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About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at |http: //books .google .com/I ^ e.y \ ' A TREATISE ON MILLING AND MILLING MACHINES Price, $1 .50 COPYRIGHT, 1916, BY THE CINCINNATI MILLING MACHINE k COMPANY CINCIJSENATI, OHIO ^■^.''- THE PLANT IN WHICH CINCINNATI MILLERS ARE MADE Thb illustration is made from a scale drawing and shows the plant as it actually is today. The machineahop building is 810 feet long; combined length of all the buildings 1300 feet. The three-story front is 380 feet wide. The entire plant, exclusive of the power plant, has eight acres (350,000 square feet) of floor space. It is the largest plant in the world devoted exclusively to the manufacture of Milling Machines and Milling Cutter Grinders. Visitors are cordially welcome to inspect this plant at all times. r. F. •^ I PREFACE The past few years have seen an unusually rapid development in the art of milling. We have carried out some very exhaustive experiments in cutter design, cutter and work cooling, and other branches of the art, which have led to marked improvements, not only in these particular branches, but in the Milling Machine itself. Although some of the data pertaining to these developments have already appeared in various publications, we believe that their compilation in complete form, as found in this book will make them of much more general use to those interested in, and responsi- ble for, efficient production from Milling Machines. A more com- plete knowledge of the action of milling cutters, the effect that action has on production, a familiarity with the different construc- tions and types of milling fixtures and holding devices, the cause of unsatisfactory Milling Machine performance and the basic prin- ciples of cutter sharpening, are all necessary for the intelligent application of the modem Milling Machine. We have in this book given considerable space to various phases of these subjects, and to this end are presenting some matter never before published. The mathematical chapters dealing with the computations involved in cutting spur, bevel, spiral and worm gears, present these subjects in a simple, detailed manner, which will, we believe, make them clear and useful to those for whom the usual method of presentation of this matter has always been too much involved. The arrangement of the various formulas and mathematical tables will prove of convenience to all who have occasion to use them. The formulas and diagrams in the chapters on gearing have been adapted from Machinery's Handbook and are printed by permission of the publishers. The mathematical chapters, especially the chapters on Shop Trigonometry, Continued Fractions, Spiral and Bevel Gears, are based on material prepared by Mr. A. L. DeLeeuw, while Chief Engineer of The Cincinnati Milling Machine Company. The Cincinnati Milling Machine Company CONTENTS CHAPTER I PAGE The Construction and Use of Milling Machines 7 CHAPTER II Erection, Care and Adjustment of Milling Machines 41 CHAPTER III Toolroom Millers — The Dividing Head, etc 55 CHAPTER IV Setting up the Machine 77 CHAPTER V An Analysis of the Process of Milling 91 CHAPTER VI Milling Machine Feeds 101 CHAPTER VII Speeds of Milling Cutters 104 CHAPTER VIII Stream Lubrication — Cutter and Work-Cooling System . . . 125 CHAPTER IX Milling Cutters — ^Notes on the Design and EflSciency of Modem Cutters 140 CHAPTER X Cutter Sharpening 172 A Treatise on Milling and Milling Machines 5 CHAPTER XI page Power Required to do Milling 182 CHAPTER XII Various Methods of Milling 186 CHAPTER XIII Milling Jigs and Fixtures 197 CHAPTER XIV The Sizing and Cutting of Spur Gears 247 CHAPTER XV Shop Trigonometry — Bevel Gears and their Calculation — Instructions for Cutting 267 CHAPTER XVI Spiral Gear Cutting — Calculations, Formulas, Tables, etc. 291 CHAPTER XVII Worm Gearing — Calculations and Methods of Cutting 310 CHAPTER XVIII Continued Fractions and their Application to Shop Prob- lems — ^Angular Indexing 319 CHAPTER XIX Change Gears for Cutting Spirals 332 CHAPTER XX Cams — Tables for Setting the Milling Machine for Milling Spiral Cams 345 CHAPTER XXI Tables of Natural Trigonometric Functions 385 The Cincinnati Milung Macmne Company High-Power Universal Cincinnati Miller Made in Six Sizes (Patent Rifthts Full; Rocryed) mm. A Treatise on Milling .and Millij^jg . J/Ja^iIin^ CHAPTER I THE CONSTRUCTION AND USE OF MILLING MACHINES Before entering into an analysis of the process of milling, the design of milling cutters, jigs, fixtures, etc., and the mathematics involved in the setting up of the machine for some classes of milling, it may be best to first examine into the construction of the machines and attachments available. Classification of Machines. In this book we will confine our- selves to the Column and Knee Type Milling Machines and the smaller sizes of Manufacturing Millers in most general use. These comprise the types of machines with which everyone is more or less familiar. They are the machines that are used in the toolroom, in the jobbing shop, for model work, repair shops and for manu- facturing. Universal Milling Machines, so called because of the great range of work that they will accommodate, are arranged with a swiveling table, and regularly equipped with a dividing head. They can thus be used, in addition to a general line of milling, for all sorts of indexing and milling work between centers, such as spur and spiral gears, and also on angular work, such as bevel and mitre gears. Each toolroom should contain one or more of these Universal Machines. Plain Milling Machines are similar to the Universals, differing only in that the Plain Machines do not have a swiveling talkie, and that their equipment does not include index centers of any sort. They are used both in the toolroom and for regular manufacturing. Vertical Milling Machines are similar to the Plain Milling Machines, with this exception — that the spindle is in a vertical position, and at right angles to the plane of the table. They are particularly adapted for the use of face and end mills in the manu- facturing department, for the milling and boring of jigs in the toolroom, and for the machining of dies. Manufacturing Millers are particularly adapted for repetition work produced in large quantities. They are, generally speaking. 8 ' Tm. CiNciNNATr MfUjNG Machine Company simpler in construction than the Knee Type Millers, and are used in large quantities in the manufacture of firearms, typewriters, auto- mobiles, etc. All of these machines will be briefly described in the following pages. The Selection of a Milling Machine. The selection of the type of Miller best adapted for the economical production of a given class of work can not be given too careful consideration. The quan- tity and quality of work that the machine will produce must justify the investment. We have gone far towards helping our customers in the solution of their milling problems and have thus gained a wider knowledge DiiTinc G>v Khe chat n dri*» ih. rMd •!«) othiag.to do w, a special order "f™" fSie are to b pwdebsttBodreHfU of the economic field of milling than can be obtained from the limited experience of one shop on one class of work. We are prepared to make complete time studies of all the milling operations on any piece of work, suggest methods, fixtures, etc., and furnish the complete equipment for doing it. Our wide experience in this work and the great variety of milling machines made by us, enable us to recommend and furnish that size. A Treatise on Milling and Milling Machines 9 _ style and type of machine which will prove most economical in view of all the conditions attendant upon its installation and use. It would hardly be appropriate to attempt to deal here with all the considerations upon which an intelligent selection of a machine depends, but mention of the most important factors will, we believe, prove helpful. Whether it should be a Cone-Driven or a High-Power Single Pul- ley type machine depends on — The quantities in which parts are made. The kind of work to be milled. Power required. Method of transmission used, whether by line shaft, group drive or individual motor drive. Whether it should be Plain, Universal or Vertical depends on — Whether it will be one of many machines or the only Milling Machine in the department. The amount of time it will be used for spiral cutting. Whether it will be used for jobbing or manufacturing. Whether for machining flat surfaces, die sinking or gang work. Whether it should be an Automatic depends on the quan- tities in which the parts are made. The suggestions contained in the illustrations of machines in operation will be helpful in the selection of the proper machine. Plain Milling Machines. These are made in both the Single Pulley Geared Spindle High-Power type and the Cone-Driven type. The rapid development of the use of Milling Machines is constantly extending their field into heavier work, demanding more power at the cutter and therefore, increased strength and rigidity in the machines. This development has led to the design of the single pulley constant speed belt machines. In their design the spindle power is not handicapped by the limitations of a driving cone, and for all practical purposes it may be assumed that the constant speed belt drive delivers the same power to the cutter at all spindle speeds, so that the operator knows just what can be expected from the machine under all conditions. 10 The Cincinnati Milling Machine Company These machines lend themselves readily to direct connected motor driving. They may be driven direct from the Hne shaft. A countershaft is not necessary. The main driving pulley is journaled on a bracket bolted to the column of the machine and is connected to the driving shaft by means of a disk friction clutch of large proportions. The machine is started and stopped through this clutch by means of a lever at the front of the machine. The spindle drive gearing is arranged as shown in Fig. 1. All the gears are steel and hardened. Those most used for speed changing are chrome nickel steel, heat treated and hardened, making an extremely durable drive. There are sixteen speeds provided. The small gear "A" in the illustration is never used for transmission but serves as a pilot when engaging the large gears. Fif. 1. Tke Complele Srindli DriTc and all the geua ore hArdened. Face gear L ie tba only E^ar keyed to the apiadle. Nogaaraarein mpab ejicep( tboeedolDS work. Pig. 2 shows the driving gears of a horizontal machine in section. In order to reduce torsional strains and consequent vibrations to a minimum, there are no gears keyed directly to shafts with the single exception of the main gear "L," which is keyed to the front end of the spindle close to the bearings. Another feature which gives these machines the strength and A Treatise on Milling and Milling Machines FH. 3. Iiulde or Sulndle Driie Bai Showina drivEne ahstt, tumbler and chain wheel far driving feed from con- stant speed sbaCt. The feed may also be driven from the spindle as shown in FiK. 1. rigidity which modem practice demands is the automatically clamped tumbler, Fig. 3 and Fig. 4. The tumbler frame is supported from the machine frame. None of its weight comes on the main driving shaft. The swinging frame carrying the tumbler gear rocks on the trunnions "C" and is operated by means of the pilot wheel on the outside of the mach" '^' ' the spiral gears "S." By means pilot wheel the entire tumbler fp adjusted laterally. When the pi turned to the right the gears are 1 mesh and the lug "D" of the swinj frame abuts on the stop pins governing the proper meshing. Now if the pilot wheel is turned farther to the right, the swing- ing frame, the tumbler frame and the spiral gears act as a system of levers and screw which lock the tumbler frame securely to its slide on the Tb.fra^'cc^'fs"te^tf™.rdimen- Diachine frame and hold the ?i<>™. jupporwd "ti™iy on the lovetaS beariBi in the drive boi, and the operation of speed ohanjing support for the tumbler gear as autoniatlMllj- cUmps it to this bearing in each 12 Thb Cincinnati Milling Machine Company firmly as if it. were permanently bolted in place. By turning the pilot wheel to the left as far as it will go, the tumbler gears are brought out of engagement. The speeds are very easily and quickly changed by means of the pilot wheel above mentioned and the two levers shown in Fig. 5. The lever positions for each speed are clearly marked. For example: to obtMn 115 r. p. m., the index plate shows corresponding to this number the ssrmbols 3-BC. It is therefore merely neces- sary to move one lever to "B," the other to "C," and move the tumbler to the No. 3 position. By pressing lightly on the treadle, while moving these levers, the gears are given a sufficient amount of motion to facilitate easy speed changing. The position of the operator FU. (. PMlliaa af OmnUc wken Cluniliw Speeds < . . j ■ l H6mov«thelev««tar88it»illgoaDdthenby WhCU chaUgmg SpCeds IS shoWn ' in Fig. 6. The feed is driven A Treatise on Milling and Milling Machines . Tke Feed Bet from the constant speed shaft and the feed plate reads in inches per minute, unless oth^'wise specified at the tune the machine is ordered. The outside of the feed box is shown in Pig. 7. The feed index and feed change levers are the same as for the drive box, but feed changing [n>m ooDsUnt Bpeed ahaft. is done best while the nmchine is running. The inside of the feed box is shown in Fig. 8. The Column, Knee, Saddle and Table. A powerful spindle drive must be supplemented by correspondingly strong main frame members. In our designs we have made use of the box section Ftt.s. ini«i<» .r PMd b*i principle. The illustra- TMs » the complete mechsnism for providing the ]« ihangrt tions show that the Col- umn is a rectangular box with openings only large enough for insert- ing the mMtt drive gearing and the feed gearing. The base deserves especial attention. It must have sufficient strength to rigidly support the machine and its work, and to with- stand the wedging action of the cutter as discussed on page 93. Any tendency to spring in the manner of a diaphragm seriously affects the alignments as well as the rigidity of the machine. As a result of careful experiments, we have changed the design of o\xr milling machine bases, giving them about six times the strength that had formerly been considered adequate. The Knee, Fig. 9, must carry the entire weight of the work and its fixture and in addition to this must resist the twisting str^ns resulting both from taking the cut and from the varying twisting moments set up through the ciianging position of the table with its work, in relation to the knee. The Cincinnati Milung Machine Company High-Power Plain Cincinnati Miller Made in Six Sizes (Patant RJftht* Fully R«Mmd) A Treatise on Milling and Milling Machines 15 It has been general practice to provide the knee with clamping levers for locking it to the column when taking a cut, but we have f oimd this rapidly distorts the knee, reduces the bearing to a small area under the clamping screws, and ultimately it becomes impossible to so clamp the knee that it will not rock on the column. To avoid this difficulty we have eliminated knee clamps entirely, have in- creased very considerably the metal in the knee where it engages the column, and provided a long taper ffb, Fig. 11, adjusted length- Tbb sbom the- ki wise, which a^rds at all times a full bearing on the column. This gib, when adjusted so as to give a nice sliding fit between these two members, provides a degree of rigidity that enables new pattern Cincinnati High-Power Millers to do heavier cutting than was previously possible and also to do accurate work within closer limits. For example, aNo. 5 Machine (which has a standard 20 h. p. . motor rating) had been for some nine months in operation in our factory on a variety of work, taking cuts which sometimes required 40 h. p., when it was called upon to mill some long bars. These are shown in the illustration. Fig. 12. They are 42' long, 4' wide, and 1^' thick. Two of them were milled with a spiral mill mounted on an arbor in the usual way, two with a shell end mill, using a Ver- tical Attachment, and two with the same mill in the spindle of the The Cincinnati Milung Machine Company A Treatise on Milung and Milung Machines 17 machine. They were machined on both sides and when placed on a surface plate as shown, they showed flat within -OOl", each holding tight eight pieces of tissue paper. This, we believe, is con- clusive evidence that with om- new construction there is no move- ment between the knee and column, nor is there any springy action in the other essential parts of the machine. The construction of the knee is clearly shown in the illustrations, and the line drawing indicates its strength at the point where it ' engages the column. Our tables have their bearings at the top of the "V" along the M™DX^?he''{^".'\hf ^-b" wrh« ffd! outer edge of the table face, thus ^°!:bV^^ti''HiJiSpo"«"Mii^-^'^unJSJ3 supporting the full width of the "*"""''■ table. The Saddle is shown in Fig. 13. Its mechanism is so constructed that the feed is direct to the table feed screw. There are no auxiliary shafts. The driving gears are close to the nut and therefore only a short section of the lead screw is in torsion. This contributes largely to the efficiency of our feeding mechanism. Centralized Control. A modem machine tool must be handy to operate. It is essential that the operator's task should be made as easy as possible. With this in mind we have grouped all our levers on that side of the machine where the operator would naturally stand when using them. The diagram, Fig. 10, shows this quite clearly. The illustration, Fig. 14, shows an added feature of handiness, resulting from placing a feed lever where the operator can control his machine from behind the table. This is indispensable when doing end milling, face milling, or boring on a large piece of work. The arrangement of the table feed levers at the front of the saddle enables the operator on a Ver- tical Machine to traverse the periphery of a rectangle without stop- The Cincinnati Milung Machine Cobipany ADd Qnlrk Betum ping either feed or speed. This makes it quite practical to mill such a piece of work without leaving an off-set where the cut ends. Power Quick Traverse and Return. All of the larger Plain and Vertical Machines are regularly equipped with our Power Quick Traverse and Return Arrangement, Fig. 15. It is driven dh-ect from the man pulley independent of the feed mechanism and provides a movement forward or back at 100" per minute. The con- trolling lever indicates the direction and when the lever is released, the table stops. The feed and power quick traverse can not both be engaged at the same time. There are limit stops which A Treatise on Milung and Milling Machines 19 prevent going beyond the limits of the table travel. All these things make for safety. Being driven from the main pulley, which does not stop when the machine is shut down, this power quick trav- erse is available for making quick table ad- justments when setting up the machine pre- paratory to milling a piece of work. This ar- rangement can be fur- nished on our smaller high-power machines as an extra attach- ment. Fix. IS. Tka P»w Qaick Tuowh md Kitain Direct-Connected Motor Drive. We have developed a sim- highly efficient arrange- hich is shown in Fig. 16. tor is mounted on a swing- t hinged to the base of the ; so that part of the weight he motor is supported by belt, keeping it at all es at the proper tension and doing away with the need for any atten- tion on the part of the operator. An endless leather belt and a metal belt guard are included in the equip- ment. This arrange- ment is suitable for any make or style of constant speed motor running not faster than 1200 r. p. m. The CmaNNATi Milling Machine Company High-Power Vertical Cincinnati Miller Made in Three Sizes (Fatant Rltfici Fully ReHned) A Treatise on Milung and Milling Machines 21 Another style of Motor Drive Arrangement is shown in Fig. 17. In this case the motor is mounted on a fixed extension fastened to the base of the machine and the drive is through reducing gears and a silent chain to the main pulley of the ma- chine. This arrange- ment is suitable for motors of any speed up to 1200 r. p. m. The reducing gears, sprockets, chain, chain guard and base are all included in the equipment. Vertical Millers. n,. it. th. ch.in «»« iw.. Arrn„Mme>.. These machines are gi^^'o^h? mMhVnf """" " ^°" "■" '"'"^ "" "'"'''''* ^' similar to the High- Power Pl^n Millers in all particulars, except that the spindle is in a vertical position. Here again we have aimed to make a machine d Snindli DriTlnl Gui 22 The Cincinnati Milling Machine Company that will have the same degree of strength in all its important parts, bearing in mind that the pressure against the cutter which must be resisted by the members carrying the spindle is the same as the pressure against the piece of work on the table. The construction of the spindle head and its driving gearing is shown in Fig. 18. All the driving gears, including the mitre gears shown, are steel and hardened. These latter have self-contained bearings. The one through which the spindle passes has a long hub bearing which takes the entire thrust of the gears, thus relieving the spindle from these strains. The spindle is as long as the spindle in the corresponding horizontal machines. Its bearings are both carried in the head frame and are always a maximum distance apart. Vertical adjustment of the spindle is obtained by moving the entire head frame carrying the spindle. This frame has long bear- ings provided with an adjustable taper gib, and when the machine is in constant operation on heavy repetition work, this frame may be securely clamped to the body of the machine, converting it temporarily into a fixed head machine. The head adjustments are quickly made by means of a pilot- wheel, the head itself being counter-balanced. There is also a slow movement provided through worm and wormwheel when . Pliln Indci Head A Tbeatisb on Milling and Milling Machines 23 Milling Machine Attachments The range of work that a Milling Machine can do is greatly increased by the use of attachments. An almost endless variety of Fll. 20. Geir-CuUIng Altuhmcnt attachments has been devised for special requirements. It is some- what difficult to determine where to draw the line between what are essentially attachments for the machine and those other devices which should be properly classed as fixtures. We always carry in stock a full variety of standard attach- ments suitable for the various sizes of machines. In their design we have ag^n followed the principle that each part of the machine should be equal in capa- city to all other parts. The Universal Indexing and Dividing Head, which forms part of the equip- ment of Universal Ma- chines and which can also be used on Plain Machines for work done between centers as well as for an- gular work, such as bevel gears, mitre gears, etc., is described in another place. The Combination Index Heads. £i'or a general line of index- ing work, the Combination Index Heads will be found extremely convenient. These can be furnished as Plain Index Centers, Fig. 19, indexing through a plate at the rear by means of an index lever mounted directly on the spindle. To this can be added the bracket 24 Thb Cincinnati Milung Machine Coupany carrying a side index plate, which makes the same divisions as our Universal Dividing Heads, for universal indexing through worm and wormwheel. This makes our Gear-Cutting Attachment, Fig. 20, and the use of this can be still further extended to include spiral milling by adding a shaft and gears for connecting it with the lead screw. In this form it is the Spiral Milling Head. These heads are made in both 12' and 16' sizes and are recommended for use not only on Milling Machines, but on other machines that are called upon to do work between centers. Another form of indexing centers for small light work is shown in Fig. 21. These centers swing work 10' in diameter and index through PK.K. uKta Nombtr indHini Aiuckmcdi a sldc ludex platc which operates through a worm and wormwheel in a manner sinailar to that employed on our Universal Indexing and Dividing Head, Gear- Cutting Attachment, and our Spiral Milling Head. The worm and wheel can readily be disengaged and the indexing may then be done direct by revolving the spindle by means of the handle attached to the disk at the rear of the head, which disk also serves as an index plate, and indexes any number dividing evenly into 24. The divisions for 3, 4, 6, 8 and 12 spaces are plmnly marked. Hi&h Number Index- ing Attachment. All our index heads using the i side index plate make an unusually large number of diviMons, as shown in the table in the chapter on Universal Toolroom Mil- lers. These divisions in- clude all numbers, odd and even up to 60, even num- bers and those divisible by 5 up to 120, and many use- „, ^ ^^ ^„^ ^^.^„ ful divisions beyond these. However, it often happens that additional divisions are required for special work in the toohvDom, or for model making and experimental A Treatise on Milling and Milling Machines 25 work. For all these requirements the High Number Indexing Attachment, Fig. 22, will be found very convenient. It consists of three plates of the same size and interchangeable with the regular side index plate. They will make all divisions, odd and even, up to and including 200, all even and those divisible by 5 up to 400, This is sufficient for practically all requirements. The indexing is all simple indexing direct through the plates and is therefore more desirable than any system of compounding or dif- ferential arrangements requiring the use of change gears. Driving Mechanism. When it is desu^ to equip a Plain Machine with a Spiral Milling Attachment and Universal Dividing Head, or Spiral Milling Head for a general line of spiral work, it is also necessary to add the Driving Mechanism shown in Fig. 23, for connecting the lead screw with the Spiral Head. This mechanism includes the 12 change gears and the segment. Undercutting Attachment. The Milling Machine is fre- quently called upon to cut gears of larger diameter than will pass under the spindle. For such work our Undercutting Attachment greatly extends the range of the machine. It consists of two 26 The Cincinnati Milling Machine Company heavy raising blocks for supporting the Dividing Head, or work- carrying member, and a special arbor support which is attached to the Knee as shown in Fig. 24, instead of through the overarm, as is regular practice. A standard arbor and either a Universal Dividing Head or a Gear-Cutting Attachment can be used. The work is sup- ported immediately above the cut by an adjustable stud in the raising block under the tmlstock, which takes the strain due to the thrust of the cutter, and thus reliev- ing the centers from any strain from this source. High-Speed Milling Attach- ment. Sometimes work requires the use of very small end milling or profiling cutters which should run at very much faster speeds than the highest speeds provided on standard FU.M-A HKn-s^d A.u.ii„.n. "^^^^^^^ machuies. For such work the High-Speed Attachment, shown in Fig. 24-A, comes in very handy. It is a geared attachment driven from the main spindle and is supported by the front box to which it is clamped. It is made in sizes suitable for use on Nos. 1 and 2 Cone-Driven Machines. Spiral Milling Attachment and Universal Milling Attach- ment. It is often desired to mill short lead spirals which have an angle that is greater than that to which the table of the Universal Machine can be swiveled. This can be easily and satisfactorily accom- plished by adding to the equip- ment of the Universal Machine, a Spiral Milling Attachment, Fig. 25, or, where the work is light- er, a Universal Milling Attach- i T?- o! 9p]Qd"*driv« gsBrs for revere speeds the table returns while the " "=«" '" ^^^ """■« ""^ "'■" '"' ^^p'** Maehine. cutter is stationary. This adds greatly to the safety of the operator and also improves the quality of the finished work. The automatic 36 The Cincinnati Milling Machine Company spindle stop can be easily disengaged when the nature of the work does not require the use of this feature. Z) ^ D B 0^ ^ E ^ F ^ •~ » — ^ ^ H — ~CTC i^— The Speeds. A choice of one of 24 spindle speeds is offered, and the gears which furnish this one speed, when reversed, will also give an additional speed in that same series. The three series of speeds and the gear ar- rangements are shown in Table A, with reference to Fig. 41. For Example. If the ma- chine is geared for 62 revolu- tions, reversing the gears will give 212 revolutions; or, if geared for 103 revolutions, reversing the gears will give 127 revolutions, and so on. The change gears are the same for each series. For ex- ample, gears that will give 31 revolutions in the low series will give 49 revolutions in the stand- ard series and 110 revolutions in the high series. But extra back gears are required for each ad- ditional series. The arrange- ment of the spindle drive gearing is shown in Fig. 41, and the ar- rangement of this same gearing for reverse speeds is shown in Fig. 42. The Feed. The feed move- ments of the machine are opera- ted in the cycles shown in Fig. 43. The fundamental cycles are: 1. Forward quick to the work, feed across the work, auto- matically stop spindle, automatically reverse and return to starting point with spindle stationary. ETC 5 ETC J tic CTC ETC N C C D ♦•tTC Fig. 43 Diagram showing some cycles of table movement obtainable with the Intermittent Feeding Mech- anism. A Treatise on Milling and Milling Machines 37 2. Forward quick to the work, feed across the work, quick forward to clear and automatically stop both feed and spindle. Then, when the work has been removed, the table may be returned quickly to the starting point by shifting the lever on the feed box. In both of the above cases the stopping of the spindle is auto- matically accomplished by tripping and applying a brake. In all cases, after the work is chucked, the main starting lever starts both feed and speed simultaneously. Under no conditions can the feed be engaged with the spindle stationary. 3. If it is desired to chuck a string of pieces on the table, dogs can be provided to produce an intermittent forward movement, by which the space between pieces is automatically traversed at the rapid rate of 100" per minute. This can be repeated for as many pieces as there are on table. A number of variations of the above fundamental cycles may be obtained by the use of additional dogs. A full representation of the most useful cycles is given in the accompanying diagram. Fig. 43. We offer a choice of one of the 12 feeds provided. These are in two series as shown in table B. Feeds are given in inches per minute. It will be seen that should a feed of 1.09" be selected, then by reversing these feed gears, 3.87" feed will be obtained. In the same way, reversing gears for 1.36" feed will give a feed of 3.12", and so on. The feed gears are the same for both series. But to use both series an extra pair of feed back gears is needed. TABLE A— SPEEDS AND GEARS CHANGE GEARS (Two speeds obtained with one pair of Change Gears by reversing on Studs D and C) StudD Outer Gear 68 T " 63 T 57 T 51 T StudC Outer Gear 29 T ' 34 T 40 T 46 T BACK GEARS AND SPEEDS Low Series Spindle F 59T Stud D Inner Gear 18T Standard Series Spindle F 52T Stud D Inner Gear 25T Speeds Gears as Shown 31 39 51 66 Gears Reversed 170 135 104 81 Speeds High Series Spindle F 37T Stud D Inner Gear 40T Speeds Gears as Shown 49" 62 80 103 Gears Reversed 268 212 163 127 Gears as Shown 110 139 . 180 232 Gears Reversed 603 477 367 285 TABLE B— FEEDS AND GEARS CHANGE GEARS (Two feeds obtained with one pair of Change Gears by reversing; on Shaft A and and Stud B) Shaft A Outer Gear "~27T 31 T 36 T StudB Outer Gear BACK GEARS AND FEEDS Low Series Shaft A Inner Gear 59T Stud B Inner Gear 19T Feeds High Series Shaft A Inner Gear 31T ^ud B Inner Gear 47T Feeds 51 T 47 T 42 T Gears as Shown .09 .36 1, 1 1.76 Gears Reversed 3 87 3.12 2.4 Gears as Shown 5.1 6.4 8.3 Gears Reversed 18. 3~ 14.75 11.3 The Cincinnati Milling Machine Company The 12-mch B. G. Plain Manufacturing Cincinnati Miller A Treatise on Milling and Milling Machines 39 12-inch B. G. Plain Manufacturing Miller This is a simple single purpose machine of the column and knee type, designed for the rapid production of small machine parts as used in the construction of typewriters, sewing machines, adding machines, registering machines, etc. Evidence of its rigid construction is very clearly furnished by the illustration. This machine is designed to run at one spindle speed, because it is usual practice to employ such machines con- tinuously on a single operation or operations which are practically identical. It can be furnished as a back geared machine as shown, or without back gears, in which case the tight and loose pulleys are mounted directly on the spindle. Quick-Acting Operating Arrangement. The operator from his position in front of and at the left-hand end of the table con- trols the feed movements with his right hand. Assuming a piece of work placed in the fixture, he moves the table forward at the rate of 2^" per turn of handwheel until the dog hits the trip, which automatically engages the power table feed. At the end of the cut a second dog disengages the table feed and stops the table, which is then returned to the starting point, bringing the fixture immedi- ately in front of the operator who, after a new piece has been chucked, repeats the above movements. An analysis of these movements compared with usual practice will show that the operator's work has been simplified and many of the usual time-consuming elements are eliminated. He may move the table forward as rapidly as he wishes, and he need not slow down when he approaches the cutter because the trip removes all need of precaution. Therefore, with the dog properly set, the work is brought rapidly close to the cutter before the power feed is thrown in, thus reducing the actual feed distance to very little more than the actual amount needed to traverse the work. Both of the foregoing machines have proven very popular with managers because they increase output, and with operators, because they very materially reduce labor. The Cincinnati Milling Machine Company Cone-Driven Plain Cincinnati Miller Made in Five Sizes (Patent Rights Fully Reserrnl) A Treatise on Milung and Milung Machines 41 CHAPTER II ERECTION, CARE AND ADJUSTMENT OF MILLING MACHINES Erection. Although the Milling Machine is a self-contained machine, it is desirable that it be set on a solid floor. It is important that it be set level and it is best when setting up a machine to place a level on the table, and then with ordinary shingles, wedge under the base until the table shows level. Shingles should then be driven under the base all around so that the weight of the machine will be distributed over the entire base. The Countershaft. The Countershaft for Cone-Driven Ma- chines, Fig. 44, should be placed as nearly as possible directly over the machine in order that the belt will clear the overhanging arm. Care must of course be taken to insure that the countershaft is level and in proper alignment with the machine. The construction of the countershaft will be clear from Fig, 45. fit- 44. The CauBMrahifi It is of the disk clutch construction and always has a driving capacity considerably in excess of the power required by the machine. When wear does take place it is easily adjusted. The clutch disk is placed on the shaft so as to face the disk on the pulley. The holder for fingers is screwed to the body of the disk, the ends of the fingers reaching over the disk on the pulley. Wear is taken up by first loosening the clamping screws and then screwing the holder for fingers 42 The Cincinnati Milling Machine Company on the clutch disk away from the pulley. Make sure that the screw is again tightened after the adjustment has been made, to insure that the holder for fingers will be tightly locked to the clutch disk. Pll. 45. Derail at Cann Single Pulley High-Power Machines are not furnished with a countershaft, but are driven direct from the line. Care should be taken when belting up the machine to be sure that the pulley runs in the direction indicated by the arrow on the pulley. A suitable pulley should be placed on the line shaft to drive the machine pulley at the proper speed. In determining the size of this pulley, follow this rule: Revolutioits of mackine pulley multiplied by the diameter of machine pulley, divided by the revolutions of line shaft, equals diameter of pulley on line shaft. For Example. Assuming a line shaft running 200 r. p. m. and a machine pulley 20" diameter running 325 r. p. m. . Then, we have — ' ^' ' = 32;^'' for the diameter of the pulley on the line shaft. This same rule, of course, applies when determining the size of the pulleys on the line shaft when driving a countershaft, except in this case we multiply the speed of the countershaft by the diameter of its pulley and divide by the revolutions of the line shaft. Oiling. It is important that a Milling Machine be well oiled. We advise the use of a good grade of mineral oil. On all our machines the oiling places are plainly marked and those places provided with A Treatise on Milling and Milling Machines 43 oilers are all in plain sight. The operator should acquaint himself with all of them and be careful not to neglect any. On pur High-Power Machines sight-feed oilers are used for the important bearings, and most of the mechanism is oiled from central oiling places. These should be filled once a day. The table bearings are oiled through oil holes provided on the front and rear sides of the table. To oil the inside parts of the saddle, bring the zero line on the table over each one of the three lines on the saddle and in each case oil through the oil hole over the zero line on the table. Be sure to keep the table in each of these positions long enough to give the oil time to pass through the tube to the place to be oiled. LOCKNUT FOR ADJUSTWC SPINDLt Fig. 46 Section through driving gears and spindle of a High-Power Machine. To Remove the Spindle from the Machine. This is an operation that is rarely necessary. When, after long and hard use, extensive overhauling makes this advisable, it is only necessary to loosen the lock nut on the Spindle, Fig. 46, at the same time driv- ing the spindle forward. After the spindle has passed through the main gear at its front end on both Cone-Driven and High-Power Machines, it will come out freely. Adjustments. The machine spindles are tapered at the front end, and are so proportioned that under ordinary service the wear on the end thrust collars and on the spindle bearing proper is about equal, so that by screwing the lock nut on spindle against the front 44 The Cincinnati Milling Machine Company box, the spindle is drawn into its taper bearing to proper adjust- ment. All machines are properly adjusted before they leave the factory, and this adjustnient is seldom necessary. When properly made, the machine should again run without further adjustment for a number of years. The white metal thrust bearing of the spindle rests against .thin washers of hard paper. By removing some of these or adding additional ones, as the case requires, an independent adjustment of the thrust bearing can be made when excessive continuous service on one kind of work may make this advisable. Adjusting Knee, Saddle and Table Bearings. These bear- ings are all provided with taper gibs. The table and knee gibs are adjusted endwise by means of a substantial screw and should be kept snug so as to take up all play, keeping these members in the con- dition of a good sliding fit. The knee gib on High-Power Machines is no longer provided with clamping levers and if kept in proper adjustment, it will be found that the machine has greater solidity between the knee and column than can be obtained by any system of locking or clamping levers. Operating Levers on High-Power Millers. The operation of Cincinnati High-Power Millers is the same for all types — Plain, Universal and Vertical. The important operating levers are indi- cated in Fig. 47. To Use the Table Feeds. Throw in the lever for the table feed gear train and then start and stop the feeds by the table feed oper- ating lever. To feed to the left, move the lever towards the left, and to feed towards the right, move the lever towards the right. To Use Cross Feeds. Throw out the lever for table feed gear train and set the lever for cross feed gear train to the position marked "cross feed" on front of knee. Operate the cross feed by operating lever at side of knee. To Use Vertical Feed. Throw out the lever for table feed gear train and set the lever for vertical feed to position marked "vertical feed," on front of knee. Operate the vertical feed by operating lever at side of knee. Move lever up to feed up, and down to feed down. To Change the Spindle Speeds. Stop the machine. Read from speed plate the lever positions for the speed wanted; for example. A Treatise on Milling and Milling Machines 45 115 revolutions requires lever positions 3-BC. Turn the pilot wheel to the left as far as it will go. Then move it along until the detent drops into the hole under 3; then turn pilot wheel to the right until you feel the gears come together; then press on the treadle lightly, which will revolve the gears slowly, at the same time turn the pilot wheel right as far as it will go, and finally pull it home tight. This sets and locks the tumbler. Next, move the levers "B" and "C." If the geai^ interfere, press lightly on the treadle and they will go into place. It is best to press on the treadle just hard enough to start the gears. The position of the operator when speed changing is shown in Fig. 48. To Change the Feeds. Change the rate of feed by means of the levers and pilot wheel on feed box in the same way as the speed changing is done. Do this while the machine is running. You need therefore not use the treadle. Before engaging either table, cross or vertical feed, it is always desirable to see that the handwheel on the end of the lead screw, cross screw, or vertical adjusting screw, is disengaged from the clutch, as otherwise, the sudden rotation of these handwheels may cause injury to the operator. 46 The Cincinnati Milling Machine Company Safety Pins. The feed mechanism of all Cincinnati Millers is provided with a safety pin, which will shear when the machine is overloaded with too heavy a feed before breakage occurs in any important part of the feed mechanism. A number of these pins are supplied as part of the regular equipment with the machine. The bushes in which these pins are located will be found just outside the reverse box on the left-hand side of the knee on the High-Power Machines, and just outside the feed bracket on the right-hand side of the column of the Cone-Driven Machines. Instructions for removing the sheared and inserting fresh pins will be found on the envelope containing the pins, which accompanies the machine. Adjusting the Clutch of High-Power Machines. This friction clutch may be set so that it will slip when very delicate cutters are used, and can also be set up so firmly that it will transmit the maximum horsepower that the belt can supply. To adjust this clutch, remove the cover from the end of the main driving pulley, release the clamping screw which holds the large threaded finger carrier, and screw up in a right-hand direction until the proper degree of friction is obtained. Tighten up the locking screw and replace the cover. Care of the Machine. The machine should be kept clean. This point can not be emphasized too strongly. The continued accuracy and durability of the machine depends upon this more than on any other one thing. All oil holes should be kept closed, and it is advisable when oiling to first wipe iron dust and chips away from oiling places before inserting the oil can. After a bearing has been allowed to run dry due to insufficient or improper oiling, and has become cut, any amount of flooding with oil will not improve its condition. It is best, therefore, to exercise proper care in the first place. When oil holes or oil tubes become clogged with gummy oil they should be thoroughly flushed with gasoline. This will not injure the bearings, but will have a cleansing effect which will insure that all bearings will again get their full supply of clean oil. The machine should never be taken apart unless absolutely necessary, and then the work should be done by a competent man who has first familiarized himself with the construction of the machine. To remedy some temporary trouble, it seldom is neces- sary to take any great portion of the machine apart. For example, trouble due to an improperly oiled bearing may always be located A Treatise on Milling and Milling Machines 47 by turning the various members of the mechanism by hand until the injured member is located. By bearing these things in mind a great deal of the time and trouble required to dismantle a machine may be saved. The careful workman will see to it that wooden coverings are provided for the front of the knee and the top of the table, so that he may place work or tools on these parts without injury to the slides or to the upper surface of the table. Attention to this will do much to maintain the original accuracy of the machine. When ordering repairs always give us the construction num- ber and letter stamped on the front face of the column immediately below the front box of the machine. Also, specify the part wanted by number. We have for some time past numbered every part entering into the construction of our machines, and these numbers are placed where they are not liable to be obliterated by wear. By specifying the part number in each case, making replacements will be very much facilitated. a Ckangint Srecf ■ f geaiB sWly turn The Cincinnati Milung Machine Company Names of Parts of Cincinnati High-Power Plain Millers and Their Use These illustrations show the location on the machine of the different parts referred to in this book. They will contribute to a better understanding of the machine and also facilitate ordering repairs. Numbers in circles are on the part to which they refer, or they are directly over that part when it is concealed, 1. Clutch lever for starting and stopping machine. 2. Table feed setting lever. 3. Power quick traverse operating lever. 4. Table feed adjustable trip dogs. 5- Table feed trip plunger. ' A Treatise on Milling and Milling Machines 49 6. Cross and Vertical feed setting lever. 7. Vertical and cross feed lever. 8. Lever for operating feed when standing behind the table, 9. Cross feed trip plunger. 10. Cross feed adjustable trip dogs. 11. Cross adjustment handwheel. 12. Vertical adjustment crank. 13-14. Quick traverse limit stops. 15. Feed change levers. 16. Pilot wheel for operating feed change tumbler. 17. Feed index plate. 18. Speed change levers. 19. Pilot wheel for operating speed change tumbler. 20. Speed index plate. 21. The treadle for giving the gears slight motion to facilitate speed changing. 22. Guide for Vertical feed trip dogs. 23. Vertical feed, adjustable trip dogs. 24. Vertical feed trip plunger. 25. Ball crank for longitudinal table adjustment. 26. Micrometer dial for longitudinal table adjustment. 27. Rack on main clutch rod. 28. Quick traverse driving belt. 29. Bracket containing left-hand bearing for table feed screw. 30. Driving keys in flanged spindle end. 31. Oil pot. 32. All steel vise. 33. Bushings in arbor bearings. 34. Table feed operating lever (concealed behind the braces in Fig. 49. See Fig. 50.) 35. Telescopic elevating (Vertical feed) screw sleeve. The Vertical screw (35-A, Figs. 50 and 51) is inside of this sleeve. 35-A. Vertical feed screw (Fig. 50). 36. Outer arbor bearing support which can be bolted to the braces. 37. Intermediate arbor bearing support. 38. Outer support, for short arbors having a bearing on the out- side of the nut. (Arbors style A, B, C, G, page 84.) 39. Adjustable bronze bush for arbor bearing. 40. Braces for tying the overarm, outer arbor support and knee together. 41. Overarm. The Cincinnati Milung Machine Company Fig. 50 42. Column of the machine. 50. 43. Drive box. 51. 44. Feed box. 45. Driving pulley. 46. Feed reverse box. 47. Saddle. 52. 48. Table. 49. Knee. 53. Bracket containing right- hand bearing for table feed screw. Bridle by which the braces are fastened to the knee. Front spindle bearing box. .J A Treatise on Milling and Milling Machines 51 54. Front face of column where the construction number and letter will be found. Always give us this numbesr and letter when ordering attachments or repairs. It identifies the machine. 55. Micrometer dial for vertical adjustment. 56. Micrometer dial for cross adjustment. 57. Front sliding covers in top of knee. Back sliding covers cor- responding with these can not be s^en. 58. Cross screw bracket at front of knee. 59. Trip plunger bracket. 60. Adjustable gib for table bearings. 61. Adjustable gib for saddle bearings. 62. Telescopic Universal joint shaft (long fork). 63. Universal joints (short forks and ball in fork). The short fork connecting with the shaft in reverse box has a flange which carries the shearing pins (safety fork). 