# Practical Treatise on Milling and Milling Machines/Chapter 8

CHAPTER VIII Milling Operations — Gear Cutting
We do not propose in this chapter to go deeply into the subject of gearing, for it would be impossible to properly treat it in so limited a space. Neither do we intend to describe the manner in which gears are cut on automatic gear cutting machines designed especially for that purpose. Our object is rather to give a few practical points applying to the cutting of different kinds of gears on a milling machine, and to show illustrations of how various gear cutting jobs and work of a kindred nature can be set up. Anyone desirous of making a detailed study of gears is referred to the many books now published that are devoted exclusively to the subject, among which are our "Practical Treatise on Gearing," and " Formulas in Gearing."
Cutting Spur Gears. The first things that are necessary to know in order to cut a spur gear, are the pitch, either diametral or circular, and number of teeth required. These must be had in order to select the correct cutter to use.
We make eight cutters for each pitch, as follows:
| No. 1 | cutter | will | cut | wheels | from | 135 | teeth | to | a | rack |
| No. 2 | " | " | " | " | " | 55 | " | " | 134 | teeth |
| No. 3 | " | " | " | " | " | 35 | " | " | 54 | " |
| No. 4 | " | " | " | " | " | 26 | " | " | 34 | " |
| No. 5 | " | " | " | " | " | 21 | " | " | 25 | " |
| No. 6 | " | " | " | " | " | 17 | " | " | 20 | " |
| No. 7 | " | " | " | " | " | 14 | " | " | 16 | " |
| No. 8 | " | " | " | " | with | 12 | " | and | 13 | " |
For those who require a finer division of the number of teeth to be cut with each cutter than can be cut with the regular numbers listed above, we can furnish half numbers in cutters from 2 to 8 pitch inclusive, as follows:
| No. 1 1/2 | cutter | will | cut | wheels | from | 80 | teeth | to | 134 | teeth |
| No. 2 1/2 | " | " | " | " | " | 42 | " | " | 54 | " |
| No. 3 1/2 | " | " | " | " | " | 30 | " | " | 34 | " |
| No. 4 1/2 | " | " | " | " | " | 23 | " | " | 35 | " |
| No. 5 1/2 | " | " | " | " | with | 19 | " | and | 20 | " |
| No. 6 1/2 | " | " | " | " | " | 15 | " | " | 16 | " |
| No. 7 1/2 | " | " | " | " | " | 13 | " | | | |
Care should be exercised that the teeth of a cutter selected are ground radially and equidistant, for the teeth are so formed that unless ground in this manner, the correct shape is not produced in the work.
If a universal milling machine is employed, the table should be set at exact right angles to the arbor by the graduations on the saddle. This precaution does not have to be taken on plain machines, as the table is fixed at right angles to the spindle or arbor.
Set Cutter Central. It is essential that the cutter be exactly central with the axis of the gear blank, especially when the gear is to be run fast, otherwise the gear will be cut "off centre," and will run more noisily in one direction than in the other. It may be set centrally as follows: Set the table or the cutter on the arbor as nearly as possible in position ; fasten the gear blank, or preferably an odd blank of about the size of the gear to be cut, on an arbor and lock it in position on the centres. Take a single cut, then remove the blank from the arbor, turn it end for end and put it back on. Permit the blank to remain loose on the arbor, and see if the cutter will pass through the groove already cut without taking any stock off on either side. If the cutter is not exactly central, stock will be cut from the upper part of one side of the groove and from the lower part of the opposite side of the groove. If this is found to be the case, the table can be slightly adjusted to compensate for the error and another trial cut taken.
Some of the gear cutters made by us have a line on the tops of the teeth that is central with the form, and for ordinary slow running gears, the cutter may be centred by bringing this line to coincide with the centre in the spiral head or foot-stock.
Measure Blanks. Measure all gear blanks carefully. It is impossible to cut correct running gears from blanks that are of the wrong diameter unless the error is small. The amount of error allowable in the diameter depends upon the pitch of the gear; the heavier the pitch, the greater the allowable error. It is better to return to the lathe any blanks that are oversize and