64. Oil pump connection with tank which is in the base of the machine. 65. Ejector rod. 66. Vertical feed nut on base of machine. 67. Location of oil pump when furnished. The following parts are shown in Fig. 50: 68. Power quick traverse pulley. 69. Quick traverse bracket on column. 70. Long fork on quick traverse shaft. 71. Extension shaft, quick traverse. 72. Cover over end of lead screw. (Remove when setting up for cutting spirals.) 73. Short forks of Universal joints. (These are identical with the forks used for driving the feed.) 74. Quick traverse bracket under saddle. 75. Quick traverse operating lever bracket. 76. Quick traverse lever shaft. 77. Quick traverse safety lever. 78. Cover over driving gears. (Remove when oiling inside parts.) Additional Parts Applying to Vertical Machines Fig. 50 79. Pilot wheel for quick adjustment of spindle (6'' per turn). 80. Knob for engaging hand feed movement. 81. Hand wheel for hand feed movement. 82. Micrometer dial for hand feed movement. The Cincinnati Milling Machine Company Fig. 51 83. One of four bolts for clamping spindle head solidly to frame of machine for heavy work. 84. Spindle head. 84-A. Rack for adjusting spindle head. 85. Lower spindle bearing box. 86. Upper spindle bearing box. 87. Head adjustment worm casing. Additional Parts Applying to Universal Macliines Fig. 51 88. Arbor. 89. Universal Indexing and Dividing Head. 90. Tail stock. A Treatise on Milling and Milling Machines 53 91. Elevating center for tailstock. 92. Front index plate on spindle for direct indexing low numbers. 93. Head center. 94. Driver for dog. 95. Side index plate. Drilled both sides, reversible. 96. Sector for convenience in indexing. 97. Index pinholder. 98. Index pin (in the holder). 99. Segment for change gears. (This segment with a complete set of change gears constitutes a Driving Mechanism.) 100. Swinging arm or bracket for idler gear. 101. Change gears for cutting spirals (12 in a set). 102. Idler gear. 103. Quick return crank handle. 104. Swivel carriage or housing. 105. Vise body. 106. Swivel base for vise. 107. Holder for adjustable bronze bush for outer arbor support. (This is substituted for the large bearing holder in the intermediate arbor support.) 108. Steady rest. 109. Universal Milling Machine chuck. 110. Vise housing. 111. Vise screw. 112. Vise jaws. 113. Swivel block in tailstock. 114. Tailstock center carrier. 115. Saddle of Universal Machine. Additional Parts Applying to Cone-Driven Machines 116. Cover over back gears. 117. Cover over back gear pinion. 118. Back gear quill. 119. Back gear operating lever. 120. Back gear locking pin. 121. Driving cone. 122. Back gear sleeve. 123. Back gear shaft. 124. Braces as used on Nos. 1, 2 and 3 cone-driven machines. 125. Bridle for attaching braces to knee. The Cincinnati Milling Machine Company Cone-Driven Universal Cincinnati Miller Made in Four Sizes (Paieot Rlghia Fully Reaerred) A Treatise on Milung and Milling Machines CHAPTER III UNIVERSAL TOOLROOM MILLERS The term "Universal" designates a Miller especially designed for automatically milling spiral forms. This, in addition to its equipment for cutting spur, mitre and bevel gears, and doing a general line of indexing and other work that is held between centers, makes the Universal Miller the gener- ally accepted toolroom machine. Such machines have the table mounted on a swiveling carri^e, permitting the work held between centers to be set at an angle with the cutter to suit the spiral being milled. Their equipment includes a Universal Dividing Head, change gears, chuck, etc. These two particulars, viz., swiveling table and Dividing Head equipment, constitute the only difference between Universal and Plain Millers. The development of modem machinery has brought with it the use of spiral gears of wider angles than that to which the table of a Universal Miller can be swiveled. To meet these require- ments we brought out our Spiral Milling Attachment some years ago to increase the range of Universal Millers to take in this work. Since then we have ar- ranged our Plain Millers so that they can be used with ^- ^- ''"'" ""'" ^"^' '" <^"'-« s**^ the Dividing Head geared to the table feed screw for generating spirals, the same as Universals. By adding to this equipment the Spiral Milling Attachment, Cincinnati Plain Millers will cut spirals of greater angle than can be cut on any Universal Miller with regular equipment. 56 The Cincinnati Milling Machine Company In recent years Plain Millers have been coming into more general use as toolroom machines than formerly, it being recognized that only a portion of toolmaking consists of spiral work and for all other purposes the Plain Machine has the advantage of greater rigidity. For a small toolroom using only one machine, it is customary to select a Universal. Additional machines may be Plain or Universal in proportion to the amount of spiral work to be done. It should be borne in mind that our Plain Millers are made to the same close limits of accuracy as our Universals. Toolroom machines are not often required to do heavy cutting. Extreme accuracy is more essential than great power. But in order to produce accurate results, it is essential that all the working parts of these machines be as rigid as it is practical to make them. This is especially important in regard to the large sliding members of the frame — such as the table, saddle, knee and column. On our machines these are constructed on the enclosed box principle, all as detailed in the preceding pages describing Plain Machines. We have based our design of each of these members on a definite knowledge of the nature of the strains to which it is subjected. The Dividing Head A modem, powerful Universal Miller is severely handicapped unless it is equipped with a Dividing Head that is strong enough to do work commensurate with the capacity of the machine itself. A Treatise on Milling and Milling Machines 57 The coiKtruction of ours is shown below. The worm and worm- wheel are unusually large, and when, after long service, wear does take place, it can be quickly taken up by means of the adjust- ing screws shown in Fig. 55. These screws are made accessible by simply removing a cover which encloses the worm casing. Thus the adjustment can be made when necessary without taking the head apart, and in the same manner and to the same degree of nicety as it is done in our shop when the heads are first assem- bled and tested. The ad- justment for wear is made in a straight line perpen- dicular to the axis of the wormwheel, the worm cas- ing being confined between two parallel vertical walls shown in section in Fig. 57. Repeated adjustments do not throw the worm and wormwheel out of alignment, and therefore do not affect the accuracy of the mechanism. The work spindle is large in diameter and its bearings are adjust- able for wear. It is provided with a clamping device. Fig. 58, by means of which it can be firmly locked during cutting operations without disturbing the acctiracy of the spacing. This relieves the worm, the wormwheel and index pin from all strain, thereby avoid- ing unnecessary wear. 58 The Cincinnati Milung Machine Company It will be noted that the front bearing tapers toward the front END. The effect of the clamp therefore is to take up whatever play exists by pxishing the spindle forward in its bearing and thus bring- ing it into perfect alignment before actually clamping it. The spindle may be set at any angle from 5° below the horizontal to 50° beyond the perpendicular position. The swiveling block is graduated about its circumference and provided with a vernier reading to five minutes, or t^ of a degree. The swiveling block swings on large trunnions (6J^" diameter on 10" head and 8J^" on 12" A Treatise on Milung and Milling Machines 59 and 14" heads), clearly shown in the illustrations, and may be held rigidly at any angle by clamping the large trunnion bearings by simply tightening two cap screws. The rigidity with which the clamps hold the trunnions is carefully tested, Fig. 59, on each head as soon as the swivel block and clamps have been fitted. Every head must carry 600 pounds 22 inches from the center of the swivel without any evidence whatever of failure on the part of the clamps to rigidly hold the swivel block in position. Fig. 59. Teal or Hinldilf of ClBRips Note the simplicity of our clamp: the large clamping surface; and that the swivel bearing is completely protected. This insures that it will not become injured so as to destroy the alignment of the head. In addition to cutting spirals, the Dividing Head is especially adapted for bevel and mitre gear cutting as described in the special chapter on that subject. 60 The Cincinnati Milung Machine Company Work of this sort should always be done with the Dividing Head spindle set at an angle away from the direction of the cut, so that any springing that may result from the small arbors that the nature of such work often requires, will be away from the cutter and prevent its gouging in. This requires that the spindle be set past the vertical position. Ours can be set to 50°. It also requires a head of the greatest rigidity. The details of ours are all very large, and the test on the preceding page shows how securely our spindle is held. The Dividing Head Tallstock. The tailstock has an adjust- able center bar which may be raised and lowered through rack and pinion. It is carried in a slide which can be swiveled to 10° above or below the horizontal to bring the centers in line with the center of taper work. It is so constructed that the cutter can pass over it without injury when set at an angle. It is provided with two centers, one for small light work and the other for heavy work, and may be reversed to bring either in position. The centers are carried in a massive slide which has V-bearings in the housing. The clamping bolt passing through the latter serves as a journal about which both the housing and the slide carrying the centers revolve. A Treatise on Milling and Milling Machines Ti5r SHMT FPU Mv- M«B ^ Soiiie Evidenccs of .^ ""^^KotJons' Dividing Head Accur- s^oTr^z ^ ./^' . ...,H^«.^^-.6^t^«€ were drawn at random D«ta,-«;^///^.«-.«t%4<^^^**^g3.^ from our files. They re- present average accuracy. They are only a few of the many similar tests which every one of our Dividing Heads must pass. We call special attention to the indexing test. This puts our regular product in the same class with instruments of precision. We are able to accomplish this because of special worm and wormwheel generating machines and other special tools which we Fi*. SI have developed for this work Fig. 60 is an example of the accuracy of our index mechanism. Six 1" diameter holes are spaced equally on a circle 141^" in diameter. They are first drilled, then bored to size. The maximum radial error is less than two ten thousandths (.0002) inch, im wmt w mv. wg^^ and the maximum chord- »~»^^-«>-"ii»*-— -*«.ta| ••,• al error is less than three- """'"""""" ^^^ quarter thousandths T.T.Z''S>:iJil,2r''y^-^^ (.00075) inch. The radial ^JrCr.r-^FZ?^ Z^:.«^:Z:: measurement is made D.<.i>.>f.a^!S/^ V a -0 c V u Q •«4 h X d (A 20 15 A 13 10 15 B 13 12 15 E 13 14 15 C 13 31 15 F 13 53 16 E 10 16 F 8 16 A 6 20 16 D 6 24 16 C 6 28 16 B 6 62 17 C 6 106 17 E 5 20 17 C 5 80 17 F 5 65 18 B 5 65 18 A 5 • ■ ■ • ■ 18 C 4 16 19 F 4 44 19 E 4 68 19 A 4 20 ANY 8 28 21 E 3 63 21 A 3 91 22 D 3 10 22 A 3 12 22 F 3 14 23 C 3 31 23 A 3 53 23 E 3 2 24 A 3 7 24 B 3 11 24 E 3 13 24 C 2 24 24 F 2 36 25 A 2 66 25 E 2 78 u 30 36 42 93 159 26 28 30 32 34 86 34 119 153 187 36 99 153 38 133 171 ANY 42 147 44 99 143 46 69 161 30 36 42 93 159 30 175 C 3 ' 01 C -a V 1: ■0 ■5 X No. of CA 1 U 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 01 c 3 h 20 26 F 26 24 26 A 91 28 26 B 169 62 27 B 81 106 27 A 189 13 28 F 28 14 28 E 42 15 28 D 77 16 28 A 91 17 29 E 87 18 30 A 30 12 30 B 36 42 30 E 42 54 30 C 93 66 30 F 159 8 31 C 93 22 32 F 28 34 32 D 32 4 32 B 36 14 32 A 48 18 33 A 99 34 C 34 38 34 E 119 133 34 F 187 36 35 F 28 81 35 D 77 117 35 A 91 34 35 E 119 51 36 B 36 119 36 A 99 20 36 C 153 24 37 B 111 28 38 F 88 62 38 E 133 106 38 A 171 18 39 A 117 105 40 ANY ANY o 14 49 91 39 91 12 18 33 39 33 10 12 14 31 53 27 7 8 9 12 21 6 21 33 4 11 13 17 4 11 17 9 2 7 9 3 A Treatise on Milling and Milling Machines 73 Index Table for High Numbers — Continued « 1 * « c o c c c « "tfl V V > V ji (A 1^ > V V N fl "5 *-4 "S "c fl "5 •3 c C/3 S c C/3 u X (A a X • c c • z i . 525 2 41 c 123 120 66 A 99 60 92 A 69 30 42 E 42 40 67 B 67 40 92 E 161 70 42 A 147 140 68 C 34 20 93 C 93 40 43 A 129 120 68 E 119 70 94 B 141 60 44 D 44 40 68 F 187 110 95 F 38 16 44 A 99 90 69 A, 69 40 95 E 133 56 44 F 143 130 70 F 28 16 95 A 171 72 45 B 36 32 70 D 42 24 96 B 36 15 45 A 99 88 70 A 91 52 96 • A 48 20 45 C 153 136 70 E 119 68 97 B 97 40 46 C 46 40 71 F 71 40 98 A 147 60 46 A 69 60 72 B 36 20 99 A 99 40 46 E 161 140 72 A 117 65 100 A 30 12 47 B 141 120 72 C 153 85 100 E 175 70 48 A 30 25 73 E 73 40 101 F 101 40 48 B 36 30 74 B 111 60 102 C 153 60 49 A 147 120 75 A 30 16 103 E 103 40 50 A 30 24 76 F 38 20 104 E 26 10 50 E 175 140 76 E 133 70 104 A 91 35 51 C 153 120 76 A 171 90 104 F 143 55 52 E 26 20 77 D 77 40 104 B 169 65 52 A 91 70 78 A 11-7 60 105 E 42 16 52 F 143 110 79 C 79 40 105 A 147 56 52 B 169 130 80 E 26 13 106 F 159 60 53 F 159 120 80 F 28 14 107 D 107 40 54 B 81 60 80 A 30 15 108 B 81 30 54 A 189 140 80 D 32 16 108 A 189 70 55 D 44 32 80 C 84 17 109 C 109 40 55 F 143 104 80 B 36 18 110 D 44 16 56 F 28 20 80 E 42 21 110 A 99 36 56 E 42 30 81 B 81 40 110 F 143 52 56 D 77 55 82 C 123 60 111 B 111 40 56 A 91 65 83 F 83 40 112 F 28 10 57 A 171 120 84 E 42 20 112 E 42 15 58 E 87 60 84 A 147 70 113 F 113 40 59 A 177 120 85 C 34 16 114 A 171 60 60 A 30 20 85 E 119 56 115 C 46 16 60 B 36 24 85 F 187 88 115 A 69 24 60 E 42 28 86 A 129 60 115 E 161 56 60 F 159 106 87 E 87 40 116 E 87 30 61 B 183 120 88 D 44 20 117 A 117 40 62 C 93 60 88 A 99 45 118 A 177 60 63 A 189 120 88 F 143 65 119 E 119 40 64 D 32 20 89 D 89 40 120 A 30 10 64 A, 48 30 90 B 36 16 120 B 36 12 65 E 26 16 90 A 99 44 120 E 42 14 65 A 91 56 90 C 153 68 120 C 93 81 65 F 143 88 91 A 91 40 120 F 159 53 65 B 169 104 92 C 46 20 121 D 121 40 74 The Cincinnati Milling Machine Company Index Table for High Numbers — Continued 0) C 'S > Q V (0 u Divisions i •*< V «8 "o Divisions ' 1 II CA X (A U ^ 1 1 tfi X • • • z 183 60 160 F 197 c 122 B 28 7 197 40 123 C 123 40 160 D 32 8 198 A 99 20 124 C 93 30 160 B 36 9 199 B 199 40 125 E 175 66 160 A 48 12 200 A 30 6 126 A 189 60 161 E 161 40 200 E 175 35 127 B 127 40 162 B 81 20 202 F 101 20 128 D 32 10 163 D 163 40 204 C 153 30 128 A 48 15 164 C 123 80 205 C 123 24 129 A 129 40 165 A 99 24 206 E 103 20 130 E 26 8 166 F 83 20 208 E 26 5 130 A 91 28 167 C 167 40 '' 210 E 42 8 130 F 143 44 168 E 42 10 210 A 147 28 130 B 169 52 168 A 147 35 212 F 159 30 131 F 131 40 169 B 169 40 214 D 107 20 132 A 99 30 170 C 34 8 215 A 129 24 133 E 133 40 170 E 119 28 216 B 81 15 134 B 67 20 170 F 187 44 216 A 189 35 135 B 81 24 171 A 171 40 218 C 109 20 135 A 189 56 172 A 129 30 220 D 44 8 136 C 34 10 173 F 173 40 220 A 99 18 136 E 119 35 174 E 87 20 220 F 143 26 137 D 137 40 175 E 175 40 222 B 111 20 138 A 69 20 176 D 44 10 224 F 28 5 139 C 139 40 177 A 177 40 226 F 113 20 140 F 28 8 178 D 89 20 228 A 171 30 140 E 42 12 179 D 179 40 230 C 46 8 140 D 77 22 180 B 36 8 230 A 69 12 140 A 91 26 180 A 99 22 230 E 161 28 141 B 141 40 180 C 153 84 232 E 87 16 142 F 71 20 181 C 181 40 234 A 117 20 143 F 143 40 182 A 91 20 235 B 141 24 144 B 36 10 183 B 183 40 236 A 177 30 145 E 87 24 184 C 46 10 238 E 119 20 146 E 73 20 184 A 69 15 240 A 30 6 147 A 147 40 184 E 161 35 240 B 36 6 148 B 111 30 185 B 111 24 240 E 42 7 149 E 149 40 186 C 93 20 240 A 48 8 150 A 30 8 187 F 187 40 242 D 121 20 151 D 151 40 188 B 141 30 244 B 188 30 152 F 88 10 189 A 189 40 245 A 147 24 152 E 133 35 190 F 38 8 246 C 123 20 152 A 171 45 190 E 133 28 248 C 93 15 153 C 153 40 190 A 171 36 250 E 175 28 154 D 77 20 191 E 191 40 252 A 189 30 155 C 93 24 192 A 48 10 254 B 127 20 156 A 117 30 193 D 193 40 255 C 153 24 157 B 157 40 194 B 97 20 256 D 32 6 158 C 79 20 195 A 117 24 258 A 129 20 159 F 159 40 196 A 147 30 260 E 26 4 A Treatise on Milling and Milling Machines 75 Index Table for High Numbers — Continued (A to (A c c B (0 '3 « > V ju w V > V jj > V jj Q 3 "5 fl ■«4 "S Q -0 ««4 "5 "3 Oi •p4 X C/) o X W •«4 X d o • iz: !z: z 260 A 91 14 305 B 183 24 355 F 71 8 260 F 143 22 306 C 153 20 356 D 89 10 260 B 169 26 308 D 77 10 358 D 179 20 262 F 131 20 310 93 12 360 B 36 4 264 A 99 15 312 A 117 15 360 A 99 11 265 F 159 24 314 B 157 20 360 C 153 17 266 E 133 20 315 A 189 24 362 C 181 20 268 B 67 10 316 C 79 10 364 A 91 10 270 B 81 12 318 F 159 20 365 E 73 8 270 A 189 28 320 D 32 4 366 B 183 20 272 C 34 5 320 A 48 6 368 C 46 5 274 D 137 20 322 E 161 20 370 B 111 12 276 A 69 10 324 B 81 10 372 C 93 10 278 C 139 20 326 D 163 20 374 F 187 20 280 F 28 4 328 C 123 15 376 B 141 15 280 E 42 6 330 A 99 12 378 A 189 20 280 D 77 11 332 F 83 10 380 F 38 4 280 A 91 13 334 C 167 20 380 E 133 14 282 B 141 20 335 B 67 8 380 A 171 18 284 F 71 10 336 E 42 5 382 E 191 20 285 A 171 24 338 B 169 20 384 A 48 5 286 F 143 20 340 C 34 4 385 D 77 8 288 B 36 5 340 E 119 14 386 D 193 20 290 e 87 12 340 F 187 22 388 B 97 30 292 E 73 10 342 A 171 20 390 A 117 12 294 A 147 20 344 A 129 15 392 A 147 15 295 A 177 24 345 A 69 8 394 C 197 20 296 B 111 15 346 F 173 20 395 79 8' 298 E 149 20 348 E 87 10 396 A 99 10 300 A 30 4 350 E 175 20 398 B 199 20 302 D 151 20 352 D 44 5 400 A 30 3 304 F 38 5 354 A 177 20 • Note. — ^These three plates have holes as follows: ^ /A— 30, 48, 69, 91, 99, 117, 129, 147, 171, 177, 189 i-LATE j 3_3g^ Q^^ gj^ gy^ jjj^ ^27, 141, 157, 169, 183, 199 p /C— 34, 46, 79, 93, 109, 123, 139, 153, 167, 181, 197 i-LATE I j)_32^ 44^ 77^ 89^ 107, 121, 137, 151, 163, 179, 193 p /E— 26, 42, 73, 87, 103, 119, 133, 149, 161, 175, 191 i-LATE j p_2g^ 3g^ 71^ 83^ iQi^ 113^ 131^ 143^ 159^ 173^ 187 76 The Cincinnati Milling Machine Company STANDARD INDEX TABLE For the Standard Index Plate Used with Dividing Head INDEXES ALL NUMBERS UP TO AND INCLUDING 6o; ALL EVEN NUMBERS AND THOSE DIVISIBLE BY 5 UP TO 120, AND ALL DIVISIONS OBTAINABLE UP TO 4OO. This Plato it drilled oa both tidet and has holes as follows: FIRST SID £—24-25-28-30-34-37-38-39-41-42-41. SECOND SIDE— 46-47-49-51-53-54-57-58-59-62-66. 1 1 « OB s 8 m s 1 S • m 1) H » •s 3 » •s 5 S U 8 S 1 i 1 1 2 ANY 20 • • 44 66 60 104 39 15 205 41 8 3 24 13 8 45 54 48 105 42 16 210 42 8 4 ANY 10 • • 46 46 40 106 53 20 212 53 10 5 ANY 8 • • 47 47 40 108 54 20 215 48 8 6 24 6 16 48 24 20 110 66 24 216 54 10 7 28 5 20 49 49 40 112 28 10 220 66 12 8 ANY 5 • • 50 25 20 114 57 20 224 28 5 9 54 4 24 51 51 40 115 46 16 228 57 10 10 ANY 4 • • 52 39 30 116 58 20 230 46 8 11 66 3 42 53 53 40 118 59 20 232 58 10 12 24 3 8 54 54 40 120 66 22 235 47 8 13 39 3 3 55 66 48 124 62 20 236 59 10 14 49 2 42 56 28 20 125 25 8 240 66 11 15 24 2 16 57 57 40 130 39 12 245 49 8 16 24 2 12 58 58 40 132 66 20 248 62 10 17 34 2 12 59 59 40 135 54 16 250 25 4 18 54 2 12 60 42 28 136 34 10 255 51 8 19 38 2 4 62 62 40 140 28 8 260 39 6 20 ANY 2 • • 64 24 15 144 54 15 264 66 10 21 42 38 65 39 24 145 58 16 270 54 8 22 66 54 66 66 40 148 37 10 272 34 5 23 46 34 68 34 20 150 30 8 280 28 4 24 24 16 70 28 16 152 88 10 290 58 8 25 25 16 72 54 80 155 62 16 296 37 5 26 39 21 74 37 20 156 89 10 300 30 4 27 54 26 75 30 16 160 28 7 304 88 5 28 42 18 76 38 20 164 41 10 310 62 8 29 58 22 78 39 20 165 66 16 312 39 5 30 24 8 80 34 17 168 42 10 320 24 3 31 62 18 82 41 20 170 34 8 328 41 5 32 28 7 84 42 20 172 43 10 330 66 8 33 66 14 85 34 16 176 66 15 336 42 5 34 34 6 86 43 20 180 54 12 340 34 4 35 28 4 88 66 30 184 46 10 344 43 5 36 54 6 90 54 24 185 37 8 360 54 6 37 37 3 92 46 20 188 47 10 368 46 5 38 38 2 94 47 20 190 38 8 370 37 4 39 39 1 95 38 16 192 24 5 376 47 5 40 ANY • • 96 24 10 195 39 8 380 38 4 41 41 • • 40 98 49 20 196 49 10 390 39 4 42 42 f • 40 100 25 10 200 30 6 392 49 5 43 43 40 102 51 20 204 51 10 400 30 8 A Treatise on Milling and Milling Machines 77 CHAPTER IV SETTING UP THE MACHINE Placing Cutters on the Arbor. When setting up the machine preparatory to milling a piece of work, care should be taken to have the cutters as close to the end of the spindle as the work will per- mit. Milling Machine arbors in general use are as a rule very much smaller in diameter than they should be, and then- weakness is simply emphasized by placing cutters at or near the middle of a long, unsup- ported arbor. Cutters on hand may have small holes, making small diameter arbors necessary, but whenever new cutters are ordered, careful consideration should be given to having them made large enough to permit of using arbors of large diameter, since it is only with properly designed cutters and arbors of sufficient size that the best results can be obtained from modem High-Power Milling Machines. (See paragraph on chattering, page 87.) Cutters should always be keyed to the arbors. The friction due to tightening up the arbor nut can not be expected to hold them. Particular attention should be paid to the proper cleansing of the hole in the spindle and the taper shank of the arbor. Unless this point is carefully watched, a true running arbor can not result, accurate work can not be secured, both the hole in the spindle and the bush in the arbor support will be spoiled. The body of the arbor, the arbor collars, and the shank should be thoroughly cleaned before the cutters and collars are placed on the arbor. Any foreign matter between these members will bend the arbor when the nut is tightened. Arbor Supports. We supply with all our machines two differ- ent styles of arbor supports. For the small arbors which have a bearing on the outside of the arbor nut, there is a suitable adjust- able bronze bush in one of the supports. The larger arbors all have one or two spacing collars that are larger than the rest, and these collars fit the bushing in the arbor bearing bracket and serve to give the arbor an additional support. This bearing collar should be as close to the cutters as practical so that the support may be close to the cutters and thus properly support the arbor. The 78 The Cincinnati Milling Machine Company braces for tying the arbor support to the knee of the machine should always be used if the work will permit. SPlNDUft ji fig. 70 Fig. 70. All short arbors are provided with a pilot bearing at the end. This fits a split bronze bushing, X, in the arbor support. Adjust this bushing to a close bearing. Fig. 71 Fig. 71. Some medium length arbors have in addition to an end pilot bearing, X, as above, an arbor bearing collar to fit the intermediate support Y. This support should be placed as close to the cutter as practical, the cutter itself being located as close to the shoulder of the arbor as conditions will permit. 6PiN0Le Fig. 72 Fig. 72. Another style of medium length arbor does not have the pilot bearing for bronze bush at end, but is furnished with a bearing collar which permits of placing the support anywhere close to the cutter. EB Fig. 73 Fig. 73. All our long arbors have two bearing collars. When- ever possible, one of these, Y, should be placed between cutters that are spaced some distance apart on the arbor and the other, Z, to which the braces are fastened, should be as close to the out- side of the gang as conditions will permit. A Treatise on Milung and Milung Machines Fig. 74. Another way of supporting a long arbor. In this case the width of the table does not permit of bringing the support Z, to which the braces are fastened, close to the cutters. The inter- mediate support Y is therefore placed close to the gang and between it and the outer support Z. Fig. 75. Sometimes the nature of the work requires the cutters to be near the outer end of the arbor. Then the intermediate support Y should be placed inside of the gang, that is, between the gang and the spindle. Fig. 76. The Wrong Way. In all of the above cases the cut- ters have been placed as near the end of the spindle as conditions permit. When this was not possible the supports have been placed close to each side of the cutters. Compare these conditions with this sketch, which shows a cutter in the middle of a long, unsupported arbor. This sort of set-up should never be tolerated. It can not possibly produce satisfactory results. The Cincinnati Milung Machine Company The Drive for Arbors and Cutters. All of our High Power Machines as well as our larger Cone Driven Machines, Automatic Machines and Manufacturing Machines have flanged spindles, as shown in Fig. 77. These flanges are fitted with hardened keys. ^m -l-MTHS.US.S ■fl FULL DEPTH OF THREAD A Treatise on Milung and Milling Machines 81 The cutter arbors are made of solid f orgings providing corresponding flanges for driving. This provides a powerful, durable drive that is not easily injured even when doing the heaviest cutting. Face mills are driven in the same way. They are slightly counterbored to fit over the flanges, thus centering them, and they are recessed to receive the driving keys. They are held in place by four screws. NO. 3 HIGH POWER SiCo'^H^wlrtR .. <.-4P.-S™..ut^-m«<. This is sunpler than the use of threaded spindle ends; it makes a more powerful drive, and mills are easily removed after doing heavy cutting. The same face mill will fit all sizes and styles of Cincinnati Millers which have flanged spindle ends. This complete interchange- ability reduces the number of face mills it is necessary to keep on hand. Complete working dimensions for use when making face 82 The Cincinnati Milling Machine Company mills to fit standard flanged spindle ends are given in the drawing. Fig. 78. Spindle Flanges for Threaded Spindles. It will be found very simple to put flanges on the older machines having threaded spindle ends, and thus gain the full advantage of complete inter- changeability of face mills between these and the later machines. On some sizes such a flange will also adapt the older machine for using the new flanged arbors. The sketches, Fig. 79, show flanges suitable for Cincinnati Millers with threaded spindles as made in recent yeara, and give sufficient dimensions to enable anyone to make similar flanges to suit the spindle ends of any other Cincinnati machines. Cutter Arbors. AH our arbors 1' diameter and larger have standard keyways as listed in the table. These are also the standard keyways used in cutters. Standard Keyways for Cutters and Arbors Diameter ot Hole (D) Width (W). Depth {A), Radius (R), in Cutter, Inchea Inches A A .020 030 AtolJ^ It^lV A 040 050 P» 2Ato2 060 2Ato3 A A 060 Cutters should be held on the arbor by keys that are a good side flt in the keyways in both the cutter and the arbor. The height of the key should be a little less than twice A, so as to have top clearance. A key that flts top and bottom like a wedge and not on the sides is bad because it will roll and ruin the arbor, and prob- ably split the cutter in two. A Treatise on Milling and Milung Machines 83 When heavy cutting is done, there is always the danger that the . side pressure will cause the key even when properly fitted, to crush in the side of the keyway in the arbor. It is beat to make the key longer than the cutter. This is especially true of narrow cutters such as saws. By using a long key the pressure ia distributed over a greater area, reducing the tendency to crush the keyway. The better method of driving large narrow saws is through a flange fitted with pins which will drive through holes drilled in the saws. For especially heavy sei-vice, the special key and keyway, Fig. 81, was designed, the idea being to substitute for the shearing action of the ordinary key, a wedging action that would have no tendency to distort either key or arbor. The arbor is first flattened and then a standard size keyway is milled into it. The keyway in the cutter is an arc of a circle and the key is made out of a piece of round stock milled in on both sides and then sawed apart lengthwise, one piece of stock forming two keys. If, for instance, the driving pressure is from right to left, the key will be forced over to the right and the flat portion of the key pressed down on the flat on the left of the arbor. This procure being almost directly downward, there is practically no side pressure, and therefore no distortion of the keyway in the arbor can result. This style of key has proven very satisfactory. Cutters so mounted can be readily removed after the heaviest milling. a B c D E F G H J .9737 A A 1 1.0518 ft n .0263 1.0378 1.1159 .0247 1.2187 iH 1.4543 IH 1.5793 .0457 1.7111 H i% 1.8361 H U .0389 1,9473 ft A 2 2.1036 ft ft 84 The Cincinnati Milling Machine Company Standard Gutter Arbors Carried in Stock SSSfffI style A Style B iPlllMiili Style C Style D Style F Style G Style J Fig. 82. MUling Cutter Arbors We carry in stock arbors as listed. We no longer put tangs on arbors, because tangs are not strong enough to do the heavy work that is now being required of milling machines. The small end of the arbor shank is tapped ^'^, 11 for drawing-in bolt, and a ^'^ bolt long enough to reach through the spindle of the machine and draw the arbor firmly into the taper, is furnished as part of the equipment of every machine. All arbors 1" diameter and over are splined for standard keys. machines on which they fit No. Style No. of Taper Diame- ter Length from Shoulder to Nut Diame- ter of Bearing Collar Flanged Code Word ^ r^U 1 ^ r^ 1/ Y^ j"^ 08 09 A A 9 9 .'^ 5 6 Brail 18" and 18" B. G Bream 1 and 2 Plain and Uni- 7 9 *10 11 13 41 43 44 45 A A A A A D D D D 10 10 10 10 10 10 10 10 10 1 1 1 6 6 8 8 8 uy2 27 27 Broth versal Cone Ma- Bugle chines: also No. 2 Bung High-Power when spindle end is threaded. 12" Plain Manufacturing Machines use Ar- bors Nos. 41 and 43. Buoy Busby 2 2 2 2ys Chime Chink Chix Choir A Treatise on Milling and Milling Machines 85 Standard Cutter Arbors— Continued machines on which they fit No. style No. of Taper Diame- ter Length from Shoulder to Nut Diame- ter of Bearing Collar FlaDged No. 3 Plain and Uni- versal Cone Type, with threaded spin- dle end. 12', 18', 24*Aut. Machines. 16 18 53 55 56 A B D D D No. 3 High-Power Plain and Univer- sal, No. 3 Plain and Universal standard when spindle end is threaded 16-C 18-C 53-C 55-C 56-C 59 57 C C F F F F F Nos. 2 and 3 High- Power Plain and Universal, No. 3 Plain and Universal Cone and Nos. 3 and 4 Plain and Universal Standard with flanged spindle end. tl2', 18', 24' Automatic with flanged spindle end. Nos. 4 and 5 Plain and Universal Cone and High - Pow- er Millers when spindle end is threaded Nos. 4 and 5 Plain and Universal High-Power, also No. 4 Plain and Universal Cone with flanged spindle end. 90 A 91 G 92 G 93 J 94 J 95 J 96 J 101 J 102 J 103 J ^4 1 10 10 2^ 2^-8 1 1 10 12 18^ 18J^ 29 29 Note 2^ 2?^ 2?^ 2?^ 2^ 23^ 16 B 1 10 2% 81 1 G m tl2 2% 83t J Wx tl8J^ 2^ 84t J I'A nm 2% 85 J IH 29 2% 86 J m 29 2% 12 12 12 12 12 12 12 12 12 12 23 C 12 1 10 Note 25 C 12 IM 12 2^ 26 C 12 m 14 2H 66 F 12 IH 26 2^ 67 F 12 IH 26 2^ 68 F 12 m 26 2^ 69 F 12 2 26 2^ 70 F 12 IH 32 2^ 77 F 12 m 32 2ys 78 F 12 IH 32 2% 71 F 12 2 32 2Vs 75 F 12 IH 36 2% 76 F 12 IH 36 2H 73 F 12 2 36 2% 'A y^ y4. 10 12 14 26 26 26 26 36 36 36 Code Word Cabal Calp CliANQ Cliff Cloud Caddy Camel Cleft Cloak Clove Codex Coach Yes Yes Cabal Czech Czar Yes ' Bryce Yes Brus Yes Brin Canal Caper Caul Calon Calza Comet Copse Copul Crier Crimp Covet Creel Crib Crave 2% Yea 2H Yes 2Vb Yes 2% Yes 2% Yes 2% Yes 2% Yes 2^ Yes 2^ Yes Blif Blup Blyo Byrt BiXY BiZA BlUD Bewe Buxe Buzz NOTE — No. 16-C and No. 23 are not furnished with a bearing collar. •When it ia necessary to use a \' arbor on the larger machines we recommend this No. 10 arbor in connection with standard collets as follows: No. 3 Cone-Type Machines with threaded spindle ends, use *'P" collet. No. 3 High-Power and No. 3 Standard Machines with threaded spindle ends, use '*PP" collet. Nos. 2 and 3 High-Power and No. 3 Standard Machines with flanged spindle ends, use "P" collet. Noe. 4 and 5 Machines with threaded spindle ends, use "H" collet. Nos. 4 and 5 Machines with flanged spindle ends, use ''N" collet. 86 The Cincinnati Milling Machine Company Arbor Equipments for Millers are as Follows: Cone-Type Machines Machine Size Arbor Included Arbor Sent on Approval 18' PI. 18' B. G. IPl. 2 PL 3 PI. 4 PI. lUn. 2Un. 3Un. 4Un. No. No. No. No. No. No. No. No. No. No. 09—1' 09—1' 11—1' 41—1' 11—1' 43— IJi' 81-lM*' 86-1^' 92—11^' 103—2' X 6' X 6' X 8' xWA" X 8' xl4H' X 12' x29' X 14' No. No. No. No. 11 1' 11—1' 16-1' X X X X 8' 8' 10' 12' x36' No. No. No. 43—1^' 86-1^" 103—2' xl4J^' x29' x36' High-Power Machines Single Pulley with Flanged Spindle Ends Machine Size Arbor Included Arbor Sent on Approval 2 PI. Std. Std. Std. Std. • No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. No. 16—1' X 10' 3 PI. 86— IH' X 29' 81 lli" X 12' 3 PI. SQ—VA' X 29' 81 IW' X 12' 4 PL 86—13^' X 29' 81 lli" X 12' 4 PL 86— li^'x29' 92 IH' X 14' 5 PL 103—2' X 36' 94_114» X 26' 2Un. 3Un. 3Un. 4Un. 4Un. 5Un. No. No. No. No. No. No. 16—1' 16—1' 16—1' 16—1' n—iii" 92— VA" X 10' X 10' xlO' xlO' xl2' xl4' 103—2' X 36' 86— IJ^' X 29' 86—11^' X 29' 86—13^' X 29' 86—11^' X 29' 103—2' X 36' 103—2' X 36' A Treatise on Milling and Milling Machines 87 Chattering Probably the greatest annoyance to which users of Milling Machines are subjected, is the peculiar action called "chattering." This is a condition of vibration that sometimes is so serious as to affect the entire machine, and frequently gives the impression that it is caused by the driving gearing. This is hardly ever the case. Chattering always starts at the cutter, and whatever vibration may result from it in other members is due entirely to this intermittent motion of the cutter as it passes through the work and this motion carried through the spindle and gears causes a corresponding and exaggerated vibration in those members. We can not emphasize too strongly that chattering always starts at the cutter, although the fault may not always lie in the cutter itself. The action of the cutter at work is fully described in the chapter on An Analysis of the Process of Milling. Now, if the cutter can spring away from the work, or if the cutter is not properly sharpened so that it alternately digs in and then slides over the work again, it throws intermittent torsional strains on the arbor and these are carried through to the gears. When investigating the trouble it is well to make sure first that the machine is in proper adjustment, especially the spindle; that the arbor is properly fitted into the spindle and securely held there; that the cutters and arbor supports are all as close to the end of the spindle as possible so as to keep the arbor from bending and springing away from the work; that the braces are properly attached and that the table, saddle and knee gibs are properly adjusted. If all these things are as they should be, the cause of the chatter lies either in the cutter, the method of mounting the cutter, the work itself, the method of holding the work, or a combination of some or all of these. Mounting the Work. The work should be mounted so as to bring the cutter as near the end of the spindle as possible and then the outer arbor support should be brought as close to the cutter as the work will allow. You can not get good results from a cutter held in the middle of a V arbor, 16'' or 18" long, supported at its outer end only. The arbor should be as large as possible. The work must be securely held either in the vise or in a properly designed fixture, and the fixture itself must be strong enough to hold the work. 88 The Cincinnati Milling Machine Company We have known of serious cases of chattering that were caused by the operator having failed to carefully clean the fixture before inserting a new piece with the result that the piece rocked in the fixture. In another case, pieces made on an automatic machine were held in an excellent fixture made to fit the pieces and hold them securely, but serious chattering resulted from the fact that when adjusting the automatic machine which made the pieces, after the tools had been sharpened, the pieces were not made to the exact size as before, and therefore did not fit the jig. Although they were held down tight enough for the milling operation, they were not properly supported and this caused all the trouble. Yet our customer did not suspect this because he felt sure that the pieces were being turned to uniform size and shape. Sometimes the work itself is so frail that it springs under the cut and this induces chattering. When the arbor is of proper size and the cutters are properly mounted; the work of sufficient strength to stand the cut and securely held in proper fixtures, serious chattering may still result because of a faulty cutter. It is certain that if each tooth of a cutter has an opportunity to take an even chip of the same size, there will be no chattering provided that each tooth has an opportunity to take a chip of adequate thickness. Cutters with teeth close together are almost sure to chatter because the chip per tooth becomes so small that it is practically impossible for each tooth to take a chip. This condition is exaggerated if a slow feed rate is used. For instance, if we have an old-fashioned cutter with 16 teeth, feeding .008*' per revolution, each one of these 16 teeth has a chance to take a maxi- mum chip only .0005" thick. It is not practical to grind a cutter that will run as accurately as this after it has been mounted on the arbor. Some of the teeth will therefore slide over the work. Even with all the other conditions as they should be, such a cutter is likely to cause those minute vibrations which produce the high pitched singing effect. If the feed in this case is increased to .030 or .040*' per revolu- tion, the difficulty is quite sure to disappear. Again, an entirely new cutter of correct design may cause chattering because the cuttermaker, not knowing on what class of work the cutters will be used, usually grinds them with about 7° clearance. This is about 50% more than it should be for cast iron and about twice what it should be for steel. Such a cutter having too much clearance will dig into the work and then spring back again at close intervals, causing the worst kind of chattering conditions. A Treatise on Milling and Milling Machines 89 Every new cutter should therefore first be properly sharpened for the work to be done. It sometimes happens that a cutter chat- ters when first put into the machine and after some use the chattering disappears. This is because the extreme cutting edge has been worn off a sufficient amount to reduce the clearance at the edge. One of the classes of milling that causes annoyance is milling keyways in shafts. These keyways usually are at the end of the shaft. The clamps are therefore some distance back from the end. The result is that when the cutter enters the work it lifts the shaft off the Milling Machine table, and of course, chattering results. On such work the trouble is exaggerated because usually milling cutters with side teeth are used. We recommend against this. A cutting-off tool in a lathe does not have side teeth, yet the action is the same. A plain milling cutter of proper width, with its sides very slightly hollow-ground will produce better results and the action of such a cutter will be still further improved if about two- fifths of the width of the teeth is ground off alternately so that each tooth will take a chip a little more than one-half, of the width of the keyway to be cut. (See Chapter on Milling Cutters.) Frequently some degree of chattering is induced by the cutter not running true and it is not unusual for the user to feel that this is caused by either the hole in the spindle of the miller or the arbor not being true. This may be the case if the arbor and the hole in the spindle are not always carefully cleaned before inserting the arbor but the trouble is frequently due to the cutter teeth not having been ground true with the hole. Remedies for Chattering — Make sure that the machine is in proper adjustment all over; make sure that the arbor is of proper size; that its shank fits the hole in the spindle; that it is clean, and that the cutters are properly mounted and the arbor properly supported. The piece of work must be securely held and properly supported so it can not spring. If the cutter is the old-fashioned kind with teeth close together, grind out every other tooth. If the clearance angle is too great, reduce it. Cutters should be of the design as described in the chapter on Milling Cutters. These cut- ters used with a suitable feed rate are sure to eliminate chattering if other conditions are anywhere near right. If everything else appears to be in proper order, it is advisable to change the feed rate. Increasing the feed frequently improves the relation of each tooth to the size of chip that it takes to such an extent, as to stop 90 The Cincinnati Milung Machine Company the chattering action. All of the above refers to Milling Machines using cutters on an arbor. When face mills are used, particularly on Vertical Machines, too wide a cutting face on the teeth of the mills may cause chatter. The actual work of a face mill is not done by the face edges of the teeth, but by the peripheral edges. The face edges should therefore, not be too wide, or they will have a dragging action on the work which will induce vibration. These face edges should be only about ^^ wide and the balance of the width of the blade should be ground back towards the center of the mill at an angle of about 7° (Fig. 83.) Since chattering is really a synchronizing of the vibrations due to the different strains set up by cutting, it will sometimes be found effective to release some member, as for instance, one side of the brace, in order to break up this synchronispi. Another point to be watched is the base of the fixture. It is not enough for the milling fixture to be strong enough to withstand the feed strain. It ought to be heavy enough to absorb the vibrations as dis- cussed in the chapter on Milling Fixtures, but it is proper to say here that the provision of adequate end supports and clamps will often do away with a good deal of chatter. This is particularly true of pieces which stand high above the table, in which case the pressures or forces resulting from the cut have a great moment around the knee. PKRIPMKRAL Fic. 83 Outline of a properly sharpened face mill. A Treatise on Milung and Milling Machines CHAPTER V AN ANALYSIS OF THE PROCESS OF MILLING The preceding pages describe the various types of Milling Machines available for the work to be done in most machine shops and toolrooms. Bearing these machines in mind, we will proceed with an analysis of the process of milling and a discussion of the tools used. Milling is the removal of metal by means of a tool which rotates while the work is advancing or feeding in a direction at some angle with the axis of the tool. When we mill with an ordinary spiral mill, the axis of the tool is the center line of the arbor or spindle and the feed takes place at right angles to this axis. When we vse a face mill on a Vertical Machine the axis of the tool is vertical, but the table again feeds at right angles to the axis. When we cut spiral gears the axis of the tool is the same as the axis of the spindle, and the table travels at an angle with this axis, but this time it is not a right angle. Classification of Milling Cutters The tools used for milling are called milling cutters. Milling cutters as we know them have a number of teeth, but it is not abso- lutely necessary that they should have a large num- ber; in fact, some milling cutters have only one tooth. Such cutt«rs are called fly cutters. With the exception of fly cutters, all cutters are bodies of revolution. A body of revolution is a body "*• ** with such a shape that it can be formed in a lathe; in other words, a body which has a central axis. The simplest bodies of revolution we know are cylinders. 92 The Cincinnati Milling Machine Company cones and spheres, but a body of revolution may have any imaginable section. When such a body of revolution is provided with cutting teeth, it becomes a Milling Cutter. When the teeth are on the outside of the cylinder, as in Fig. 84, it is called a Spiral Mill. When the teeth are on the base of the cylinder, as in Fig. 85, it is called a Face Mill. When a face mill is of small diameter and of rela- tively great length, it is called an End Mill, Fig. 86. When the teeth are cut on a truncated cone, Fig. 87, it is called an Angular Mill; and when it is neither a cylinder nor a cone, but has an irreg- ular outline, it is called a Form Cutter, Fig. 88. "'*■ «' From these five fundamental forms of cutters a great variety of shapes and styles of cutters for different purposes has been developed. The Action of a Milling Cutter Most of the difficulties in milling arise from the peculiar shape of the chip. The action of a milling cutter at work is therefore a very important thing to keep in mind. It will readily be seen with- out much discussion that the chip as taken by an ordinary milling cutter, a formed cutter or an angular cutter, is approximately of the shape as shown in Fig. 89, in the shaded portion. The cutter enters at A and leaves at B. When it enters, the chip has no thickness, theoretically speaking; when it leaves, the chip has its maximum thickness. Fig, 90 gives us a somewhat ^"' ** better idea of the shape of such a chip, but, whereas Fig, 89 completely overlooked certain things. Fig. 90 grossly exaggerates these same points. Here a milling cutter A Treatise on Milung and Milung Machines 93 is shown with its center at 0|. This same cutter is also shown with its center at Oj, and it is supposed that the cutter has advanced in relation to the work from Oj to O2 during the time it made one revolution; in other words, that this distance OiOa K the feed per revolu- tion. (As a matter of fact, it is not the cutter which advances, but the work. However, the ef- fect is the same and the problem is simplified by assuming that the cut- ter has advanced as shown.) The cutter Fi(. ST which we have repre- sented here is supposed to have only one tooth and this tooth is shown in the position it would be in when the center of the cutter has arrived at O2- The line XY shows the top of the work when rough. The line VW shows the top of that part of the work which is finished. The curve YV has been swept out by the tooth of the milling cutter when its center was at Oi. It will be seen that the tooth ABC strikes the work at the point B, and that this point B is a little higher than the finished line VW. It will also be seen that at this moment the cutting edge of the tooth advances not only to the left, but also slightly downward, following the curve BR, and that it has to compress the metal of the work before it gets to the vertical position. This is not true cutting of metal because some of the parts of the metal have to be squeezed downward into the work. It is more like a punching operation. The metal has to flow away from the cutter to give the cutter _ ^ a chance to enter. Fig. 91 gives a better and less exaggerated idea of what actually happens. The distance O1O2 ia more than is ordinarily used in practice. It is true that such an amount of feed, or even more, is used per revolution, but not per tooth, and we are assuming a cut- 94 The Cincinnati Milling Machine Company Fig. 89 ter that has only one tooth. Fig. 91 shows that the tooth enters almost, but not quite, in a vertical position, and that the height of this little hill as shown at B in Fig. 90, is very small indeed, and that, therefore, there is perhaps more of a chance that the cutter will slide over the metal to be removed than that it will penetrate. This is actually what happens in practice — the tooth does not penetrate at once, but slides over the work. In doing so, the cutter and the arbor are lifted or sprung up and put an increasing amount of pressure on the work. This pressure finally becomes great enough to make the tooth of the cutter penetrate into the metal. From that moment on the chip is being removed. There is something that makes the action described even more pronounced, and that is that a cutter is never absolutely sharp. However nicely a cutter tooth may be ground, it will be found that its edge is slightly rounded when viewed under a strong enough magnifying glass. It is obvious that such a rounding helps the tooth to slide over the work and delays the moment when the tooth actually begins to penetrate. All these things are not visible to the casual observer because the distances are so small and the cutter goes around so fast, but an analysis of the cutter ac- tion shows that these oc- currences must actually take place. Fig. 92 shows the cut- ter in various positions, each position being ahead of the previous one the amount of the feed per revolution. This sketch again is much exagger- ated to show that the finished surface as obtained is not an absolutely smooth surface, but has ridges running across. We are all familiar with these ridges. They determine the quality of the finish of the milled piece. It is plain that these ridges must be close together in order to give a toler- able finish. For mere roughing operations, the distance between the Fltf. 90 A Treatise on Milling and Milling Machines 95 ridges is of no importance, but for finished work these ridges must be close together, and the better the degree of finish required the nearer these ridges must be to each other. Revolution Marks. These ridges are sometimes called "tooth- marks." They are not toothmarks at all — they are revolution marks. If these marks were really toothmarks, then it would be possible to get the ridges very close together by simply putting more teeth in the cutter. However, as I I / * matter of fact, the number of the teeth in the cutter does not affect the distance between these marks at all. This can be proven I by putting two cutters next to each PI J, other on the same arbor. The cut- ters should preferably be of the same diameter and should have different numbers of teeth. They should be so placed that a pair of teeth are in line with each other. Then take a cut with both cutters at the same time over one piece of metal and you will find two important things. In the first place, the two cuts side by side have exactly the same number of ridges per inch, showing that the number of teeth has no influence. In the second place, you will find that the ridges made by the two cutters are not in line with each other, notwithstanding the fact that we took care to line up one tooth of the one cutter with a tooth of the other. Referring ag^n to Fig. 92. The cutter positions are shown with a distance between them equal to the feed per revolution. We can calculate the height of the ridges if we know the diameter of the cutter, and the amount of the feed per revolution, and if we as- sume THAT THERE IS ONLY ONE TOOTH IN THE CUT- "''^ TER. The calculations show that for a 314" cutter, and with a feed of fifty thousandths per revolution, the height of the ridge is .00019, or practically two-tenths of a thousandth; with a feed of thirty thousandths, it would be .00007, or less than one-tenth of a thous- andth; with a feed of twenty thousandths, it would be .00003, or 96 The Cincinnati Milling Machine Company three hundredths of a thousandth. Since there is only one tooth at work, it might be inferred that, if there were ten teeth, making the feed per tooth in the first instance not fifty thousandths, but only five thousandths, the height of the ridge would be much less than .00019''. But this is not so, because a milling cutter never runs absolutely true. In order that a cutter shall run true every tooth of the 10-tooth cutter must be on exactly the same diameter. Fie 93 and describe a circle around exactly the same center, and in order to make this all perfect the cutter must be absolutely round; its hole must be absolutely round, its hole must be absolutely concen- tric with the outside; it must be mounted on an arbor without any clearance whatever; the arbor must be absolutely round and of even diameter; the center of the arbor must be absolutely in line with the center of its taper; the taper must be absolutely round and must fit into the hole of the spindle which again must be absolutely round; this hole in the spindle must be absolutely concentric with the bearing of the spindle; this bearing must be absolutely round and must work without any clearance in the front box. This is a condition which is impossible. In a practical machine all of the points mentioned here will have some variation. The highest de- gree of workmanship would not avoid some little error in all of these places, and it is fairly certain that the resultant error will be an accumulation of some of these. If the sum of these errors is only two ten thousandths of an inch (and this would certainly be remarkably good workmanship), then the ridge made by the cutter willbe two ten thousandths, regardless of how many teeth are at work. It is the swing of the cutter which makes the ridge. It is only then, when the swing of the cutter is less than two ten thousandths of an inch, that the ridge will be less deep. It is clear, therefore, that the ridge we see is a revolution mark and not a toothmark. However, if we should increase the feed per revolution to .300*^, then the height of the revolution mark would be approximately .0006", and in that case, it is very likely that the number of teeth in the cutter will reduce the size of the revolution mark. Fig. 93 A Treatise on Milling and Milling Machines 97 represents revolution marks produced by an extremely coarse feed and is the picture of the inaccuracies of the cutter, arbor, spindle, etc., which produce the revolution marks, and superimposed on this are slight depressions representing the toothmarks. It must be remembered that this represents a cut taken with an extremely fast feed per revolution, and that the faster the feed per revolution, the more pronounced the toothmarks will become. An analysis of the action of the cutter will show that the tooth immediately following the low one (corresponding to the high point on the curve) will reduce the height of the revolution mark some- what, making it less than the amount actually represented by the error in the cutter, arbor, spindle, etc., but it must be noted that even in these extreme cases the principal mark left on the work is the revolution mark, although the cutter no longer acts as if there were only one tooth. With a fine feed per revolution, such as is more generally used, the cutter does act,, so far as marking the work is concerned, as if it had only one tooth. Referring again to Fig. 90, it will be seen how difficult it must be for the tooth of the cutter ABC to penetrate into the metal. The conditions shown here are worse than found in actual practice, but only in amount; the nature of the conditions is the same. If we should make the tooth in the form AiBC, then it would be easier for the tooth to penetrate; there would be no necessity for the tooth to compress the metal downward, and there would be a true cutting action, such as we get with a lathe tool. This form of tooth would have a face which is not radial, but points back of the center; in other words, the tooth is undercut; or to express it as we do with lathe tools, the tooth has rake. Using a cutter with rake makes the action much easier. We will treat this subject more at length in the chapter on Milling Cutters. Action of a Face Mill. In the previous paragraphs we have studied the action of the teeth of ordinary milling cutters, but this is not the action of the teeth of face mills or end mills. The tooth of a face mill acts like a planer tool, or shaper tool, the only difference being that instead of moving over the work in a straight line, it moves in a circle. Fig. 94 shows a section of a face mill, the body shown in cross- section lines and two teeth projecting. XY is the top of the rough work, and VW is the top of the finished part of the work. 98 The Cincinnati Milling Machine Company OmCCTiON Of FCCD Fig. 94 The work feeds against the cutter in the direction of the arrow. It will be seen at once that it is the peripheral edge of the tooth that does the work, taking away a slice every time a new tooth enters, as shown in cross-section, two slices having been represented in the sketch. It is often thought that the face edge of the tooth of a face mill does the cutting, but this is not so; the sketch shows clearly that th€[ cutting is done by the peripheral edge of the tooth. Fig. 95 is a top view of this same face mill with one tooth shown in position. BW is the portion of the work already trav- ersed by the tooth and XY is the metal about to be cut off. The cutter turns in the direction of the arrow, and takes a slice as shown in cross-section. In order to have a true cutting action, the line AB of the cutter tooth must clear the already finished portion, and the line BC must fall back of the center, the angle /p OBC being called the rake, and the angle ABD the clearance angle. These rake and clearance angles may vary for different kinds of material and different conditions, but there must be some clearance angle or else the cutter will refuse to cut, and if we wish to cut with some degree of efficiency, there also must be a rake angle, else the metal will be pushed off (the action of a punch) instead of being cut off (the action of a knife). The chips made by a properly designed face mill resemble planer chips; in fact, it would be impossible to say what machine has produced the chip by simply looking at it; but, if the cutter is not properly designed, then the chips produced will be short and badly crushed — entirely different from those produced by a proper planer tool. The power required to remove metal will be very much more if the proper angles are not provided, and the life of the cutter. Fig. 95 A Treatise on Milling and Milling Machines 99 and, for that matter, the life of the machine also, will be very much shortened. Action of a Side Mill. A side milling cutter has both peripheral and side teeth. It is a fact, however, that the greater part of the cutting is done with the peripheral teeth, unless the amount of stock to be removed is very small. Fig. 96 shows a Side Milling Cutter at work on a piece of material cutting on both periphery and side. The amount of metal to be removed is indicated by the dotted lines. Sup- pose the thickness of this stock is 3^" and the other dimensions as given in the figure; at a speed of 70 feet per minute, we run 54 revolutions per minute. If the feed is very fast, say, 20" per minute, there will be re- moved per revolution |}, and as there are 11 teeth, each tooth has a feed of ^W, or practi- cally ^/ao'^. It will be seen that at the bottom of the groove, and for a width of %'^, the cutter acts exactly as a spiral mill; that is, it does all the cutting with its peripheral teeth and removes a comma-shaped chip which is V30" thick at its thickest part. For the other 3^" of the width of the cut, the cutter also acts like a spiral mill, the only difference being that here the cut is J^" deep instead of ^s^. The surface traversed by each side tooth is 3^" high and V30" wide, that is, it is as wide as the chip is thick. This area therefore is ^ /eo of a square inch. The surface traversed by the peripheral edges of each tooth consists of two parts; one part is ys" wide and y/ high; the other is ys' wide and y/ high. The first part has an area of ^ x 3^ equaling ^ square inches, and the other part has an area 3^ x 3^ equaling ^ square inch, altogether ^ square inch, therefore it traverses practically nine times as much surface as a side tooth. If the feed were less than 20" per minute, the surface traversed by the side teeth would be proportionately smaller. It will be seen then that the side teeth perform only a small portion of the total work, and their only function is to clean Fi2. 96 100 The Cincinnati Milling Machine Company up the side of the groove or slot, thus acting merely in a finishing capacity, and at the same time, of course, provide space for the accommodation of the chips produced. AN ILLUSTRATION O E MILLS IN ACTION The mills in Fig. 96-A are 13 J^" in diameter, and, in combina- tion with a pair of spiral mills 3" in diameter, they take a cut J^' deep across these surfaces, having a width of 273^" at a table travel of 4^' per minute. They work at a speed of 14 r. p. m. and re- move altogether IIH" of metal per minute. A final finishing cut brings the pieces accurate to within .001". The work is done on a No. 4 Plain High Power design miller. rr -J? fa A Treatise on Milling and Milling Machines 101 CHAPTER VI MILLING MACHINE FEEDS The feed of the Milling Machine is the movement of the table which advances the work against the cutter. On knee and column type machines there are three possible movements of the table; namely, lengthwise of the table (longitudinal feed), crosswise of the table and vertical. In some machines all three feeds are auto- matic; that is, they are power-driven, but in quite a large number only one power feed is provided, namely, the longitudinal feed. Two Systems in Use. There are two well-known feed systems in general use — ^feed in thousandths of an inch per revolution of spindle, and feed in inches per minute. With the first system the feed is driven from the spindle, so that when the spindle speed is increased, the amount of feed per minute will be increased in pro- portion, but the ratio between the advance of the table and the feed of the cutter will remain the same. The distance between revolution marks will therefore remain the same. With the second system, the feed is arranged in such a way that for any given position of the feed lever there is a fixed amount of feed per minute, regard- less of how fast the spindle runs. A change in spindle speed will not affect the quantity of output unless the feed rate is also changed at the same time. Standard American practice is to make all Cone-Driven Millers with the feed driven from the spindle, and therefore, reading in thousandths of an inch per revolution of the spindle. It would be difficult to arrange such machines with feeds reading in inches per minute, because to do this requires a constant speed shaft to drive from and there is no constant speed shaft on a Cone-Driven Miller. Cincinnati Cone-Driven Millers are provided with 16 feed changes, ranging in the smaller machines from .006 to .250 of an inch per revolution, and in the larger sizes from .007 to .300 of an inch per revolution of spindle. Standard practice on Millers with constant speed drive is to arrange the feed to read in inches per minute. This is a simple • • • • « f • .•.• • • t 102 The Cincinnati Milling Machine Company matter on these machines, because the main shaft always runs at constant speed and the feed is driven from it. There are some advantages in the older system used on Cone-Driven Machines, but except in special cases, these advantages are outweighed by those of the newer system, reading in inches per minute, as will be seen from what follows. Feeds in Thousandths per Revolution. Let us first con- sider a machine with feeds reading in thousandths per revolution. Assuming a small end mill requiring a fast speed, say 350 r. p. m. The finest feed available on a large Cone-Driven Machine is .007 per revolution. On some work this feed may be entirely too fast for this small, frail cutter. Now, let us assume a large cutter requiring a slow speed, say 14 r. p. m. The coarsest feed is .300 per revolution, and the fastest table travel we can get at 14 r. p. m. is 14 times .SOO*' or 4.2*' per minute, which is entirely too slow in many cases. These extreme cases indicate the limitations of this system. Most milling comes between these extremes and for the usual work the feeds provided are entirely satisfactory. This system has the advantage that it indicates at once the grade of finish; that is, the distance between revolution marks. Feeds in Inches per Minute. Let us consider a machine with feeds in inches per minute. Assume again a small end mill running 850 r. p. m. The finest feed on Cincinnati High-Power Millers is Yi per minute. This results in the present case, in a feed of about .0015" per revolution, certainly fine enough for the frailest cutter. Now assuming a large cutter at 14 r. p. m., using the coarsest feed of 20" per minute. We, of course, get a table travel of 20" per minute, which is a very satisfactory rate of production. This system also has the advantage of indicating at once the rate of production. Cincinnati High-Power Millers are all arranged with feeds reading in inches per minute, the feed box providing 16 changes, ranging from y^' to 20" per minute. Influence of Feed on Production. The rate of production depends directly on the rate at which the work passes under the cutter. It follows, therefore, that the feed used should be as fast as practical. There are certain conditions which frequently arise in practice, which limit the rate of feed that can be used. Quite often the piece is of such a nature that it can not be held rigidly in the holding fixture. In still other cases the piece itself may be too frail A Treatise on Milung and Milling Machines 103 to stand the pressure due to a heavy feed. In such cases there are only two things possible; either reduce the feed (table travel) and do the work slower, or if the machine is cone-driven, reduce the feed per revolution and increase the speed. On a High-Power Machine this latter result is accomplished by simply increasing the speed of the cutter, because this automatically reduces the feed per revolution, therefore, producing smaller chips and consequently less pressure against the work. However, high speeds have a tendency to burn out the cutter, and therefore, if we want to increase production by increasing speeds, we must do something to keep the cutter from burning. This will be discussed more fully in the chapter on Stream Lubrication. Roughing and Finishing Cuts. Some work is milled with only one cut to produce the desired surface. Other work requires two cuts. In the latter case the roughing cut may be taken without regard to the finish produced, and the only elements to be con- sidered are: the strength of the piece itself, the power of the machine, its ability to stand the strains and the condition of cutter, arbor and fixture. If only one cut is taken, then the finish must also be considered. Using spiral mills, end mills or formed mills, a very satisfactory commercial finish is produced with from .035 to .050" per revolution. Such a feed, and often even higher feeds may be used for surfaces which are bolted together and which are not re- quired to be oiltight, but for a great variety of work, a finer feed is necessary. Work which must be scraped or which is finish ground will easily stand .030", whereas work which must have a high finish and does not get any subsequent operation may require a feed as low as .020" per revolution. When very small end mills are used for such work as die sinking, and rounding out the ends of keyways, and various other delicate operations, a finer feed must be used, not because of the finish, but because of the frailty of the cutter. The relation of feed to speed on a great variety of cuts in cast iron and steel is given in the diagrams in the following chapter on Speeds of Milling Cutters. 104 The Cincinnati Milling Machine Company CHAPTER VII SPEEDS OF MILLING CUTTERS We are all familiar with the fact that if a piece of work in a lathe runs too fast, the lathe tool will bum out. This term "burning out" is incorrect. What is meant is, that the tool becomes so hot that the temper of the extreme cutting edge is drawn out, and this edge be- comes so soft that it refuses to cut further. This holds true whether the tool is a lathe tool, a planer tool, or a milling cutter, the only difference being that with the lathe and planer tool the work moves while the tool is fed into it, whereas with the milling cutter the condition is reversed^^the work is fed under the cutter while the milling cutter rotates. A milling cutter is a complicated tool as compared with a lathe or planer tool and we will therefore use the latter in our analysis of the action of cutting tools. Action of a Lathe Tool. When a lathe tool takes a chip, feeding, say, from right to left, its front end is up against the finished part of the work, its top face is partly covered by the chip as it comes off the work, and its left side is pressed against the work trying to feed into it. There is considerable pressure between the work and the front edge, heavy pressure between the top and the chip, and also heavy pressure between the left side and the work. Meanwhile the work is moving and this movement under pressure causes friction and friction generates heat. It can be easily seen under a magnifying glass that the chip as it comes off the work is broken up into a great number of fine laminations which slide over each other. The breaking up of the chip and the sliding of the laminations both generate heat. Heating. If a lathe tool takes a chip 3^" deep with a feed of i^" per revolution, the chip as it comes off has a section much greater than 3^ X ^", and a different shape; it is not rectangular, but triangular. All this breaking up, sliding, and changing of shape causes a great deal of heat to be developed. In fact, much less than 1% of all the work done on a lathe is used for separating the chip from the work, and all the rest of the work is spent in breaking up A Treatise on Milling and Milling Machines 105 the chip, overcoming the friction between tool and work and between tool and chip. At the same time this useless work is converted into heat, which heats up the tool. Of course, the tool loses some of this heat. If we run at a low speed, taking a fine chip, and using a fairly large tool, the amount of heat generated is relatively so small that the tool can carry it off and conduct it into the body of the machine or radiate it out into the atmosphere as quickly as it receives the heat. It warms up a certain amount until its rate of radiation and con- duction are as great as the rate at which it receives heat. From that moment on the tool does not become any hotter, regardless of how long we keep on cutting. If we should cut faster or take a heavier cut, then the tool will become much warmer before this equilibrium is reached. If we go still further increasing the speed, we finally reach the point where the tool receives more heat than it can dissipate, and then the tool "bums out." We find, however, that the body of the lathe tool is perhaps slightly warm, but cer- tainly not hot, showing that this body had ample capacity to carry off all the heat generated. Why then does the tool bum out? Imagine that we cut a lathe tool up in slices, starting at the shank end and proceeding toward the cutting edge. The sections become smaller and smaller, and the section close to the cutting edge is very small. This last section, therefore, can not carry off much heat, and besides being completely covered by the work and chip can not radiate heat. In fact, it is protected because both chip and work themselves are hot and may even add to the heat of the tool. We find, moreover, that it is only the extreme cutting edge which is affected. Application to a Milling Cutter. All that was said about a lathe tool is applicable to a milling cutter. A milling cutter has an advantage in so far that the tooth of the milling cutter stays in the work for only a short time and then rotates through the air, giving it a chance to cool down. If the cut is shallow, the tool is in the work for only a short period of time. If the cut is deep the con- ditions are somewhat less favorable, but in almost all cuts the period of time during which it cools in the air is much greater than the period of time during which it accumulates heat. If a milling cutter is properly designed and made it is possible to run it at a higher rate than a lathe tool. Unfortunately, most milling cutters are made without rake, and must do three or four times as much work as a lathe tool in order to remove the same amount of metal. All of 106 The Cincinnati Milling Machine Company this eictra work is converted into heat, and this more than offsets the favorable conditions under which a milling cutter works. The speed of a tool is limited by the fact that it gets so hot that it loses its temper, and this heat is developed by useless work being done, namely, by bending and breaking up chips, and so on. There are three different ways by which we could speed up a tool. One, by finding some material of which to make the tool which would not lose its temper no matter how high the temperature. This was partly accomplished by the invention of high-speed steel. A second way, by making a tool of such shape that it merely separates the metal and performs no useless labor. Such tools may be invented some day, and, in fact, a lathe tool has been made which will remove metal without breaking it up. A third way to increase the speed would be to carry off the heat as fast as it is generated. If we can do this, then it makes no difference how much heat is developed by the action of cutting, for all of this heat will be carried off immediately and the tool will become no hotter. Under such conditions, as far as burning out is concerned, any speed would be permissible. To obtain the very best results we should employ all three of these methods; that is, we should have the cutter made of some material which will retain its temper even at a high temperature; it should be constructed in such a way that it does as little unneces- sary work as possible, and there should be means of carrying off the heat as fast as it is generated. Under these conditions we can get the highest possible speeds. Conditions Determining Proper Speeds. It is impossible TO STATE definitely AT WHAT SPEEDS CUTTERS SHOULD BE RUN, BECAUSE THIS DEPENDS ON TOO MANY CONDITIONS. It depends in the first place on the kind of cutter, in the second on the amount of material to be removed per minute and, not only that, but it depends on the relation between the depth of cut and feed. A cut of }/s' depth and J^" feed per revolution can be taken at a higher speed than a cut at a depth of J^" and with a feed of ■^'^ per revolution, though the amount of material removed per minute would be the same in both cases. It further depends very largely on the rigidity of the machine and the fixture in which the piece is held. It depends also on the rigidity of the piece itself, and last, but not least, on how often we think it economical to regrind the cutter. We can run at almost any speed if we are willing to regrind A Treatise on Milling and Milling Machines 107 the cutter every five minutes, but this would not be economical. It is also possible to regrind the cutter only once every six months, but we would have to run so slow that again this would not be economical. There is a point where we get the highest efficiency and when a shop has to mill a great number of pieces of one kind, a few figures should be put on paper to determine which is the most economical speed at which to run the cutter. Influence of Speed on Production.* To illustrate: A shop has to mill 1,000 pieces, and employs two cutters for this purpose, one of which is being reground while the other is in action. We run at such a speed that it takes six minutes to mill one piece. We will assume that it requires three minutes to place the piece in the jig and remove it again, 60 minutes to regrind a cutter, and 40 minutes to reset the machine while the new cutter is put in place. Assume that the speed is such that the cutter must be reground after every 100 pieces. We then have 3,000 minutes to put them in the fixture, 6,000 minutes to mill them, 600 to grind the cutter and 400 to set the cutter. While the grinding of the cutter is being done, the milling still goes on, so that though we have to figure in the labor cost of grinding the cutter, the milling machine is never standing idle, except during the time that we reset the machine for the new cutter. The total time, including sharpening and setting cutters for these 1,000 pieces is 10,000 minutes. (The machine time is 9,400 minutes and the grinding time 600 minutes.) If we should run the cutter so much faster that the milling could be done in five minutes instead of six minutes per piece, under those conditions we have to grind the cutter more frequently than once in every hundred pieces, as in previous examples. Let us assume that X represents the number of times we must grind the cutter per hundred pieces, then we would like to know how often we may grind this cutter without losing time. In order not to lose time we must mill all these 1,000 pieces in 10,000 minutes, and we must remember that if we grin d the cutter X times as often, we also must *In order to keep this illustration as simple as possible, so that the principle involved may not be confused with the wage factor, it is assumed that the value of an hour's work on the cutter grinder equals that of an hour's work on the milling machine. If, in the illustration which assumes the use of only oiie cutter, the milling machine operator also does the cutter sharpening, the result appears to be better, because the operator is not idle, but the milling ma- chine is idle and milling production suffers. The important thing is to keep the milling machine going at the right rate, and as nearly continuously as possible. 108 The Cincinnati Milling Machine Company reset the machine X times as often. The cutting now takes place in 5,000 minutes. It takes 3,000 minutes to put the piece in the fixture; X times 600 minutes to grind the cutter; X times 400 minutes to reset the machine; altogether 10,000 minutes. 5,000+3,000+400 X+600X=10,000. Therefore, X-2. In other words we may grind the cutter once for every 50 pieces. The machine time in this case is 8,800 minutes and the grinding time may be 1,200 minutes. CUT SPEfD This means if we reduce the cutting time from six minutes to five minutes, we may grind the cutter twice as often as before and not lose time. If we find that we have to grind the cutter less than twiee as often, we would gain time, but if we find that we have to grind the cutter more than twice as often, we lose time. The figures show a rather striking result. A reduction of the cutting time from six minutes to five minutes, that is, an increase in speed of 20%, would allow us to regrind the cutter twice as often provided we had two cutters. If we increase the cutting speed so as to reduce the cutting time from six minutes down to four minutes. A Treatise on Milung and Milung Machines 109 we might grind the cutter three times as often and not lose time. If we had only one cutter the machine would stand idle during the additional time that the cutter is being reground and we would get an equation very similar to the previous one, except that we must figure in the time during which the machine stands idle, which is just as long as the time during which the cutter is being reground. Assuming that the machine and operator are both idle while the cutters are being ground, then the machine time (which includes the times the machine is actually milling, is standing still for the cutter to be removed and reset, and standing still while the cutter is being resharpened) is 10,000 and grinding 600 as before, making the total time 10,600. This equation then would be: 5,000+3,000+400 X+600 X- 10,600, and therefore, X = n or V. In other words, under those conditions, we may regrind the cutter only one and five-eighths times as often as before. It will be readily seen that if it takes a longer or shorter time to grind a cutter or to reset the machine, and if the proportions between 110 The Cincinnati Milung Machine Company chucking time and cutting time are different, the value of X will be diffenent also. In our own practice parts are made in comparatively small lots— several hundred at a time — and we aim to use such a com- bination of feed and speed as will enable the cutter to stand up for one complete lot of pieces without resharpening. Boinhing W' desp, oast iron. Practical Cutting Speeds. The diagrams, Figs. 97 to 109, were developed from our own practice. We make parts in comparatively small lots and plan our feeds and speeds so that a cutter will mill a complete lot without resharp- ening. The life of the cutter is therefore a factor entering into these curves. They are applicable to modern machines equipped with the latest design cutters and ample lubrication, where lubricant is used. They do not show the maximum feeds and speeds that can be used, but are a safe guide for those who are responsible for pro- duction. It is entirely practical to very greatly exceed these feeds and speeds on some work, but if the equipment consists of the usual form of standard cutter as found in stock, it is necessary to reduce A Treatise on Milling and Milling Machines 111 the results shown by these speed curves a very substantial amount before they can be applied. Roughing Cast Iron with Spiral Mills. The diagram in Fig. 97 shows cutting speeds and feeds when milling cast iron at different depths of cut with a 3' diameter cutter. The variables are the depth of cut, the feed in inches per minute, and the cutting speed. That part of the curves shown to the right of the heavy vertical line .460 i CUT SPEED fl(. IM. Srbml Hllk Rodgblac A' deep, cut imn. drawn at 70 feet per minute cutting speed, represents good practice. The use of these curves will be evident from the following: Suppose we are to take a cut J-^" deep in cast iron and wish to run 80 feet per minute cutting speed. The curves will show that the most efficient feed rate to be used, providing the work and cutter will stand it, is 22' per minute. On the other hand, suppose we have a piece of work which we feel should go through the machine at a feed of 12' per minute. If the cut is again ■^" deep, we may run as fast as 88 feet per minute cutting speed. It must be noted that the above diagram does not iake into account that influence the diamet^ 112 The Cincinnati Miixing Machine Company fA the cutt^ has on the pomissible speed. It is good tor cuttos from 3' to 3^4' in diameter. The diagrams in figs. 98, 99, 100 and 101 should thenion be refared to for mne exact results tar cuttos irf otho* diameters. The curves in Pig. 98 are based on cuts ^' deep. Now, assuming a cutto- 4' in diantetcr and a rou^iing cut at .240* pa- revolution: It will be safe to nm the cutter 92 feet per minute. Similariy, the curves in Fig. 99 show that undo- these same conditioDS and with a cut ^s' deep, the best cutting speed is 84 feet pa- minute. Fig. 100 shows that with a cut i^' deep the best speed is 76 feet pa- minute, and Fig. 101 shows that with a cut H' deep the best speed is 65 feet pa- minute. These figures show a range in speed from 65 to 92 feet cutting speed. GCTiaally speaking, 70 to 75 feet cutting speed is good IN-actice when milling a hi^-grade of cast iron, such as is used in the betto- class of machine tools. The above curves are based on wide spaced, wide angle cuttors. A Treatise on Milling and Milling Machines 113 When using these curves in connection with the older form of standard cutters as found in stock, the results shown on these curves should be reduced to from one-third to one-half of their values before applying them. Finish Milling Cast Iron Using Spiral Mills. Fig. 102 shows curves based on good practice for finishing cuts -ss" and ^' deep, but this again does not take into consideration the influence of diameter of cutter. These curves are a good guide for general practice. For more exact results, refer to Figs. 103 and 104, which are based on the use of cutters of different diameters. The values of these curves shown between the heavy horizontal lines drawn at .050" and .060" per revolution indicate the feeds and also the corresponding speeds which we consider good practice for finishing cuts on surfaces which will afterwards be polished. For producing the finer grades of linbh, suitable for scraping, the values of the curves shown between the horizontal lines drawn at .024" and .030" feed per revolution should be used. If the cutters are sharp and the 114 The Cincinnati Milling Machine Company equipment is in good order, this feed rate will produce an excellent finish. Assuming again our 4' diameter cutter and a feed of .023' per revolution: Fig. 103 shows that with a finishing cut ^" deep, it is safe to run the cutt^B 130 feet per minute, and Fig. 104 shows that for a finishing cut 3^" deep, it is safe to run the cutters 120 feet per minute. CUT SPEED tit. lOJ. Spfrnl MIUb FiuiibiDE ii' deep, cast iroD. Speeds and Feeds for Shell End Mills. The diagram. Fig. 105, shows curves based on good practice when using end mills, taking cuts from ^i" to ■^'' deep in cast iron. In all of these curves the depth of cut remains constant, the variables being as before, the feed in inches per minute, the cutting speed and diameter of the cutter, and there is also the additional variable, width of cut. We find from these curves that if we want to take a cut 2" wide with a 3" diameter end mill, we can run about 75 feet cut speed and at a feed of 11" per minute. Should we wish to take a cut 3' wide, with a 3^" diameter cutter, we find that we can run practically 60 feet cut speed and use a feed of SJ/^" per minute, and so on. A Treatise on Milling and Milling Machines 115 A very interesting additional feature of these curves is found below the 50-foot cut speed curve, the application of which is as follows: Suppose we are taking a cut 2J4' wide with a 2J-^" diameter cutter at 50 feet cut speed. We can feed safely 6J-^' per minute. However, if for some reason we should find it preferable to feed only 3* per minute, then we can run 100 feet cut speed with safety. In the same way, with a 3J-^" diameter cutter, taking its full width of cut, namely 3^^", the proper speed is 50 feet and the corresponding feed is 8)4*. However, at 5^" per minute feed on this same cut, we can with safety run 80 feet cut speed, and so on. From this it will be seen that all of the diagram lying above the 50-foot cut speed curve shows the relation between feed, speed, diameter of cutter and width of cut. That part of the diagram which is below the 50- foot curve applies only to the maximum width that each cutter can take, it of course being clear that a 3' diameter end mill can not take a cut greater than 3* wide. This part of the diagram is useful in showing the extent to which the cut speed may be increased when 116 The Cincinnati Milling Machine Company the feed is reduced, the diameter of the cutter and the width of cut remaining constant. This diagram is based on actual practice in our shop, using modem wide-spaced shell end mills. For the older style of end mills as found in stock, the values shown by these curves should be reduced by 25% to 35%. W1DTM Of CUT. Fif. itg. sua End Min* Broken corners. Roughing, esM iron H'-A' deep. Face Milling Cast Iron. Fig. 106 shows a set of curves for High Power Face Mills and Standard Face Mills for both roughing and finishing cuts which have a width approximately equal to the diameter of the cutter. From these we find that at a feed of 12" per minute a High Power Face Mill can very safely run 62 feet cutting speed for roughing and 82 feet for finishing. A Standard Face Mill, that is, one of the lighter design, should run about 50 feet cutting speed for roughing and 73 feet for finishing, and so on. At a feed of 8" per minute, the speeds become for a High Power mill 68 feet for roughing and 89 feet for finishing, and for a Standard mill, 56 feet for roughing and 79 feet for finishing. Spiral Milling in Steel with Stream Lubrication. Fig. 107 is a general diagram based on cuts ^'', K". i%" and J^' deep. A Treatise on Milung and Milling Machines 117 taken with a wide spaced, wide angle spiral mill with rake, in cold- rolled machinery steel with an ample supply of cutting lubricant. Assuming a feed of 8" per minute, the corresponding speed for a cut }4' deep is 62 feet; for •^° deep, 80 feet; for H" deep, 104 feet, and for iV" deep, 128 feet per minute. Finishing cuts yj" to j^" deep in machinery steel under the above conditions of ample lubri- cation, should under good shop conditions be taken at a cutting CUT SPEED Fl(. lOe. Face MtUa RoufbiDi and FiaiBbioE. out iroD. Depth of cut, miighing H to H- Qnisbinc itiof,. speed of 150 to 160 feet per minute. When the equipment consists of the older form of cutters, such as can be bought from stock, and the lubricant is used in limited quantities, the above figures should be reduced to from M to M of the values shown in the curves before they are applied. Face Milling Steel. Fig. 108 is used in exactly the same way as Fig. 106, except that it shows the relation between feed and speed when milling steel, whereas Fig. 106 applies only to cast iron. This diagram is again based on roughing cuts from }4' to t^" deep, and finishing cuts ^'' to ^" deep on cuts having a width equal to from y^' to 5^" the diameter of the cutter. 118 The Cincinnati Milung Machine Company If we want to take a roughing cut at 16' per minute the diagram shows at once that we can use about 80 feet cut speed. A finishing cut at 16* per minute can be safely taken at 94 feet cut speed, and so on. The separate curve at the left of the diagram applies to rough- ing cuts J^" deep and 6' or more in width. These exceptionally heavy cuts of course can not be taken at such high speeds and fast Machinery steel. Stream lubjication. feeds. For instance, at a feed of 12" per minute the cut speed should not be more than 60 feet. Keywaying. Fig. 109 is again based on modem cutters supplied with ample lubricant and milling nickel steel drop forgings 1 ^% N., ,30 to .40 carbon, .40 to .60 Chr., and also when milling the grade of machinery steel known as hub stock. There are two sets of curves shown. We will first consider the curves based on a 2}-^" diameter cutter. This is a cutter of our latest design, as described in the chapter on that subject, and it will be seen that with a feed of 8* per minute, a cutting speed of 30 feet can safely be used in chrome nickel steel, and in hub stock a cutting speed of 73 feet A Treatise on Milling and Milling Machines 119 is about right. With cutters of the older design these results should again be reduced. The other two curves, which refer to a special staggered tooth cutter, are based on the use of the cutter shown in Fig. 110. This is a cutter 4' in diameter, ^' face, with inserted teeth, as shown. Its construction makes it possible to take advantage of the best cutting angles and it will be noted that the teeth are far apart and Cin SPEED Flf. 108. Fue Mini SMel nutinis and machiiiery ttert. Width of cut, H to !i the diameter of the cutter, each tooth removes a chip which is only part of the full width of the cut. It therefore has not only a free cutting action, but the chips are entirely free to get out of the way throughout all stages of the cut. Referring to the diagram, it will be seen tliat at 8' per minute feed this cutter mills clirome nickel steel safely at 102 feet cutting speed, and a corresponding increase over the other cutter when milling hub stock. These curves and this cutter are shown to indi- cate what was meant in a preceding paragraph which stated, that for special cases, the speeds and feeds given in these curves can be very greatly exceeded. 120 The Cincinnati Miixing Machine Company The Cincinnati Milling Machine Company recently carried out extensive experiments to determine maximum cutting speeds that could be taken with a modem milling machine equipped with proper cutters and provided with ample cutting lubricant or coolant properly applied. Machinery steel was cut at speeds of 400 to 450 feet per minute when taking cuts not deeper than J^", 250 to 350 feet per minute when taking cuts J^" deep, and keyways %° wide and %" deep were milled at a cutting speed of 400 feet per minute. Nickel steel, heat-treated, was milled at 150 feet cutting speed, taking cuts %" wide, T^" deep. Vanadium steel of great hardness was milled at a cutting speed of 190 feet per minute. Tool steel, 1.25% carbon, such as is used for certain classes of reamers, was milled at a cutting speed of 200 feet per minute. The results of these tests are given in detail in Chapter VIII, on Stream Lubrication. Safe Practical Speeds. In general practice the following cutting speeds can be safely used with modem cutters, and an A Treatise on Milling and Milling Machines 121 ample supply of coolant for the cutter on that work which requires coolant: Cast Iron Spiral Mills Rough milling 65 to 75 feet Finish milling 80 to 120 feet Face Mills Rough milling 65 feet Finish milling 80 to 110 feet Machine Steel Spiral Mills Rough milling 70 to 75 feet Finish milling. 100 to 140 feet Face Mills Rough milling 60 to 85 feet Finish milling 90 to 110 feet Tool Steel — Annealed Spiral Mills Rough milling 50 feet Finish milling 70 to 80 feet Chrome Nickel Steel (.30 to .40 carbon drop Forgings) Rough milling 45 feet Tobin Bronze Spiral Mills with Lubricant Rough milling 90 feet Finish milling 125 to 150 feet Brass 200 feet Aluminum 600 to 1,000 ft. Other Factors Which Determine the Life of the Gutter. The failure of the cutter is not always due to excessive speed. When the metal is gritty a grinding action takes place, which by and by dulls the cutter. This is especially true when cutting cast iron. For that reason special attention must be paid to the clearance angle of cutters, which will be taken up more in detail in the chapter on construction of Milling Cutters. The Cincinnati Milling Machine Company m. 110. AdliuUbl* littMiMl TMth SloUlnc CnUw (Patent applied Cor) Then there is also the legitimate wear on the cutter caused by the edge rubbing over the work and the pressure of the chip against the teeth. This wear is not greater with fast than with slow speeds, but, if with slow speeds the cutter will be dulled in two days, with twice the speed it may become dulled in one day. The amount of work performed by the cutter will be the same for the same amount of wear, but the time required for doing it with fast speeds will be very much less than when slow speeds are used. For example: Assuming a piece of work that can be milled at 100 rev., and that the feed per revolution should be .200'. The resultant table travel will be 20' per minute. Now, if we run the cutter 50 rev. and use the same feed rate, the table feed will be 10' per minute, only one-half as fast as before. The cutter will be doing only one-half as much work and will last twice as long. On the other hand, if we feed 10" per minute at 50 revolutions and then increase the speed to 100 revolutions, but do not increase the feed, production will not be increased and the cutter will, theo- retically, last only half as long when milling the same number of pieces, because the cutter makes twice as many chips and therefore comes in contact with the work twice as often since the chips are only half as big as before. Some data confirming this are given in the next paragraph. iNCRBftSlNG THE speed alone dobs not increase production. Life of Cutters When Milling Cast Iron. Some very valu- able experiments were made by the Cincinnati MiUing Machine Company on the effect of cutting lubricant on the life of the cutter when milling cast iron. The result of these tests is shown in the accompanying table. The cast iron bar milled was in each case A Treatise on Milling and Milling Machines 123 36'^ long. All cuts were taken on scale. The cutter used was our standard slotting cutter, but with only one tooth operating, all the other teeth having been removed. Cutter — 5*" diameter, %' face. Arbor — IJ^*'. Speed of cutter — 12 r. p. m. Cut — ^'^ deep, %" wide. Effects of Use of Lubricant and the Size of Chip on the Life of a Gutter Milling Cast Iron No. of Cuts Feed per Min. Feed per Tooth Total Distance Traveled per Sharp- ening Total Wear of Tooth (Radial) Wear of Tooth per 100' Traverse Remarks CO CO CO CO .5 l!0625 1.0625 .0069 .0069 .0147 .0147 108' 108' 108' 108' .0035 .003 .0035 .00325 .00324 .00277 .00324 .0030 Lubricant. No Brace Dry. No Brace Lubricant. No Brace Dry. No Brace 3-e 3-f 3iS 3-h 6-i 6-i 6-m 6-n 1.0625 1.0625 .5 .5 2.25 2.25 1.0625 1.0625 .0147 .0147 .0069 .0069 .03125 .03125 .0147 .0147 108' 108' 108' 108' 216' 216' 236' 236 .0015 .001 .00275 .003 .0005 .00025 .002 .00375 .00138 .00092 .00254 .00277 .00023 .000125 .00084 .0015 Lubricant. With Brace Dry. With Brace Lubricant. With Brace Dry. With Brace Dry. With Brace Lubricant. With Brace Dry. Braces Lubricant. Braces The above tabulation shows some very interesting things. For instance, cuts a, b, c and d were taken with the outer end of the arbor supported from the overarm, but not tied to the knee with braces. This, therefore, allowed a slight amoxmt of vibration, not sufficient to be noticeable, but it nevertheless existed and had its effect on the life of the cutting edge of the cutter. Comparing cut c for instance, with cut e, shows that with the braces, the wear on the cutting edge was not quite one-half as much as without braces. In the same way, comparing cut a with cut g, an improve- ment is again shown when the braces are used. We will consider here, only those cuts taken when the machine was equipped with braces. Let us first consider the effect of lubri- cant. Cuts e and f show that there was less wear when running dry, while cuts g and h show slightly in favor of lubricant. This is also true when we compare i and j. In the same way, comparing m and n, the result seems to indicate that it is better to run dry on cast iron. 124 The Cincinnati Milling Machine Company The conclusion to be drawn from all this is, that there is no advantage in using lubricant when milling cast iron, if we consider alone the question of the life of the cutter. However, it has been very clearly demonstrated that when milling frail pieces at a high speed rate, there is a decided advantage in using fast feeds and lubri- cant, when milling cast iron parts of this character, because of the cooling effect of the lubricant, which prevents the heating of the piece and in consequence, warping out of shape. It must be noted, however, that we do not recommend this, because whenever it has been tried on manxifacturing operations it was found that thej lubricant carried small particles of iron into the bearings of the machine, and caused su6h rapid deterioration that it was not practical to keep the machine in proper adjustment to do rapid, accurate work. Effect of Size of Chip on Life of Cutter. Even more interest- ing than the effect of lubricant is the effect of the size of the chip as shown by these figures. Comparing cuts e and g we find that with a feed of 1'' the wear on the cutter is .00138, whereas when feeding 3/^" the wear on the cutter is .00254 when the distance milled in each case is 108". In other words, feeding 3^'' per minute, the cutter came in contact with the work twice as often in milling a distance of 108", as it did when feeding V per minute, and the wear on the cutter was approximately twice as great. Again comparing cuts h and i. Cut i was taken with a feed 43^ times as fast as cut h, while the wear on the cutter at the slower feed per 100" of traverse was nearly 10 times as great as the wear on the cutter at the faster feed. These figures indicate quite clearly that the dulling of the cutter is in direct proportion to the number of contacts which the cutter- tooth makes with the work in a given length of travel. We believe that an entirely safe conclusion is that the wear per contact, that is to say, the wear per chip produced, is approximately the same for different sizes of chips when milling cast iron within the practical limits of milling. In other words, if we use a chip per tooth of .007", the cutter will make as many chips and in consequence will be dulled to the same extent when milling a piece 100" long as it will when taking a chip .014" thick, milling a piece twice the length, that is, a piece 200" long. All this shows the desirability of using the fastest feed that other conditions will permit. A Treatise on Milling and Milling Machines 125 CHAPTER VIII STREAM LUBRICATION CUTTER AND WORK COOLING It was found by experimenters that lubricant on a tool does something else besides producing a smooth surface. It also acts as a coolant and there has been a great deal of discussion as to whether the benefits are due to the fact that the fluid lubricates, or whether they result from its cooling effect. We will not consider here the action of the fluid as a lubricant, but only as a coolant. The limitation of the cutting speeds results from the fact that the act of cutting makes the extreme edge of the tool hot enough to draw its temper. Carbon steels lose their temper at a relatively low heat. High-speed steels differ from carbon steels in this respect only — ^that they can stand a much higher temperature before losing their temper. Generation of Heat by Cutting Tools. Most of the experi- ments above referred to were carried out on the lathe, and are briefly discussed in the preceding chapter. But what applies to a lathe does not necessarily apply to a milling machine. A lathe tool is constantly embedded in the work and the top of the lathe tool is constantly covered by the chip, so that the cutting edge of the tool, which is the part to be kept cool, receives very little, if any, of the lubricant, consequently it gradually acciunulates heat, but it does not burn out because it also loses part of this heat. Finally a point is reached at which it loses heat about as fast as it receives it and, therefore, remains at an approximately constant temperature. When this temperature is the highest the tool will safely stand, then the speed, which produces this temperature, is the highest safe speed for that tool under the conditions assumed. A milling cutter works under entirely different conditions. A tooth enters the work, removes a chip and leaves the work, then travels through the air for the greater part of a revolution. It therefore has a better chance to dissipate the heat received than a lathe tool. But what is far more important, the fact that the cut- ter tooth is free of the work a large part of the time, gives an oppor- 126 The Cincinnati Milling Machine Cobipany tunity to apply artificial means for carrying away the heat as fast as generated and thus keep the cutter cool at high speeds. The Cincinnati Milling Machine Company has carried on a long series of experiments to determine the most effective method of applying cutting lubricant and the extent to which speeds and, therefore, production, can be increased by the use of a sufficient volume of lubricant properly applied. It was found that the nature of the lubricant does not affect the cutting speed, provided the quantity is sufficient. It was further found that in the majority of cases the quality of finish is equally good with the cheaper compounds as with pure lard oil, when suf- ficiently large quantities of lubricant are used. The speed at which it is possible to run the cutter depends primarily upon the volume and method of application of the lubri- cant. The average small stream as usually provided, is by no means sufficient to secure ample cooling. After numerous trials we developed a system which deluges the cutter and work with lubricant, and as a result, we are able to greatly increase the speeds over those formerly attainable, and still keep cutters and work cool. These experunents formed the subject of an editorial in the "American Machinist," by the editor, Mr. L. P. Alford. It appeared in the issue of April 16, 1914, and as it gives important data on the experiments as recorded by an impartial observer, the editorial is reproduced on the following pages. Editorial from the American Machinist, April 16, 19H: "Progress in the art of cutting metals, as in all other lines of human endeavor, has been a slow advance with occasional sudden, pronounced jumps, followed by the same slow advance. One such jimip came in 1900, with the announcement of the development of high-speed steel. This was first presented to the American Ma- chinists' readers in the issue of August 9, 1900. The feature was high speed. The editorial note said : The appearance of a large lathe turning a IV steel shaft at this speed (150 feet per minute) is nothing less than startling. This article, I believe, is the annoxmcement of the beginning of another jump in this curve of progress, at least as it affects multi- toothed cutting tools. The startling feature as in the case of high- speed steel, is the speed. Tests have iihown peripheral cutter A Treatise on Milling and Milling Machines 127 speeds and work feeds in steel, some eight to twelve times greater tiian those used in ordinary milling practice. minute. W«k feed SO>i' per minute. Depth of cut H*' U&terial, muhinery ited.0.2ca The Cincinnati Milling Machine Company's Progressive Experiments. The conditions which have made these tests pos- sible are the direct result of the work that the Cincinnati Milling Machine Company, Cincinnati, Ohio, has done during the past six or eight years. In 1908.the American Machinkt showed the line 128 The Cincinnati Milung Machine Company of Cincinnati High-Power Millers. Since that time this line has undergone progressive improvement, particularly in the selection of better materials. At the Pittsburgh meeting of the American Society of Mechanical Engineers in 1911, A. L. De Leeuw, until recently chief engineer of the company, presented a paper on Milling Cutters and Their Efficiency. A feature of this was data on the use of cutters with wide spaced teeth. This paper was abstracted on pages 753 and 787 of Vol. 35. Last year was shown this firm's Semi-automatic Miller, which was adapted for much higher cutting speeds and table feeds than were in common use for that general type of machine when it was designed. These developments set up the conditions of powerful, heavy machines, an extensive use of cutters with wide-spaced teeth, which permitted increased feeds, and experience with feeds and speeds somewhat higher than average practice. From this foundation experiments were begun with much higher work feeds and cutter speeds. The illustrations. Pigs. Ill to 123, inclusive, show in graphic fashion some of the results. Details of the system have been made the subject of patents. To show what these results are, I can do no better than to give the records of the tests that I have witnessed. The machine upon which the high-speed tests were run is shown in Fig. 111. This is a No. 5 High-Power Cincinnati Miller driven by an independent motor, with a speed of the con- stant-speed pulley 50 per- cent greater than that for no which the machine was *"'' ^""""^ """■ designed. The steel cut was a mild machinery steel, 0.2 carbon, 0.5 manganese, having an ultimate tensile strength of from 55,000 to 65,000 pounds per square inch. The cutters were all of high- A Tbbatisb on Milling and Milung Machines 129 Test No. 1. Cutter, spiral mill, 25° angle, SJ^" diameter, 9 teeth, 10° rake, 6' long. Arbor IJ^" diameter. Depth of cut K', width 5", length 18". Speed of cutter 500 r. p. m., peripheral speed 458 feet per minute. Feed 30^* per minute. Finish good for com- mercial milling where surfaces are to be bolted together. Test No, 2. AH conditions the same as for Test No. 1, except that the depth of cut was reduced to 0.02', and the feed to 7.23" per minute. The finish in this case was good enough to polish. Test No. 3. Cutter, a helical mill Zi4" diameter, 6" long, 3 teeth, angle with axis 69°, rake 15°, arbor IJ^", cutter speed 510 r. p. m., peripheral speed 470 feet per minute, feed 303-^" per minute. Two cuts were taken, the first with a depth ■^'y the second with a depth of iV- Test No. 4. A slotting cutter with sharp-cornered teeth 1" wide, 61^" diameter, rake 15°, 16 teeth, arbor 13/^". Alternate teeth slope in opposite directions with the axis of the cutter. Cut- ter speed 510 r. p. m., pe- ripheral speed 835 feet per minute, feed 30 J^" per min- ute. Cuts were taken at a depth of -1^5' and J^". The finish was a good commer- BlKsm lubrication ^B^mi-^yHomita Miller; hood Clal fiulsh iu Cach CaSC. lilwd a»»y f^m ^iu,, U. .bow co.«l^uotion. ' ^^^^ ^^ ^ High-feed test, gashing with a gear cutter. Cutter 7 diametral pitch with extra hub, 12 teeth, 3}^" diameter, 10° rake, arbor l}^" diameter. Cutter speed 218 r. p. m., peripheral speed 200 feet per minute, feed 112' (9J/^ feet) per minute. Material of the same composition as for the blocks in the preceding test, in the form of a cylinder 1814" long and of a diameter representing a 30-tooth, 7-pitch gear. The machine upon which this test was made was a 28" Cincinnati Semi-automatic Miller. Repeated cuts were taken without any signs of distress of machine or cutter. 130 The CiNcmNAn Milling Machinb Company Test No. 6. A feature of all the preceding tests was a copious supply of lubricant to cany off all the heat. In each case as soon as the cut was finished, cutter and work were felt and neither showed an appreciable rise in temperature. To show the effect of cutting dry the block and cutter of Test No. 1 were replaced and a cut started with a depth of J^', feed at 20' pet minute, and a cutter speed of 87 r. p. m., peripheral speed Cut ipwd 77 I. p. m. Cot ^ daep by t' widb Fsed ITA* pM minute UJWO Iba. Miuite itienttli ateeL 80 feet per minute. This cut was started dry and the cutter showed distress after running about 2J^'; it was stopped, and the edges of the teeth were found to be blued. As a comment on the length of life of some of the cutters working under these conditions, a record is given of a cutter of the same description as the one used in Test No. 5, run to destruction. It milled 6,700', not including the cutter approach. This is equivalent to completely cutting 223 gears, 1' face, 7 pitch, 30 teeth. The cutter began to show distress at about the fourth cut from the last, and from this point to destruction the breakdown was rapid. Dis- counting these last three or four cuts, the cutter milled the equivalent of 220 gears of the dimensions specified. A Treatise on Milling and Moung Machines 131 Stream Lubrication. The copious use or deluging of cutter and work with a lubricant or coolant has been mentioned. This is arranged for on Knee and Column Type Machines, as shown In Figs. Ill and 113. Around the miller table is placed a light steel frame to confine the liquid. In the base is set a centrifugal pump capable of delivering 12 gallons per minute. This is some 10 times the quantity delivered by the geared pumps ordinarily used. The reservoir capacity is large, and in this the pump is submerged, so FK. IM. _ . . ... - jhsrp corne.. Bp«ed aiSr. p. m. Cutter SM' ain"t«- Tetd wptei. Peed 112" Ual«risl SS.OOO-lb. maohinerv atrel. 7 pitah Uublnerr eteet cutter etudatd elottiM ti nihing cutter. 12 ti^tb. Cut fulldoptbof tootb, wHb shArp corun. .-" " ""' Speed 218 r. p. m. Cutter SM' diameter, "— " -■ "—■•■'- — that there is no suction piping or necessity for priming. The lai^e capacity provides enough fluid so that an appreciable accumulation of heat is avoided. In addition, the surface of the table over which the lubricant spreads in a wide sheet acts as a means of cooling. The pump discharge under considerable pressure passes through a fle^ble hose to the cutter, or cutter hood, having in the line a large, quick-acting gate valve. From the table a large flexible steel tube returns the lubricant to the machine base. The preferable means of distributing the lubricant to the cutter is by means of a special cutter hood. This is shown in Figs. 113, 114, 117 and 118. It completely surroimds the cutter. The advantages of the hood are principally three. It confines the large flow of lubricant dh^ctly to the cutter and work, thus securing an inverted bath or flowing stream and making all of the 132 The Cincinnati Milling Machine Company lubricant do its share in cooling. It washes the chips from the teeth of the cutter so that they can not be carried back into the cut, thus clogging it, dulling the cutter and marring the finished surface. It prevents the splashing of lubricant when used in large quantity. Incidentally, it is also a milling cutter guard, guarding against accidental injury to the operator. Effects of Stream Lubrication and High Speeds. It is instructive to consider in brief fashion the possible effect of these high speeds and lubrication upon the various limiting factors that enter into milling machine practice. Power of machine: Increased speed in milling means a slightly increased power consumption per cubjc inch of metal removed. Tests made by the Cincinnati Milling Machine Company indicate that an increase of 100 percent in speed means an increase of about 10 percent in power consumption per cubic inch of metal removed. Thus increased speed means more powerful machines. Ability of the cutter to remove metal : The ability of a cutter to cut is increased with an increase of speed, the feed per minute remaining unchanged, for the reason that the chip taken by each tooth is decreased. This means a decrease of strain, wear and heating effect. The total or final heating effect is increased, but this can be counteracted by copious lubrication. Size of arbor and its spring: The size of the arbor is one of the limitations in present milling practice, being governed by the sizes of commercial cutters. The feed per minute is a measure of the strain on the arbor; thus an increase of speed, giving a lessened pressure per tooth, reduces the arbor strain and tends to do away with the limitation of arbor size. To illustrate, if a given set of conditions permit of a feed of 2" per minute, then by maintaining this rate per revolution, but multiplying the revolutions per minute by 10, we get a permissible feed of 20*^ per minute with the same arbor stress. Heating of the cutter: The heating of the cutter is often the limitation. This can be removed by using a quantity of lubricant or coolant sufficient to remove the heat as soon as it is released and keep cutter and work cool. Wear of the cutter: The wear of a milling cutter is dependent upon the number of linear inches milled if the depth of cut and feed per revolution are kept constant. Thus, increase of speed increases wear per unit of time. When the speed is sufficiently high so that by the aid of copious lubrication the chips are completely washed A Treatise on Milling and Milling Machines 133 away, wear is somewhat reduced by avoiding the grinding action due to the cutting up of chips. Breakage of cutters: Frail cutters are a limitation in milling practice, because only a certain maximum feed per revolution can be taken, dependent upon their strength. If this feed is kept con- stant, production is increased directly as the speed is increased, without increasing the cutter strain or danger of breaking. m r, p, m. Feed UT per i Heating of work: Uneven local heating when milling produces surfaces that are not fiat because swelled portions are cut away. This is a progressive action as the cut advances, for the total heat- ing increases. Further, some work springs after removal from the fixture, due to its temperature when removed. The absence of heating will do away with this limitation. Spring of the work: A weakness and frailty of the work is another limitation, which is minimized for the same reasons brought out under "Breakage of cutters" above. Spring of the fixture: The analysis given for "Breakage of cutters" applies here. In many cases we might get greater production if the time for putting work into and removing it from fixtures could 134 The Cincinnati Milling Machine Company be reduced. However, the frailty of fixture or work prevents the use of quick-acting clamping devices, as eccentrics, cams, levers and the like. Thus, if the pressure per tooth in cutting is reduced, the pressure required for holding may be reduced, and clamping devices may be made to operate more quickly. Thus the influence of speed in this respect should be to increase production. Spring in the machine: The arguments presented xmder "Spring in the fixture" apply here. Distance of revolution marks on the work: It is claimed that output today is controlled in perhaps 90 percent of cases by the distance between revolution marks. Polishing or some following operation limits this distance. These marks must be near together, or the following operation can not be properly performed. An increase of speed with imchanged feed, bringing these marks closer together, is one obvious remedy. Smoothness of cut: One feature in high-speed milling is the throwing away of the chips, which resembles nothing so much as the throwing off of shavmgs and chips in planing wood. This complete removal of the chips, both by the effects of speed and copious flooding with lubricant, does away with the grinding effect oh the finished surface. Thus, with a fixed distance between revolu- tion marks, high speed tends to give a smoother surface. It is possible that the fljnvheel effect of the rapidly rotating parts con- nected to the arbor influences this action. Cleaning fixtures and work: The washing effect of the lubricant on the work and fixture, when the lubricant is used in great quantity and imder considerable pressure, may aid in increasing production. Chips from High-Speed Milling. The illustrations, Figs. 121, 122, 123, show chips from high-speed milling, and the notes below indicate the conditions imder which each was produced. Fig. 121. (A) From machinery steel, cutter spiral mill 3J^' diameter by 6*" long, IJ^' arbor. Cut 5*" wide, 3^' deep, cutter speed 500 r. p. m., feed SOJ^*" per minute. Stream lubricated. (B) Conditions as for A except depth of cut ^'^. (C) From machinery steel, cutter helical mill 33^' diameter, 6*" long, 3 teeth, IJ^*" arbor, cut 5*" wide, -^^ deep. Cutter speed 500 r. p. m., feed 303^*" per minute, stream lubricated. (D) Conditions as for C except depth of cut 3^*". Fig. 122. (E) Conditions as for C except depth of cut f^*", cutter speed 86 r. p. m., feed 20' per minute. A Treatise on Milling and Milling MACinNES 135 (F) From machinery steel, kejnvay cutter, 6^" diameter, V face, IJ^'' ar- bor, cut a slot 1" wide, ■^'^ deep. Cutter speed 500 r. p. m., feed SOJ^*^ per min- ute. Stream lubricated. (G) Conditions as for F, except depth of cut J^*'. Fig. 123. (H) From ma- chinery steel, 7-pitch spur gear cutter, 4*^ diameter, cutting full depth. Cutter speed 220 r. p. m., feed 112 per minute. Stream lubri- cated. (I) Conditions as for A except depth of cut f^*", cutter speed 86 r. p. m., feed 20*" per minute. Stream lubricated. The removal of metal was at the rate of 31 cubic inches per minute. (J) Conditions as for I except that the cut was made dry. It ran for only about 2^*" when the cutter showed signs of distress. These chips were colored dark blues and purples in contrast to all of the other chips, which were bright and without any discolora- tions. The differences of all these chips from ordinary chips are evident. One fea- ture of these chips is that when they are produced A B C D Fit, 121 136 The Cincinnati Milung Machine Company with suflBicient lubricant they are entirely devoid of color. Here is one of the radical differences between high-speed milling and high- speed turning. In the origin- al article in the American Machinist, describmg the announcement of high-speed steel, occurs this sentence: 'The chips themselves left the tools at a temperature which drew them to beauti- ful blues and purples; this coloring of the chips is a practical shop test of the correct speed of the work.' In contrast, the absence of color in high-speed mill- ing chips is a practical shop test of the practicability of the feed and speed in use. Kinds of Lubricant. These tests seem to show that the nature of the lubri- cant does not affect the cut- ting speed provided the quantity is sufficient. That is, the principal action is one of cooling, and with even the cheapest cutting com- pounds there is sufficient lubricating effect, provided the quantity used is great enough to produce the necessary cooling." The Pump. The pump is of the centrifugal type and is capable of delivering 1/ Fig. 122 A Treatise on Milling and Milling Machines 137 from 12 to 15 gallons of lubricant per minute. This is many times the quantity delivered by the geared pumps used on milling machines at the time these experiments were con- ducted. This pimip is lo- cated in a large reservoir in the base of the machine, and is completely sub- merged, therefore, needing no suction pipe or priming. This large reservoir is necessary so as to provide a large enough body of lubricant to prevent it from accumulating an ap- preciable amount of heat. In addition, the lubricant spreads itself in a wide sheet over the table of the Milling Machine, and is thus aircooled before it re- turns to the reservoir. The supply is carried through a line of ^" piping to a large quick-acting gate valve, by which the volume is regulated, thence through a flexible hose and down pipe to the cutter hood. This down pipe is clamped to the overarm and may be firm- ly secured in any desired position. The Cutter Hood. This cutter hood (pa- tented) is attached to the H I n m ^ mm 2L ii7SArfi,V i^ 3 4 5 6 7 RH|Ht|tmi[tiimng u Fie 123 138 The Cincinnati Milling Machine Company delivery pipe and partly encloses the cutter. The functions of the hood are: 1. To confine the large flow of lubricant directly to the cutter and work, thus securing an inverted bath, and making all the lubri- cant take part in the cooling of the cutter. 2. To wash the chips from the teeth so that they can not be carried back into the cut, causing the cut to become clogged and the cutter to be dulled. 3. To prevent splashing of lubricant. A drain table (patented) consisting of a light steel frame is pro- vided to confine the lubricant to the table. This drain table is provided with a stramer of large area, and is so designed that a tight fit to the table is not required. A flexible metaJ return tube of ample capacity is provided to return the lubricant to the reservoir. This cutter and work-cooling system can be applied to all sizes of Cincinnati Single Pulley High-Power Millers, Plain and Vertical (but not Universal). It should be attached in our factory before the machine is shipped. The Standard Equipbient includes: 1 centrifugal pimip 1 set of %" piping, gate valves, flexible hose, etc. 1 standard hood 1 drain table 1 flexible return tube The standard hoods furnished as part of the equipment are as follows: No. 2 Plain and No. 3 Standard Machines: Hood for spiral mill Z" diameter, 3' face, l^i" hole. No. 3 Plain and No. 4 Standard Machines: Hood for spiral mill 3J^' diameter, 4' face, IJ^*" hole. No. 4 and No. 5 Plain Machines: Hood for spiral mill 4*" diame- ter, 6*" face, 2" hole. For Vertical Machines, Face Millers and Duplex Millers, the hoods must be made up special to suit the cutters and work and can only be furnished when we have definite information. Sometimes work is of such a nature that the hood can not be used with a face or end mill. The practical value of being able to use faster speeds, with the resulting faster table travels, is clear. On a number of regular A Treatise on Milling and Milling Machines 139 milling operations in our manufacturing department, the increase in feed, because of the faster speeds with stream lubrication, averages 125% faster than the best previous practice. Light Cuts with Stream Lubrication. The very large ma- jority of all milling work allows only relatively light cuts. This is either because the cutter is of delicate construction or the arbor is small; or the piece itself is frail or of such a shape that it is not feasible to hold it rigidly in a fixture, or because heavy feeds would heat or spring the work too much; and finally, because the revolution marks may have to be close together in order to get a presentable finish. Running the cutter at very high speeds makes it possible to take light cuts at a high rate of feed per minute with the following advan- tages: The pressure on the work is light. The work does not spring. The spring in the arbor is reduced allowing the use of smaller arbors and smaller cutters. Lighter fixtures can be used. Irregular pieces can be held in fixtures with less danger of being pulled out. The pressure between cutter and work being slight, there is not the danger of springing the arbor and consequently the finish is better, and the piece is finished to closer accuracy as to size. There is no heating of the piece, and in many instances it is possible to finish a piece with one cut, where heretofore two cuts were required. Heavy Cuts with Stream Lubrication. Not only is this large fiow of lubricant very beneficial on light cuts, but it also makes it possible to take the heavier cuts at very much higher cutting speeds, thereby permitting a smaller cut per tooth, thus reducing the strains on work and arbor. The volume of lubricant also car- ries away most of the chips, thus reducing the necessary cleaning of the jig to a minimum. 140 The Cincinnati Milling Machine Company CHAPTER IX MILLING CUTTERS In Chapter V, milling cutters and the fundamental principles of their action were discussed, but without going into the details of cutter construction. In this chapter we will discuss the design of cutters in detail. We will first consider the simple case of ordmary milling cutters. An ordinary milling cutter is a cylindrical body of steel with a hole through the center and with teeth running parallel or at some angle with the axis. If the teeth are parallel with the axis, the cutter is called a plain mill, and if they are at angle, the cutter is called a spiral mill. When cutters are of relatively small size, they are made of a solid piece of steel. When of sufficiently large size, the body and teeth are separate and the cutters are then called inserted tooth mills. Solid Mills. The most important things about the body of the mill are the material of which it is made, and the thickness of the metal between the kejnvay and the bottom of the teeth. The metal is either carbon tool steel or high-speed steel. Carbon steel cutters are used less and less nowadays, but stream lubrication, discussed in the preceding chapter, makes it possible to use them to better advantage than before. Carbon steel cutters are often used for finishing operations on extremely exacting work, while high-speed steel cutters are used for roughing. Carbon steel acquires a finer edge than high-speed steel. This latter material is more or less brittle and the edges of a high-speed steel cutter under the mag- nifying glass sometimes show small serrations, which affect the quality of the finished surface when an extremely fine surface is to be produced. The end surfaces of the body of the cutter should be as nearly flat, parallel and at right angles to the axis of the bore as it is possible to make them. The result of defective ends of the cutter is that the arbor will be sprung when arbor collars and cutters are clamped A Treatise on Milling and Milling Machines 141 together by the nut at the end of the arbor; the cutter will not run true, and the effect is the same as if one tooth were considerably higher than the others. This one tooth, therefore, does much more / Fig. 124 A modern spiral mill with wide spaced undercut teeth. work than the others and dulls before the other teeth are affected. In other words, the cutter must be resharpened much sooner than if all the teeth were doing their share of the work. M 5TDKEYWAV ALL CUTTERS TO HAVE 25» SPIRAL. 10 TEETH Fie 125 One of the earlier spiral mills with nicked teeth, having radial faces. This style of cutter has been superseded by the one shown in Fig. 124. The bore of the cutter should be true to size and perfectly round. As a rule, the bore is partly relieved as is shown in Fig. 124. This relief is not provided when the cutter is short. 142 The Cincinnati Milling Machine Company FbRi«i Rcucr- ChiI* BftCMKKR ENLMftaco FIc. 126 When milling cutters were first invented they were made with a very large number of teeth. The cutter was merely a rotating file, but as such, was a great improvement over a hand-operated file. Gradually the number of teeth was diminished, but it was soon f oimd that if the teeth were relatively far apart, each tooth would have to take a fairly heavy chip. At that time cutters were either not groxmd at all, or ground by hand, and, of course, this made it impossi- ble to have the teeth on an approximately uniform diameter. Under these conditions some teeth would not cut at' all and others would have to take twice or three times their legitimate share of the work, or maybe more. Not xmtil cutter grinding machines were regularly used for sharpen- ing cutters, was it i)ossible to use the milling cutter for reasonably heavy work. Faults of Cutters with Too Many Teeth. Until quite recently, teeth of plain mills and spiral mills were spaced about %" apart, and even now cutters may be foxmd in use on which the teeth are even closer together. These teeth were made with Radial Faces as in Fig. 125, so that their action was as shown in Fig. 90. The tooth was forced into the metal, causing spring in the arbor, or in the work. Imagine a cutter cutting steel at a speed of 70 feet per minute with teeth spaced %" apart, then 2,240 teeth will work every minute, and if we further imagine that the feed is 2" per minute, then each tooth takes a chip of which the greatest thickness is TiVir of an inch, or less than one thousandth of an inch. It will be readi- ly seen that this chip is so thin that, as a rule, the tooth will refuse to bite into the metal, thus leaving a chip of double thickness for the next tooth. This tooth is perfectly capable of taking this double chip, but it is compelled to do this extra work because of spring in the arbor. In other words, something which is wrong must happen first before the cutter will cut at all. DIRECTION OF CUTTING NEGATIVE ^^^-^^^ CLERRflNCE ^^ ^**«*„,,,CLERRRNC6 FIc. 127 A Treatise on Milling and Milling Machines 143 Fie. 128 Correct Design of Spiral Mills. A few years ago The Cincin- nati Milling Machine Company carried through a series of eiqperi- ments as to the best spacing of the teeth of milling cutters. It was f oxmd that a much wider spacing than was then customary would give very much better results, and from these experiments a set of dimensions for various styles of cutters was developed. Fig. 124 shows our latest design of Spiral Mill, 43/^*" in diameter. This mill has 10 teeth correspond- ing to a spacing of about l.V. At first we followed usual practice with an angle of spiral of about 10° or 12°, but this was soon increased until now this angle is made 25°, unless there should be end teeth, as in end mills, when the angle is kept down to 20°. The faces of the teeth are not made radial, but are undercut; in other words, they have rake. The amoimt of this rake should be about 15° for steel, and this is the way the cutter should be made if used for steel only, but as a standard cutter may be used for either steel or cast iron, this rake angle is kept down to 10°. Due to this xmdercut the section of the tooth would be materially weakened, and for this reason the back of the tooth is milled with a double angle as clearly shown in the illustration. This actually gives a stronger tooth than on the older mills made without rake. The bottom of the tooth is made with a large fillet, for two reasons: In the first place, this fillet strengthens the tooth, and in the second place, it prevents chips from lodging between the teeth. It was found quite early in the investigation of milling cutters that a long cutter, that is, one with wide face, would cause con- siderable spring and chatter, and that this condition might be partly remedied by making nicks in the teeth, Fig. 125, thus cutting down the length of the chip. These nicks, or chipbreakers, have long been a regular feature of milling cutters. However, it was also f oimd that a milling cutter with chipbreakers would not produce as fine a finish as one without them, so that quite often an additional 144 The Cincinnati Milling Machine Company cutter without chipbreakers had to be used for finishing. An analysis of this condition showed that this rough finish was due to the fact that one side of the chipbreaker had negative clearance. Fig. 127 will show this clearly. This side of the chipbreaker, there- fore, could not cut, but was dragged over the metal, and this pro- duced a torn finish, and besides, this point of the chipbreaker became the weak point of the cutter; in other words, it was the starting point for the breaking down of the cutter when at work. To over- come this, chipbreakers were made as shown in Fig. 128. They were produced by milling two notches crossing each other at the front edge of the tooth. The same result was obtained later on by con- structing the chipbreaker as shown in Fig. 126. These chipbreakers were necessary when the angle of spiral was 10° or 12° and were kept until this angle was gradually increased to 25°. The chip- breakers with clearance on both sides do not produce the torn finish caused by the ordinary kind of chipbreakers, so that the same style of cutter can be used for roughing and finishing cuts. How- ever, the comer of the chipbreaker still remains the weak point of the cutter and begins to dull first. It was also found that the edge of the tooth following dulled faster immediately be- hind each chipbreaker than the other parts of the cutting edge. All this goes to show the de- sirability of doing away with chipbreakers. Twenty-Five Degree Angle Spiral Mills. The angle of 25° is a great improvement over the old angle, for, with this angle no chip- breakers are needed, as will be clear from what follows. There is another reason why this angle of 25° is preferred. The wide spacing of the teeth allows one tooth of a 12° spiral mill to get entirely out of action before another tooth enters, and this causes more or less hammering. If the cut is deep, then this hammering is not noticeable, because one tooth is still in the cut when the next one ¥12. 129 A Treatise on Milling and Milling Machines 145 enters, but when the cut is shallow the hammering becomes quite pronounced. The angle of 25® does away with these conditions. Unless the cut is very shallow indeed, there will always be two teeth in action. Besides, with the 10® or 12® angle, the cutting action is not so free, and therefore the difference between chip and no chip means a great deal of difference in pressure exerted against the work and therefore a great deal of difference in the spring of the arbor. With the angle of 25® the length of the tooth embedded in the work is never very great, and therefore the spring in the arbor is very much less and consequently the hammering is very much reduced. To illustrate this with figures, we shall assume a piece of work 4" wide and a cutter of 3J^" in diameter, with nine teeth. We shall further assume that the depth of cut is J^*' and < 1 that the angle of the spiral is 10® (see Fig. 129). The curve - AB represents the path of the cutter in the work. Under the conditions given above, the angle AOB is 31® 15 minutes. The angle between two ad- joining teeth, AOC, is 40®, be- cause there are 9 teeth in the cutter, so that when a certain point of the tooth OA is just ready to leave the work, a corresponding point of the next tooth OC has not yet entered. It may be, however, that another point of OA still is in the work; in fact, this must be so, because the tooth is not parallel with the axis, but is cut with a spiral. This will be clear from Fig. 130, which shows a development of this cutter. Imagine a piece of paper wrapped around the cutter, the edges of the teeth having been painted with red lead and the piece of paper then taken off the cutter and laid out flat. All the teeth will show on the paper as red lines. Ai represents one of these lines. The angle which this line Ai makes with a line AC at right angles with the edge of the paper is 10®. The length of this line AC is 4", this being the width of the work. Of course it may be that the cutter is longer than 4*^, but we are only contemplating that portion of the cutter which is engaged with the work. From the dimensions of AC and the angle 10®, we find that AiC is .70532^ In Fig. 129, A is just ready Fi(. ISO 146 The Cincinnati Milling Machine Company to leave the work, but the other extreme point of this tooth Ai has still ^/lo" to travel before it is in the same relative position. A simple calculation will show that the angle AOAi is 28° 30 minutes and, therefore, that the angle AiOC is IV 30 minutes. We have found that any point of the cutter travels through the work through an angle of 31° 15 minutes, which is more than IV 30 minutes, so that the point Ai of the tooth OA is still in the work when the point C of the tooth OC enters. However, we see also that it is in the work for only a short time longer and, consequently, if the depth of cut were less than J^'' the tooth OA would be completely out of the work before the tooth OC would enter. If, now, we should make the spiral angle 25° instead of 10°, we would have the same general conditions, but the actual figures would be changed. The angle AOB, Fig. 129, would still be 31° 15 minutes, but the line AiC, Fig. 130, would now be 1.86524" instead of .70532,*' and the angle AOAi would now be 32° 15 minutes, so that the angle AiOC would be only 7° 45 minutes. In other words, the tooth OC would be in action long before the tooth OA would leave the work and, consequently, the depth of cut might be very much less than J^'' and yet there would be always at least one tooth in the cut. It will, of course, also be clear that the part of the tooth which first enters the work will be entirely clear again before the farther end of the s^me tooth enters, even in a cut J^'^ deep. In a shallower cut the section of tooth in engagement at one time will, of course, be less. This fact together with the free cutting action due to the shearing effect of the wide angle combine to produce a smoother action and the removal of more metal per horsepower than is possible with the older cutters. Results of Tests on Milling Cutters. The results of experi- ments on milling cutters referred to in the previous paragraph are summarized in the several test records printed below. Space does not permit of giving all the details here, but the data given will indicate quite clearly the great advantages possessed by cutters of the Cincinnati design. Three series of tests will be considered here, as follows: a. To show the influence of wide-spaced teeth. b. To show the influence of rake or undercut teeth. c. Tests on cutting capacity of face milling cutters. All of these cutting tests were made in a machinery steel bar having 55,000 pounds tensile strength, containing .20 carbon and .50 manganese. Because of the great variation in the cutting qualities A Treatise on Milling and Milling Machines 147 of different pieces of cast iron, it is difficult to formulate exact data, and the results published herein will therefore be confined to milling tests on uniform steel bars as above. Influence of Wide-Spaced Teeth, The tests given in table A were made with three spiral mills, all of which were 3* in diameter, with a 134" hole, 25° angle spiral, teeth ground with 5° clearance, but with the faces of the teeth radial, that is, no undercut or rake. The cutters differed only in the spacing of the teeth. Cutter A had 22 teeth, spacing about .dS'^. Cutter B had 16 teeth, spacing about .59*; Cutter C had 10 teeth, spacing about .94"^. The cuts were taken in a machinery steel bar 2^" wide, and the cuts were exactly the same depth in each case. Table A— Showing Influence of Wide Spaced Teeth Cutter Width of cut Depth of cut Revolutions Actujal feed in inches per minute. Cubic inches of metal removed per minute Amperes Volte Actual h. p. at machine cor- rected for motor efficiency. . . Cubic inches of metal removed by 1 h. p. in one minute A— 22 Teeth 80.4 11.70 5.94 60 200 13.44 .442 >A 80 14.8 7.63 70 200 15.75 .484 >a 80 18.46 9.52 74 198 16.5 .577 B— 16 Teeth 2H 82 11.9 6.14 54 196 11.77 .522 2M 68 15.11 7.79 56 198 12.32 .631 '4, 67 18.64 9.62 64 198 14.28 .674 C— 10 Teeth 2Ji 69 11.9 6.14 46 195 9.84 .625 2H 68 15.11 7.79 52 197 11.39 .684 2H 68 18.77 9.68 60 196 13.24 .731 The above figures show very conclusively the advantage of wide spacing alone. Cutter B, for instance, removed an average of 21% more metal than cutter A, and cutter C removed an average of 36% more metal than cutter A. Influence of Rake or Undercut Teeth, Tables B, C and D show the results of cutting tests made on a steel bar 5" wide, with cutters 33^^^ diameter, 6'^ face, used on an arbor l}^'^ diameter. Cutter A, Cincinnati Design Spiral Mill as in Fig. 124, 25® spiral angle, 10 teeth, 1.11* spacing, with 10° undercut or rake. This is shown in operation in Fig. 131. Cutter B, a Cincinnati Design Cutter similar to the above, but with radial tooth faces, that is, without rake. This is shown in operation in Fig. 132. Cutter C, a Helical Mill as shown in Fig. 151. This is shown in operation in Fig. 133. 148 The Cincinnati Milung Machine Company All of these tests were made on a No. 5 Plain High-Power Cin- cinnati Miller, direct connected to a 35 h. p. motor and fitted with our stream lubrication system. The feeds and speeds as given in the tables are corrected for loss of speed in the motor and the horse- power delivered to the machine is corrected for motor efficiency. Table B— Showlnft the Influence of Rake CjtB A' deep. Machine set for 18' teed permtnute. -55- sa B "25^s5iTSr .^7 c»\TESiii™urri™iidbi-ib:p; A Treatise on Milling and Milling Machines 149 Table B shows cuts that were taken ^' deep with the machine set at 16* feed per minute. The data obtained from the cuts with the helical mill are included in these tables as a matter of interest only. We are chiefly concerned with the relative value of cutter A with rake, and cutter B, which is similar to it, but has radial teeth. The figures show that the cutter with rake removed approximately 48% more metal per horsepower minute than the cutter without rake. SpitBl mill 3M' diar Cutter A— 2fl° Spira "-fo" »ll E— Helical Mill 7 OS S6 23. S4 t 23.60 .7 la & Feed In Inches per inlnutB (actual) Cubic tnchea of metal removsd per minute . 'fil Total b. p. at machine corrected for motor 27 57 Cubic Inches of metal remoTed by i b. p. at machine In one minute ,938 150 The Cincinnati Milling Machine Company Table C shows Bimilar tests but with cuts %' deep. Here it will be seen that the cutter with rake removed more metal per horse- power minute than in the previous case when taking a iV' cut. However, the cutter without rake did not do so well on the deeper cut. In fact, in this case, the cutter with rake removed approxi- mately 60% more metal than the one without rake. Table D-^howinft Influtoice of Rake CuM H' deep. Macblne aet for 20' teed pet minute. Cutter A-25» S^^^ B— 25° Spiral E— Helical Mill f 29.82 1.10 1». .7flO 8^9 Feed In Incbea peT minute Isclual) Cubic Inches of metal removed per minute. Total h. p. at machine corrected tor motor Cubic fncheB of metal remoTed by 1 b. p. at .&66 It rake could uot take this ci h (he feed set for 20' per miuule. A Treatise on Milling and Milling Machines 151 Table D compares these same cutters again, but with the machine set for 20* feed per minute. This comparison is not entirely fair, because the cutter with no rake could not be made to take the cut at this fast feed, and the figures given in this table therefore, com- pare the results obtained from the cutter with rake with the machine set at 20*^ per minute and the cutter without rake with the machine set at 123^*" feed per minute. The results of these tests are very illuminating, showing sepa- rately as they do, the great advantages; first, of wide-spaced teeth; second, the still greater advantage of rake. Of course it must be borne in mind that the ordinary form of nicked tooth high-speed steel spiral mill, which is considered standard and regularly car- ried in stock, could not successfully take some of the cuts shown in tables B, C and D. Tests on Face Mills. The tests in table E were made with a lO*' High-Power Face Mill as shown in Fig. 139, and the coolant was applied with one of our standard oil pimip equipments. In these tests proper corrections have been made on feed and speed to com- pensate for the loss of speed in the motor and the horsepower delivery to the machine is corrected for motor efficiency. Table £— Gutting Tests on Face Mills Actual Cutter Speed Actual Feed Inches per Min. Amperes Actual H. P. at Machine Metal Removed Depth of Cut Total Cu. In. per per Min. Cu. In. by 1 H. P. in 1 Min. W W H' Vs' Vs' Vs' H' 15H 15^ 15 16 15 15^ 15Ji 15J^ 15Ji 15Ji 16 16 15Ji 4.61 4.61 4.65 5.81 5.81 5.81 7.56 7.63 7.56 7.66 7.63 7.70 7.68 7.63 50 51 51 66 63 64 52 52 50 50 50 44 44 45 12.53 12.83 12.83 16.91 16.11 15.82 13.10 13.10 12.53 12.53 12.83 10.90 10.90 11.16 11.52 11.52 11.62 14.52 14.52 14.52 14.17 14.30 14.17 14.37 14.30 12.02 12. 11.92 .919 .898 .907 .86 .903 .918 1.082 1.091 1.131 1.148 1.114 1.103 1.101 1.069 The above figures are comparative only in relation to the cubic inches removed per horsepower per minute with this mill at dif- ferent depths of cut. They indicate that this mill showed its highest efficiency on cuts %'' deep, and that there was a decided falling off of efficiency with cuts J^*' deep. 152 The Cincinnati Milung Machine Company Relation of Depth and Width of Cut and Feed to Efficiency. This relative efficiency applies to this cut only. At some other width of cut and some other feed the relative efficiencies of cuts of different depths will show different results. It must be remembered that the efficiency of the cutter, that is, the metal it will remove with one horsepower in one minute, depends on three factors: width of cut, depth of cut, rate of feed. As proof of this we need only call attention to extreme cases: 1. An extremely wide cut. For instance, a cut in steel 10*^ wide, ^2^ deep, will not prove efficient as compared with the above cut T^^ X y at the same rate of feed, although the cut has the same area of section. 2. An extremely deep cut. For instance, a §aw ^'^ wide can not possibly take a cut 10'' deep, although this will again have the same area of section. The above figures will prove very valuable when estimating the capacity of a Miller for a given piece of work, or when estimating production on a given piece of work to be done on any particular machine. While the above tests are confined to the use of spiral mills and face mills, they will indicate that similarly good results may be expected from end mills, side mills and other cutters when made in accordance with the Cincinnati design. (See Chapter IX, Power Required to Do Milling.) Some examples of these different styles of mills are shown on the following pages and will serve as a guide for anyone desiring to make his own milling cutters. However, we recommend that CUTTERS ALWAYS BE BOUGHT from a reliable cutter maker. This is a special business and those who have made it a study and have a fully equipped plant and men experienced in this work can invari- ably furnish a better cutter than can be made in a shop that is not specially equipped for doing this work. Besides, when all the expense is figured in, the purchased cutter will be found to be cheaper. We do not make cutters ourselves, but will always gladly refer others to reliable concerns who make that their business. End Mills with Shank. Fig. 134 shows End Mills with taper shanks. It will be noticed that on these the angle of the spiral is 20® instead of 25°. This is done because the spiral angle also becomes the rake angle of the end teeth. A 25° angle would be too great. At the same time it is desirable, for the reasons given above, to keep the spiral angle as wide as is practical. A compromise A TBEATISB on MlLUNG AND MlLUNG MACHINES 153 angle of 20° has proven satisfactory. It will be noticed that these end mills also have their teeth undercut 10° and the faces of th(^ end teeth are cut back of the radial line this same amount. With the older design these things would have been out of the question because the teeth would have become entirely too weak. The mills shown in the drawings have the backs of the teeth formed with double angles, pving them ample strength. ^ It used to be the practice to continue the end teeth of an end mill down to the center, or at least as close to the center as it was possible to go. This served no purpose whatever. If the 2' end mill shown in Fig, 134 takes a cut, say, J^" deep, with y^ feed per 154 The Cincinnati Milling Machine Company revolution, then each of the teeth will take a bite of ^'^. It may seem that this is a very small cut for this size end mill, but at a speed of 70 feet per minute the cutter will make 135 revolutions per minute, and as we have j/s" feed per revolution, the feed per minute will be lej^*. This illustration also shows that it is the peripheral teeth of the end mill and not the face or end teeth which do the cutting, and it further shows that only ^^ of the edges of the face teeth come into play. In the end mill shown the body is counterbored. This is done mainly to provide for many regrindings. The comers of the teeth are rounded or beveled. These extreme comers, if made sharp, are the weak points of the cutter. A rounding or beveling of this comer adds much to the life of the cutter. COTTERS-f AND WIDER HAVE 12* SIDE CLEARANCE ON EACH SIDE 12 TEETH HSS Fit* 135 Side Mills. A modem Side Mill, 5" diameter, is shown in Fig. 135. As practically all of the work done by a side milling cutter is done by the peripheral teeth, it is important that these teeth should be undercut. When side milling cutters are to be used for milling slots in which the periphery and both sides are in action, and if the correct width of the slot is known, then a cutter may be designed with rake in all directions by simply building the cutter out of two similar A Treatise on Milling and Milung Machines 155 cutters placed side by side with the peripheral teeth cut spirally, one-half being right-hand and the other half being left-hand (see Fig. 136). The cutter as shown is made in such a way that the proper width of cut can be maintained by placing spacers between the two halves. If the two halves of the cutter were flat where they join each other, then the spacing out would leave an opening between them and this would leave a ridge in the work. For this reason they are made interlocking and the teeth of one-half overlap those of the other. The construction as shown has another advantage, namely, that though the teeth are wide-spaced, there will be no hammer blow because the teeth of one-half are in action before those of the other half are out of action. Shell End Mills. Fig. 137 shows a 2^" Shell End Mill. Shell end mills are in all respects similar to the taper shank end mills, except that the angle of the spiral is 15° instead of 20°. This style of cutter is seldom used as a spiral mill. Its action is the same as that of face mills described later. These cutters are driven by shrinking them on to a short arbor, about .0005' larger in diameter than the standard size of the hole in the cutter. Placing the cutter in boiling water heats it sufficiently to let the arbor enter. In addition, the arbor is provided with a driv- ing key. Reference is made to the action of this style of cutter in Chapter V. The action is entirely different from that of a plain or spiral 156 The Cincinnati Milling Machine Company mill. The face mill makes a chip like that of a planer tool, the only difference being that the tooth of a face mill sweeps in a circular path, whereas the planer tool removes the chip along a strmght line, the side of the tooth doing the cuttmg. Face Mills. Fig. 138 shows a 9^' Cincinnati Standard Face Mill, and Fig. 139 the corresponding size of High-Power Face Mill. They are similar in most respects, the difference being that the High Power Face Mill is especially built for the heaviest kind of duty. Both styles consist of a body in which slots are milled for the insertion of the blades. These bodies are made of steel. The slots for the blades are milled in the body at an angle of 7° with the center line. The blades themselves are made out of rectangular stock, ground to a driving fit into these slots. The blades are held in place by pins which are flattened on one side, thus making a wedge as clearly shown in the illustration. This brings the backs of the blades up against solid metal, and the amount of this metal is sufficient to support the blades under the heaviest cuts. A heavier stock is A Treatise on Miixing and Milling Machines 157 ,|J 158 The CiNaNNATi Milling Machine Company used for the blades of the High Power Face Mill than for those of the Standard Face Mill. Though the blades are driven in and held by the taper wedge, it is possible to take such heavy cuts that the blades will move endwise and it is for this reason that the High Power i li I Face Mill is provided with a backing-ring, which is bolted on to the body of the mill. This backing-ring holds screws supporting each blade individually. This arrangement also permits of setting the blades forward as wear takes place. A Treatise on Milung and Milling Machines 159 Particular attention should be paid to the angles. The rake angle, that is, the angle which the face of the blade makes with the radial line is 15°. The clearance angle on the peripheral edge is 7°. That portion of the blade which has this clearance angle is only j^" wide, and the blade is ground away at an angle of 25" back of this narrow land ; that is, at 10° with the tangent at this A lii' diameter intwlocked splinias cutter. point. This is done mainly to avoid unnecessary grinding when regrinding the cutter. The face edges have a clearance of 10° and are ground away at an angle of 20°; that is, 13° with the body of the mill. The blades are set at an angle of 7°, with the axis of the mill, so as to provide some rake at the point where the face edge of the blade slides over the finished work. Though, theoretically speaking, this face edge does no cutting, in reality it does remove a small amount of metal which is left there due to the spring in the work, the fixture, or the machine. It should also be noticed that the face edge of the blade is not left straight, as it is in taper shank end mills. There is first a rounded comer with a i^' radius, then a flat part -^' wide, and then the rest of the face edge of the blade is ground away with an angle of 7 to 10°. As there are 16 blades in the 10" face mill, and as these blades are 134" wide, there would be 20' of cutting edge resting on the work if these blades were not ground back. If the width of the work is somewhat less than 10", 160 The Cincinnati Milung Machine Company somewhat less than 20* of blade would be resting upon it, but in either case this would have a tendency to chatter. Too much stress can not be laid on the necessity of making both the body of the cutter and the blades as heavy as it is practical to make them. We can only give here sufficient information to enable the toolmaker to comprehend the principles on which correct cutter design is based. Lack of space forbids us to go into detail and we will only show here a few additional examples of milling cutters with notes as to their principal features. Splinlng Cutters, Saws, Slotting Cutters, etc. Fig. 140 shows a Splining Cutter made interlocking, and particular attention is called to the simple method of interlocking, the entire half of each part being made thinner than the other half. This design works well for cutters from -^° face up. Fig. 141 shows a Saw arranged to be driven not only by the key, but also by two pins which are held in a flange keyed to the arbor. Fig. 142 shows a thin Slotting Cutter. These thin slotting cutters are quite capable of doing very rapid milling, except for the fact that the body is liable to break through the keyway, and even if A Treati^ on Milung and Milung Machines 161 they do not break, the small amount of bearing which the cuttw has on the key is liable to indent the key, making it very difficult to remove the arbor collars. For this reason such narrow cutters should be made with hubs as shown. 0^ Fig. 143 is a Thread Milling Cutter. The particular screw to be cut has no finish except on the threaded portion, and the cutter is arranged in such a way that it turns up the outside while it mills the thread. This cutter, also, is provided with a hub. Fig. 144 shows another cutter provided with a hub, and which has some features that are worth noting. It will be seen that the teeth have alternate side rake in opposite directions, and further, that the teeth are not the full width of the cut to be taken. This arrangement allows the chips to come out freely, makes a very smooth side cut and prevents the chips from sticking in the cut. It often happens that when the chip is the full width of the cut the expansion of the chip wedges it in the cut and this causes not only excessive power consumption, but also more especially, a rough side finish. Fig. 145 shows a cutter of much the same peculiarities except that it has no side cutting teeth. Each tooth, however, is given side rake and the teeth are agam relieved so as to prevent wedging of the chips. It will be observed that the relief consists of beveling the edge of each tooth alternately and is always found on the side 162 The Cincinnati Milling Machine Company of the tooth where there is no rake because it is the rake side only that is expected to do work. Formed Cutters. Fig. 146 shows a Form Relieved Cutter, for finishing parts to an exact outline. These cutters are sharpened by grinding the faces of the teeth, and they retain their original outline, providing the teeth are always ground radially and straight. Cutters for cutting the teeth in gears belong to this class. Fig. 147 shows a Gear Stocking Cutter on which the alternate teeth are provided with right and left-hand side rake, all teeth having 10° undercut. This cutter has proven extremely satis- factory for roughing out gears. Fig. 148 shows an inserted tooth End Mill made in one piece with the shank. In the smaller sizes this makes a stronger mill than when the body and shank are separate, since in that case TOP View Of TtrrM.tMifW6Eo- side vnnft- Rf . 1« Fig. US the end of the shank must be quite small in diameter because the body of the mill will not admit of a large bore. Fig. 149 shows an Angular End Mill made in one piece with the shank. Fig. 150 shows an Angular Milling Cutter for use on an arbor. Helical Mills. Fig. 151 shows what we call a Helical Cutter, because its most striking feature is that the teeth are formed in a helix around the body. This cutter has several peculiarities which A Treatise on Milling and Milling Machines 163 make it capable of doing some work which can not be done with ordinary cutters, and which, on the other hand, limit its usefulness in other directions. This cutter is made as shown in the illustration as a single cutter, or sometimes as an interlocked cutter, right and left-hand. It might be supposed that the end thrust must be con- siderable with such a cutter, and for this reason the first cutters of this nature were made right and left. Tests have shown, however, 164 The Cincinnati Milling Machine Company s!::.n::::rj|i —.r *)R A Treatise on Milling and Milling Machines 165 that a cut which requires 80 amperes current with a right and left- hand cutter, requires 85 amperes with a single cutter, so that the end thrust amounts to only about 6% of the power required for the cut. The distinctive features of this cutter are that it cuts with a shearing cut; that it pushes the chips off sidewise; that it makes toothmarks, and not revolution marks; and that it does not spring away from the work. This latter property makes it especially valuable for cuts on thin work. If, when a cut is in progress, the feed be stopped while the cutter still rotates in contact with the work, it will be found after the feed has been reengaged and the cut finished that no mark is left on the finished surface at that point where the 166 The Cincinnati Milung Machine Company feed temporarily ceased. The only indication of the stopping of the feed will be that a somewhat different gloss will be observed at that point. This property of the cutter makes it possible to start a cut by feeding the work upward and then chan^ng the direc- tion of the feed, say, to the horizontal, without causing a depression where the change of direction took place. Thin plates, springy work, copper bars, test pieces of boiler steel, etc., have been very suc- cessfully milled witii this cutter. An example of work that this cutter will do successfully, and which is practically impossible with any other equipment, is shown in Fig. 152. This consists of milling steel test bars to size. Fig. 153. "*■ "^ As Is well known, these bars must have an accurate section and the sides must be parallel, and to size. In the illustration shown a number of pieces were clamped together for convenience in holding. The total width of the cut was 434". the depth H", and the feed A%' per minute. The work is first fed vertically to the cutter, then the horizontal feed is thrown in, and the cut is taken the proper distance. Because of the free cutting action of this cutter the work can be fed first vertically, then stopped and fin- ally fed horizontally without leav- ing an offset, thus insuring bars of the same sectional area throughout the entire length, with sides paral- _ fk ih lei and accurate for size. Any other form of milling cutter will dig into the work and leave a groove in the work at the time when the vertical feed is stopped and before the table feed can be engaged. Another illustration of this ciltter at work and one which also A Treatise on Milling and Milung Machines 167 shows the nature of the chip is shown in Fig. 133. An even more definite idea of their form may be obtained from the chips at D in Fig. 121, and at E in Fig. 122. Fig, 154 shows a modification of this cutter milHng the steel Universal Joint Shafts for Cincinnati Milling Machines. These shafts are turned with a head, the diameter of the head being equal to the largest diameter seen in the illustration. The cross feed brings the cutter into proper depth; the longitudinal feed then is used, after which the circular feed forms the rounded end; the longitudinal feed is then used once more on the opposite side of the piece and this finishes the operation, F^g. 155 shows another modification of this Helical Mill as used for milling out the ends of connecting rods. A single hole is drilled, the cutter inserted and the table is fed first horizontally and then vertically so that the cutter, traversing a rectangular path, cuts the desired opening into the end of the rod. A final finishing cut then brings the opening to size and proper finish. Rods 5" thick have been successfully milled with a cutter 1%" diameter at a roughing feed of M" and a finishing feed of ZH" per minute. Making Spiral MilMog Cutters. The Milling Machine is shown set for making spiral cutters in Fig. 156. The table is swiveled The Cincinnati Milling Machine Company to the proper angle and the Dividing Head is geared, all as given in the table, page 170. Setting the Cutter. The cutter should be set before the table is swiveled. Since spiral mills are always cut with a double angle cutter, usually one that has a 12° angle on the side which forms the A Treatise on Milling and Milling Machines 169 cutting face of the tooth, it is necessary to adjust the work off center, so that when the cutter is the right height above the head centers to give us the proper depth of cut, a straight edge placed along the edge of the tooth on the 12° side will line up with the dividing head center. This will give us radial teeth as shown in Fig. 157. However, the new cutters with undercut faces and wide-spaced teeth require two cuts. The setting of the cutter in relation to the work is shown in Fig. 158. In this case it will be noticed that the work must be offset more than in the previous case. It should be offset so that a straight edge placed along the edge of the cutter on the 12° side will form an angle with a line drawn from the outside diameter of the work to the center of the headstock of 10° for 10° xmdercut, and 15° for 15° undercut cutters. This leaves the tops of the teeth entirely too wide as at a, Fig. 158. A second cut is then taken to bring the teeth to proper form as at b and c. Fie. 157 He 158 170 The Cincinnati Milling Machine Company Leads, Change Gears and Angles for Making Spiral Milling Cutters Angle for Diameter Lead Gear 1st 2d Gear Setting of in on Intermedi- Intermedi- on Milling Cutter Inches Worm ate Gear ate Gear Screw Machine Table M 3.24 28 48 40 72 25H Vs 4.17 40 64 48 72 25H H 4.68 40 64 56 72 25% Vb 6.12 56 40 28 64 24J4 1 6.67 64 56 28 48 25M IH 8.33 48 32 40 72 25J^ IH 10.29 72 40 32 56 24Ji m 11.66 56 32 48 72 25H 2 13.33 64 32 48 72 25J^ 2H 15.24 64 28 48 72 25 2H 16.87 72 32 48 64 25 2% 18.75 72 32 40 48 25 3 19.69 72 32 56 64 25H ZH 21.43 72 28 40 48 25M 33^ 23.33 64 48 56 32 25^ ZH 25.57 100 64 72 44 24% 4 26.67 64 28 56 48 25H 4K 28.67 86 48 64 40 25 4J^ 30.71 86 32 64 56 24% 4H 32.73 72 32 64 44 24M 5 32.73 72 32 64 44 25% 5Ji 34.72 100 24 40 48 25H 6^2 37.04 100 24 64 72 25 6?i 39.29 100 28 44 40 24% -6 39.29 100 28 44 40 25^ Leads, Change Gears and Angles for Making Spiral End Mills Angle for Diameter Lead Gear 1st 2d Gear Setting of in on Intermedi- Intermedi- for Milling Mill Inches Worm ate ate Screw Machine Inches Gear Gear Table y^ 2.08 24 64 40 72 203^ Vs 3.24 28 48 40 72 19% y^ 4.17 40 64 48 72 20K> Vs 5.44 56 40 28 72 20 % 6.48 40 48 56 72 20 y% 7.41 40 48 64 72 20% 1 8.33 48 32 40 72 20K IK 9.70 64 48 32 44 20 ij ! t- Si 1 : I ^1 K} ^i 1 £d CS] # Fig. 186 A Treatise on Milling and Milling Machines 209 from the one vise while cutting takes place on the other and in con- junction with an elevating movement of the knee, also allows of the insertion of unfinished work in the same vise, thereby giving a continuous milling operation. Fig. 185 shows the same two vises, each of which grips one end of the same plate in which it is desired to mill a slot. There is nothing that could be devised for this par- ticular job that would be more efficient and at the same time less costly. In addition to the use of vises, a standard fixture can be designed on which there are a number of adjustable jaws, which jaws may in turn be moved from point to point on the main or base plate of the fixture, so that the one fixture could easily be adapted to hold quite a large variety of pieces, both as to dimensions and shape. The details of such a fixture are seen in Fig. 186. Standard Parts of Fixtures. While on the subject of a standard fixture, it is proper to look at what may be regarded as standard constructions. There are but few of these, since conditions vary so largely in milling fixture design and it has seldom been found practical to carry in stock a number of such standard parts as may very well be done in connection with the designing of drill jigs. However, the use of certain well-defined types even though differing in dimensions can be advantageously followed and we will discuss a few of these types. Support Pins. These are of two types — Fixed and Adjustable. The Fixed Support Pins when used in conjunction with a finished surface may generally be as Fig. 187, consisting of a flat-headed shoulder screw, having a hardened head, the top of which head may be surface-ground when in position. No adjustment need be pro- vided. When used for supporting rough castings, a good con- struction is that shown in Fig. 188, consisting of a screw with hexa- gon head and rounded top, tapped into the body of the fixture and provided with a lock nut so that the points may be elevated or lowered according to the variation in the castings. Adjustable Support Points may be divided into two classifica- tions: those that are brought into contact with the work through a spring and those which are hand-actuated. The first of these is shown in Fig. 189 and consists of a plunger which rests on a com- pression spring. Its vertical movement is limited by the point of a screw which projects over into a slot cut in the plunger. This prevents the spring from pushing the plunger far out of the fixture 210 The Cincinnati Milling Machine Company and is also a preventive against the plunger being lost when the fixture is in, or being transported to the toolroom. The plunger is clamped in position by either a sleeve directly operated on by a screw, or by a split sleeve, both halves of which are pulled together with a screw, the first of these methods being shown in the illus- tration. It will be evident that in both methods of clamping the support is entirely dependent upon the friction between the side of the plunger and the clamping member. For heavy work or work where a jarring effect is produced, to have a more solid form of adjustable support. A standard construction for this is shown in Fig. 190, and consists of a vertical plunger guided and restricted in its movement by the point of a screw and having its lower end beveled at an angle of 45°. This end rests on a similar surface on the end of a horizontal sliding plunger which is moved forward by a screw in the fixture. This construction has the merit of being cheap, simple and self-locking. It is not usually considered desirable to put a spring on this plunger to force it down when the adjusting screw is released. It is rather better to rely upon the operator forcing the plunger down with his finger, which operation insures the cleanliness of the top of the supporting point. Clamps. The standard constructions of these can again be divided into two types: those which press the work directly down on to the supporting member and those which hold by a side pres- sure, as in the case of vise jaws. The general principles of clamps have been touched on, on page 202, and the illustrations here given A Treatise on Milling and Milling Machines 211 212 The Cincinnati Milling Machine Company clearly show the application of some of these principles. The simplest form of Slotted Clamp, Fig. 191, is provided with a cound heel and beveled gripping portion. The rounding of the heel is so that the clamp may adjust itself on a three-point bearing, two of these points being on the work, the third on the supporting part of the fixture. Theoretically, such a clamp should be used in con- junction with a ball washer, but practically the ordinary flat washer serves. The Swiveling Clamp, Fig. 192, having the same gripping portion and heel is restricted in its swinging by the pin shown in the clamping stud. The Swinging Clamp, Fig. 193, is used only when the work is so large and unwieldy as to require a good deal more space for insertion than is usually necessary. This construction consists of a clamp swinging around a horizontal axis having provision at the gripping end for a one-point contact only, and since its plane of swinging is fixed, the clamping bolt swings into the clamp from the side so that when the clamp is released the bolt falls down below the work and the clamp is swung back entirely behind the pivot. The Cam, Fig. 194, has an angled surface, and in the one move- ment effects three pressures; it tends to force the work down on to the support over against the side stop and up against the end stop. Clamps which hold by gripping the work sidewise are shown in Figs. 195 and 196, The heel of the clamp is angled so that the grip- ping of the piece tends also to pull it down on to the supporting points. It is usually desirable to serrate or file- cut the gripping surfaces and the hole must, of course, be slotted in order to allow of slight vertical adjust- ment. The heel is again rounded and a compression spring provided to keep the heel of the clamp up against the undercut surface of the fixture. The simplest and one of the most satisfactory standard forms of Side Clamp is shown in Fig. 196 and consists of a simple screw having a hardened, pointed end, said screw being set to point down- ward to an angle of approximately 5°, so that its advance also produces a downward pressure. This, of course, puts certain Fig. 192 A Trbati^ on Milung and Milling Machines 213 o ;e> 214 The Cincinnati Milling Machine Company indentations in the work, but where these are not objectionable this form of clamping has much to commend it on the score of simplicity and strength. For Side Locations there are practically no standard con- structions. The usual practice is to press the work against flat or pointed screw heads. Sometimes it is desired to locate from some surface in conjunction with a boss, in which case flags may be utilized. The fl^ consists of a swinging member, the end of which termi- nates in a profile which agrees with the boss from which it is desired to locate. After the work has been chucked in the fixture the flag is swung into position over the boss, and the operator by means of various screws and clamps, wedges the work over until the flag and boss are in agreement. A good example of this is shown in Fig. 197. In other cases the location must be from the surface that is to be machined, ^^' '" so that the locating member must be removed before the cutter passes over the work. A comparatively simple way of doing this, shown in Fig. 198, entails the use of a bracket having either a formed locating piece or two screws which may be set in any desired plane. This bracket can be slid along the front of the fixture so that the work having been lined up by it will be left free for the cutter when the bracket has been slid to the next piece, or out to the end of the fixture. There is with this con- struction, of course, the "<■ "* danger that the operator may forget to remove his locating piece, and for certain high-production jobs a method similar to that shown in Fig. 199 can be followed. A Treatise on Milung and Milling Machines 215 The fixture is so arranged that the side locating points are auto- matically removed from the path of the cutter by the advance of the table. The illustration shows the details of this construction. A pair of swing brackets, A, carrying the locating point proper, are caused to rotate around the pivot by the movement of the plungers B, which are in turn actuated by the cam C that is fastened to the stationary headstock. Setting Pieces are often used in milling fixtures to insure the proper relationship between the machined surface and some other rough or previously machined part. These setting pieces may be divided into those that are hardened and placed in such a position as to be entirely free from the action of the cutter, and those which are soft and can not be so placed. The first type is well illustrated in Fig. 200, which shows a large angle bracket fixture carrying a casting which is to be operated on by a comparatively complicated gang. On the face of this angle bracket and well removed from the 216 The Cincinnati Milling Machine Company cutters will be noted two hardened gauges, A, having one flat and one angular side. These correspond with the important surfaces to be machined. In setting up a job the cutters are placed on the arbor and the fixture brought up so that the cut ters are between the setting points, pieces of tissue* paper bei ng used to determine their proximity. The cutters being set in the p roper relationship, the table is moved back CaTT£-^^ Fig. 198 to the chucking position, the work inserted and the pieces all milled. It is possible for the operator to test the continued accuracy of alignment at any time by simply repeating this process. It is not, of course, intended that he should do this for each piece. The other type of setting piece shown in Fig. 201 is based on the use of a soft steel piece, A, fastened to the end of the fixture and having stamped on its surface a dimension, which dimension is supposed to be measured by the toolkeeping department as soon as the fixture is turned in after use. If by any accident, the setting *ln our own practice the gauges or setting points are made .010*' undersize, and a .OlO*' steel thickness gauge is used instead of tissue paper. A Treatise on Milling and Milling Machines 217 piece has been damaged by the cutters, it is a simple matter to replace the same and to always secure exact duplication. (B is a swinging gauge for testing the piece before it is removed from the fixture.) This latter method is to be recommended more where the cutters are delicate and liable, on account of the nature of the job, to be brought in contact with the setting piece and also where the setting piece itself is comparatively difficult to reproduce as a hardened unit. Simple Fixture for One Piece. Passing then to the more specific types of fixtures, we will first consider the simple fixture designed to hold one piece for use either on a Horizontal or Vertical Milling Machine, an adequate illustration being found in Fig. 202 and detailed in Fig. 203. It will be noted that the work rests on three fixed screw heads and is supported at intervals by additional adjustable points. The supporting points and side clamping screws are all of the standard types described above and prove adequate to hold the work under a heavy roughing feed of 20" per minute. After the surfaces have been roughed and the side clamping screws slightly slackened up to release the bowing effect attendant on the 218 The Cincinnati Milling Machine Company side pressure, the finishing cut is taken at the same feed, resulting in a very flat surface with a degree of smoothness sufficient to meet the requirements. This fixture is of about as simple a construction as can be evolved for such a job as that illustrated. Tandem Fixtures, String Jigs. Following the simple fixture to hold one piece only, comes either two such fixtures set in tandem Fi|. IMI No S High-Power Miller. T.Hrgest cuttersU'diuneter.JSrcviilutione. Cut. S'A' vide, f,' deep. Feed i -G, ^iE r^^rj7 / r ^-& .^__^ :-:Bt. t-f ^ fl i^W-^ s 222 The Cincinnati Milling Machine Company Loading Fixtures. In certain limited fields the loading fixture can be very advantageously employed. Particularly is this the case where the length of cut or time taken for the cut is extremely short, and where the chucking of the piece consumes a very large proportion of the total time. In such cases a pair of fixtures can be used, one of them being on the table of the milling machine, the «. Uriwt«ult«r8 4M'diair leter, 23e CM per m,Qi.t*. iB.'feed .On^aW' pM'mLnuSS* Production 3 to 4 other on a convenient bench where either the operator or a helper can be removing the finished and inserting fresh, unfinished pieces. Fig, 205-A shows an arrangement for milling spark plugs in which this method is utilized. There are two work holders, each provided with a number of collets for gripping an individual piece. The work holder proper takes care of 37 plugs. The plugs are chucked in the fixture which is lifted to the table, dropped over a locating pivot attached to the table and clamped with bolts sliding in the T slots. It is located accurately by means of a plunger fitting between the sides of the T slots and sliding in a bush carried in the fixture. The work is then milled, indexed through 60° by means of other bush- ings in which the plunger fits and then re-indexed, making three A Treatise on Milung and Milling Machines 223 ) 1 B£gEEIB( I I I D m Ik s E © ^:£ jsjjja S w Wm K 224 The Cincinnati Milling Machine Company passages in all, which completes the milling of all six sides of the 37 plugs. The fixture is then released, lifted off the table, and the other fixture containing new plugs dropped in its place. The opera- tion is then repeated. With this arrangement the helper can be working all the time on the fixture that is off the milling machine table, and he can further be assisted by the machine operator in the intervals between reversing the feed, removing and inserting -24-. No. 1 Plain Cone-Driven Miller with loadinc fixtures the fixtures. For the successful operation of this method, reason- ably quick devices must be used for the clamping of the loading fixture to the table, cams and compressed air having been success- fully applied for this purpose. Right Angle or Square Fix- ture. In all of the above cases we '—-^'•-VT-j^vs*. yi^ — qr-^ j only use the table feed of the machine I *n iTV— !_/ k-i in one direction with a consequent I I \\ ' " ) I I '^'^ return stroke which may or may 'w«>vM« - rl-/ — Tv— **" ^^^ ^^ utilized to give a finishing ^ — *_' cut. To eliitiinate this return stroke "«■ *•*■■ we can, where the work is small enough, use a right angle or square fixture as referred to in the comparison of methods previously made. Such a fixture as shown in Fig. 206 does away with any idle travel whatever and often will, from the point of view of production, compare favorably with the rotary method. A Tebatisb on Milung and Milling Machines 225 In the fixture illustrated there are four compartments, the pieces being set as shown in the line cut, Fig. 207. All four pieces are milled by using a combination of table and cross feed. The methods of support are similar to those previously illustrated, the only notable points being the arrangement of the clamp, which it will be seen consists of a flat plate having trunnions which rotate in the fixture, being operated by a screw to which is attached per- O-^ manently a crank handle. The fulcrum of this plate, or clamp, is set back of the surface to be gripped so that the downward ten- dency is secured. The end of the screw operating these clamps is 226 The Cincinnati Milling Machine Company tiimed down and provided with a screw head so that while the crank handle can easily be slipped off the square it can not be entirely removed from the screw and lost. This arrangement means that the operator can always set the crank handle in an easy position for gripping the work and still make allowance for variation in the thickness of the casting. Another point to be observed on this fixture is that all of the four handles for gripping the work are brought either to the front or side of the fixture. Such an arrangement is, of course, absolutely necessary if any kind of speed in clamping is to be maintained. One of the advantages of this type of fixture as compared with the rotary fixture, is that a more solid union is effected between the fixture and the milling machine, due to the abolition of the extra rotary attachment members. This method consequently lends itself rather more to those jobs that call for a reasonably heavy material removal in addition to a high production. Rotary or Continuous Milling Fixtures. The rotary method of milling gives a high rate of production on certain classes of work. This has been dealt with in the earlier chapter on Milling Methods and we now show in Fig. 208 a fixture designed for holding pole pieces while milling the base surface. The location of this piece is rendered simple since a previous grinding operation provides a finished surface on which the piece may be located. The only points to be watched then are the method of gripping and the dis- position of chips. For gripping the piece, reliance is placed on a central ring, this ring having a number of facets to correspond with the number of pieces held in the fixture. These facets are undercut at an angle which corresponds approximately with the curvature of the piece and they are additionally provided with file-cut surfaces which embed slightly into the surfaces of the pole piece and make a very efficient gripping device. The outer or movable gripping member is a cam provided with longitudinal serrations and pivoting around studs carried in the frame of the casting. The end of the cam projects in the form of a lever which is either tightened by hand or by blows from a lead hammer. The fixture itself is practically in two halves, the central half carrying the locating ring and the outer half carrying the gripping cams, these two halves being joined together by a series of ribs. In between these ribs the chips fall clear of the top surface of the Circular Attachment into a trough sur- rounding said attachment, from where they may be easily removed. A Treatise on Milling and Milung Machines 227: The foregoing illustrations cover practically the full line of stand- ard methods of milling with face mills on both Horizontal and Vertical Machines. Redprocal Fixtures. When it is desired to mill either one or two faces parallel to each other, the reciprocating No. 2 Vertical Milfer with contiDUDUs millins fixture liolding 12 polepi«ce forgings, with aurfacea ZH'^y. Cutter fdiameUr, as [evolutioua. feed 12^' per minuU. Pri^fuction 4 pec miuute. method is often used in conjunction with a gang of side mills. A good example of this is shown in Fig. 209, where a gang of four milling cutters machine at one passage two sides of two large hexagon nuts. To make the fixture comparatively universal, the studs on which the nuts o£,sm*~a (they have not been previously threaded) I'^L I rest may be removed and substituted by - -^ other sizes. The nut is gripped to these studs by means of the two angular plates A, which move in slots BB, set at _ right angles to the surface to be gripped. / // These plates move downward through the U right and left-hand screw D, operated "*• ^•* by the crank handle C, shown on the right-hand side of the fix- ture. By this means two pieces are gripped with one movement rr^ 228 The CmaNNATi Milling Machine Company of the lever and a wide range of sizes can be easily accommodated with the one fixture. There is nothing special to be noted in the construction of this other than the arrangement of the gripping pieces above described. An elaboration of this method is found in Fig. 210, which shows a p£ur of hand-indexed fixtures arranged for cutting slots in the flanges of automobile hubs. It is, of course, obvious that this method leaves a curve at the bottom of the slot corresponding to the diameter of the cutter. The work is gripped by a contracting collet or split end of the spindle of the attachment, the circular surface of the work having been previously turned. Attention is drawn here to a device that should more often be applied to milling fixtures; that is, the ejecting mechanism. It very often happens that a very well-designed fixture that is entu^ly satis- factory in every other point fails in that the closeness of fit between the gripping device and the work rendera it difficult for the opCTator to remove the piece without a certain amount of manual labor that ought to be avoided. In this fixture a lever is provided, located conveniently at the rear of the fixture, which on being slruck or pushed ejects the work. The details of the indexing are not par- ticularly important and will be dealt with in that part of the chapter devoted to indexing fixtures. A Treatise on Milling and Milung Machines 229 Automatic Releasing Fixtures. Following the hand ejecting of work, one naturally conies to the automatic releasing and ejection of same. Fig. 211 shows an equipment for holding magneto base plates while milling the tops and edges. The piece rests on three fixed supports and is clamped by the central plate A, having knife edges, said plate being attached solidly to the fixture. The No. 3'High-PDwer Miller with reciprocal hand index fiitursa Enisbing four slots 1' wide, 1' deep in Butomobils hubs. Feeding 4^' per minute, removing H' metal in l.S mmutes per oomplele hub. gripping is through two levers, B, with their fulcrum to the rear of the gripped surface, the gripping being actuated by a balanced cam, which in turn is connected to the handle C projecting from the front of the fixture, the details of this mechanism being shown in Fig. 212. There is nothing particu- larly interesting about this part, but >3js attention is drawn to the small lever ,-j3C_*,>5t r D carrying the pin E shown pro- -.-— : ■d _L t-^ 1 |*W»I '■■ ■ "\ '■- '. %/■ : ; - .1 A fffi ■LOCK. I , >■ .. ... r . < . . , T .T III III 1 1 I I Fig. 223 at A. To accomplish these results the indexing was made through a pair of hardened plungers being brought into contact with similar hardened plungers in a block fastened to the stationary portion of the fixture B. These plungers, which were set up solid when in final position, also were arranged so that adjustment could be made by the toolmaker when assembling the fixture. To insure perfect contact between the fixed and indexing plungers, cam C was used, this cam being mounted on the bracket or fixed plunger support, and so being self-contained as far as the strains set up in insuring this contact were concerned. By this means the danger of a close and hard, alternating with a light and easy, contact were overcome. The indexing mechanism was, therefore, made to serve but one func- tion, that of indexing, and had no connection with the rotating A Treatise on Milling and Milling Machines 243 mechanism, which takes the form of a semi-circular dovetail slide D, rotating around a corresponding complete dovetail E in the base plate. (Fig. 224.) Entering into and forming the other half of the bearing or dovetail is a dovetail slide F, Fig. 223, which is forced forward and released by means of the cam G, shown at the rear. The effect of the angularity of the sliding member and .the angularity of the circular dovetail portion is to pull the rotating member firmly on to its seating over its full surface, which ar- Fig. 224 rangement can hardly be accomplished by any combination of horizontal and vertical locking mechanisms, since in this design the horizontal and vertical adjustments are made simultaneously. An unusual rigidity in the locking mechanism and unusual mainte- nance in correct bearing is secured with this construction, which can be strongly recommended for work where acciu'acy and long life are desired. Separation of Swiveling from Indexing Functions. It is always particularly desirable in accurate indexing mechanisms to separate those parts which are responsible for the entirely different functions of swiveling and indexing, A comparatively simple and extremely rigid indexing fixture is that shown in Fig. 226. This fixtiu'e was designed for cutting grooves either straight or angular in cutter blanks. When cutting the straight grooves the fixture was mounted directly on the table of the machine and when cutting angular grooves on an angled raising block A, as shown in the 244 The Cincinnati Milling Machine Company illustration. The interesting features of this fixture are the extremely liberal index teeth and the arrangement of the index plunger. The details of this are shown in Fig. 227. It will he noted that the index plunger proper is a separate piece of hardened steel fastened to a pivoting member B, the pivot being placed so that it is as nearly as possible in a line perpendicular to the straight side of the index tooth and starting from the end of that tooth. With this arrange- ment it is impossible to cause engagement between the tooth and index slot until the index plate shall have rotated past the desired position. The driving home of the index tooth, therefore, causes sliding action between the angular surfaces of the index tooth and A Treatise on Milung and Milling Machines 245 slot and brings the straight sides of these members together with- out any sliding friction and consequent wear. As a result the accuracy of indexing is much more permanent than when this little point is neglected. It can, of course, be easily seen that if wear is permitted to take place indiscriminately on both sides of the index plunger and is not confined to the one unimportant nonaligning FU. 2it ndei fixture cuttini 30 slota W nide, IH' deep, inU a 12' diBoietfr ita. feeding a* per minute in 78 minulee par body oomplele. side we will have much less certainty as to the accuracy of the indexing than when such precautions are observed. For driving the index plunger home a cam C is used, this consisting of a disc having a flat milled on it and having a hole bored eccentric to the circular contour. This is a very simple construction and gives not only a powerful lock but also a quick release and is done without any elaborate cam construction. In place of the usual arrangement for pulling out the index pin which, as a rule, consists of a spiral spring in tension anchored to some convenient part of the fixture, a spiral 246 The Cincinnati Milling Machine Company SPRING in compression is used, this spring being let one-half into the fixture and one-half into the index plunger or pivoting plate. The details of this are clearly shown in the drawing and it is recom- mended as a very convenient and satisfactory spring arrangement in that the spring can be given a small travel with less likelihood of permanent set and at the same time is thoroughly concealed and Fig. 227 guarded from injury either in use or transit from the machine to the toolroom. The foregoing description covers most of the standard milling fixture construction. It can not do more than indicate the different types and it must not be understood that these standard types will cover all classes of milling. For every individual job a different set of conditions arise, demanding a separate study. The proper designs for fixture and cutter are essential if the milling machine is to be an efficient tool. Lacking these, there is but little chance for any satisfactory results to follow its installation. A Treatise on Milling and Milling Machines 247 CHAPTER XIV THE SIZING AND CUTTING OF SPUR GEARS If two smoothly turned rolls are mounted on parallel shafts with their surfaces in close contact, as shown in Fig. 228, and one is turned through an arc, then the other will also revolve. If the circumferences of the end faces are divided into equal parts, and at the start two division lines are placed opposite each other, then, as we turn, the other division lines will come in line with each other. In other words, the circumference of the driven roll moves as many inches as the .circumference of the driver. If the driver has 6" circumference and the driven 12", then it takes two entire turns of the driver to bring the driven roll around once. We see, therefore, the number of turns of the two rolls are in inverse ratio to their circumferences, and consequently to their diameters. This is, of B — course, only theoretically true, as in actual practice there would be B ^=i=t ^ --A slippage. To prevent slippage both rolls are provided with teeth. It would not be safe to provide roll A alone with teeth on the outside, as these teeth would have no place to go un- less we cut corresponding grooves into roll B. To make all such re- volving parts of similar construction, we provide them with teeth above and grooves below their friction surfaces. Although the friction surface itself has then disappeared entirely, it remains the most im- portant factor in the design of such parts. The diameters of these two friction surfaces determine the ratio of the number of revolutions of these rolls. Rolls with teeth are called gear wheels.* When the rolls are cylin- ders, as shown, the gear wheels are called spur gears. The original friction surfaces are called pitch surfaces or pitch cylinders. A section of the pitch surface at right angles to the axis is called a pitch circle, or more generally the pitch line. Fig. 22S 248 The Cincinnati Milung Machine Company As there is no slippage possible between the teeth of these wheels, our rule now becomes absolutely fixed. The relative number of revo- lutions of two mating spur gears is in inverse ratio to their pitch circumferences, and consequently to their pitch diameters. In order to get a smooth uniform action of one gear on the other, the teeth must be of a certain definite shape. It is possible to make the teeth of one of the rolls of almost any shape, provided the teeth of the mating roll are shaped to suit. It is desirable, however, to make gear wheels in such a way that a given wheel can run with many others and not solely with the one with which it is mated, because in many mechanisms gear wheels must be interchangeable. The experience of a great many years has gradually limited the shapes of gear teeth to only one system; namely, the involute shape of tooth. Circular Pitch. If the rolls shown in Fig. 228 were provided with a tooth at every point where a mark appears, the distance between these marks would be called the pitch of the gear wheel. We say, therefore, that: The pitch of a gear wheel is the distance from center to center of two adjoining teeth, measured along the pitch circle. This pitch is called the CIRCULAR PITCH, Chordal Pitch. Years ago, when practically all gear wheels were cast and when the patternmaker had to construct the gear wheel, he used his dividers to space the teeth of his pattern. The dividers were set to the length of the chord and not the arc, between the centers of two adjoining teeth. This distance was therefore called "chordal pitch." This chordal pitch is not used in metal gear cutting and will not be considered here. Diametral Pitch. When the diameter of a circle is an even number of inches, or some simple fraction, the circumference of that circle becomes a decimal fraction which never expresses exactly the length of the circumference, however many decimals we might use. If the diameter is V, then the circumference is 3.1415926535. Of course it would not be practical to use all these figures, nor would it be practical to work to such a degree of accuracy, and therefore the circumference of the V circle is often expressed by 3.1416, and sometimes even by 3.14. There are also common fractions which 22 express the length of the circumference very closely, such as, -— A Treatise on Milling and Milung Machines 249 355 for ordinary work, and for more accurate work. In either case 113 the circumference is an odd fraction when the diameter is a simple figure or fraction, and vice versa, the diameter would be an odd figure if the circumference were an even figure. The use of circular pitches, therefore, leads to awkward fractions when computing a set of gears. To simplify the matter. Diametral Pitch has been uniformly adopted. This makes it easy to determine any factor in the design of a gear when some of the others are known, as for instance, to find the number of teeth when diameter and pitch are given, and so on. The diametral pitch is a number expressing how many teeth there would be in a gear of 1'' pitch diameter. If, for instance, the diametral pitch is 10, then a gear V pitch di- ameter would have 10 teeth, a gear 2'^ pitch diameter would have 2 X 10 = 20 teeth. This 2*^ diameter gear would have 2 x 12 teeth if the pitch were 12, and 2 x 16 teeth if the pitch were 16, and so on. From these simple data we derive the following rules: To find the number of teeth of a gear, multiply the diametral pitch by the pitch diameter. To find the pitch diameter of a gear, divide the number of teeth by the diametral pitch. To find the diametral pitch of a gear, divide the number of teeth by the pitch diameter. To find the center distance of two mating gears, divide half the sum of their teeth by the diametral pitch. To find the sum of the numbers of teeth of two mating gears, multiply their center distance by the diametral pitch and multiply this product by 2. In all that follows, "Pitch" is understood to be the Diametral Pitch, unless otherwise designated. It will be represented by the letter P. Circular Pitch by P'. Addendum and Dedendum. It is not only necessary to have a certain standardized shape of the gear teeth if we want the gears to be interchangeable, but it is also necessary that all gears of the same pitch should have the teeth project the same fixed height above the pitch surface and the grooves the same fixed depth below. A number of considerations enter into this matter and there has been established a definite relation between these dimensions of the 250 The Cincinnati Milling Machine Company teeth and the pitch. The system most common at the present time makes the height of the gear tooth above the pitch line (pitch sur- face) equal to 1 divided by the pitch. For a 5-pitch gear this height would be V. For a 10-pitch gear it would be tV, etc. This is called the addendum. The depth of the tooth below the pitch surface is made equal to the height above the surface. This is called the dedendum. If gears were actually made this way they would have to be absolutely perfect and their center distance would have to be absolutely cor- rect, otherwise the top of a tooth might interfere with the bottom of a groove of the. mating gear. For that reason the grooves are cut somewhat deeper than this theoretical depth. This additional depth is called clearance. The sum of addendum and dedendum is called working depth. The difference between working depth and the full depth is called clearance. Outside Diameter.* If we have a gear of 20 teeth, 10 pitch, 20 then its pitch diameter is — = 2*^. The addendum of such a gear ^ ^ 10 would be rr and, as this addendum is added to the radius of the gear, the outside diameter of this gear will be 2.2". This outside diameter is the same as the pitch diameter of a gear of 22 teeth, 10 pitch, so that we find the following rules: The outside diameter of a gear is found by adding 2 to the number of teethy and then dividing it by the pitch. The number of teeth of a gear is found by multiplying the outside diameter by the pitch and then subtracting 2, Circular Pitch, Clearance and Full Depth. We have seen that a gear V pitch diameter, 10 pitch, has 10 teeth. Such a gear would have a pitch circumference of 3.1416, so that the circular pitch of this gear would be 3.1416 divided by 10 = .31416; *If there are two mating gears on a pair of shafts, and there should also be another pair of gears on these shafts opposite each other, but which must clear each other, then the outside diameters of these gears added together must be somewhat smaller than the sum of the pitch diameters of the mating gears. In other words, the sum of the numbers of teeth of the two gears which must clear each other must be at least four less than the sum of the numbers of teeth of the mating gears. As the slightest error in the size of the mating gears, or the center distance, would cause the other gears to interfere, it is customary to either make the sum of their numbers of teeth five less than that of the mating gears, or else turn them down a slight amount. A Treatise on Milling and Milling Machines 251 To find the circular pitch, divide 3. HI 6 by the diametral pitch. It is customary to make the clearance at the bottom of the teeth equal to ^ of the circular pitch. The total depth of a tooth being composed of the addendum, dedendum and clearance, is found as follows : Since the circular pitch equals -^- — then A of the circular pitch = — X — = that is . 157 divided by the pitch. ^ P 20 P Since the 1 Addendum = 1 divided by the pitch = — P Dedendum = 1 divided by the pitch = — P 157 Clearance = . 157 divided by the pitch = ^ P We have by adding these 1 1 .157 2.157 u 1 ^ ^u 1 1 = = whole depth. P P P P From the above we deduce these rules: The whole depth is 2,157 divided by the pitch. The clearance is 0,157 divided by the pitch. Pressure Angles. Fig. 229 shows a pair of teeth of two mating gears in such a position that a point on the pitch circle of one gear is pressing on a point of the pitch circle of the mating gear. The direction of this pressure depends on the shape of the teeth. The most common form of tooth used at the present time is such that the direction of the pres- — ^ sure AB makes an angle 143^ _ degrees with the tangent com- mon to the pitch circles at this point. This line AB in the direction of the pressure is called the line of action. In later years many builders of machinery have adopted a sys- 252 The Cincinnati Milling Machine Company tern of gearing by which this line of action makes an angle of 20 de- grees with the common tangent. It was formerly thought that such an angle of 20 degrees would cause too much pressure on the bearings, too much wear on the gear teeth and a less smooth action between the gears, but recent thorough investigation has shown that this is not so. It has been found, on the other hand, that the teeth are stronger, the pressure on the bearings is not perceptibly more, the action is as smooth, and the wear on the teeth is not greater. A rack belonging to the system of gears which has an angle of action of 143^ degrees, has teeth with straight sides which make an angle of 14 J/^ degrees with the vertical. When the angle of action is 20 degrees, the rack teeth will also be straight, but make an angle of 20 degrees with the vertical. Not all makers of gear wheels make the addendum and dedendum as indicated above. Sometimes the teeth are made shorter and are called stub teeth. These, however, will not be discussed here. It is customary to make the tooth and the space equal in width, therefore the thickness of the tooth on the pitch line equals half the pitch. Selecting the Cutter. The shape of the tooth changes with the number of teeth of the gear, so that the exact shape of a tooth of a gear with 179 teeth is different from the proper shape for a 180- tooth gear. The difference would be extremely small in this case, but it would be somewhat greater for gears of 20 and 21 teeth respec- tively. This difference in shape becomes more marked in gears with the smaller number of teeth. For most practical purposes these varia- tions can be ignored to a certain extent. It is common prac- tice to cut gears with any number of teeth, but, of course, all of the same pitch, with eight different shapes of teeth, so that a set of only eight cutters is required for one pitch to cut any gear from 12 teeth up to a rack. The eight cutters adopted are: No. 1 to cut a wheel from 133 teeth to a rack. No. 2 to cut a wheel from 55 teeth to 134 teeth. No. 3 to cut a wheel from 35 teeth to 54 teeth. No. 4 to cut a wheel from 26 teeth to 34 teeth. No. 5 to cut a wheel from 21 teeth to 25 teeth. A Treatise on Milling and Milling Machines 253 No. 6 to cut a wheel from 17 teeth to 20 teeth. No. 7 to cut a wheel from 14 teeth to 16 teeth. No. 8 to cut a wheel from 12 teeth to 13 teeth. These eight cutters are made with the correct shape for the lowest number of teeth which they are supposed to cut. If then, we want to cut a gear with 48 teeth we must select the No. 3 cutter, which will cut of gears from 35 to 54 teeth, but we know that the shape of the tooth will not be entirely correct. The shape thus pro- duced will be found sufficiently accurate in a large number of cases where high speeds and great smoothness of running are not essential. However, if gears must be cut very accurate, then it becomes neces- sary to use a special cutter made to the correct shape for that par- ticular number of teeth. Cutter makers are prepared to furnish such cutters. Cutting Gears on the Milling Machine. Until within the last few years, practically all cut gears were made by means of a rotary milling cutter of such a shape as to produce the correct shape of teeth. Now, many gears are made by the process of bob- bing or shaping. In this discussion we are concerned only with the process of milling the teeth. Ordinarily, gear wheels are milled on automatic gear-cutting machines, which are specially designed for this one class of work. However, the installation of a gear cutter may not be advisable in a shop that has not much gear cutting to do. In such cases this work is done on the milling machine. A milling machine will cut the teeth as rapidly as a gear cutter, and it does not take longer to set up the milling machine than the gear cutter. Aside from having an indexing worm wheel of large di- ameter, the only advantage it has over the milling machine is that it automatically indexes the gear and returns the cutter at a rapid rate. The gear cutter then does not require any further attention after a job has once been started, whereas the milling machine requires the attention of an operator for indexing and advancing the work and throwing in the feed. This, however, does not amount to anything where only one or a few gears of a kind have to be cut at one time, so that, even in shops where there are gear cutters, odd jobs of gear cutting are frequently done on the milling machine, because this machine lends itself to rapid setting up and no par- ticular preparation for indexing is required. Fig. 230 shows the milling machine m operation milling a spur gear. 254 The Cincinnati Milling Machine Cobipany Setting the Machine. When setting up the machine for cutting a spur gear, care should be taken to see to it that the machine is in correct adjustment in every respect, all as discussed on pages 65-66 in the paragraphs on the use of the Dividing Head. It is of the utmost importance that the cutter be kept sharp. This is discussed in det^l in Chapter X, on Cutter Sharpening. A properly sharpened cutter should be mounted on the arbor as close to the end of the spindle as permissible, and it may be well to use an intermediate support as in Fig. 230 to give additional stiffness to the arbor. Now, adjust the table so as to bring the dividing head center up close to the cutter and then make transverse adjustments to bring the dividing head center to coincide exactly with the center of the face of the tooth of the cutter. Since gear cutters are all provided with a central line on the outside of their teeth this can be very easily done by simply bringing the dividing head center to coincide with this line on the cutter. We can now lower the table, A Treatise on Milling and Milung Machines 255 place our piece of work between centers and properly secure it by means of a dog to the driver, making sure that there will be no chance for back lash. The index pin must be set to the proper circle of holes as deter- mined from the index tables ; the plate itself must be securely locked, making sure that there is no back lash at this point; the index pin should be brought around in the direction in which the indexing will be done, which is preferably in the direction of the hands of a clock and allowed to drop into one of the holes. Th^i set the sector for the proper spacing; tighten the spindle clamp at the rear of the dividing head; start the machine; raise the work up carefully until the revolving cutter liegins to show the first slight evidence of touching the work; then set the elevating dial to zero, run the table to the right clear of the cutter and then raise up the required amount for the proper depth, all of which may be read from the dial; dis- engage the elevating crank so as to reduce the possibility of the adjustment being dis- turbed, and now we are ready to proceed with the milling. Cutting Large Gears. It sometimes happens that the milling machine is called upon to cut gears which are so large in diameter that they can not pass be- tween the table in its lowest position and the cutter on the arbor. Such work can be done in two different ways. First, by using the Un- dercutting Attachment, described on page 25. ni- ^i This attachment makes ..'^''"i,'"'.^ ^ T'F"i °S, *''»>'"«'« . MMhir» by »t- tmg the oiviQiDA h«aa apinciJe vettical anti iiaiHK tbfl uptwd. it possible to cut gears of large dimensions and coarse pitches on machines of moderate size. Second, by setting the spindle of the Dividing Head in a vertical position as shown in Fig. 231. It will be quite clear that by holding 256 The Cincinnati Milling Machine Company the work in this position a very large gear can be accommodated, but instead of using the longitudinal table feed we must now use the vertical feed, and we should feed up so that the pressure of the cutter on the work will be down towards the table. This makes it comparatively simple to place a supporting rest under the rim of the gear as close as x)ossible to where the cut is being taken. It must of course be remembered that although the dividing head is made to a close degree of accuracy, nevertheless, as the gears grow larger the index errors which do exist will be correspondingly multi- plied. However, these methods make it possible to cut very satis- factory gears whenever an occasional odd size gear must be cut. Table of Tooth Parts Whole Thickneas Working Diametral Circular Depth of at Addendum Depth of Pitch Pitch Tooth Pitch Tiine Tooth IH 2.5133 1.726 1.257 .8000 1.600 m 2.094 1.438 1.047 .6666 1.333 IH 1.795 1.233 .898 .5714 1.1429 2 1.570 1.078 .785 .5000 1.000 2H 1.396 .959 .698 .4444 .888 2J^ 1.256 .863 .628 .4000 .800 2H 1.142 .784 .571 .3636 .727 3 1.047 .719 .524 .3333 .666 3H .897 .616 .449 .2857 .571 4 .785 .539 .393 .2500 .500 5 .628 .431 .314 .2000 .400 6 .523 .360 .262 .1666 .333 7 .448 .308 .224 .1429 .285 8 .392 .270 .196 .1250 .250 9 .349 .240 .175 .1111 .222 10 .314 .216 .157 .1000 .200 11 .285 .196 .143 .0909 .181 12 .261 .180 .131 .0833 .166 14 .224 .154 .112 .0714 .142 16 .196 .135 .098 .0625 .125 18 .174 .120 .087 .0555 .111 20 .157 .108 .079 .0500 .100 22 .142 .098 .071 .0455 .090 24 .130 .090 .065 .0417 .083 26 .120 .083 .060 .0385 .076 28 .112 .077 .056 .0357 .071 30 .104 .072 .052 .0312 .066 32 .098 .067 .049 .0294 .062 The "whole depth of tooth" is the depth to be cut in gear. A Treatise on Milling and Milling Machines 257 Rules and Formulas for Dimensions of Spur Gears For the sake of convenience the useful rules that can be deduced from the foregoing discussion of spur gears, together with their formulas, are given on the following pages. In view of the fact that practically all the gear problems arising in the machine shop are based on the use of diametral pitch, we have tabulated the rules and formu- las for diametral pitch by themselves and give in a supplementary table similar rules and formulas for circular pitch for use when such gears are to be made. We believe this separation of the data for diam- etral pitch from those for circular pitch will avoid the confusion that sometimes arises when they are all placed in one table. In these tables the following notation is used : P = diametral pitch. P' = circular pitch. N = number of teeth; (if the num- ber of teeth in both gear and pinion are referred to, Ng = number of teeth in gear, and Np — number of teeth in pinion). D « pitch diameter. C = center distance. S » addendum. F = clearance. W « whole depth of tooth. T = thickness of tooth. O = outside diameter of gear. ClWCULWW PitCM Fi2. 232. Gear Tooth Parts The circular pitch is defined as the distance from center to center of two adjacent teeth alons^ the pitch circle. The diametral pitch is a number found by dividing the number of teeth by the pitch diam- eter. In other words, it gives the number of teeth for each inch of pitch diameter. 258 The Cincinnati Milling Machine Company Rules and Formulas for Dimensions of Spur Gears Made to DIAMETRAL PITCH To Find Rule Formula Diametral Pitch Divide number of teeth by pitch diameter. N P = — D Number of Teeth Multiply pitch diameter by diametral pitch N =^ P X D Number of Teeth Multiply the outside diameter by the pitch and subtract 2 X P - 2 Total Number of Teeth in a Pair of Gears Multiply the center distance by the diame- tral pitch times 2 C X P X 2 Pitch Diameter Subtract two times the addendum from outside diameter D = - 2 S Pitch Diameter Divide number of teeth by diametral pitch. N D = P Outside Diameter Add two times the addendum to the pitch diameter = D + 2 S Outside Diameter Add 2 to the number of teeth and divide the sum by diametral pitch N -h 2 n — P Whole Depth of Tooth Divide 2. 157 by diametral pitch 2.157 IF — P Addendum Divide 1 bv diametral pitch 1 s - p Dedendum Divide 1 by diametral pitch 1 p Clearance Divide 0. 157 by diametral pitch 0.157 F — P Thickness of Tooth Divide 1 . 5708 by diametral pitch 1 . 5708 T — 1 — P Center Distance Add the number of teeth in both gears and divide the sum by two times the diame- tral pitch Ng -f- Np C = 2 P Center Distance Divide the sum of the pitch diameters of a pair of crears by 2 D + D 2 Length of Rark" Multiply number of teeth in rack by 3.1416 nnH HiviHp Hv diamptTal nit.oh 3.1416 N X\a\^]X P A Treatise on Milling and Milling Machines 259 Rules and Formulas for Dimensions of Spur Gears Made to CIRCULAR PITCH To Find Rule Formula Diametral Pitch Divide 3 1416 bv circular nitch 3.1416 p P' Circular Pitch Divide 3. 1416 by diametral pitch 3.1416 P' — P Pitch Diameter Multiply number of teeth by circular pitch and divide the product by 3. 1416 NP' D — 3.1416 Center Distance Multiply the sum of the number of teeth in both gears by circular pitch and divide the product by 6.2832 {Ng + Np)P' C = 6.2832 Addendum Divide circular nitch bv 3 1416 P' S - 3.1416 Clearance Divide circular pitch by 20 P' F - 20 Whole Depth of Tooth Multiply 0. 6866 by circular pitch W = 0.6866 P' Thickness of Tooth Divide circular pitch by 2 P' T - 2 Outside Diameter Multiply the sum of the number of teeth plus 2 by circular pitch and divide the product by 3 . 1416 (N + 2) P' = 3.1416 Circular Pitch Multiply pitch diameter by 3.1416 and divide by number of teeth 3.1416D P — N Pitch Diameter Subtract two times the addendum from outside diameter D = - 2S Number of Teeth Multiply pitch diameter by 3.1416 and divide the product by circular pitch 3. 1416 P A7 — PJ — P' Outside Diameter Add two times the addendum to the pitch diameter ^ D +2S Length of Rack Multiply the number of teeth in the rack by circular pitch L « NP' 260 The Cincinnati Milling Machine Company GomparatiTe Table of Circolar and Diametral Pitch Table No. 1 shows the diametral pitches with the cxMresponding circular pitches. Table No. 2 shows the circular pitches with the corresponding diametral pitches. Table No. 1 1 Table No. 2 i Djftmetral Pitch Circular Pitch Circular Pitch Diametral Pitch 2 1.571 in. 2 in. 1.571 2Ji 1.396 IH 1.676 2H 1.257 IH 1.795 2Ji 1.142 IVs 1.933 3 1.047 VA 2.094 3H .898 lA 2.185 4 .785 IVs 2.285 5 .628 lA 2.394 6 .524 IH 2.513 7 .449 lA 2.646 8 .393 13^ 2.793 9 .349 lA 2.957 10 .314 1 3.142 11 .286 H 3.351 12 .262 Vs 3.590 14 .224 H 3.867 16 .196 H 4.189 18 .175 H 4.570 20 .157 Vb 5.027 22 .143 A 5.585 24 .131 H 6.283 26 .121 A 7.181 28 .112 % 8.378 30 .105 A 10.053 32 .098 Va. 12.566 36 .087 A 16.755 40 .079 y% 25.133 48 .065 A 50.266 Metric or Module System of Gear Teeth. The metric sys- tem of measurement does not use diametral pitches, but instead, the dimensions of gear teeth are expressed by reference to the MODULE of the gear. The module is equal to the pitch diameter in A Treatise on Milling and Milung Machines 261 millimeters divided by the number of teeth in the gear. For example, if the pitch diameter of a gear is 50 millimeters and the number of teeth 25, then the module equals 50 -j- 25 = 2. The accompanying table gives a comparison between diametral, circular and metric pitches, together with their decimal equivalents. To convert module or metric (for example M 2) into the equivalent diametral pitch, proceed as follows: M 2 = .247'', or in other words, it is the same as a circular pitch of .247^ P = 3 . 1416 P' in Inches P = 3 . 1416 "T247" 12.70. Comparative Table of Diametral, Metric and Circular Pitches, with Decimal Equivalents Diametral Pitch, P = Number of Teeth 3.1416 Pitch Diameter in Inches Circular Pitch in Inches Pitch Diameter in Millimeters Circular Pitch in Millimeters Module = Number of Teeth 3.1416 Pitch Diameter in Inches X 3.1416 Circular Pitch, P' = 3.1416 Number of Teeth Diametral Pitch in Inches Dia- me- tral Pitch Mod- ule Cir- cular Pitch Deci- mal Equi- valent Dia- me- tral Pitch Mod- ule Cir- cular Pitch Deci- mal Equi- valent Dia- me- tral Pitch Mod- ule Cir- cular Pitch Deci- mal Equi- valent 26 .121 .124 .125 .131 .143 .155 .156 .157 .175 .185 .187 .196 .216 .219 .224 .247 .250 .262 .278 .281 .286 .309 .312 .314 2% "W .340 .344 .349 .371 .375 .393 .433 .437 .449 .495 .500 .524 .556 .562 .571 .618 .625 .628 .680 .687 .698 .742 .750 .785 7 "% .866 1 "Vs .875 9 3H .898 24 3 '"h 8 • • • • •' • 1 .989 22 1.000 IH "a' 8 3 1.047 s'A "a" 9 "m 1.113 20 1.125 18 7 2% 1.142 VA ■'a' 4 '"a 10 "VA 1.237 1.250 16 6 2M 1.257 m '"'il' 4M ' ' ' V ' 16 11 "Wi 1.360 1.375 14 53^ 2H 1.396 2 "'k' 5 "ys 12 "i'H 1.484 1 500 12 5 2 1.571 2M "a" 5H "'ii' 14 "m 1.732 1.750 11 4>^ IH 1.795 2H "'a' 6 "h 16 "2" 1.979 2.000 ib 4 VA 2.094 262 The Cincinnati Milling Machine Company g o •p-i .^ > ••^ no bO ^ ti ^ .S o '^ C9 c^ Pi S ^ fe c «4-l ^ ^ p h u o CO b no o Q> ^M Q> ^ fe ^ o; ^ ^ H C4 Eh o ^ -i-> bO a •»-i 03 P 1- -noqj, 05 05''^^''^ O) O ^ ""^ ^ •A9a -noqj, -^ CO r* t>. 1-t o '^cooo •AaH 1 1- sq^pmra -noqj, ooor^oiO'^eoOOiOO»00»OQ COt^O"^I'-i-4'«^CO«00 f-H rH 1-4 C^ C^ ^ •A8H cococococococccococo sq^piras -noqj, OOCOTji(NOOQOTt<-?5 rH t-H 6l »-« »H C^ •ABH ^rti ^3^ ^3^ ^^ ^^^ ^9^ ^tji ''tji ^^n ^^n |8 sq^pmn -noqj, Tl4COt^CO'HO"*i'COC^t>. t-« tH d 1-1 C^ 1-1 tH •ABH ^rtl ^^^ ^5^ ^3^ ^^T^ ^9^ ''wi ^5^ ^^^ ^^^ 1:^ sq^pmn -noqj, r*Tt. •AaH iOiO^^^^>OOiOU3 1:^ sqtpim -noqj, O(N00"«^OC0-'^OC0i-H •ABH CO o CO CO o CO CO CO CO to g §^ fl a -»> M ^ P5 I ;l S fl* ^ to ^ « o d o »4 1S|| ^i i 6ps« S 8 O JSoo-S^ A Treatise on Milling and Milung MAcraNES 263 a a o o .23 > Q GJ9 ^ In O 09 Eh bO .s t3 .15 c^ p4 s piia •So sif^ptras o CO 05 ifh r*^ SSS Pitch 40 sif^pcnra -noqj, 05C5r^OiOTj.'-i05ooc^ioosco?5 Pitch 32 sq^pmra -noqj, 9S SS 2: £2 2 2S 5S ;3I S? S OiO"'T^^OOOOOOCOCO Pitch 30 -noqj, i.OOiOO»00»00»OQ Oi-«or*c^cocoo50»5 t-H d 1-1 rH c^ *-« Pitch 28 sq^tpires -noqj, f-i(N 00 t^ CO -^ C^ v-i C^ »-i *-< *-< 1^ Pitch 26 sq^pmra -noqj, 1-1 - 00 05 . '-H '^cooo 1-H 1-H CI 1-H *-« ^ sq^pnTO -noqx t>- Tt< 1-1 00 »0 C^ »0«0C^ i 1-h f— I CO coo cot> iq^pavB -noqj. »OQ»00»OOiO tH tH C^I »-• C^ f-l Bq^pms -noqj, C0-C^COi-l^ 1— I rH C^ 1-H 1-^ (N sqtpnBS -noqj, T}iOOC^«OOTtTi<(Ma>cO'^i-«^ CnI 1-H tH tH v-t 01 iq^pires -noqj, f-iC^C0'^Ot^00OO5l •Aan sq^pinra -noqx C0t>.O'^00^ COt*i-H 1— I tH rH C. CO O 1-1 1>- Tt< t3 c8 e a 0) o o 03 pC CO 9 Cd O H a 08 I O O 14 OQ I 264 The Cincinnati Milling Machinb Company Table for Cutting Racks— Continued (Using the Cross Screw for making divisions.) Pitch Pitch Pitch P 2 2H 4 2K ( d OD ^ QQ -4J ■*^ •*J i a c3 • a • a • a • > O > O > Q > & ,£3 ^ jq ^ M H H 6 H 6 H 5 7 171 196 57 7 142 6 192 6 114 5 7 113 6 188 6 171 5 7 84 6 184 6 28 5 7 55 6 180 6 85 5 7 26 6 176 6 142 7 197 6 172 6 199 5 7 168 6 168 6 56 5 7 139 6 164 6 113 5 7 110 6 160 6 170 5 Pitch 2% ■♦a § OQ I 142 84 26 168 110 52 194 136 78 20 Pitch 3 5 5 5 5 5 5 5 5 5 5 OQ S o 47 94 141 188 35 82 129 176 23 70 Pitch > 4 4 4 4 4 4 4 4 4 4 I a o H 98 196 94 192 90 188 86 184 82 180 Pitch 4 5> 3 3 3 3 3 3 3 3 3 3 OD q o H Pitch 5 185 3 170 3 155 3 140 3 125 3 110 3 95 3 80 3 65 3 50 3 O H 28 56 84 112 140 168 196 24 52 80 Pitch 6 2 2 2 2 2 2 2 2 2 2 Pitch 7 124 2 49 48 2 98 172 2 147 96 2 196 20 2 45 144 2 94 68 2 143 192 2 192 116 2 41 40 2 90 q o H Pitch 8 P^ 1 1 1 1 1 1 1 1 1 1 CQ a o H 193 186 179 172 165 158 151 144 137 130 Pitch 9 Pitch 10 Pitch 11 Pitch 12 Pitch 14 3 ^ 3 09 ■♦a ^^ ■*» •^ 13 TS n: T § § § § • 3 • P • a a > Q > g > O >> O > a p^ e ^ ^ ^ e ^ 149 114 86 62 98 ' 28 172 124 47 142 58 186 196 56 144 48 145 170 30 110 94 84 116 172 43 198 2 34 192 112 88 96 141 26 174 158 90 140 60 20 OD 13 a o H 24 48 72 96 120 144 168 192 16 40 A Treatise on Milling and Milling MAcmNES 265 Table for Cutting Racks — Continued (Using the Cross Screw for making divisions.) Pitch Pitch Pitch Pitch Pitch Pitch Pitch Pitch Pitch Pitch Pitch Pitch 16 18 20 22 24 26 28 30 32 36 40 48 09 03 OQ OQ OQ s S s 09 s s •4^ ■♦a •4^ ■♦a •*» ■«-» ■*» -M •4^ ■♦a ■*» ■*» TJ t TJ 'T TJ T 'T t: TJ TJ t: T § ■§ a § a I § § o8 § 5 i a 3 OQ OQ § a a OQ a a O o o O o O O O o o O O JH ^ M ^ ^ M M M JH U3 M M H H H H H H H H H H H H 196 175 157 143 131 121 112 105 98 87 79 65 192 150 114 86 62 42 24 10 196 174 158 130 188 125 71 29 193 163 136 115 94 61 37 195 184 100 28 172 124 84 48 20 192 148 116 60 180 75 185 115 55 5 160 125 90 35 195 125 176 50 142 58 186 126 72 30 188 122 ■ 74 190 172 25 99 1 117 47 184 135 86 9 153 55 168 56 144 48 168 96 40 184 96 32 120 164 175 13 87 179 89 8 145 82 183 111 185 160 150 170 30 110 10 120 50 180 70 190 50 Directions. — For example: To cut a 16-pitch rack, adjust the work to the cutter and set the micrometer dial of cross screw to zero. For the next tooth turn the cross screw crank until the mi- crometer reads 196 thousandths; for the following tooth continue to turn until the reading is 192 thousandths; and so on until you reach the last number in the above table; then without moving the cross screw set the micrometer dial to zero, and commence over again, con- tinuing as before. For cases in which one or more revolutions are required, make the number of revolutions and the necessary num- ber of thousandths beyond for each tooth, as shown in the table. For example: To cut a 3-pitch rack. Adjust the work to the cutter and set the micrometer dial on the cross screw to zero. Then mill the first tooth. For the next tooth, turn the cross screw crank through five complete revolutions, plus an additional amount until the micrometer dial reads 47 thousandths. When this tooth has been cut, index for the next tooth by turning the cross screw crank through five complete revolutions again and continue until the micrometer dial reads 94 thousandths. For the next spacing make five revolutions of the crank and continue around until the microm- eter dial reads 141 thousandths, and so on. 266 The Cincinnati Milling MAcmNE Company Indexing Table for Use in Connection with Rack Indexing Attachment for Gone-Driven Millers Diametral Diame- tral Pitch 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 22 24 26 28 30 32 Gear on Stud 88 88 88 88 88 88 88 88 88 88 88 88 44 88 88 88 88 88 88 88 44 Gear on Crank Shaft 28 35 42 49 66 63 70 77 84 91 98 105 56 63 70 77 84 91 98 105 56 Turns of Index Plate Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Half Half Half Half Half Half Half Half Circular Cir- cular Pitch Gear Gear on on Crank Stud Shaft 84 28 77 28 70 28 63 28 66 28 98 56 56 35 84 56 56 42 70 56 56 49 84 42 56 70 42 56 56 84 56 98 28 56 28 56 Turns of Index Plate Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Half Whole Whole Whole Whole Whole Half Indexing Table for Use in Connection with Rack Indexing Attachment for 'AH Millers of High-Power Design Diametral Diame- tral Pitch. 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 22 24 26 28 30 32 Gear Gear on on Crank Stud Shaft 88 56 88 70 44 42 44 49 44 56 44 63 44 70 44 77 44 84 44 91 44 98 44 105 33 84 44 63 44 70 44 77 44 84 44 91 44 98 44 105 33 84 Turns of Index Plate Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Whole Half Half Half Half Half Half Half Half Circular Cu-- cular Pitch f 16 i i } 1 8 i 1 i 7 i Gear on Stud 84 77 70 63 88 49 56 42 56 70 56 42 56 42 56 56 42 Gear on Crank Shaft 56 56 56 56 44 56 70 56 42 56 49 84 70 56 84 98 84 Turns of Index Plate Whole Whole Whole Whole Half Whole Whole Whole Half Half Half Whole Half Half Half Half Half A Treatise on Milling and Milling Machines 267 CHAPTER XV SHOP TRIGONOMETRY— BEVEL GEARS The name Trigonometry has a formidable soimd to those who have had no special training in this branch of mathematics, but whose work frequently requires them to use it in their everyday shop work. It is intended here to cover only enough ground, and that in simple language, to enable anyone with a knowledge of arithmetic to solve the ordinary shop problems involving angles, and we have, therefore, headed this chapter Shop Trigonometry. This word is composed of two other words, which translated in their proper order mean — ^triangle measurement. In other words, trigo- nometry is simply the measurement of triangles. The basis of all the computations is the circle, which, as we all know, is divided into 360 divisions called degrees. 1 degree = 60 minutes. 1 minute = 60 seconds. In all mathematical calculations, the following sjonbols are used: ° = degrees, thus 3 degrees = 3° ' = minutes, thus 5 minutes = 5' '^ = seconds, thus 12 seconds = 12" which is written 3°5'12", and reads "three degrees, five minutes, twelve seconds." The Right Angle Triangle. Of all the different triangles we can make the right angle triangle lends itself best to simple calcu- lations by means of trigonometry. One of the first things to be remembered is that the sum of the three angles of a triangle is 180°. A right angle triangle is a triangle, one of whose angles is a right angle. If one of the angles of a triangle is a right angle, or 90°, then the sum of the other two angles must also be 90°, because the sum of all the angles is 180°. From this we always know that one angle of the right angle triangle is 90°. If we know a second angle it is an easy matter to 268 The Cincinnati Milling Machine Company figure the third. If, for instance, a right angle triangle has an angle of 30°, then there must be another angle of 60°. The way we would figure is simply this: The three angles together are 180°. One of them, the right angle, has 90°. This leaves 90° for the other two angles. One of these two is 30°. Therefore the other must be 90° - 30° = 60°. If we know that the line BC in the drawing ABC (Fig. 234) is 16'' long, and that AC is half as long as BC, then we know that AC must be S*'. This is trigonometry. Trigonometry simply gives (^ the proportion or ratio between the sides of right angle triangles, and the problem of trigo- S^ nometry is simply to find one of the sides \ when you already know another side and the \ proportion between these two. \ If we draw a line DE parallel with AC, \ p then BE will be twice as long as DE because j^ -QQ jg ly^f^Q as long as AC, and if we had drawn \ DE somewhere else this same thing will hold \ true. If BC were twenty times as long as \ AC, BE would also be twenty times as long as \ DE. Any proportion which may exist between ^ ^ Q BE and DE remains unaltered no matter where F*«- 234 we draw the line DE. This proportion is not changed so LONG as we do not change the angle at b. Very complete tables have been made which give the proportion between AC and BC for any size of angle B. For a certain angle this proportion may be one-half, for another it may be one-third, for still another seven-eighths, for still another .4635, and so on. If you know that BC is 16" and you want to find AC, you will natu- rally want to know first what is the proportion between AC and BC. If you learn this proportion is one-half, you multiply 16 by one-half and find that 8 is the length of AC. If you know that the propor- tion is ;4635, you multiply 16 by .4635 and find 7.4160 is the length of AC. If you do not know the proportion between AC and BC, but instead, know the size of the angle B, you refer to the tables aiid find what the proportion is for this angle and then multiply 16 by that figure, the same as before. In other words, knowing the size of the angle is just as good as knowing the proportion, provided you have the table. If you know the proportion and want to know what the angle B is, you can, of course, find it in the same way by using the same table. A Treatise on Milling and Milling Machines 269 These tables not only give you the proportion between AC and BC when you know the angle B, but they also give you the pro- portion between AB and BC. They also give you the proportions between AB, AC, between AC, AB, between BC, BA and between BC, AC. Six of these proportions are given in the table, and a single multiplication will give you at once any of the sides of a right angle triangle if any of the other sides is given, or if you know one of the angles. Definitions of Sine, Tangent, etc.* Trigonometry would not seem so formidable if its terms were given in English instead of Greek and Latin words. "Measuring triangles" sounds much simpler than "Trigonometry," but it means the same thing. We find in the tables the terms: Sine, Cosine, Tangent, Cotangent, Secant and Cosecant. These words do not describe anything that Fie. 235 Fie 236 *It has been customary to teach trigonometry by showing the angle as made by two radii of a circle in which the length of the radius — 1' (see Fig. 236). It is possible to show angle AOB by the two radii CO and AO. If we drop the perpendicular CD on the line AO, and if we further assume that the radius OC of the circle is 1" in length, then the line CD is the sine of the angle COD, and OD is the cosine of this angle. If we erect a perpendicular at the point A, then this line will intersect the extension of the radius OC at the point B. In this case the radius AO is 1'^ in length, and the line AB is the tangent of the angle AOB. In the same manner the line EF is the cotangent of the angle AOB. These lines are tangents to the circle, and their length is determined by the points where these tangents intersect the legs of the given angle. This is the reason why the proportions mentioned are called the tangent and cotangent of the given angle. In Fig. 236 the radius OG is again 1'^, and the intersecting line, or secant, HG, is as many inches long as the value of the secant of the angle OGH. Tlh Toe Cixjs%aii yinusc yiMxssE Cohpaxt wrj^ m er€rj O A a Addendum Dedendum + clearance S-hA Whole Depth of Tooth Space Thickness of Tooth at Pitch Line Pitch Cone Radius Rule Divide the number of teeth in the pinion by the number of teeth in the gear to get the tangent Divide the number of teeth in the gear by the number of teeth in the pinion to get the tangent The sum of the pitch cone angles of the pinion and gear equals W .... Divide the number of teeth by the diametral pitch; or multiply the number of teeth by the circular pitch and divide by 3 . 1416 Divide 1 by the diametral pitch; or multiply the circular pitch by 0.318. Divide 1.157 by the diametral pitch; or multiply the circular pitch by 0.368 Divide 2. 157 by the diametral pitch; or multiply the circular pitch by 0.687 Divide 1.571 by the diametral pitch; or divide the circular pitch by 2 . . . Formula D Multiply the radius — by the cose- 2 cant of the pitch cone angle Np tan oc p = Na n^ tan « y ~ Np a p + a^ = 90** N NP' P •:: 1 S P = 0.318 P' 1.157 ^ \ A — p = 0.368 P' 2.157 w — Vf — P = 0.687 P' 1.571 P' T — — P 2 D C=^Co8ecDX— 2 A Treatise on Milling and Milling Machines 289 Rules and Formulas for Calculating Bevel Gears with Shafts at Right Angles — Continued No. 10 11 12 13 14 15 16 17 18 19 20 21 To Find d o •a A o W> M -♦a 2 o s Addendum of Small End of Tooth Thickness of Tooth at Pitch Line at Small End Addendum Angle Dedendum + Clearance Angle Face Angle Cutting Angle Angular Addendum Outside Diameter Apex Distance Apex Distance at Small End of Tooth Number of Teeth for which to Select Cutter Proof of Calcu- lations by Rules Nos. 9, 12, 14, 16 and 17 Rule Subtract the width of face from the pitch cone radius, divide the re- mainder by the pitch cone radius and multiply by the addendum Subtract the width of face from the pitch cone radius, divide the remain- der by the pitch cone radius and multiply by the thickness of the tooth at the pitch line Divide the pitch cone radius by the addendum to get the cotangent . . . Formula s = S X C-F t = T X C-F Cotan = S Divide the pitch cone radius by the dedendum 4- clearance (S 4- A) to get the cotangent Subtract the sum of the pitch cone and addendum angles from 90** Subtract the dedendum angle from the pitch cone angle Multiply the addendum by the cosine of the pitch cone angle Add twice the angular adxlendum to the pitch diameter Multiply one-half the outside diame- ter by the tangent of the face angle. Subtract the width of face from the pitch cone radius; divide the re- mainder by the pitch cone radius and multiply by the apex distance Divide the number of teeth by the cosine of the pitch cone angle The outside diameter equals twice the pitch cone radius multiplied by the cosine of the face angle and divided by the cosine of the adden- dum angle Cotan =■ S + A 8=90°-(a+0) C = a - * K=S Xcos oc O = D -{-2K O J= — Xtan 5 2 i=Jx C-F N' = N cos « = 2 CXcos 8 cos 290 The Cincinnati Milling Machine Company Rules and Formulas for Calculating Miter Bevel Gearing Fig. 247 Fig. 248 Use Rules and Formulas Nos. 22, 4-8, 23, 10-13, 24-26, 17-19, 27 and 21 in the order given. All dimensions thus obtained are the same for both gears of a pair. No. To Find Rule Formula 22 Pitch Cone Angle Pitch cone anele equals 45° a = 45° 23 Pitch Cone Radius Multiply the pitch diameter by . 707. C = 0.707 D 24 Face Angle Subtract the addendum angle from 45° 8 = 45° _ 25 Cutting Angle Subtract the (dedendum -h clearance) anele from 45° ; =, 45° - v^ 26 Angular Addendum 1 Multiply the addendum by . 707 . . . i IC = . 707 S 27 Number of Teeth for which to Select Cutter . .. Multiply the number of teeth by 1.41. N' = 1.41 iV A Treatise on Milling and Milling Machines 291 CHAPTER XVI SPIRAL GEAR CUTTING Spiral gears may have their axes parallel, the same as spur gears, or the axes may be at an angle with each other. A spiral gear differs from a spur gear in that the teeth are not placed parallel with the axis, but are wound spirally around the pitch circle. The name "spiral gears" is really wrong. The teeth are not wound in a SPIRAL, but in a helix around the pitch circle. The distinction between a spiral and a helix will be clear when we remember that the main spring of a watch is a good example of a spiral, while the threads on a lead screw form a helix. However, in our discussion, we will use the name "spiral gears," as this is the name by which the average mechanic know^ them. This chapter will not treat of all the properties of spiral gears, but only of such as need be known in order to design or make them. If we have two shafts with a center distance of 7J4", and we must drive one shaft from the other with a given speed ratio, we will find considerable trouble if we try to use spur gears. If, for instance, the speed ratio is 4 to 5, we will not be able to use spur gears except by making them 18 pitch. The sum of the diameters is 143^'', being twice the center distance, and we must select the pitch so that the sum of the numbers of teeth of the two gears can be split up into two numbers which have a ratio of 4 and 5. If we should select 4 pitch for the gears, we would find that the sum of the numbers of teeth of these two gears is 4 times the sum of their diame- ters, or 4 times 14 J/^ equals 58. However, 58 can not be split up into two numbers which have a ratio of 4 and 5. In order to do so, 58 should be divisible by 4 plus 5 which equals 9. If we should select 5-pitch gears, then the sum of the numbers of teeth of the two gears would be 5 x 143^ = 72 J^, and this, of course, is impossi- ble, as the sum of the number of teeth of two gears must be an integral number. If we make the pitch 18, then the sum of the numbers of teeth of the two gears would be 18 x 14J^ = 261, and 292 The Cincinnati Milling Machine Company 4 5 one gear would have — of 261 teeth, and the other gear — of this num- ber. However, 18 pitch is probably entirely too fine for the work we have to do, so that we must choose one of two things. We must either make special cutters with an odd pitch, or we must be satis- fied with a compromise as to the gear ratio. The first of these two things is costly and consumes a great deal of time and the other may be absolutely prohibitive if an exact gear ratio is required. Substituting spiral gears for spur gears would solve the question at once. Definitions — Pitch, Lead, Normal Pitch, etc. A tooth of a spiral gear is much like the thread of a screw. It does not have the same cross section, nor is it meant to do the same kind of work, but in many respects the two are very similar. The distance from a point on a screw thread to the corresponding point on the ne5d: thread is called the pitch. The distance the screw travels in an axial direction, if we give it one complete turn, is called the lead. These same terms apply in the same way to a spiral gear. There is, however, this distinction : We measure the pitch of a screw along the axis of the screw, whereas, we measure the pitch of a spiral gear around the circumference, that is, at right angles to the axis. However, there are two things which are called pitch in the spiral gear. The pitch, as we described it, that is, the distance between two cor- responding points of two adjoining teeth measured at right angles to the axis, is called the real pitch, whereas the distance between two corresponding points of two adjoining teeth, measured in a direction AT right angles to the direction of the teeth, is called the normal pitch. The normal section, which would give us the normal pitch, would show us the true section of the teeth. A section, taken at right angles to the axis, would give us the dis- torted view^of the shape of the teeth as seen when looking at the end of a spiral gear. A section through the axis would also give a distorted view. If the spiral angle is 45°, then the distorted views of the teeth would be the same whether we take the sections through the axis, or at right angles with the axis. If the angle of the spiral with the axis is less than 45°, that is, if the spiral gear approaches more nearly a spur gear, then the right angle section would give a less and the axial section a more distorted view. This is reversed if the angle of the spiral with the axis is more than 45°, that is, if the spiral gear approaches more nearly the shape of a worm. A Treatise on Milling and Milling Machines 293 Gutting Spiral Gears. Spiral gears are ordinarily cut with common spur gear cutters. The normal pitch is, therefore, given in the same way as the pitch of spur gears, that is, we talk of a 5, a 7, or a 10-pitch gear. The real pitch is measured along the cir- cular section of the gear, and if this pitch is P and the number of teeth of the gear is n, then the length of the circumference of the normal section is np. RB s RXIS T « TOOTH LINE N» NORMRL PITCH P » RERL PITCH L*SPlRnLRN6LE Fig. 249 Fig. 249 shows that the normal pitch and real pitch bear such a relation to each other that the normal pitch is a right angle side of a right angle triangle, of which the real pitch is the hypotenuse and the tooth line is the base. If the angle between the tooth line and the axis is called L, and if the normal pitch is P, then the real pitch is P-secant-L. If we know the pitch of the cutter, the number of teeth and the spiral angle, we can easily figure the pitch diameter of the spiral gear. We figure as if it were a spur gear and then multi- ply the diameter by the secant of the spiral angle. For instance, a 294 The Cincinnati Milung Machine Company spiral gear with 16 teeth, 5 pitch, and a spiral angle of 37 degrees, will have a diameter of 16 divided by 5 and multiplied by the secant of 37 degrees. If we were dealing with a spur gear the pitch diameter wouldbe - = 3.2'. 5 From a table of secants we find sec 37° = 1.2521. have 3.2 X 1.2521 = 4.0064', the pitch diameter of the The pitch circumference is 4.0067 x x - 4.0067 x 12.587'. If we should make a wooden cylinder with a diameter pitch diameter of our spiral gear, and then cut out a angle triangle. Fig. 250, of which one right angle side the circumference of the pitch circle, and the opposing Then we spu^gear. 3.14159 = equal to the paper right is equal to angle equal Fic. 250 to the spiral angle, and wrap this triangle aroimd the cylinder, we will find that the hypotenuse describes a spiral line around the cylinder, and that the end of the hypotenuse will come in line with the beginning. In other words, the two ends of the hypotenuse will be a distance apart on the cylinder equal to the lead of the spiral. If now we unwrap the paper triangle we have in this triangle all the important elements of a tooth of the spiral gear. One right angle side is the circumference of the pitch circle, the second right angle side is the lead, the hypotenuse is the length of a tooth wrapped once around the pitch cylinder, the angle opposite the circumference is the angle of the spiral with the axis of the gear. This is commonly called the spiral angle or helix angle. It is the angle to which the milling machine table must be set. The angle opposite the lead is the angle which the tooth makes with the body of the gear. A Treatise on Milling and Milling Machines 295 Addendum, dedendum and clearance are the same as in a spur gear of the same pitch as the normal pitch of thd spiral gear. Selecting the Cutter. It is now possible to figure all the dimensions of the spiral gear and turn up the blank in the lathe. However, when it comes to cutting the teeth, a new element comes in. Although the gear may have 16 teeth, 5 pitch, this does not mean that we can use a 16-tooth, 5-pitch gear cutter for this spiral gear. It is true, we will have to use a 5-pitch cutter, but not for 16 teeth. We must select a spur gear cutter for a different number of teeth. The rule usually given is to divide the number of teeth of the spiral gear by the cube of the cosine of the spiral angle. This gives good results for gears having a spiral angle in the neighborhood of 45°, but anyone who has followed this rule for gears with a spiral angle differing greatly from 45° will have found that such gears do not run properly and the running of the gears becomes worse as the spiral differs more from 45°. For such gears we recommend the following rule: Divide the number of teeth of the spiral gear by the product of the square of the cosine multiplied by the sine of the spiral angle, N = in which N is the number of teeth of the Cos L^ X sin L selected gear cutter, and n is the number of teeth of the spiral gear. Taking the above case N = ^ = ^^ = '1 ^ 41. Cos 372 X sin 37 .79864^ x .60182 .6378 x .60182 We should select a cutter suitable for cutting a gear with 41 teeth. The speed ratio of two spiral gears is, as with spur gears, the ratio of their numbers of teeth. For instance, a 16-tooth gear driving a 32-tooth gear will cause this latter gear to run half as many revolutions per minute as the former. The center distance between two spiral gears, as with spur gears, is equal to half the sum of their pitch diameters. Shafts Parallel. Computation of a pair of spiral gears which are to be used in place of spur gears. If we have two shafts, say 8" apart, and wish to drive one from the other by means of spiral gears with a given gear ratio, and, if we desire to use standard gear cutters we should proceed as is shown in the following example: 296 The Cincinnati Milling Machine Company The two gears shown in Fig. 251 must have a ratio of 2 to 1; a center distance of 8*^, and in order to make them of the proper strength the teeth must have about 5 pitch. As we want to use standard gear cutters, we will make the pitch exactly 5. SMRU GIMA NUMBER OP TECTHin<2S •riRnt MN6Let2o*2r Right hand LRRGE GEAR NUMBER OP TEETH>2nt90 BPIRRL RNGLE » SO^Zl' LEPT M«NO Fig. 251 A pair of spiral gears on parallel shafts to give a speed ratio of 2 to 1. Number of Teeth and Spiral Angle. Taking the number of teeth in the small gear = n, and the number in the large gear = 2n, and the spiral angle of the teeth in the small gear L, we have: n sec L Pitch diameter small gear = , and Pitch diameter large gear = , because, in a pair of spiral 5 gears with shafts parallel, the spiral angle is the same in both. The sum of the pitch diameters of the gears is, therefore, n sec L 2n sec L ~ "T Z and this sum equals double the center distance. A Treatise on Milling and Milling Machines 297 Therefore, n T 2n T 1/? — sec L H sec L = 16. 5 5 Multiplying both sides of this equation by 5, in order to simplify it, we get n sec L + 2n sec L = 80. This is a very simple equation, but unfortunately there are two unknown quantities: The number of teeth n, and the spiral angle L. However, there is one thing we know about n; it must be an integral number. There is still another thing we know, and that is that we would like the angle to be about 20 degrees, for this gives the maximum efficiency of the gear system. We will, therefore, try the equation by giving L the value of 20°: sec 20 = 1 .0642, and therefore the equation n sec L + 2n sec L = 80 becomes (n x 1 . 0642) + (2n x 1 . 0642) = 80. 3n X 1.0642 = 80. n X 3.1926 = 80. n = 25.058. 2n = 50.116. As n must be an integral number, we will assume a value of n = 25, and therefore 2n = 50. Substituting in the above equation, we get 25 X 1.0642 + 50 X 1.0642 = 79.815. Since the second member of the equation should be 80 and not 79 . 815, it is evident that the assumed value of 20° for L, the spiral angle will not do, if we decide to use 25 and 50 teeth. In proceeding to find the correct angle, we will first determine whether the angle should be more or less than 20°. For trial, we will select 19° and 21°. With 20° the value of the second member was too small. Therefore, it must be increased. Since our value is too small we will try a larger angle, 21°: sec 21 =» 1.0711. Substituting this in our equation, we get 25 X 1.0711 + 50 X 1.0711 = 80.3325. 298 The Cincinnati Milling Machine Company The value, using 20°, was . 185 too small. Our new value is . 3325 too large. The correct angle is, therefore, between 20° and 21°. By trial, we find that 20°22' (sec 20°22' = 1.0667) gives us 25 X 1.0667 + 50 X 1.0667 = 80.0025, or .0025 too large, and 20°21' (sec 20°21' = 1.066) gives us 25 X 1.0666 + 50 X 1.0666 = 79.9950, or .005 too small. We will, therefore, choose as our value of L, 20°21'. Let us try this out and find what the new center distance between the gears will be. Since the gears are 5 pitch and we have taken 2 x center distance for our second member of the equation, then the center distance is 1^^^^ = 7.99950 2x5 which is .0005" short, which is close enough for all practical pur- poses.* Our gears, therefore, will have a spiral angle of 20°21', the small one with 25 teeth and the large one with 50 teeth. Selecting the Cutter. Referring back to the rule given on page 295, we have for the small gear XT n 25 N = cos2 20°21' X sin 20°21' .93759^ x .34775 25 = 81, .8780 X .34775 and for the large gear 50 50 .937592 X .34775 .8780 x .34775 = 163. Therefore, the cutters should be selected for 81 and 163 teeth respectively. * We have already decided that the center distance between the shafts on which these gears will work in our machine is 8*. Were we to use an angle of 20° 22', our gears would have a center distance .00025*' too large, and they would not go into place, or at least they would work too tight if all other dimen- sions were correct. We therefore choose 20° 21' which makes gears that are .0005' small and will have just this much working clearance. This is satisfac- tory for ordinary work. If closer accuracy is required we must either change our center distance in the machine or continue trying by selecting angles read- ing in seconds until a satisfactory one is found. A Treatise on Milling and Milling Machines 299 Computing the Lead. Referring to Fig. 250: We know angle L = 20°21'. However, we do not know the pitch circum- ference. We must therefore first find the PITCH diameters Pitch diameter = — x sec L. P Then for the small gear we have — X sec 20^21' = — X 1.0666 = 5.3330, 5 5 and for the large gear — X sec 20°21' = — X 1.0666 = 10.666 5 5 Since the outside diameter equals the pitch diameter plus twice 2 the addendum, OD = PD h — therefore, 2 outside diameter of small gear = 5.3330 h = 5.7330"; 5 outside diameter of large gear = 10.6660 + — = 11.0660". 5 The PITCH circumferences are: small gear 5.333 x 3.1416 = 16.754 large gear 10 . 666 x 3 . 1416 = 33 . 508. T H - Pi^ch circumference _ 16.754 _ 16.754 At^.-intf Tangent L Tangent 20°21' " . 37090 " for the small gear, and 2 x 45.17" = 90.34" for the large gear. We now proceed to select the change gears by following the instructions given in the chapter on Change Gears for Cutting Spirals. Our gears are as follows, shafts parallel : Pitch = 5. Number of teeth in small gear = 25. Number of teeth in large gear = 50. f iff 300 The Cincinnati Milling Machine Company Spiral angle small gear = 20^21' right hand. Spiral angle large gear = 20''21' left hand. Pitch diameter small gear = 5 .3330' Pitch diameter large gear = 10 . 6660' Outside diameter small gear = 5 .7330' Outside diameter large gear = 11.0660' Lead small gear = 45 . 17'^. Lead large gear = 90.34'^. Cutter for small gear = for 81 teeth. Cutter for large gear = f or 163 teeth. Center distance (exact) = 7.99950^ Center distance (actual) = 8. 00". The above example is not at all unusual, since spiral gears are coming more into general use for transmission members on parallel shafts in place of spur gears. Shafts at Right Angles. We will now consider the case of a pair of spiral gears on shafts that are at right angles with each other. Fig. 252, using the same general data as above. Speed ratio = 2 to 1. Pitch = 5. Center distance = 8. Spiral angle of small gear = L. Spiral angle of large gear = 90° — L. or = complement of L. Number of teeth in small gear = n. Number of teeth in large gear = 2n. There is an important point of difference between this and the previous case. With shafts parallel, we prefer a spiral angle of about 20° to reduce the end pressure on the shafts. With shafts at right angles, we prefer a spiral angle of as near 45° as we can make it, for this gives the maximum efficiency of such a gear system. Number of Teeth and Spiral Angle. Since the spiral angle of the large gear is the complement of L, we must use the cosecant in finding its number of teeth. Our equation then is A Treatise on Milling and Milling Machines 301 RIGHT HBND SPIRRL nxis OF SMRLLGERR L«46*30'RraHTHRno HNCit Op LRnoK Genu (90-LJL r ^3»30'R, hbmo RIGHT HAND SPIRRL «XIS OP Fig. 252 Spiral gears with shafts at rfght angles. n sec L , 2n cosec L ^ ^ + = 16, or n sec L + 2n cosec L sec 45° = 1.4142 cosec 45° = 1.4142 = 80. and therefore, the equation n sec L + 2n cosec L == 80 becomes n X 1.4142 + 2n X 1.4142 = 80. 3n X 1.4142 = 80. n X 4.2426 = 80. n = 18.85. Since n must be an integral number, we will assume n to have a value of 19, and therefore 2n equals 38. Substituting these values in our equation, we get 19 X 1.4142 + 38 X 1.4142 = 80.6094. 302 The Cincinnati Milling Machine Company Since the second member of the equation should be 80, it is evi- dent that our assumed value of 45° for L, the spiral angle, is incor- rect for 19 and 38 teeth. In proceeding to find the correct angle, we will first determine whether the angle should be more or less than 45°. For trial, we select 44° and 46°. With 45°, the value of the second member was too large. Therefore, it must be reduced. If we find that 44° gives a smaller value than 45°, then we know that the angle should be less than 45°, but if the value is greater, then we know that the angle must be more than 45°. Of course, we don't expect that either 44° or 46° will be the correct value of the angle, but making a trial with both will show us in the first place, in which direction we must go, and in the second place, how much a change of one degree affects the result. Assuming an angle of 44°: sec 44=1.3902 cosec44 = 1.4395 we then have 19 X 1.3902 + 38 X 1.4395 = 81.1148. This is more than the value resulting from 45°. Therefore, we must select an angla greater than 45°. Assuming an angle of 46°: sec 46 = 1.4395 cosec46 = 1.3902 we then have 19 X 1.4395 + 38 X 1.3902 = 80.1781. This is closer to 80 than we found when L was assumed at 45°, but it is still too large. We will, therefore, try an angle of 47°. sec 47 = 1.4663 cosec47 = 1.3673 we then have 19 X 1.4663 + 38 X 1.3673 = 79.8171. This is too small, whereas the value L = 46 was too large, there- fore, the true value of L must be somewhere between 46° and 47°. A Treatise on Milling and Milling Machines 303 We note further that the value f or L == 46 is . 1781 too large and for L = 47 is . 1829 too small, so that we may expect the true value of L to be very close to 46°30'. We will try this, assuming L = 46°30'. sec 46°30' = 1.4527 cosec46°30' = 1.3786 then 19 X 1.4527 + 38 X 1.3786 = 79.9881. This value is so close to 80, that it is worth while to try it out and see what the center distance of these gears will be. In our first equation we made the second member 2 X center distance x the pitch = 2 x center distance x 5 = 80. Therefore, the center distance of our new gear will be, 79 9881 center distance = — '■ = 7.99881. 2x5 This differs from 8^^ only a little more than .OOl*^, which is close enough for all ordinary requirements. However, we do not need to stop here if extraordinary accuracy is required. In that case we would note that the value of the second member is too small and that, therefore, the angle is too large. We would, therefore, try 46° 20' or 46°25' and gradually narrow down until the error is inside of the permissible limits. By following the same methods as in the previous example, we find other needed data as follows: Selecting the cutter for the small gear we have XT KfC " cos2 46°30' X sin 46°30' " .3437 " ' and for the large gear N = 5 = J8_ = 105, cos2 43°30' X sin 43°30' .3622 therefore the cutters should be selected for 55 and 105 teeth respect- ively. Computing the Lead. Pitch diameter = — x sec L. There- 304 The Cincinnati Milling Machine Company fore, we have for the small gear — X sec 46^30' « — x 1.4527 = 5.52026, 5 5 and for the large gear — X sec 43°30' = — x 1.3786 = 10.47736. 5 5 2 Outside diameter small gear = 5 . 520 h = 5 . 920"^. 5 Outside diameter large gear = 10.477 + — = 10.877'. 5 The pitch circumferences therefore, are small gear 5.520 x 3.1416 = 17.341 large gear 10.477 x 3.14X6 = 32.914 T J Pitch circumference Lead = Tangent L We have for the small gear J , 17.341 17.341 -^ .^^, Lead = = = 16.465*^ Tan 46°30' 1.05378 and for the large gear Lead==-^2,M_ =3^914^34 684,, Tan 43°30' .94896 We can now proceed to select the change gears as described in the chapter on Change Gears for Cutting Spirals. Our gears are as follows — shafts at right angles: Pitch = 5. Number of teeth in small gear = 19. Number of teeth in large gear = 38. Spiral angle of small gear = 46°30' right hand. Spiral angle of large gear = 43°30' right hand. Pitch diameter of small gear = 5.520". A Treatise on Milling and Milling Machines 305 Pitch diameter of large gear = 10 .477". Outside diameter of small gear = 5.920". Outside diameter of large gear = 10.877". Lead of small gear = 16.465". Lead of large gear = 34 . 684". Cutter for small gear = for 55 teeth. Cutter for large gear = f or 105 teeth. Center distance (exact) = 7.99881". Center distance (actual) = 8. 00". Shafts at an Angle of Less than Ninety Degrees. We will now consider the case of a pair of spiral gears on shafts at an angle of 60° with each other, Fig. 253, using again the same general data as in the two previous cases. Speed ratio = 2 to 1. Pitch of cutter = 5. Center distance = 8. Spiral angle of small gear = L. Spiral angle of large gear = 60° -L. Number of teeth in small gear = n. Number of teeth in large gear = 2 x n. nxis OF RIGHT HHNO SPIRAL RIGHT HBND SPIRRL Grwi Lt2fn HtHuhoi Fig. 253 Spiral gears with shafts at an angle of less than 90 degrees. 306 The Cincinnati Milling Machine Company (a) If the spiral angle of each gear is less than the angle between the shafts, then the sum of the spiral angles of the gears will equal the shaft angle and the gears will be of the same hand spiral. (b) If the spiral angle of one of the gears is greater than the shaft angle, then the difference between the spiral angles equals the shaft angle and the gears will be of opposite hand spirals. Number of Teeth and Spiral Angle. Our equation is again n X Sec L 2n x Sec (60°-L) -^ -f ^ -= 16, or 5 5 n X Sec L + 2n X Sec (60°-L) = 80. We now have to find the angle L by trial. Let us assume L = 20°, then n X 1.0642 + 2n X 1.3054 = 80, or 1.0642n -f 2.6108n = 80 3.675n = 80 n = --— = 21.8 teeth. 3.675 Suppose we select n = 22 and find the spiral angle L by assum- ing L = 20°, then 22 X Sec 20° + 2 X 22 X Sec (60°-20°) = 80, or 22 X 1.0642 + 44 X 1.3054 = 80 23.414 + 57.437 = 80.850, which is too large. Suppose L = 21°, then 22 X Sec 21° + 44 X Sec 39° = 80 23.5022 + 56.6148 = 80.117, which is still a trifle too large. After trying a few more examples, with angles ranging from 21° to 22°, we find L = 21°17', which gives 22 X Sec 21°17' + 44 Sec 38°43' = 80 23 . 6104 + 56 . 3904 = 80 . 0008, which is close enough for all practical purposes. H" - j: Tl^ A Treatise on Milling and Milling Machines 307 Diameters, Circumferences, etc. Then, Pitch dia. of small gear = 22 x Sec 2V1T ^ 4 722". TDu u A' 4? 1 44 X Sec 38°43' ,. ^-o. Pitch dia. of large gear = = 11.278'^. Center distance = J^ (4.722 + 11.278) = 8.000/ Outside dia. of small gear = 4.722 + ^ = 5.122^ 5 Outside dia. of large gear = 11.278 + ^ - 11.678". 5 The pitch circumferences are: Small gear = 4.722 x 3.1416 = 14.834" Large gear = 11.278 x 3.1416 = 35.430" and the exact leads are for the Small gear -^i^ii- = 38.081" Tan 21°17' Large gear ' = 44.198" Tan 38°43' Selecting the size of cutter, we have for 22 Small gear, N = == = 27 . 2 teeth Cos2 21°17' X Sine 21°17' 44 Large gear, N = : = 115.6 teeth. Cos2 38°43' X Sine 38°43' From the table of leads (page 344) we find the closest lead for the small gear is 38.182 and the large gear 43.977, and the corresponding change gears, 72, 24, 56, 44 and 86, 44, 72, 32. This example indicates the procedure for computing a pair of spiral gears with shafts at any other angle. 308 The Cincinnati Milling Machine Company It is important that drawings should be complete with all data, needed by the shop before they leave the Engineering Department, For example: The data that the drawing for the above spiral gears should contain are as follows: Small Gear Large Gear 6 22 4.722' 6,122' 8.000' .200' .4314' 21° 17' 38,081' 38. 182' 27 (No. 4 Cutter) 72 24 56 44 11 278' 8.000' Spiral ai^le 38° 43' 43,977' Number of teeth tor which to select The change gears for cutting thb spiral 44 72 32 bI gear on a Pbiio MiUer A Treatise on Milling and Milling Machines 809 The equipment shown in Fig. 254 is a No. 3 Cincinnati Miller with Dividing Head and Spiral Milling Attachment. The blank is steel, 3' diameter, 3 pitch, 60° spiral, and is fed past the cutter 1" per minute. This equipment will mill spirals of any angle up to about 70°. It will also cut racks. Fig. 255 shows a Cincinnati High-Power Universal Miller with its regular equipment of Dividing Head, etc. The table may be swiveled 52° for either right or left hand spirals. For spirals having a larger angle the Spiral Milling Attachment must be used. 310 The Cincinnati Milling Machine Company CHAPTER XVII WORM GEARING If, in a pair of spiral gears, the driver has a very small number of teeth, as for instance, one, two, three or four, and the driven gear a proportionately large number; in other words, if the velocity ratio is very great then we get a gearing arrangement which is com- monly called endless screw or worm gearing. The driver, which is called a worm, is a screw with single or multiple threads of such a fdrm that its cross section is the same as that of a rack and its teeth must mesh with a special form of spur gear called a wormwheel. In a worm and wormwheel with shafts at right angles, the teeth of the wormwheel form an angle with the shaft which is the same as the complement of the spiral angle of the worm; that is, 90° minus the spiral angle of the worm. A wormwheel may therefore be a plain spur gear with its teeth at an angle with its axis. Such worm- wheels are in common use. But the more efficient form of worm- wheel used in machinery of the better class has its teeth made to fit the worm thread accurately. This is the form of wormwheel that should preferably be used wherever efficiency and durability are essential. The velocity ratio of a worm and wormwheel is independent of their relative pitch diameters; if the worm has a single thread the velocity ratio is equal to the number of teeth of the wormwheel; with a double-threaded worm it is one-half; with a quadruple- threaded worm one-fourth of the number of teeth of the worm- wheel, and so on. Careful distinction should be made between the terms "pitch" and "lead." The distance between the center of two adjacent threads is termed the "pitch" or more correctly, the "linear pitch," while the "lead" is the distance which any one thread advances IN ONE revolution of the worm. Therefore, the lead and pitch of any single-threaded worm will be equal, while for a double- threaded worm the lead is twice, and for a quadruple-threaded worm four times the linear pitch, and so on. A Treatise on Milling and Milling Machines 311 Worm threads, that is, the teeth of a worm, have straight sides at an included angle of 29°, Fig. 256. The Worm Cutting Tool. The width at the end of the lathe tool used for chasing a worm, or the width of the top of the tooth of the cutter when the worm thread is milled, equals the linear pitch P* of the worm multiplied by .31. This is also the width of the bottom of the space between the threads. We have, therefore Width of cutting tool at end = P x .31. The included angle between the sides of the tool = 29°. The full depth or cutting depth of the worm thread = P x . 6866. A worm cut to this depth with a correct tool will have a width at top of thread = P x .335. The Outside Diameter. The outside diameter of the worm blank is obtained by adding twice the addendum to the pitch diameter. The addendum S = P x .3183 or - ^ . 3 . 14159 The outside diameter o = P + 2S. The accompanying table gives the important dimensions of worm thread parts. •P is linear pitch of worm and circular pitch of wheel, therefore, all these calculations are based on circular pitch. 312 The Cincinnati Milling Machine Company Fie 257 To compute the necessary dimensions for a worm gear drive, the following formulas should be used in connection with Figs. 256 and 257. P = circular pitch of wheel and linear pitch of worm. I = lead of worm. n = number of threads in worm. S = addendum. d = pitch diameter of worm. D = pitch diameter of worm wheel. = outside diameter of worm. O = throat diameter of worm wheel. 0' = diameter of worm wheel over sharp corners. b = bottom diameter of worm. N = number of teeth in wormwheel. W = whole depth of worm tooth. T = width of thread tool at end. B = helix angle of worm. — B = gashing angle of wormwheel. U = radius of curvature of wormwheel throat C = center distance. A Treatise on Milling and Milling Machines 313 Rules and Formulas for Worm Gearing To Find Rule Formula Linear Pitch Divide the lead by the number of threads. It is understood that by the number of threads is meant, not number of threads per inch, but the number of threads in the whole worm — one, if it is single- threaded; four, if it is quadruple-thread- ed, etc I P = - n Addendum of Worm Tooth Multiply the linear pitch by 0.3183. ..... S = 0.3183 P Pitch Diame- ter of Worm Subtract twice the addendum from the outside diameter d = - 2 S Pitch Diame- Multiply the number of teeth in the wheel by the linear pitch of the worm, and divide the product by 3. 1416 NP D — wheel 3.1416 Center Dis- tance Be- tween Worm and Gear Add together the pitch diameter of the worm and the pitch diameter of the wormwheel, and divide the sum by 2 D + d C = 2 Whole Depth of Worm Tooth Multiply the linear pitch by 0. 6866 W = 0.6866 P Bottom Di- ameter of Subtract twice the whole depth of tooth from the outside diameter 6 = - 2 TT Worm Helix Angle of Worm Multiply the pitch diameter of the worm by 3. 1416, and divide the product by the lead; the quotient is the tangent of the helix angle of the worm Tan B .= 3.1416 d I Width of Thread Tool at End Multiply the linear pitch by 0.31 T = 0.31 P Throat Di- ameter of Worm wheel Add twice the addendum of the worm tooth to the pitch diameter of the worm- wheel ^ D +2S Radius of Worm wheel Throat Subtract twice the addendum of the worm tooth from half the outside diameter of the worm U = - - 2S 2 Outside Di- ameter of Add together the pitch diameter and twice the addendum = d + 2 S Worm Pitch Diame- ter of Worm Subtract the pitch diameter of the worm- wheel from twice the center distance. . . . d = 2C - D Diameter of Wormwheel to Sharp Corners Multiply the radius of curvature of the wormwheel throat by the cosine of half the fye angle, subtract this quantity from tne radius of curvature, multiply the remainder by 2, and add the product to the throat diameter of the wormwheel. . . 0' = 2([7- [7X °^\ cos - 1 -f- 2/ Gashing Angle of Gear Divide the lead of the worm by the cir- cumference of the pitch circle. The result will be the tangent of the gashing angle Tan (90° -B) = 1 X d 314 The Cincinnati Milling Machine Company Table of Important Dimensions of Worm Thread Parts Circular Circ. or Height Depth Thick- Width of No. of or Linear Linear of Tooth of Space Whole ness of Thread Width of Threads Pitch, Pitch, above below Depth of Tooth on Tool Thread per In. Inches Decimal Equivs. Pitch Line Pitch Line Tooth Pitch Line at End at Top i 2 2.0000 0.6366 0.7366 1.3732 1.0000 0.6200 0.6708 i IH 1.7500 0.5570 0.6445 1.2015 0.8750 0.5425 0.5869 VA 1.5000 0.4775 0.5524 1.0299 0.7500 0.4650 0.5031 i IH 1.2500 0.3979 0.4603 0.8582 0.6250 0.3875 0.4192 1 1 1.0000 0.3183 0.3683 0.6866 0.5000 0.3100 0.3354 iM 1 0.7500 0.2387 0.2762 0.5149 0.3750 0.2325 0.2515 1>2 8 0.6667 0.2122 0.2455 0.4577 0.3333 0.2066 0.2236 2 i 0.5000 0.1592 0.1841 0.3433 0.2500 0.1550 0.1677 2^ i 0.4000 0.1273 0.1473 0.2746 0.2000 0.1240 0.1341 3 1 8 0.3333 0.1061 0.1228 0.2289 0.1667 0.1033 0.1118 s'A 1 0.2857 0.0909 0.1053 0.1962 0.1429 0.0886 0.0958 4 0.2500 0.0796 0.0920 0.1716 0.1250 0.0775 0.0838 4H 9 0.2222 0.0707 0.0819 0.1526 0.1111 0.0689 0.0745 5 1 0.2000 0.0637 0.0736 0.1373 0.1000 0.0820 0.0670 6 i 0.1667 0.0531 0.0613 0.1144 0.0833 0.0516 0.0559 7 1 0.1429 0.0455 0.0526 0.0981 0.0714 0.0443 0.0479 8 i 0.1250 0.0398 0.0460 0.0858 0.0625 0.0387 0.0419 9 i 0.1111 0.0354 0.0409 0.0763 0.0556 0.0344 0.0373 10 A 0.1000 0.0318 0.0369 0.0687 0.0500 0.0310 0.0335 12 A 0.0833 0.0265 0.0307 0.0572 0.0416 0.0258 0.0279 14 iV 0.0714 0.0227 0.0263 0.0490 0.0357 0.0221 0.0239 16 . A 0.0625 0.0199 0.0230 0.0429 0.0312 0.0194 0.0209 18 1 19 0.0556 0.0177 0.0205 0.0382 0.0278 0.0172 0.0186 Practical Example. When computing a worm and wormwheel it is customary to assume the outside diameter of the worm (if possible make it so you can use an existing hob) and the linear pitch. The velocity ratio is, of course, given. We will take for our example a single-threaded worm, two threads per inch. The linear pitch is therefore 3^''. Assume the outside diameter to be 2 . 000" and the velocity ratio 40 to 1. As the worm is single threaded, n = 1. Therefore, l=Pxn = 3^xl = J^". (The lead equals the linear pitch in this case, since the worm is single threaded.) S = .3183 X P = .3183 x .5 = .15915". d = 2 - (2 X .15915) = 2 - .3183 = 1.6817^ D = P X N 40 X .5 20 3 . 1416 3 . 1416 3 . 1416 = 6.3662". A Treatise on Milling and Milling Machines 315 C = ^_±i = y^ (6.3662 + 1.6817) = 4.0239. w = .6866 X P = .6866 x .5 = .3433. b = o-2w = 2-(2x .3433) = 2 - .6866 = 1.3134. rp , T5 X X d 3.1416 X 1.6817 ,^ ^^^, ., . Tangent B = — - — = = 10.5564 therefore, 1 .5 B = 84°36', the helix angle of worm. The gashing angle of wormwheel (90° - B) = 5°24'. T= .31xP= .31 X .5= .155", the width of thread tool at end. = D + 2 + S = 6.3662 + .3183 = 6.6845", the throat diame- ter of the wormwheel. Cutting the Wormwheel. Cutting a wormwheel on a Milling Machine requires two operations; first, gashing the teeth, and second, hobbing the teeth to correct size and shape. The gashing operation consists of roughing out the gear teeth. The cutter should be an involute cutter of the same diameter and pitch as the worm threads. The wormwheel to be gashed is held between centers. Fig. 258, and the table of the machine Ls moved longitudinally to bring the cutter central over the work, having first made sure that the cutter is central with the dividing head center, as when cutting spur gears; then the milling machine table is swiveled to an angle corresponding with the gashing angle. For wormwheels driven by a right-hand worm, that is, wheels finished by a right hand hob, swivel the milling machine table toward your right hand (when facing either end of the table), and for wormwheels driven by left- hand worms, swivel it to the left. The work is fed vertically into the cutter to the desired depth for each tooth. The work is indexed the same as a spur gear. This gashing operation should be carried out so as to leave only a small amount of metal on the sides and bottom of the teeth for the final finishing or hobbing opera- tion. The Gashing Angle. The gashing angle for the gear depends on the diameter and lead of the worm. It is found by dividing the lead of the worm by the circumference of its pitch circle which gives the tangent of the desired angle. The Cincinnati Milling Machine Company _ 4. r I,- I Lead of worm langent of gashing angle = Circumference of pitch circle that is, . The angle may then be read from a table of natural tangents. The gashing angles for wormwheels for a variety of worms from %" to 6" diameter and from Vio' to I'j/^" lead may be taken directly from the table at the end of this chapter. For example: Suppose we have a worm 3' pitch diameter, J^' lead or two threads per inch, which is the same thing. We find in the column opposite 3^^' lead and under 3" P. D., 3°2', which is the gashing angle for the gear that will work with that worm. A Treatise on Milling and Milling Machines 317 Hobbing the Wormwheel. For the hobbing operation the wormwheel must be so held between centers that it can revolve freely, because it must be driven by the hob. If the worm and wormwheel have shafts at right angles (which is the usual form) the table of the milling machine must be set straight; that is, at right angles with the cutter arbor, Fig. 259. The gashing cutter must be replaced by a hob of proper size and pitch. The hob must, of course, be central over the rim of the wormwheel and the table should be locked in position to insure against movement. When the machine has been started, raise the knee until the hob has cut to the proper depth. If excessive stock has been left to be removed, or if an exceptionally good finish is wanted, it is best to revolve the wormwheel under the hob a number of times, bringing it to final finish depth for the last cut or revolution. Special hobbing attachments are sometimes provided for the milling machine, which are arranged for positively driving the work 318 The Cincinnati Milung Machine Company spindle by means of gears from the machine spindle so as to insure positive rotation of the gear in exactly the correct ratio with the hob. With such an attachment the preliminary gashing operation can be omitted. Gashing Angles for Wormwheels A Treatise on Milling and Milling Machines 319 CHAPTER XVIII CONTINUED FRACTIONS ANGULAR INDEXING Angular Indexing. The tables on pages 329-30-31 will be found convenient for angular indexing when it is desired to space holes or notches a given number of degrees and minutes apart. These tables contain all that is required in the great majority of cases. They give angles that may be obtained with the index plate regularly furnished with the Cincinnati Universal Dividing Head and are accurate to within one-half a minute, with the exception of those few in heavy type. In these the error is somewhat greater and may amount to a minute or slightly more. The tables give angles advancing by minutes from 3' up to 9°, which corres- ponds to one full turn of the index handle. For larger angles we make one full turn for each 9° plus the reading in the table cor- responding to the fractional degrees and minutes. For example, to index spaces 20°15' apart, two turns give an 18° space, and for the 2°15' we find in the table a spacing of 7 holes in the 28 circle. The entire spacing is, therefore, using the 28 circle, 2 turns 7 holes. When it is desired to space angles to closer limits than those given in the tables the spacing can be computed by following the com- paratively simple method of Continued Fractions described below. Computing the Spacing. Suppose the drawing comes to the shop showing a spacing of 37°34'29", and the nature of the work makes it desirable to come as close to this as is practical with a Universal Dividing Head. One turn of the index crank produces an angle of 9° because 40 turns produce one complete turn of the spindle, or 360°. We note right away that we can make four complete turns which makes 36° and there is left an angle of 1°34'29". The question is now, what circle of holes shall we use and how many spaces should be indexed. One complete turn of the index crank makes 9°, or 32400''. We must make an angle of 1° (which is 3600 seconds), 34' (which is 2040 seconds), and 29", or altogether 5669". It is, therefore. 320 The Cincinnati Milling Machine Company necessary to make - - of a full turn of the index crank. This ^ 32400 would be easy enough if we had a circle with 32,400 holes, but, of course, this is not the case. We must, therefore, find some other fraction which has a much smaller denominator and a value very close to the given fraction. If we can find one in which the denomi- nator is the number of holes in one of the circles, we have an easy way of spacing this angle. Greatest Cominon Divisor, If two numbers have a common divisor, such, for instance, as 21 and 77, which have the common divisor 7, then, if we should subtract 21 from 77 the remainder will also have this divisor 7 as a factor; and if we subtract several times 21 from 77 that remainder also has the factor 7; in other words, if 21 and 77 have a common divisor, and we should divide 21 into 77, the remainder of the division can also be divided by 7. If then we should divide this remainder into the 21, the remainder of this new division would also have this factor 7. We could keep this up, always dividing the remainder of the last division into the divisor of this last division, until finally the division would leave no remain- der, then the last divisor would be the greatest common divisor. 21)77(3 ' 1-4)21 ( I ~^) 14(2 14 O Seven being the last divisor is the greatest common divisor. Continued Fractions. In the following example, we will assume a fraction . Here we will find that there is no greatest 1727 common divisor. A Treatise on Milling and Milling Machines 321 943) 1727 C I 943 784)94-3 ( I 7S4.^ / 159)784(4 636 ^ 148) 159 ( I ^ 148 I 1)148(13 11 38 33 5)11(2 l)|(5 o We will now show how it would be possible to find the original figures, 943 and 1727, if nothing but the quotients were given. We know that the last divisor was 1, the remainder is and the quo- tient is 5, therefore the dividend must have been five times 1, or 5. The previous divisor, therefore, is also 5. The quotient was 2 and the remainder was 1, so we find that the dividend there must have been 2 times 5 plus 1 equals 11. The previous divisor, therefore, was 11, and the dividend was 13 times 11 plus 5 equals 148. Con- sequently, the previous divisor was 148. We could go on this way by always multiplying the last quotient by the last divisor and adding the last remainder, and using this resulting number as the previous divisor. But there is a much simpler way of doing this very thing. Prepare a diagram as in Fig. 260 and place the quotients from our continued fraction in the spaces above the line from left to right beginning with the last quotient. Fig. 260 In the spaces below the line, but beginning two spaces to the left of the last quotient we write 0, which was the last remainder, and to the right of it 1, which was the last divisor. 322 The Cincinnati Milling Machine Company By following a system of multiplication and addition, as indi- cated above, by following the arrows in Fig. 260, we get 5x1 + = 5, which was the next to the last divisor. This is placed in the space to the right of the last divisor, which brings it below the last quo- tient. In the same way 2 x 5 + 1 = 11 and 13 x 11 + 5 = 148, 1 X 148 + 11 = 159 and so on until we finally get back to the original numbers 943 and 1727. Now it is a peculiar property of numbers that, if we should cut off part of this operation, say along the line A; in other words, if we should start with 13 instead of 5, making a diagram as in Fig. 261, we will get another fraction but which is very close in value to the original fraction. 13 ; 1 4 1 1 1 13 ; 14 Fig. 261 69 83 152 Another peculiar property of numbers is that if we should cut off at A and find that the resulting fraction is a little too large, then, if we cut off at C, one place further to the right, the fraction would be a little too small, and if we should start at E the fraction would be too large again, and so on. The value of these approxi- mating fractions would move somewhat like the wave line in Fig. 262. Fig. 262 The straight line represents the true value of our original frac- tion and the wave line represents the value of the approximating fractions. It will be seen that these approximating fractions go alternately above and below the real value and that they gradually go farther and farther away from that value. The diagram. Fig. 261, shows that the resulting fraction if we 83 ' started on the line A would be . If we reduce the original frac- 152 943 — — - to a decimal fraction we get .54603, and reducing the tion A Treatise on Milling and Milling' Machines 323 83 approximate fraction — we get . 54605, or a difference of . 00002 . In other words, we have an error of 2 in a total of 54600, which is a very small error indeed. If this fraction had been used for spacing, the holes or notches thus spaced might have been nearly 53^" apart with an error of only .0002. Returning now to our problem of 5669 spacing . We carry a continuous division, 32400 5669)32400(5 28345 , 4055)5669(1 4055 1614)4055(2 3228 ^ ""527)1614(1 787)827(i 787 40)787 (l 9 387 360^ "r7)40(l 27 (3)27(2 I )l3(l3 13. O just like in the previous example and then we ignore the last four quotients, keeping only the quotients 5, 1, 2, 1 and 1, Fig. 263. 1 2 Fie 263 2 1 5 5 1 7 40 We set these five quotients up in our diagram as before, and find the approximate fraction — , which means that we have to take 7 7 7 7 spaces on the 40 hole circle. - of a circle is — of 9°, or — of 32400 40 40 40 324 The Cincinnati Milling Machine Company seconds. This is 5670 seconds, whereas what we want is 5669 seconds. This shows that we have missed our angle by one second. However, we meet a new difficulty here. We find that we must take 7 spaces on a 40 hole circle, but there is no such circle on the standard index plate. If there should be great need of extreme accuracy a special plate with a 40 hole circle could be made, but, as a rule, the accuracy required is not so great, nor would the dividing head permit of such extreme accuracy as an error of less than one second. Such extreme accuracy is only foimd in the most refined astronomical instruments and has no place in the machine shop. Instead, then, of making a special plate with a 40 hole circle we cut off the next quotient, leaving only the quotients 1, 2, 1 and 5, Fig. 264. 3 Fig. 264 1 5 4 23 This will give us the fraction - , and this is easily obtainable 23 by using the 46 hole circle and taking 8 spaces. of 9° gives us 5635 seconds, whereas we wanted 5669 seconds, so that our space is 34 seconds too small. Even this is a high degree of accuracy, the error being only about of what it would be with the ordinary method of circular indexing. We could have cut off still another quotient and used only the 3 figures 2, 1 and 5, in which case we would have found the fraction Fig. 265. 17^ 2 1 1 2 FK. 2«S 3 17 This means that we would have had to use the 34 hole circle and take 6 spaces. The result would have been 5717 instead of 5669 seconds, or an error of 48 seconds. Even this is a great im- provement over the regular method. You will note that with five A Treatise on Milling and Milling Machines 325 quotients we were 1 second large; with four quotients 34 seconds small; and with three quotients we were 48 seconds large.* The method of continued fractions is useful in a great many other instances, of which two examples are given. Application to Gearing a Lathe to Cut Metric Threads. We know that if we have a standard lead screw on a lathe and want to cut metric threads we must introduce a pair of compound gears which will make up for the difference between metric and English pitches. If, for instance, we have a 34" pitch lead screw and want the lathe to work as if the pitch of the screw were 6 millimeters, we put a pair of compound gears in the feed mechanism of 125 and 127 teeth respectively. If the pitch of the lead screw is }/2 and we want to make the lathe work as if the lead screw had a pitch of 10 millimeters, we introduce a pair of compound gears of 100 and 127 teeth respectively. Now, such gears of 100 and 127 teeth are quite large and it will generally be found that it is impractical to put such gears into an existing mechanism. The numbers 100 and 127 are relatively prime and it is not possible to find another fraction of the same value by canceling. We resort, therefore, to our method of continued fractions. We make the continuous division of 100 and 127 and ignore first one and then perhaps two or more of the last quotients until we find a fraction which is sufficiently small, and then we test this fraction for its accuracy. Ignoring the last 37 quotient we obtain the fraction — , which means that we will have to use two gears of 37 and 47 teeth respectively. These numbers are quite practical and it should be easy to introduce a pair of gears of that size into a mechanism. In order to test out the accuracy *It does not matter which of the two numbers comprising a fraction is divided into the other. It is simplest to divide the smaller into the larger to avoid decimals. However, in arranging the figures composing our new equivalent fraction we must remember that b. If we use the denominator as a divisor, the last divisor produced becomes the NUMERATOR of our equivalent fraction since the natural relation is not disturbed. c. If we use the numerator as the divisor, which happens to be the case in the examples given here, we have reversed the natural relation and now the last divisor produced becomes the denominator of the equivalent fraction, thus, 943 83 1727- ''^^''^'^ = 162 326 The Cincinnati Milling Machine Company of this fraction we reduce — and - to decimal fractions and find 127 47 that there is a difference of 17 in a total of 78740, which is quite accurate enough for all but the very finest work. If we had cut off one more quotient we would have found the approximating 26 fraction , which is quite convenient, but not quite so accurate. The error in this case is 48 in a total of 78740; in other words, nearly three times as much as with the fraction ^ 47 Application to Computing Change Gears for Cutting Spirals. Another application of this method is to be found in com- puting the change gears required to cut a spiral of given lead. A Dividing Head is furnished with a certain number of change gears which are quite sufficient for all ordinary work, and this book contains a table of the leads which can be cut with these change gears. The teeth in reamers, taps, cutters, etc., can easily be cut with these change gears. Even spiral gears can, as a rule, be cut without using any other change gears than the ones supplied. How- ever, some times spiral gears must be cut with great accuracy and a relatively small variation in the lead is not permissible. In Chapter XVI, on spiral gear cutting, we showed that the lead is found by the simple formula: T H - P^*^'^ circumference tangent of spiral angle and from this it follows that the lead is usually a decimal fraction and it would be strange indeed if this fraction could always be found in the table of leads. Assume that we have to cut a spiral gear having a lead of 5 . 8042'^. Consulting our table of leads we find that the nearest leads given are 5.788 and 5.833. Neither of these two leads is close enough , X 1 o- XT. driven gears lead* - for very accurate work. Smce the = our frac- drivmg gears 10 tion is — . This is an awkward fraction to reduce into suitable 10 form for conversion into change gears. We will therefore carry out our method of continued fractions. For convenience we multiply *See Chapter XIX, page 332. A Treatise on Milling and Milling Machines 327 both numerator and denominator by 10,000 in order to get rid of the decimal. This, of course, does not change the value of the . ^. , . , . 58042 fraction, which now is . 100000 We now have 58042) 1 00000(1 58042 ^1958)58042(1 U_958^ 16084)41958(2 32168 . 9790)l6O84(| 9790 6294) 9790(1 6294- 34-96)6294(1 3496 2798)3496(1 2798 698)2798(4 2792 5)698(116 6l 9 6 38 36 2)6(3 6 Dropping the last three quotients and applying our diagram, we get 1 1 1 1 i 1 2 ! 1 1 1 2 2 4 6 ; 10 26 36 62 I Our approximately equivalent fraction is therefore . Testing this for accuracy, we divide 62 into 36, which gives us .580645. However, we must remember that we started with a fraction which represented the lead divided by 10. This approximate equivalent is therefore also tV of the lead. Multiplying it by 10 we therefore 328 The Cincinnati Milung Machine Cobipany get 5.80645 as our approximate lead, which compared with the actual lead of 5 . 8042 shows that our new approximation is . 00225" long. This, however, is so small an error that it is not likely to lead into difficulties. We will, therefore, split up our fraction and convert it into 62 suitable change gears. Thus 36 4x9 62 6.2 X 10 4 10 40. 9 6 6.2 ^ 10 62' 10 ^ 6 54 60 Our change gears therefore are 40 X 54 _ driven gears _^ 2d Intermediate x Gear on worm 62 X 60 driving gears 1st Intermediate x Gear for screw We therefore put the 40 tooth gear on the second intermediate stud, the 54 tooth gear on the worm shaft, the 62 tooth gear on the first intermediate stud, and the 60 tooth gear on the stud in the segment, which runs at the same speed as the screw. A Treatise on Milling and Milling Machines 329 Table for Angular Indexing on the Universal Dividing Head . 1 1 . 1 1 1 p 1 2 3 8 1 1 53 54 55 0) o 51 30 59 5 3 6 Q 3 .2 S 45 46 47 1 a 41 51 30 8 10 6 1 .3 S 37 38 39 o 2 o 62 41 51 2 2 2 18 12 isi* 1 . 15 4 137 56 58 6 48 30 6 2 40 54 16 5 107 57 57 6 49 54 11 2 41 47 14 6 181 2 58 28 3 50 54 11 2 42 30 9 7 77 59 46 5 51 34 7 2 43 53 16 8 66 54 6 52 53 11 2 44 66 20 9 59 1 62 7 53 43 9 2 45 59 18 10 54 2 43 5 54 57 12 2 46 39 12 11 49 3 43 5 55 47 10 2 47 42 13 12 46 4 59 7 56 28 6 2 48 58 18 13 42 5 25 3 57 37 8 2 49 51 16 14 39 6 49 6 58 59 13 2 50 54 17 15 37 7 24 3 • 1 59 59 13 2 51 41 13 16 34 1 1 8 24 3 2 54 12 2 52 66 21 17 62 2 9 47 6 2 1 58 13 2 53 53 17 18 30 1 10 54 7 2 2 62 14 2 54 59 19 19 57 2 11 38 5 2 3 66 15 2 55 37 12 20 54 2 12 30 4 2 4 39 9 2 56 46 15 21 51 2 13 37 5 2 5 39 9 2 57 58 19 22 49 2 14 51 7 2 6 30 7 2 58 58 19 23 47 2 15 43 6 2 7 51 12 2 59 54 18 24 47 2 16 57 8 2 8 38 9 3 54 18 25 43 2 17 42 6 2 9 46 11 3 1 54 18 26 62 3 18 62 9 2 10 54 13 3 2 59 20 27 59 3 19 41 6 2 11 66 16 3 3 59 20 28 58 3 20 54 8 2 12 49 12 3 4 47 16 29 37 2 21 66 10 2 13 49 12 3 5 38 13 30 54 3 22 66 10 2 14 28 7 3 6 58 20 31 53 3 23 39 6 2 15 28 7 3 7 49 17 32 34 2 24 58 9 2 16 28 7 3 8 66 23 33 49 3 25 38 6 2 17 59 15 3 9 57 20 34 47 3 26 25 4 2 18 47 12 3 10 54 19 35 62 4 27 62 10 2 19 66 17 3 11 51 18 36 30 2 28 43 7 2 20 54 14 3 12 59 21 37 58 4 29 54 9 2 21 57 15 3 13 42 15 38 57 4 30 54 9 2 22 38 10 3 14 39 14 39 42 3 31 47 8 2 23 34 9 3 15 47 17 40 54 4 32 47 8 2 24 30 8 3 16 66 24 41 66 5 33 58 10 2 25 41. 11 3 17 66 24 42 51 4 34 46 8 2 26 37 10 3 18 30 11 43 25 2 35 57 10 2 27 66 18 3 19 38 14 44 49 4 36 62 11 2 28 62 17 3 20 54 20 45 24 2 37 39 7 2 29 58 16 3 21 43 16 46 47 4 38 66 12 2 30 54 15 3 22 43 16 47 46 4 39 49 9 2 31 25 7 3 23 53 20 48 34 3 40 54 10 2 32 39 li 3 24 53 20 49 66 6 41 59 11 2 33 53 15 3 25 58 22 50 54 5 42 53 10 2 34 49 14 3 26 42 16 51 53 5 43 42 8 2 35 66 19 3 27 47 18 52 62 6 44 57 11 2 36 38 11 3 28 39 15 330 The Cincinnati Milling Machine Company Table for Angular Indexing on the Universal Dividing Head . 1 s 1 s 1 p s v 0) H 0) g S d 0} S V 2 0) S a .3 S 29 2 O 62 St 24 P .a 21 1 O 62 QQ 30 P a 13 1 38 1 22 .a 5 1 O 37 CQ 3 4 5 6 25 3 30 54 21 4 22 66 32 5 14 43 25 6 6 59 40 3 31 41 16 4 23' 39 19 5 15 24 14 6 7 25 17 3 32 28 11 4 24 47 23 5 16 41 24 6 8 66 45 3 33 38 15 4 25 53 26 5 17 46 27 6 9 41 28 3 34 53 21 4 26 53 26 5 18 34 20 6 10 54 37 3 35 53 21 4 27 53 26 5 19 66 39 6 11 51 35 3 36 30 12 4 28 54 27 6 20 54 32 6 12 58 40 3 37 57 23 4 29 54 27 5 21 37 22 6 13 42 29 3 38 57 23 4 30 54 27 5 22 62 37 6 14 39 27 3 39 37 15 4 31 199 100 5 23 62 37 6 15 59 41 3 40 54 22 4 32 137 69 5 24 30 18 6 16 66 46 3 41 66 27 4 33 89 45 5 25 30 18 6 17 53 37 3 42 51 21 4 34 67 34 5 26 53 32 6 18 30 21 3 43 46 19 4 35 53 27" 5 27 38 23 6 19 57 40 3 44 41 17 4 36 47 24 5 28 28 17 6 20 54 38 3 45 24 10 4 37 39 20 5 29 41 25 6 21 34 24 3 46 43 18 4 38 66 34 5 30 54 33 6 22 41 29 3 47 57 24 4 39 62 32 5 31 62 38 6 23 62 44 3 48 57 24 4 40 54 28 5 32 39 24 6 24 38 27 3 49 66 28 4 41 25 13 5 33 47 29 6 25 66 47 3 50 54 23 4 42 46 24 5 34 42 26 6 26 28 20 3 51 49 21 4 43 42 22 5 35 58 36 6 27 53 38 3 52 51 22 4 44 57 30 5 36 53 33 6 28 39 28 3 53 51 22 4 45 53 28 5 37 24 15 6 29 25 18 3 54 30 13 4 46 34 18 5 38 24 15 6 30 54 39 3 55 62 27 4 47 47 25 5 39 43 27 6 31 58 42 3 56 62 27 4 48 30 16 5 40 54 34 6 32 62 45 3 57 41 18 4 49 43 23 5 41 38 24 6 33 66 48 3 58 59 26 4 50 54 29 5 42 30 19 6 34 37 27 3 59 43 19 4 51 39 21 5 43 66 42 6 35 41 30 4 54 24 4 52 37 20 5 44 66 42 6 36 30 22 4 1 47 21 4 53 59 32 5 45 47 30 6 37 34 25 4 2 58 26 4 54 57 31 5 46 39 25 6 38 38 28 4 3 58 26 4 55 66 36 5 47 42 27 6 39 46 34 4 4 62 28 4 56 62 34 5 48 59 38 6 40 54 40 4 5 66 30 4 57 58 32 5 49 34 22 6 41 66 49 4 6 57 26 4 58 58 32 5 50 54 35 6 42 47 35 4 7 59 27 4 59 47 26 5 51 54 35 6 43 59 44 4 8 37 17 5 54 30 5 52 46 30 6 44 28 21 4 9 39 18 5 • 1 43 24 5 53 49 32 6 45 28 21 4 10 54 25 5 59 33 5 54 58 38 6 46 28 21 4 11 43 20 5 3 41 23 5 55 38 25 6 47 57 43 4 12 30 14 5 4 41 23 5 56 47 31 6 48 49 37 4 13 47 22 5 5 62 35 5 57 59 39 6 49 66 50 4 14 34 16 5 6 30 17 5 58 59 39 6 50 54 41 4 15 53 25 5 7 51 29 5 59 54 36 6 51 46 35 4 16 57 27 5 8 28 16 6 54 36 6 52 38 29 4 17 42 20 5 9 28 16 6 1 54 36 6 53 51 39 4 18 46 22 5 10 54 31 6 2 58 39 6 54 30 23 4 19 25 12 5 11 66 38 6 3 58 39 6 55 39 30 4 20 64 26 5 12 57 33 6 4 46 31 6 56 39 30 A Treatise on Milling and Milling Machines 331 Table for Angular Indexing on the Universal Dividing Head 00 0) 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 OQ 1 V 63 1 d 57 O 57 «8 OQ 44 Q a s 28 7 58 62 48 7 29 59 58 45 7 30 54 42 7 31 1 59 46 7 32 2 59 46 7 33 3 37 29 7 34 4 28 22 7 35 5 47 37 7 36 6 38 30 7 37 7 43 34 7 38 8 53 42 7 39 9 34 27 7 40 10 54 43 7 41 11 30 24 7 42 12 30 24 7 43 13 51 41 7 44 14 51 41 7 45 15 41 23 7 46 16 57 46 7 47 17 42 34 7 48 18 37 30 7 49 19 59 48 7 50 20 54 44 7 51 21 49 40 7 52 22 66 54 7 53 23 39 32 7 54 24 62 51 7 55 25 57 47 7 56 26 46 38 7 57 27 58 48 7 58 J2 47 47 54 43 43 62 25 38 58 39 66 66 54 41 62 42 57 43 51 37 30 38 54 47 24 24 49 58 59 43 43 0) 39 39 45 36 36 52 21 32 49 33 56 56 46 35 53 36 49 37 44 32 26 33 47 41 21 21 43 51 52 38 38 bfi GO d 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 0) 62 54 46 28 38 58 59 30 51 62 53 54 66 34 46 47 24 49 38 51 66 54 57 43 58 30 62 47 49 34 53 0) 03 02 55 48 41 25 34 52 53 27 46 56 48 49 60 31 42 43 22 45 35 47 61 50 53 40 54 28 58 44 46 32 50 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 qQ :3 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 54 57 58 59 62 43 66 47 49 51 54 28 30 62 34 37 39 42 46 49 54 59 66 51 54 55 56 59 41 63 45 47 49 52 27 29 60 33 36 38 41 45 48 53 58 65 1 Turn 332 The Cincinnati Milung Machine Company CHAPTER XIX CHANGE GEARS FOR CUTTING SPIRALS We have seen in the chapter on spiral gears how the lead of the spiral is calculated. We shall now see how the machine is arranged to produce a given lead. The wormwheel in the Universal Dividing Head has 40 teeth and the worm is single threaded, therefore, 40 revolutions of the worm are required to make one revolution of the dividing head spindle. The table screw is so geared to the segment that the first change gear on this segment starting from the screw end makes one revolution for 34" table movement. If equal change gears were used the wormshaft would also make one revolution for each )4!' table travel, and as the worm has 40 teeth, the table would have to move 40 x J^'' = lO*' for one full turn of the wormwheel and, therefore, for one turn of the spindle of the dividing head. In other words, a spiral of 10*^ lead will be produced if we use even change gears. If we want less lead we must speed up the wormshaft, and for more lead we must slow it down. This we do by means of the change gears furnished with the driv- ing mechanism of the dividing head. If the lead is to be one-third of 10'' then we must speied up 3 to 1, and if the lead were three times 10", then we would slow down one- third of the speed of the first change gear. The Lead Divided by Ten is the Change Gear Ratio. For instance, to cut a spiral with a lead of lOJ/^", divide lOJ^ by 10. Writing this as a common fraction we find that the change gear ratio is - = , or — . We would get this result by placing a 10 100 20 J^ H 6 20-tooth pinion on the first segment stud and a 21-tooth gear on the wormshaft. As these gears would be too far apart we would place two equal idlers somewhere between the two gears so as to connect them. However, looking up our list of change gears we find that we have neither a 20 nor a 21-tooth gear. Nor do we have mul- tiples of both. It is true we have a 40-tooth gear which is 2 times 20, A Treatise on Milling and Milling Machines 333 but we have no gear with 2 times 21 teeth. We must therefore try to select our gears in such a way that we can compound them. 21 This we do by splitting the fraction — into two other fractions 20 whose product equals the original fraction. This might be done in 21 7 X 3 different ways; for instance. = . We might now look for 20 4x5 a pair of gears with a ratio of 7 to 4 and another pair with a ratio of 3 to 5; but, as we would like to have the gears as nearly of even size as we can get them, we multiply the numerator of the second fraction and the denominator of the first each by 2, which, of course, 7x6 does not change the value of the product. We then get — — . Mul- 8x5 tiplying both numerator and denominator of a fraction does not change its value. We may, therefore, make such a multiplication to raise the figures composing these fractions so they will correspond to the number of teeth in standard change gears furnished with the J. .J. 1 1 rni- 7 8 56 J 6 8 48 dividmg head. Thus — x = and x = . 8 8 64 5 8 40 The original ratio is not changed in value when written . 64 x 40 We saw above that if we had a 20 and a 21-tooth gear we could have placed the 21-tooth gear on the- wormshaft and the 20-tooth on the first segment stud (called in the tables, gear for screw) and with two equal toothed idlers between to fill the space (which would not have affected the ratio) we could have proceeded to mill our spiral of lOJ/^" lead. In this case the 20-tooth gear would have been the driver and the 21-tooth the driven gear. In the case of our compound gears, therefore, 64 and 40 are the drivers and 56 and 48 are the driven gears. We place 64 on the first segment stud (gear for screw) and let it drive 56 (2d intermediate) and 48 on the wormshaft and drive it by 40 (1st intermediate), all as shown in Fig. 266. From this example the following rules may be deduced. 334 The Cincinnati Milling Machine Company 1st. = Change gear ratio, that is Lead __ Driven gears To" "" Driving gears 2d. Resolve this fraction into two fractions. 3d. Multiply the numerator and denominator of each fraction by some number (not necessarily the same number for both frac- tions) so as to get numbers corresponding to the number of teeth in standard change gears furnished with the machine. These numbers will then represent driven gears _ 2d interm. x gear on wormshaft _ lead driving gears 1st interm. x gear for screw 10 lead Application of Continued Fractions. The fraction 10 is not always by any means as simple a fraction as the ones used in the preceding cases to illustrate the principle involved in com- puting change gears. Suppose, for example, it is desired to determine the proper change gears for a lead of 9 . 643''. Our fraction now is — ^ . Multiplying this by 1000 to get rid of the decimal, we have the fraction . Proceeding now as in the last example given 10000 * in Chapter XVIII on Continued Fractions, we get the following: 9643) 10000 9643 ; 3 57)9643(27 71-4 2503 2499 , 4)357(89 32 "37 1)4(4- 4: O A Treatise on Milling and Milling Machines 335 Omitting the last two quotients and placing the others in our diagram as before, we get 27 1 27 1 27 28 27 and our approximately equivalent fraction is, therefore, - . Before we proceed further let us prove the accuracy of this fraction. We find by dividing 27 by 28 we get . 96425. We must remember that lead our original fraction was , the value of which of coxirse is one- ^ 10 tenth the lead. That is approximately what we get when we divide 27 by 28, as above. We must, therefore, multiply this result by ten in order to compare it with the original figure representing the lead. This gives us 9 . 6425, which subtracted from the actual lead, 9 . 643, shows a difference of . 0005, entirely too small an amount to give us any concern. We may, therefore, proceed to split up our 27 fraction — so as to reduce it into fractions representing suitable change gears. Thus 27 ^ 3x9 28 4 X 7 3 16 48 , 9 8 72 - X - = — and — X - = 4 16 64 7 8 56 48 X 72 We therefore have in which 48 and 72 are the driven gears 64 X 56 and 56 and 64 are the driving gears. We therefore proceed to place these on the machine as shown in Fig. 266, placing the 48-tooth gear on the second intermediate stud, the 72-tooth gear on the worm shaft, the 64-tooth gear on the first intermediate stud and the 56-tooth gear on the stud in the segment next to and running at the same speed as the screw. In this connection it should be noted that it is permissible to transpose the 48-tooth gear and the 72-tooth gear and also the 56- tooth gear and the 64-tooth gear. This may make a more convenient combination to set up and does not affect the result at all. The Cincinnati Milling Machinb Company Fig. 266 shows the Divid- ing Head as used on a High- Power Universal Miller, geared up for a right-hand spiral, 103^' lead. We make a variety of machines and spiral cutting heads, and since the use of the idler varies with different combinations of spiral heads and machines, the following tabulation will prove of No. 1 and No. 2 Cone-Driven Machines Right-Hand 1 Left-Hand Spiral Spiral Do not use Idler Use Idler Uae Idler ! Do not use Idler All High-Power Deaign Right-Hand Left-Hand Spiral Spiral Head ir or" 16" Spir. Head I!se Idler Do not use Idler Do not use Idler Use Idler The table of leads on pages 338 and 339 gives a selected number of leads with corresponding combinations of change gears, angles, etc., for spirals up to 6" diameter and angles up to 45°. The table on pages 340 to 344 gives a complete list of leads up to 80", that can be obtained with the change geai^ regularly sup- plied without interference when they are placed on the machine. This will be found of great convenience, as the proper combination for almost any desired spiral can be taken from this table. For example: We want the proper gearing for a spiral of 21.1" lead. Consulting the table we find a lead of 21,116", and since this is only .016" longer than the theoretically correct lead, this gear combination can be used for all ordinary work. ■Always withdraw the index plate stop before starting to cut spirals, because the index plate must be free to revolve with the index pointer. After the head has been geared up the table should always be moved by hand to insure that all parts are free to move, before throwing in the power feed. The Dividing Head should be placed in that slot of the table which is directly over the lead screw. A Treatise on Milling and Milling Machines 337 Leads, Change Gears and Angles for Milling Twist Drills These tables are used in connection with standard cutters for milling twist drills. Diameter of Drill Pitch in Inches Gear on Worm 1st Inter- mediate Gear 2d Inter- mediate Gear Gear for Screw Angle of Spiral A 1.67 24 64 32 72 ir 27' M 1.94 28 64 32 72 2r A 2.92 28 64 48 72 20° Vs 3.24 28 48 40 72 21** A 3.89 32 64 56 72 20** 10' M 4.17 40 64 48 72 20** 30' A 4.86 40 64 56 72 20° 'A 5.33 32 40 48 72 20° 12' H 6.12 56 40 28 64 19° 30' M 6.48 40 48 56 72 20° H 7.29 56 64 40 48 19° 20' Vb 7.62 48 56 64 72 19° 50' H 8.33 48 32 40 72 19° 30' 1 8.95 86 56 28 48 19° 20' IH 9.33 48 40 56 72 20° 40' Twist drills are milled with the center part increasing in thick- ness toward the shank end. For different size drills this thickness varies as shown in table below. Ji' drill is A* thick at the point, and A*^ thick in the back. J^* drill is A* thick at the point, and A* thick in the back. Ji* drill is A* thick at the point, and A* thick in the back. 1' drill is A*' thick at the point, and Ji" thick in the back. 114" drill is l/i" thick at the point, and A* thick in the back. Other size drills vary in about the same proportion. Tpie Cincinnati Milung Machine Company I* p. s «s if. 11 11 o s •s S A Treatise on Milling and Milling Machines zv^ The CDSC13CXA7T MnXDiC >lACHDiE COHPANT Leads from MW to 3.14S' 3dxW 10 I>m« J 1 Ifitx: 1 J f 1 f & » ? 5 .r & ^ ■^ *" ^^ ^ "^ ^^ ^ ^ fr & ^ & -, s S c ^„ £ 5 'c if ,_ S 5 a > .« s 5^1 1 g ^ -1 s & :: & ^ > Z > it ft. 5^ 2 - £ ■*?? y A- • T c &. •S 5 »- ix tx S k ^ t; «- S'Z &-C o-C ^ ^ ^^ ^^ ^•v ^^ •* «» ^* ^» ^^ ^l* ^^ %mm ^^ •» r^ J- *««» -^ ^^ •— ^> 1 i^ ?5 24 1 1 I 40 56 24 lOO 1 28 1 .^70 ^4 1.714 2 442 64 ' 48 85 .7»1 24 86 28 M) 1.744 24 64 40 ^ 2 444 40 ! 72 , 44 100 ,W) 24 72 24 100 1-750 28 64 40 100 2.450 56 ; 64 28 100 ,¥^ 24 86 32 100 1.778 32 72 40 100 2.456 44 i 86 ! 48 100 Mfjfi 24 64 24 100 1.7S6 32 M5 48 100 2-481 32 1 72 ! 48 86 //30 24 72 24 86 1.809 28 72 40 S6 2.4>9 32 .100 56 72 '^JiZ 24 72 28 100 1.823 28 100 56 86 2.500 24 , 64 48 72 r029 : 24 56 24 100 1-860 24 •72-48 S6 2-514 44 ! 56 I 32 100 I 042 28 86 32 100 1.867 28 72 48 100 2.532 28 , 72 ; 56 86 1 047 24 61 24 86 1.886 44 56 24 100 2.537 24 j 44 ! 40 86 Km 24 64 28 100 1.919 24 64 44 S6 2.558 32 1 64 44 86 lJfj^i7 24 72 32 100 1.925 28 64 44 100 2-567 44 . 48 28 100 LrjS5 24 72 28 86 1,944 28 64 32 72 2-6l» 28 i 40 32 86 1.116 24 86 40 100 1.956 32 72 44 100 2.619 24 ; ^ 44 72 \.v.m 2A '56 24 86 1.990 28 72 44 86 2.658 32 ! 56 40 86 L2rjO 24 64 32 100 1,993 24 . 56 ! 40 86 2.667 40 172 48 100 L221 ! 24 64 28 . 86 2.000 32 64 ' 40 100 2.674 28 64 44 72 1.22H 24 86 44 100 2.030 24 44 i 32 86 2.713 28 48 40 86 L240 24 72 32 86 2.035 . 28 ■ 64 i 40 86 2.743 48 56 32 100 1,244 28 72 32 100 2.047 ; 40 ' 86 : 44 100 2.750 40 64 44 100 1.302 1 28 86 40 100 2.057 48 56 : 24 100 2.778 32 64 40 72 1.333 24 72 40 100 ' 2.067 32 72 . 40 86 2.791 1 32 64 48 • 86 1.340 24 80 48 100 2.083 ' 24 64 ! 40 72 2.800 56 64 32 100 1.371 32 56 24 100 1 ! 2.093 . 24 64 i 48 86 . 2.842 40 72 44 ; 86 1.305 24 64 32 86 1 . 2.100 . 28 64 48 100 2.849 28 64 56 86 1.400 28 04 32 100 ' 2.133 32 72 48 100 ' 2.857 24 56 48 72 1.433 28 80 44 100 2.171 28 72 48 86 2.865 44 100 56 86 1.447 28 72 32 86 ' 2.178 28 100 56 72 ' 2.880 48 40 24 100 1.458 24 04 28 72 2.182 40 44 24 100 > 2.894 32 72 56 86 1.407 24 72 44 100 ! 2.193 24 56 44 86 • 2.917 28 64 48 72 1.488 32 80 40 100 1 2.200 32 64 44 100 ; 2.924 32 56 44 86 1.500 40 04 24 100 1 2.222 28 56 32 72 2.933 44 72 48 100 1.550 24 72 40 86 2.233 40 86 48 100 • 2.946 44 56 24 64 1.550 28 72 40 100 2.238 28 64 44 86 2.960 28 44 40 86 1.503 28 80 48 100 2.274 32 72 44 86 2.984 28 48 44 86 1.505 24 50 32 86 2.286 32 56 40 100 3.000 40 64 48 100 1. 000 24 72 48 100 2.292 24 64 44 72 3.044 24 44 48 86 1.028 28 04 32 80 2.326 32 64 40 86 3.056 32 64 44 72 1.037 32 80 44 100 2.368 28 44 32 86 3.070 24 40 44 86 1.050 44 04 24 100 2.381 24 56 40 72 3.101 40 72 48 86 i.mi 24 04 32 72 2.392 24 50 48 86 3.111 40 100 56 72 1.705 24 72 44 80 2.400 32 64 48 100 3.126 48 100 56 86 1.711 28 72 44 100 2.431 28 64 40 72 3.143 40 56 44 100 A Thbatise on Milling and Milung Machines 341 Leads from 3.175" to 6.667* 3.333 3.349 3.360 3.411 3.422 3.429 3.733 3.750 3.771 3.907 3.920 3.979 I 5,093 ; 5.104 I 5.119 ! 5.133 56 48 28 80 56 24 5G I 48 44 5.185 32 ir 56 5.209 56 40 32 5.226 86 64 28 5.238 44 56 48 5.316 40 66 64 5.333 32 40 48 5.347 44 64 56 5.357 48 64 40 5.412 64 44 32 5.426 40 48 56 5.444 56 40 28 5.568 56 44 28 5.625 72 48 24 6.657 32 44 56 a. 714 64 24 5.759 86 56 24 5.788 56 72 64 5.833 48 64 56 5.847 44 56 64 5,893 48 64 44 5.920 40 44 56 5.926 64 48 32 5.954 64 40 32 5.969 44 48 56 5.972 86 48 24 6.061 40 44 48 6.109 56 44 48 6.125 56 40 28 6,136 72 44 24 6.140 44 40 48 6.160 56 40 44 6.202 40 48 64 6.222 64 40 28 6.234 64 44 34 6,349 40 56 64 6,364 56 44 32 6,379 48 66 64 6.429 72 56 32 6.465 64 44 32 6.481 40 48 56 6.515 86 44 24 6,563 72 48 28 6.667 64 56 28 342 The Cincinnati Milling Machine Company Leads from 6.720' to 12.444' Lead Driven 2d x Worm 10 Drivers 1st x Screw a f-H a 1 OQ <1 1-1 ri o 56 ^ Ist Intermediate Gear ® (Driver) O s 48 Q Gear for Screw ^ (Driver) 1 a a •a OQ H-1 00 Gear on Worm ^ (Driven) OS 1st Intermediate Gear ^ (Driver) »u 2d Intermediate Gear **^ (Driven) o 72 Lead of Spiral in Inches a 1.4 a> O 86 c;, 1st Intermediate Gear *^ (Driver) ^ 2d Intermediate Gear ^ (Driven) Gear for Screw (Driver) 6.720 8.212 10.238 72 6.750 72 40 24 64 8.250 48 64 44 40 10.286 72 40 32 56 6.765 40 44 64 86 8.312 64 56 32 44 10.313 72 64 44 48 6.806 56 32 28 72 8.333 48 32 40 72 10.370 56 48 64 72 6.822 44 48 64 86 8.361 86 40 . 28 72 10.390 64 56 40 44 6.825 86 56 32 72 8.377 86 44 24 56 10.419 56 40 64 86 6.968 86 48 28 72 8.485 48 44 56 72 10.451 86 64 56 72 6.984 44 56 64 72 8.532 86 56 40 72 10.476 64 56 44 48 7.000 56 40 32 64 8.551 86 44 28 64 10.500 56 64 48 40 7.013 72 44 24 56 8.555 44 40 56 72 10.558 86 64 44 56 7.071 40 44 56 72 8.571 72 56 32 48 10.667 48 40 64 72 7.104 48 44 56 86 8.682 64 48 56 86 10.694 56 32 44 72 7.111 64 40 32 72 8.687 86 44 32 72 10.714 72 56 40 48 7.130 44 48 56 72 8.839 72 64 44 56 10.750 86 40 32 64 7.159 72 44 28 64 8.889 56 28 32 72 10.859 86 44 40 72 7.163 44 40 56 86 8.930 48 40 64 86 10.909 72 48 32 44 7.167 86 40 24 72 8.958 86 56 28 48 10.938 56 32 40 64 7.273 64 44 28 56 9.000 72 40 28 56 10.949 86 48 44 72 7.292 56 64 40 48 9.143 64 40 32 56 11.111 64 32 40 72 7.330 86 44 24 64 9.166 48 32 44 72 11.168 86 44 32 56 7.333 44 40 48 72 9.214 86 40 24 56 11.169 72 48 64 86 7.407 40 48 64 72 9.333 48 40 56 72 11.198 86 64 40 48 7.465 86 64 40 72 9.351 72 56 32 44 11.250 72 32 28 56 7.500 72 48 32 64 9.375 72 64 40 48 11.313 56 44 64 72 7.601 86 44 28 72 9.385 86 56 44 72 11.402 86 44 28 48 7.619 48 56 64 72 9.406 86 40 28 64 11.518 86 64 48 56 7.679 86 64 32 56 9.429 48 56 44 40 11.667 56 32 48 72 7.714 72 40 24 56 9.471 56 44 64 86 11.688 72 56 40 44 7.778 64 32 28 72 9.524 64 56 40 48 11.758 86 32 28 64 7.814 48 40 56 86 9.545 72 48 28 44 11.786 72 56 44 48 7.839 86 48 28 64 9.556 86 40 32 72 11.852 64 24 32 72 7.875 72 40 28 64 9.568 72 56 64 86 12.000 72 40 32 48 7.955 56 64 40 44 9.598 86 64 40 56 12.031 56 32 44 64 7.963 86 48 32 72 9.625 56 64 44 40 12.040 86 56 64 72 8.000 64 40 28 56 9.643 72 64 48 56 12.121 64 48 40 44 8.021 56 64 44 48 9.697 64 48 32 44 12.178 72 44 64 86 8.036 72 64 40 56 9.722 56 32 40 72 12.216 86 64 40 44 8.063 86 40 24 64 9.773 86 44 32 64 12.222 48 24 44 72 8.081 40 44 64 72 9.778 44 40 64 72 12.273 72 64 48 44 8.118 48 44 64 86 9.844 72 32 28 64 12.286 86 40 32 56 8.148 44 48 64 72 9.954 86 48 40 72 12.318 86 64 44 48 8.182 72 44 28 56 10. 159 64 28 32 72 12.375 72 40 44 64 8.186 44 40 64 86 10.227 72 64 40 44 12.444 56 40 64 72 A Treatise on Milung and Milling Machines 343 Leads from 12.468' to 24.635" Lead Driven 2d x Worm 10 Drivers 1st x Screw s M 1.1 hes t^ 1 t-t f^ a 0) o g3 o t— 1 09 o OS O o .a •a QQ I Worm ven) rmediate ver) rmediate ven) r Screw ver) • QQ L Worm ven) rmediate ver) •mediate ven) r Screw ver) a CQ L Worm ven) rmediate ver) •mediate ven) r Screw ver) •s ar on (Dri > Inte (Dri Intel (Dri ar f 0] (Dri ar on (Dri Inte (Dri Intel (Dri .2*2 ar on (Dri Inte (Dri Intel (Dri 3'^ c8 J O 04 GO 1— ( 66 48 O 44 J 9i o 72 56 48 o 40 J 9i O 86 QQ 1—1 32 CM 40 o 12.468 15.429 19.196 56 12.500 56 28 40 64 15.469 72 32 44 64 19.286 72 32 48 56 12.542 86 40 28 48 15.556 64 32 56 72 19.592 64 28 48 56 12.571 64 56 44 40 15.636 86 40 32 44 19.636 72 44 48 40 12.698 64 28 40 72 15.677 86 64 56 48 19.688 72 32 56 64 12.798 86 56 40 48 15.714 64 32 44 56 19.708 86 48 44 40 12.833 56 48 44 40 15.750 72 64 56 40 19.907 86 24 40 72 12.857 72 28 32 64 15.926 86 48 64 72 20. 156 86 64 72 48 12.963 56 24 40 72 16.071 72 32 40 56 20.204 72 28 44 56 13.030 86 48 32 44 16.125 86 64 48 40 20.364 64 44 56 40 13.091 72 40 32 44 16.288 86 48 40* 44 20.455 72 32 40 44 13.125 56 32 48 64 16.296 64 24 44 72 20.476 86 56 64 48. 13. 139 86 40 44 72 16.424 86 32 44 72 20.571 72 56 64 40 13.333 64 32 48 72 16.500 72 48 44 40 20.625 72 48 44 32 13.395 72 40 64 86 16.722 86 40 56 72 20.741 64 24 56 72 13.438 86 32 28 56 16.753 86 56 48 44 20.903 86 32 56 72 13.500 72 64 48 40 16.797 86 32 40 64 20.952 64 24 44 56 13.636 72 48 40 44 16.875 72 32 48 64 21.000 72 48 56 40 13.651 86 28 32 72 16.893 86 56 44 40 21.116 86 32 44 56 13.714 64 56 48 40 16.970 64 48 56 44 21.429 72 28 40 48 13.750 56 28 44 64 17.063 86 28 40 72 21.818 72 48 64 44 13.935 86 24 28 72 17.102 86 64 56 44 21 . 939 86 28 40 56 13.961 86 56 40 44 17.143 72 56 64 48 21 . 989 86 64 72 44 13.968 64 28 44 72 17.277 86 64 72 56 22.041 72 28 48 56 14.026 72 56 48 44 17.374 86 44 64 72 22.338 86 56 64 44 14.063 72 32 40 64 17.455 64 44 48 40 22.396 86 32 40 48 14.077 86 56 44 48 17.500 56 24 48 64 22.500 72 28 56 64 14. 143 72 56 44 40 17.551 86 28 32 56 22.803 86 48 56 44 14. 259 56 24 44 72 17.679 72 56 44 32 22.857 64 24 48 56 14.286 64 32 40 56 17.777 64 28 56 72 22.909 72 44 56 40 14.318 72 64 56 44 17.917 86 32 48 72 23.036 86 56 72 48 14.333 86 40 48 72 17.959 64 28 44 56 23.333 64 48 56 32 14.659 86 64 48 44 18.333 64 48 44 32 23.455 86 44 48 40 14.667 64 48 44 40 18.367 72 28 40 56 23.516 86 64 56 32 14.694 72 28 32 56 18.429 86 56 48 40 23.571 72 28 44 48 14.781 86 64 44 40 18.477 86 32 44 64 23.889 86 32 64 72 14.815 64 24 40 72 18.667 64 48 56 40 24.000 72 48 64 40 14.931 86 32 40 72 18.701 72 56 64 44 24.133 86 28 44 56 15.000 56 28 48 64 18.750 72 32 40 48 24.188 86 64 72 40 15.202 86 44 56 72 18.770 86 28 44 72 24.432 86 32 40 44 15.238 64 28 48 72 18.813 86 64 56 40 24.545 72 44 48 32 15.273 56 44 48 40 19.091 72 48 56 44 24.571 86 56 64 40 15.357 86 28 32 64 19.111 86 40 64 72 24.635 86 48 44 32 844 The Cincinnati Milling Machine Company Leads from 24.750" to 80.625" Lead _^ Driven _ 2d x Worm 10 Drivers 1st x Screw 24.750 25.083 25. 130 25.455 25.595 25.714 26.061 26.182 26.250 26.327 26.667 26.875 27.000 27.302 27.364 27.500 27.643 27.922 28.000 28.052 28. 155 28.636 28.667 29.091 29.318 29.388 29.563 29.861 30.000 30.234 30.714 B u to o 72 86 86 64 86 72 86 72 72 86 64 86 72 86 86 72 86 86 64 72 86 72 86 64 86 72 86 86 72 86 86 o I B ^ u > OQ 40 48 56 44 28 56 48 44 48 28 28 28 40 28 44 24 56 28 40 28 28 44 48 28 48 28 40 24 48 64 56 o to HH — ' 44 56 72 56 40 64 64 64 56 48 56 56 48 64 56 44 72 40 56 48 44 56 64 56 72 64 44 40 64 72 64 to o 32 40 44 32 48 32 44 40 32 56 48 64 32 72 40 48 40 44 32 44 48 32 40 44 44 56 32 48 32 32 32 J o a •g 9* 30.857 31.111 31.273 31.354 31.500 31.852 32.000 32.250 32.576 32.727 32.847 33.507 33.786 33.939 34.205 34.286 34.554 35.000 35. 102 35. 182 35.833 36.000 36.857 37.403 37.625 38.182 39.091 39.417 39.490 40.000 40.313 o 72 64 86 86 72 86 64 86 86 72 86 86 86 64 86 72 86 72 86 86 86 72 86 72 86 72 86 86 86 72 86 e8 o o Intermediate (Driver) Intermediate (Driven) 1^ C<1 28 48 24 56 44 64 48 56 40 56 24 64 28 56 48 72 24 40 44 64 24 44 28 48 28 44 24 56 44 56 28 64 56 72 24 56 28 64 44 72 48 64 40 64 28 48 28 64 40 56 24 56 44 64 24 44 28 72 24 64 48 72 u. > Q 40 48 40 32 32 72 40 40 44 32 48 44 40 44 32 48 32 48 56 40 32 32 40 44 32 44 32 40 56 48 32 o a 2 -s 40.952 41.143 41.806 42.232 43.000 43.636 43.977 44.675 45.000 45.606 46.071 47.778 48.000 48.375 49.143 50.167 50.260 51 . 429 52.121 53.750 55.286 57.333 58.636 60.000 61.429 62.708 64.500 69.107 71 . 667 80.625 B o d 'p O 08 O S p3 B 3> 86 72 86 86 86 72 86 86 72 86 86 86 72 86 86 86 86 72 86 86 86 86 86 72 86 86 86 86 86 86 03 28 28 24 28 40 24 44 28 28 24 28 24 24 40 28 24 28 28 24 28 28 24 24 24 28 24 24 28 24 24 O 08 1 s ^ o 4) > SP. 64 64 56 44 64 64 72 64 56 56 72 64 64 72 64 56 72 64 64 56 72 64 72 64 64 56 72 72 64 72 OQ 0) t- > o-C o8^-^ O 48~ 40 48 32 32 44 32 44 32 44 48 48 40 32 40 40 44 32 44 32 40 40 44 32 32 32 40 32 32 32 A Treatise on Milling and Milling Machines 345 CHAPTER XX MILLING SPIRAL CAMS In this chapter we give detailed tables for setting Cincinnati Millers for Milling Screw Machine Cams and other spiral cams with leads between .600" and 6.00" advancing by .001", The cutting of accurate screw machine cams is one of the most difficult jobs that comes to the toolroom, because of the intricate computations necessary to determine the correct settings. Such cams are required in great variety, each differing from the other by only a few thousandths and with practically no duplications, making the use of master cams out of the question. These cams usually have shorter leads than can be obtained on a dividing head by any practical combination of change gears. It is therefore necessary to use a vertical attachment in connection with the dividing head and set both of them to that angle, which, together with the lead produced by the change gears, gives the correct lead to produce the required cam. It is the computation of these angular settings in connection 346 The Cincinnati Milling Machine Company with the proper change gear combinations that involves mathe- matics which is sometimes too confusing for the toolmaker. In the tables following all the information is given, and it only remains for the milling machine operator to select the lead of the desired cam from the tables and set up to the corresponding change gears and angles. Example: To set the machine for a cam having .717" lead. Setting tlie Vertical Attachment. Read the angle direct from the dial and set the spindle 39J^° from* its vertical position. Setting the Dividing Head. Subtract the angle in the table from 90°. The difference represents the angle to which the spindle must be raised from the horizontal position. 90° - 393/^° = 503^°. Set the dividing head spindle 503^° up from the horizontal position. This angle is read direct from the dial. Follow this same method when setting up for any other similar cams. 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15 1.499 28 72 401 100 15)% A Treatise on Milling and Milling Machines 353 • o Z t Id a hi a 111 t lU q: tn z • Z ■ Id a III z Id Hi lil 0: U Z • 0: z Id a Id 1 Id a: • id tc CO z • a o •- Z ^ IT -1 • 5 IT mmm 1 1 5 iij • 0: Hi i id -J < < • • < < • • A • • 0^ Id kJ til 9 Id z kJ bJ a 9 ^ z 111 § M a A z J O «-• M "^^ J e r4 ti <3 ^ J «-i N < 1.600 "IS T? ■40 100 31 1.550 "44 "64 I4 100 20 Teoo 44 "56 "W 100 21" 1.501 32 86 44 100 23/2 1.551 44 64 24 100 20 1.601 28 64 32 86 101% i.5oe 28 86 48 100 16 1.552 24 72 48 100 14 1.602 24 64 32 72 16 1.503 28 72 40 100 15 1.553 28 64 32 72 37 1.603 28 64 32 86 10 1.504 24 72 40 86 14 1.554 24 64 40 86 27 1.604 32 86 44 100 ll)% 1.505 24 64 32 72 25»^ 1.555 44 64 24 100 l9*/ft 1.605 40 56 24 100 201% 1.506 28 72 40 100 14y>t 1.556 24 64 32 72 21 1.606 24 64 32 72 15V% 1.507 24 72 40 86 I3V^ 1.557 28 64 32 86 17 1.607 32 86 44 100 11 1.508 24 72 48 100 19 Mk 1.558 24 72 44 86 24 1.608 44 64 24 100 13 1.503 28 64 32 86 22 1.559 24 72 48 100 13 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1.574 32 86 44 100 16 1.624 24 64 32 72 13 1.525 28 72 40 100 \\¥i 1.575 24 72 44 86 22 h 1.625 44 64 24 100 10 1.526 24 72 40 86 10 1.576 24 72 48 too 10 1.626 24 72 44 86 17>% 1527 28 72 40 100 11 1.577 32 86 44 100 15^ 1.627 24 64 32 72 12)% 1.528 32 86 44 100 21 1,678 44 64 24 100 17 1.628 24 64 32 72 12 V% 1.529 28 86 48 100 12 1.573 28 100 56 86 30 1.629 32 72 40 86 38 1.530 28 72 40 100 lOVii 1.580 28 64 32 86 14 1.630 24 64 32 72 l^ 1.531 28 72 44 100 26^ 1.753 32 86 48 100 II 1654 24 72 44 86 14 1.704 28 64 40 72 45y^ 1754 28 72 48 100 20 1.655 28 64 40 too 19 1705 28 64 40 100 13 1.755 28 72 40 86 14 1.656 28 72 44 too 14 '/l 1.706 24 64 40 66 12 1.756 32 86 48 100 10% L657 28 72 44 100 14)^ 1707 40 86 44 100 33»^ 1.757 28 100 56 86 15% 1.658 24 72 44 86 l3Vk 1.708 26 64 40 100 I2S^ 1.756 32 72 44 100 26 1659 24 64 40 86 16 1.709 24 64 40 86 WVk 1.759 32 86 48 100 10 1660 28 72 44 100 14 1.710 26 72 40 86 19 1.760 26 72 48 100 ie% L66I 24 72 44 86 13 1.711 32 72 44 100 29 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72 40 86 11 1.677 28 72 44 100 WVi 1.727 32 72 44 100 26 1.777 32 56 40 too 39 1.678 28 64 40 100 \S*h 1.728 32 72 40 100 i3y& L778 44 56 24 too 19% 1.679 24 72 44 86 10 1.729 32 72 40 100 l9Mi 1.779 26 72 40 86 10% L680 28 72 44 100 11 1.790 28 72 40 86 17 1.780 28 100 56 66 12% L68I 24 64 40 86 15>^ 1.731 24 72 48 66 21 V^ 1.781 28 72 40 86 10 I.68Z 28 72 44 100 \0V2i 1732 32 72 40 100 13 1.762 32 64 40 100 27 L683 40 56 24 100 11 1.733 32 66 48 100 14 1.763 28 100 56 86 12 1.684 32 86 48 100 19^ L734 28 72 40 86 I6V^ 1.764 24 56 40 66 26% 1.685 28 72 44 100 10 1.735 28 72 40 86 I6M1 1.785 28 72 46 too 17 1.686 28 64 40 100 l5Vtt 1736 32 72 40 100 I2V^ 1.766 28 100 56 86 11% 1.687 32 64 40 100 32^ 1.737 32 86 48 100 IbYi 1.767 32 72 44 too 24 1.668 40 56 24 100 10 1.738 32 56 40 100 AOYi 1.768 24 72 48 86 16 1.689 32 86 48 100 19 1739 32 72 40 100 12 1.769 26 100 56 66 II 1.690 28 64 40 100 15 1.740 32 86 48 100 13 1.790 28 100 56 66 11 1.691 32 72 40 100 18 1.741 28 72 44 86 29 1.791 24 64 44 66 21 I.69Z 24 64 40 86 14 1.742 32 72 40 100 ll>^ 1.792 26 100 56 66 10% 1.693 24 72 48 86 245^ 1.743 28 72 40 86 15>^ 1793 26 too 56 86 10% 1.694 32 72 44 100 30 1.744 32 86 48 100 I2»^ 1.794 44 56 24 100 18 1.695 44 56 24 100 26 1.745 32 72 40 100 II 1.795 28 100 56 86 10 1.696 24 64 40 86 I3>& 1.746 24 64 44 66 24y^ 1.796 26 64 32 72 22^ 1.697 28 72 44 86 31 V^ 1.747 32 86 46 100 12 1.797 24 72 48 86 15 1.696 26 64 40 100 14 1.746 32 72 40 100 10% 1.798 24 64 44 66 20% 1.699 24 64 40 86 13 1.749 28 72 48 100 20% 1.799 Ja 72 46 100 15% A Treatise on Milling and Milung Machines 355 356 The Cincinnati Milung Machine Company ui liJ ■ • UI "?" ■ hi R" — ^ • O o l&J 5 iij bJ q: o t IE O o hJ 1^ 5 bl bl o CO • a: o 5 St o hi o bl 1 hi K O to 2 IK liJ lil z z II* Id bl z z hJ bl Z « o ■AJ g o UJ • o ■■v Z o bi • o 1 o hi a K Z oe: o d: Z K -1 O tt Z o: J < < ■ • < < < • • j5 O < ^ ■ M* < O iij » a a bl z Id iij » i z bl ^ Sil a ^ z -J 9-i (U O < .-i i3 r-l M P < J o W99 1-4 cu O < 1.950 "IS "72 "44 "8? iT^ ^000 "48 "56 "24 too 19*^ 2.050 28 "64 "48 loo 12 'A 1.951 24 44 32 86 16 2.001 28 64 40 86 10^ 2.051 24 64 40 72 to 1.95« 40 86 44 100 17*^ 2.002 40 86 44 KO 12 2.052 28 64 44 86 23W 1.955 28 72 44 86 11 2.003 26 64 44 86 26*/i 2.053 28 72 48 86 19 1.964 24 64 48 86 21 2.004 28 64 40 86 10 2.054 28 64 48 100 12 L955 32 72 48 86 36 2.005 28 100 56 72 29 2.055 24 64 48 86 II 1.956 32 72 48 100 tv/% 2.006 40 86 44 100 llVk 2.056 40 86 48 too 25 1.957 24 64 40 72 20 2.007 40 86 48 100 26 2.057 40 44 24 100 19^ 1.958 40 86 44 100 17 2.008 48 56 24 100 12Vi 2.058 24 64 48 86 I0S4 1.959 28 72 48 86 25>^ 2.009 40 86 44 100 11 2.059 28 72 48 86 WA 1.960 28 72 44 86 10 2.010 32 72 40 86 13Ml 2.060 32 72 48 100 15 1.961 24 44 32 86 15 2.011 32 72 48 100 19)^ 2.061 24 64 48 86 10 t.96e 48 56 24 100 I7J% 2.012 48 56 24 100 12 2.062 24 56 40 72 30 1.965 24 56 40 86 10 2.013 40 86 44 100 10S4 2.063 40 44 24 100 19 1.964 24 64 40 72 I9ya 2.014 32 72 40 86 13 2.064 44 48 28 100 361^ 1.965 24 44 32 86 14^ 2.015 40 86 48 100 ZbYz 2.065 28 64 48 too \0\A 1.966 28 64 40 86 15 2.016 40 86 44 100 10 2.066 32 56 40 86 39 1.967 32 64 40 too 10>V 2.017 24 64 40 72 14 V4 2.067 32 64 44 too 20 1968 40 86 44 100 16 2.018 32 72 40 86 12^^ 2.068 28 64 48 too 10 1.969 24 64 40 72 19 2.019 48 56 24 100 II 2.069 40 44 24 100 IbVz 1.970 32 64 40 100 10 2.020 28 72 48 86 ZVA 2.070 32 72 48 100 14 1971 32 72 40 86 I7J^ 2.021 24 64 40 72 14 2.071 28 72 48 86 17^1 197Z 48 56 24 100 16^ 2.022 32 72 40 86 12 2.072 32 56 40 100 25 1973 40 86 44 100 15^^ 2.023 48 56 24 100 lOVk 2.073 28 64 40 72 3l'/i 1974 24 44 32 86 1354 2.024 28 64 48 100 15 V4 2.074 52 72 48 100 15>^ 1975 28 64 40 86 14 2.025 32 72 40 86 \\yi 2.075 40 44 24 100 18 1976 28 64 44 86 28 2.026 48 56 24 100 10 2.076 28 72 48 86 17 1977 40 86 44 100 15 2.027 28 100 56 72 2I!4 2.077 28 100 56 72 I7li 1978 24 44 32 86 13 2.028 28 64 48 100 15 2.078 32 72 48 100 15 L979 28 64 40 86 13!^ 2.029 32 72 40 86 II 2.079 40 72 44 86 43 L980 28 64 48 too 19 kk 2.030 24 64 40 72 19 2.080 IZ 64 44 too 19 1.981 24 64 40 72 18 2.031 24 64 48 86 14 2.081 40 44 24 too 17/1 1982 24 44 32 86 I2Wl 2.032 32 72 40 86 \0^ 2.082 32 72 48 100 12 yk 1983 28 64 40 86 19 2.033 28 64 48 100 I4yk 2.085 28 100 56 72 17 1.984 28 48 40 86 43 2.034 24 64 40 72 I2'A 2.084 28 64 40 72 51 L985 24 64 48 86 It/i 2.035 24 64 48 86 15!^ 2.085 24 64 48 72 33V^ 1.986 24 44 32 86 12 2.036 32 72 40 86 10 2.086 32 72 48 too 12 1.987 28 64 40 86 \V/i 2,037 24 64 40 72 12 2.087 28 72 48 86 16 L988 28 56 32 72 261^ 2.038 28 64 48 100 14 2.088 28 100 56 72 16)4 1.989 24 44 32 86 W/t 2.039 24 64 48 86 15 2.089 28 64 44 86 21 1.990 28 64 40 86 12 2.040 32 72 48 100 17 2.090 32 72 48 too llVfai 1.991 28 64 40 86 12 Z04I 24 64 40 72 lt!4 ^091 28 44 32 86 28 1.992 48 56 24 100 14^ 2.042 28 64 48 100 I3>4 2.092 28 72 48 86 i5y% 1.993 24 44 32 86 11 2.043 24 64 48 86 12^ 2.093 32 72 44 86 25 1.994 28 64 40 86 IIV^ 2.044 40 44 24 100 ZOYi 2.094 52 72 48 100 11 1.995 40 86 44 100 19 2.045 24 64 40 72 M 2.095 28 56 32 72 19«/r 1.996 24 44 32 86 10)4 2.046 28 64 48 100 15 2.096 28 64 44 86 ZOYi 1.997 32 72 40 86 15 2.047 24 64 48 86 12 2.097 32 72 48100 \oyt 1.998 28 64 40 86 II 2.048 24 64 40 72 10)^ 2.098 32 64 44 too MYt 1.999 24 44 32 86 10 2.049 28 64 56 86 44 2.099 28 100 56 72 Wh 1 A Treatise on Milling and Milling Machines 357 o ui a o Of UJ DC ■ «0 • hi 5 bJ Z U T 3: hJ • • hJ bJ 0: 111 kJ 5 Id ■ Id CO z 111 bJ z z llJ z z Id Z • o o ■u Z 1 a: ■ ^ ■ liJ • 0: lU z Z Id -J < Id < UJ sa • a < z < UJ UI »' \ < <3 z < Id < fid iS i -J o cu < J <3 T-l (U *** J <3 tH CVI < t.ioo "28 ■4? ■32 "b^ 27>5 Z.I50 "32 "72 ■44 86 19 2205 "24 "56 ■40 "72 22J^ MOl 32 72 48 too 10 2.151 28 56 52 72 14)^ 2.201 28 64 44 86 1014 ZAOZ 28 72 48 86 I4y^ 2.152 32 64 44 100 12 2202 32 72 44 86 14^ 2.103 40 44 24 100 15>^ 2.155 56 64 28 too 26^ 2203 32 56 40 100 I5y£ 2.104 28 too 56 72 15 2.154 24 64 44 72 20 2204 28 64 44 86 10 2.105 40 86 48 100 19 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52 72 1014 2235 44 86 48 100 lAVz ZI36 28 56 32 72 16 2186 32 72 44 86 16 2236 32 72 44 86 lOi^ 2.157 32 72 44 86 20 2187 40 72 44 100 ZVh 2237 24 56 40 72 20 2.138 28 72 48 86 10 2188 28 56 32 72 10 2.238 24 64 44 72 \Vh 2.159 52 64 44 100 W/t 2189 28 64 44 86 12 24t39 32 72 44 86 10 2.140 24 56 40 72 26 2190 32 56 40 86 34S^ 2240 32 56 40 100 1IV% 2.141 28 56 32 72 155^ 2191 48 100 56 86 45 V^ 2241 32 64 40 86 I5'4l 2.142 28 100 56 72 10»^ 2192 40 66 48 100 11 2242 24 64 44 72 12 2.145 56 64 28 100 29 2193 28 64 44 66 1154 2243 28 64 44 72 33 ZI44 40 72 48 100 36 Vt 2194 28 64 40 72 25V^ 2.244 32 56 40 too 11 2.145 28 too 56 72 10 2195 28 64 48 86 26 2.245 28 64 S6 86 38 2.146 28 56 52 72 15 2196 40 86 48 100 I0»^ 2.246 24 64 44 72 IIV4 ^147 40 86 48 100 16 2197 28 64 44 86 11 2247 32 64 40 86 15 2.148 44 86 48 100 29 2196 44 86 48 100 ZhVx 2248 32 56 40 100 1054 2.149 40 44 24 100 10 2199 40 86 48 108,10 1 2249 32 72 48 86 25 358 The Cincinnati Milling Machine Company • cr o z O liJ bJ liJ 5 UJ It U K Z « Z z ■ It Id "kT hi T ft: bJ bJ q: CO z • DC Z bi 5 bJ Itl bi hi It bJ • hJ It 10 Z o 1- liJ ■ bJ • 1- bf o o: z Z cc -J a: Z Z K si 0: z Z tc -J < < ■ • < C < 25 . • • a < < < ■ • < kJ bJ &i i » z bJ til S Z bJ ^ til a m z _j O (U < ^ T-l Al < -J »H (VI < 2.250 "24 "64 "44 72 n 2.900 "24 "56 ■40 72 15 2.3iio "28 "64 "44 "72 2857 2.251 32 56 40 100 10 2.301 32 64 48 100 l6*/£ 2.351 28 48 40 72 A^Yi 2.252 32 64 40 86 14 v^ 2.302 28 64 48 86 I9yk 2.352 32 64 48 100 IPA 2.253 40 64 44 too 35 2.303 28 44 32 86 13)^ 2.353 32 72 48 86 1271 2.254 24 64 44 72 lOVi 2.304 26 72 56 86 24yi 2.354 28 64 40 72 14 'A 2.255 32 64 48 100 20 2.305 24 56 40 72 14 V^ t955 44 86 48 too i6*A 2.256 28 64 48 '86 22 S4 2.306 44 56 32 100 23^1 2.356 32 64 48 100 II 2.257 24 64 44 72 10 2.307 28 44 32 86 19 2.357 24 64 48 72 19^1 2.258 28 44 32 86 \7'A 2.308 44 86 48 100 20 2.358 32 56 40 86 2754 2.259 32 64 44 86 28 2.309 28 64 48 86 19 2.359 28 64 40 72 14 2.260 44 66 32 100 26 2.310 24 56 40 72 14 ^360 32 64 48 100 lO'A ^261 44 86 48 100 23 2.311 40 72 44 100 19 2.361 40 72 44 too 15 2.262 32 64 40 86 \VA Z3I2 28 44 32 86 12 yk 2.962 44 56 32 100 20 2.265 44 72 48 100 39 !4 e3l3 32 64 48 100 l5'/t 2.363 32 64 44 86 23 2.264 40 64 48 100 41 2.314 44 56 32 100 29 2.364 32 64 48 too to 2.265 28 44 32 86 17 2.315 24 56 40 72 I3V^ 2.365 24 56 48 86 8V1 ^266 32 64 40 86 13 2.316 28 44 32 86 12 2.366 40 72 44 100 14 'A ^267 28 40 32 86 23)^ 2.317 24 40 44 86 41 ^367 56 64 26 too 15 2.266 40 72 48 86 43 2.316 32 64 48 100 15 2.368 24 44 40 86 21 2.26d 32 64 48 100 19 2.319 28 48 44 86 39 2.369 28 64 40 72 19 2.270 28 44 32 86 I6»% 2.320 28 44 32 66 11^ 2370 44 56 32 100 19 'A 2.271 32 64 40 86 \^yl 2.321 28 40 32 86 27 2371 40 72 44 100 14 2.272 28 64 48 86 ZVA 2.322 28 72 56 86 23V^ 2372 56 64 28 100 14^ 2.275 44 100 56 86 b7'/ti 2.323 48 100 56 86 42 2.373 28 64 40 72 12*A 2.274 46 56 32 100 34 2.324 32 64 48 100 I4'A 2.374 32 100 56 72 I7A 2.275 32 64 40 86 12 2.325 28 44 32 86 M 2.375 28 64 48 86 13*A 2.276 28 44 32 86 16 2.326 24 64 48 72 21^ 2.376 40 72 44 100 I3>^ 2.277 24 56 40 72 17 2.327 24 44 40 86 23 'A ZV77 56 64 28 too 14 2.278 44 56 32 100 25 2.328 28 44 52 86 10 'A 2.378 28 64 40 72 12 2.279 32 64 40 86 ll*/k 2.329 24 56 40 72 It 2.379 28 64 46 66 19 2.280 26 64 44 72 i\yt 2.330 40 100 56 72 4171 2.380 32 100 56 72 17 2.281 40 64 44 86 44'/a 2.931 28 64 40 72 I6V% 2.381 40 72 44 100 15 2.282 28 44 32 86 15^ 2.332 28 44 32 86 10 2.382 28 64 40 72 H*A 2.285 32 64 40 86 II 2.333 24 56 40 72 ll'A 2.383 44 86 48 100 14 2.284 28 64 40 72 20 2.334 24 64 48 72 21 2.984 28 64 48 86 IZYt 2.285 44 86 48 100 2I*A 2.335 28 64 48 86 17 2.385 32 72 56 66 34 W 2.286 28 64 44 72 31 2.336 44 86 48 100 18 2.386 28 64 40 72 II ^287 32 64 40 86 lOV^ 2.337 24 56 40 72 n t387 56 64 28 100 15 2.288 44 56 32 100 ZAik 2.336 32 64 48 100 19 2.388 44 66 48 too I9V4 2.289 24 56 40 72 16 2.339 40 64 44 86 43 2.369 28 64 48 66 12 2.290 24 44 40 86 25S^ 2.340 24 56 48 72 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48 24 64 25 4.999 40 48 44 72 n 5.049 64 40 32 66 52 5.099 44, 64 56 72il7S% A Treatise on Milling and Milung Machines 377 378 The Cincinnati Milling Machine Cobipany O • u O hJ a hi J i u • q: o hi o hi i hi hi s • hi ft , 1 • flt 5^ e i z kJ u z z f^ 1 ^ ;z w 'H S ' . 1 • o K o • o HJO fci 1 • H t O: ki 1 a ac Z Z K a 0: z ^ 0: : -J 9 1 ^ z ^ flt -J i J < ti i < u -J < 1 a * 9 < hi ; Z < hi 1 hi • ■ a Qi § < B.tSO "56 40 26 "64 51 5.500 40 "44 "48 72 29 5.350; 72 ^ ^4 "64116 1 5.Z5I 40 44 56 86 27>^ 5.501 86 56 24 64 23 5.351 64 40 32 86 26 s.zwt 52 40 48 72 10 5.502 72 48 24 64il9yi 5.352 64 40 32 66 26 S.Z5S 40 48 56 66 I4*A 5.505 64 48 32 7ZZhyi 5.353 56 40 28 72 loyi 5.Z54 64 56 28 46 56 5.504 56 40 28 72119 5.354 40 56 64 72 32 V4 5.Z55 44 56 64 86 26 5.505 64 40 32 66^27 5.355 40 56 64 72 52V4 5.2S6 64 46 52 72 27>^ 5.506 64 40 28 72 3IKI 5.356 72 40 24 64|57'4 5.Z57 64 40 52 86 28 5.507 40 46 56 86 12 5.357 56 40 28 64 29 5.256 44 64 56 72 1094 5.506 46 64 56 72 24>^ 5.558 86 56 24 64 2iV4 5.259 48 64 40 56 II 5.509 40 48 56 72 35 5.359 64 56 26 48136)4 5.260 64 48 24 56 25 5.510 56 44 28 64 MYi 5.560 64 44 32 72 34 5.261 66 56 24 64 24 5.511 44 56 64 72 AOYi 5.361 56 40 28 72 10 S.IVL 64 44 52 86 W/i 5.512 64 44 32 86 II 5.362 46 64 44 56 24'/i 5.265 52 44 56 72 Z\Vi 5.513 64 44 32 86 11 5.363 44 40 48 72 45 5.264 52 44 56 72 Z\)\ 5.514 72 44 24 64 30 5.364 72 48 24 64 MYz 1 5.265 46 64 56 72 25>\ 5.515 56 40 28 72 1214 5.365 44 48 56 66126 1 5.266 44 64 56 72 10 5.516 64 46 24 56 21*^ 5.566 56 44 26 64 15V4| 5.267 56 72 64 86 24V«i 5.317 40 48 56 86 WYi 5.367 56 72 64 86 22 1 5.266 72 46 24 64 20 '/i 5.316 44 46 56 86 27 5.368 86 48 24 72!26 1 5.269 72 46 24 64 20^ 5.319 46 64 44 56 25'4 5.369 48 64 56 72 23 5.270 44 48 56 66 28 5.320 44 56 64 66 24V4 5.370 64 46 24 56 20 5.271 56 40 26 72 I4V^ 5.321 66 48 24 72 27 5.371 64 48 32 72 25 5.272 86 44 24 64 44 5.522 64 44 32 86 10V4 5.372 72 44 24 56 40 5.275 86 48 lA 72 26 5.323 44 40 56 86 42 5.373 40 48 64 72 43)4 5.274 48 64 44 56 26V^ 5.324 86 64 40 72 44h 5.574 64 40 32 86 25/1 5.276 40 44 56 86 27 5.525 56 40 28 72 12 5.375 86 44 28 72 45 5.276 48 64 40 56 10 5.326 64 48 32 72 26 5.376 56 64 40 48 42V4 5.277 44 56 64 86 25V^ 5.383 48 64 44 56 24 5.284 64 44 32 66 MVi 5.334 64 48 24 56 21 5.384 48 64 44 56 24 5.285 64 40 52 72 42 5.335 64 48 24 56 21 5.385 56 72 64 86 21*/4 5.286 48 64 56 72 25 5.336 40 44 56 72 41 5.386 64 48 24 56 19 '/I 5.287 46 64 56 72 25 &337 40 44 56 72 41 5.387 44 48 56 86 25)4 5.288 56 72 64 66 24 5.338 66 48 28 72 40 5.388 44 48 56 86 25'/4 5.289 48 56 64 86 54 5.339 56 44 28 64 I6V4 5.369 48 64 56 72 22'4 5.290 56 44 46 100 50 5.340 86 56 24 64 22 5.390 86 48 24 72 25)4 5.291 56 44 48 100 50 5.341 48 64 44 56 25 5.391 56 44 26 64 14*4 5.292 72 44 24 56 41 5.342 44 48 56 86 26V^ 5.392 64 48 32 72 Z^Yi 5.295 72 44 24 56 41 5.343 40 44 56 86 25 '/2 5.393 72 48 24 64 16)4 5.294 44 48 56 86 27>i 5.344 86 48 24 72 26/% 5.394 86 56 24 64 20/1 5.295 44 48 56 86 27^1 5.345 86 48 24 72 26/* 5.395 32 44 56 72 I7V4 5.296 56 44 28 64 16 5.346 86 48 28 64 47 5.396 64 40 32 86 25 5.297 86 48 24 72 27 J4 5.347 56 72 64 86 22 '/a 5.397 56 44 32 64 32 5.296 40 44 56 86 26^ 5.348 56 72 64 86 2254 5.398 40 48 64 86 29V4 5.299 44 56 64 86 25 5.349 32 44 56 72 19 5.399 64 44 24 56 30 A Treatise on Milling and Milling Machines The Cincinnati Milling Machine Company A Treatise on Milling and Milling Machines 381 The Cincinnati Milung Machine Company A Treatise on Milling and Milling Machines Instructions for Using Cam-Milling Attachment The attachment consists of a head stock E, mounted on the slide C, having its ways in the bed plate A, which is bolted to the table of the machine. The work spindle is driven through wonns and wormwheel G by a belt from a separate countershaft running on pulley P. There is also provision for applying a crank for hand feeding. Power feed is recommended because it gives a more even motion than can be obtained by hand. The work spindle is left large so it can be turned down to suit the master cam and the blanks of the cams being milled. The attachment is set up as follows: Secure the master cam to the work spindle so as to engage the roller R, which is located on a bracket fixed to the base plate. The slide C is held in working engagement with this roller by the weight W. The weight regularly furnished is heavy enough for only the lightest work; when heavy milling is to be done, sufficient weight must be added. 384 The Cincinnati Milling Machine Company The table of the machine must be adjusted vertically to bring the center of the roller on the same horizontal plane with the center of the cutter. The cam being milled is mounted on the work spindle as shown. As the spindle revolves, it follows that a revolving motion is imparted to the cam being milled, and in combination with this revolving motion there is also a lateral movement caused by the master cam rolling against the roller R, which is fixed to the base A. If the master cam is properly constructed the resulting cam will be satis- factory. When cams are cut out of solid stock, a roughing cut should be taken first, leaving a small amount for finishing. The finishing cutter must always be the same diameter as the roller with which the finished cam shall work. The Master Cam. In case it is found preferable to use for the master cam a cam which is exactly like and the same size as the cam to be made, the roller R must be the same diameter as the finishing cutter. In general, the master cam should be larger than the cam being milled, and the roller R should be as large in diameter as possible. In laying out such a master cam, decide upon a size for the roller R (which may be any convenient size), and then lay out the MASTER CAM, CONSIDERING IT AS A CAM WHICH, WHEN OPERATING IN CONNECTION WITH THIS ROLLER, WILL HAVE THE SAME THROW AND THE SAME TIME AS the cam being made. These instructions hold for both face and cylindrical cams. A Treatise on Milling and Milling Machines 385 CHAPTER XXI NATURAL TRIGONOMETRIC FUNCTIONS Giving the Values of Sines, Cosines, Tangents, Cotangents, Secants and Cosecants for all Degrees and Minutes from Degrees to 90 Degrees These functions are arranged in 45 tables, each of which contains the values of these six functions for one angle and its complement. This, we believe, makes very much simpler and more useful tables than those arrangements which place in separate tables. Sines and Cosines, Tangents and Cotangents, Secants and Cosecants. For Angles Less than 45°. For all angles up to 45°, the readings are made direct from the table. The angle is given at the top left- hand comer of the table and the minutes are imder the left-hand column headed M. Suppose we want to know the value of the Sine of an angle of 36°12'. We turn to the table which has the angle 36° at its top as on page 398, and then we follow down the column headed Sine to the figure opposite 12 (in the left-hand column under M), and we find the value .59060. This is the Sine of 36°12'. The Cosine, Tangent, Cotangent, Secant and Cose- cant are found in exactly the same way. In fact, if these several functions are wanted at the same time they may be read from the table when we are reading the Sine of the angle. For Angles Greater than 45°. We now reverse the above process. The names of the functions are given at the bottom of the table. The angle is at the bottom right-hand comer and minutes are given in the right-hand column OVER M. We must always READ UP. Suppose we want to know the value of the Sine of an angle of 54°21'. Turning to that table which has the angle 54° at the bottom, as on page 397, we find our function over the Sine as given at the bottom of the table. We read up in the column over M at the right-hand side of the page imtil we come to 21, then read across to the left and in the column over Sine we find the value .81259. This is the Sine of 54°21'. The value of the Cosine, Tangent, Cotangent, Secant and Cosecant are found in exactly the same way. 386 The Cincinnati Milung Machine Company u £ Si^c^'ftKss As;s^9^;;<«!999:;!»%9}i^p>«^^;3(^AP^i9^^!i f;ii 19^9!) a 8 ?s !:^ :?7:?s s s i»«o M n •*) <« M o Okoo t««e w) ^ f^ TC M o S IlllllllllllllllllllllllllOlffiiiiliiiiiiiiiiiiiiiiiiiiiSiti M o «■«« JT JT JT J? Jri5'8i?'«'8 » » » » » s ^ ^ ^ s JT ff » » ff J? ff a ^ ^ CO O o o a o CO ' ^ S 21 A A V ffi "^ t j2 f^ •< wo ^"* «'> fo 1 « o « t'g S ff 8 S 8 tS> S>^ d« S 9> 8>o I/) r>) n M OkOO

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S^SSS^ ^OkCD 00 OQOQOQaOOQOOQOOQOQOQOCQCQQ c U C^ kOpfn«-o^r»i-i «noo 5iioOkfn©Qk«r»p^»r~i-« "»ao c«iAOk»o»o»'» v^ t ioi')V9<0• >r . . V Ok <^moQ«v Wrier c*>c*;p)P)r7WWcOC')< 'P u e \Q Q '"50 5 ** t ** tqi ** "^SS '* "' $?*''■'& p'*>(^>-' 2* 1— irojuugOkfOf^p ts M 2 8* o OoooSooooooOook gk Ok & o gk g'9^9>9'g'9'9'ekSk 8>» o i-S' 3 ° ** « '^*">« '-« <»'2 S 2 ^JtJ'S J:S ?8 S S P^J?"8 JJ-S l?RSiaSSJJ!"ftP5^^^5;iJ5?5?'i5''&?SiRRj;?S?!S'aR%Rk2 S A Treatise on Milling and Milling Machines 401 Table of Decimal Equivalents in inches of Millimeters and Fractions of Millimeters mm. Inches mm. Inches mm. Inches ^}, = .00079 18 = .02047 2 = .07874 j'ff = .00157 iJ = .02126 3 = .11811 A = .00236 18 — .02205 4 = .15748 A = .00315 13 = .02283 5 ss .19685 /. = .00394 18 = .02362 6 = .23622 i«. = .00472 U = .02441 7 = .27559 3'. = .00551 Vo = .02520 8 = .31496 A = .00630 n = .02598 9 = .35433 j'o = .00709 li = .02677 10 = .39370 J8 = .00787 45 = .02756 11 == .43307 41 = .00866 48 =s .02835 12 = .47244 i! = .00945 42 = .02913 13 = .51181 U = .01024 48 — .02992 14 =s .55118 ii = .01102 89 50 = .03071 15 =B .59055 i§ = . 01181 48 = .03150 16 = .62992 is = .01260 41 50 = .03228 17 = .66929 n = .01339 n = .03307 18 s= .70866 48 = .01417 n = .03386 19 = .74803 is = .01496 u = .03465 20 = . 78740 18 = .01575 48 =: .03543 21 = .82677 fi = .01654 48 = .03622 22 = .86614 li = .01732 48 = .03701 23 ^ .90551 !J = .01811 48 = .03780 24 — .94488 n = .01890 48 = .03858 ' 25 =s .98425 18 = .01969 1 = .a3937 26 =1 L . 02362 10 mm. 10 cm. 10 dm. 25.4 mm. 1 Centimeter = 0.3937 inches. 1 Decimeter = 3.937 inches. 1 Meter = 39.37 inches. 1 English inch. 402 The Cincinnati Milling Machine Company Table of Decimal Equivalents of Fractions of an Inch 8thB. 32d8. 64th8. 64ths. H ^ .125 A - .03125 A - .015625 « = . 515625 K - .250 A = .09375 A - .046875 « = .546875 Vs = .375 A - .15625 A = .078125 a = . 578125 H - .500 A - .21S75 A « . 109375 H = .609375 ^ = .625 A - .28125 A - .140625 a = . 640625 H - .750 H - .34375 tt = . 171875 tt = .671875 H - .875 H - .40625 tt « .203125 tt = .703125 leths. tt - .46875 H = .234375 tt = . 734375 A = .0625 • H = .53125 tt = .265625 a = .765625 A « .1875 tt = .59375 Jl - .296875 tt = .796875 A - .3125 H - .65625 ii = .328125 tt = . 828125 A - .4375 H - . 71875 « = . 359375 w = .859375 A « .5625 « - .78125 if = .390625 H = .890625 H = .6875 H - .84375 ii - .421875 K = .921875 H = .8125 « - .90625 H - . 453125 *i = .953125 If = .9375 H « .96875 fi = .484375 H = . 984375 Index 403 INDEX Accuracy of Dividing Heads, 61 Adapters for Flanging Threaded Spin- dle Ends, 82 Adjustment, Care and Erection of Milling Machines, 41 Adjusting Knee, Saddle and Table Bearings, 44 Adjusting the Spindle, 43 Care of the Machine, 46 Changing Feeds, 45 Changing Spindle Speeds, 44 Countershaft, 41 Erection, 41 High Power Machines, 42 Oiling, 42 Operating Levers, 44 Ordering Repairs, 47 Removing the Spindle, 43 Speed of Countershaft, How to compute, 42 To use the Table, Cross and Ver- tical Feeds, 44 Addendum, 249 Angles and Leads for Spirals, Table of, 338 Angles, Leads and Change Gears for Cutting Spiral End Mills, 170 Angles, Leads and Change Gears for Cutting Spiral Milling Cutters, 170 Angles, Leads and Change Gears for Cutting Twist Drills, 337 Angular Indexing, 319 Angular Indexing, Table for, 329 Arbors, 82 Arbors, Carried in Stock, 84 Arbor Equipment for Millers, 86 Arbors, Keyways for, 82-83 Arbors, Method of Driving, 80 Arbors, Proper Arrangement of Sup- ports and Cutters on, 78-79 Arbor Supports, 77 Attachments, Milling Machine, 23 Cam Milling Attachments, 30 Circular Milling Attachments, 30 Dividing Heads, 56 Driving Mechanism, 25 High Speed Attachment, 26 Index Heads, Combination, 24 Indexing Attachments, High Num- ber, 24-66 Oil Pumps, 31 Rack Indexing Attachments, 28 Rack Indexing Attachment, Table for, 266 Rack Milling Attachments, 28 Slotting Attachments, 28 Spiral Milling Attachments, 26 Undercutting Attachments, 25 Universal Milling Attachments, 27 Vertical Milling Attachments, 27 Vises, All Steel, 33 Vises, Plain, Swivel and Tool- maker's, 32 Automatic Clamping and Releasing Fixtures, 195-230 Automatic Indexing Fixtures, 237 Automatic Millers, 35 Automatic Releasing Fixtures, 229 B Bevel Gears, Computations for, 273 Computing the off-set, 284 Cutting Bevel Gears on a Miller, 278 Formulas for Bevel Gear Calcu- lations, 287 Outside Diameter of Blank, 277 Selecting the Cutter, 277 Setting the Machine, 282 The Shape of the Tooth, 278 Tooth Elements, 280 Cam Milling Attachment, 30-383 Cams, Spiral Milling, 345 Care, Erection and Adjustment of Milling Machines (see Adjust- ment), 41 Change Gears, for Cutting Spirals, 332 Application of Continued Fractions to, 334 Change Gear Ratio, 332 Leads, Change Gears and Angles, 311 Leads, Change Gears and Angles for Cutting Spiral End Mills, 170 Leads, Change Gears and Angles for Cutting Spiral Milling Cut- ters, 170 Leads, Change Gears and Angles for Cutting Twist Drills, 337 Leads, Table of, 340 to 344 Placing Change Gears on the Ma- chine, 336 Chattering, Causes of, 87 404 Index Chattering, Remedies for, 89 Chip, Influence of Size of, on Life of Cutter, 124 Chips from High Speed Milling, 134 Chordal Pitch, 248 Circular Milling Attachment, 29 Circular Pitch, 248-260 Clamping Devices for Fixtures, 210 to 216 Classification of Milling Machines, 7 Clearance for Cutters, 176 Column and Knee Construction, 13 Continued Fractions, 319-320 Angular Indexing Tables, 329 Application to Angular Indexing, 319 Application to Computinp; Change Gears for Cutting Spirals, 326- 334 Application to Gearing a Lathe for Metric Threads, 326 Greatest Common Divisor, 320 Continuous Milling, 192 and 226 Control, CentraKzed, 17 Coolant, Use of, on Cutters (see Stream Lubrication), 126 Cosecants, Table of, 386 to 400 Cosines, Table of, 386 to 400 Cotangents, Table of, 386 to 400 Cut, Relation of Size of, and Feed to Efficiency, 152 Cutter and Work Cooling System (see Stream Lubrication), 126 Cutter Arbors, 84-86 Cutter Sharpening, 172 Cutters, Milling, 140 Action of, 92 Capacity of. When Milling Cast Iron, 184 Capacity of, When Milling Steel, 183 For Cutting Gears, Table of, 252 Eflfe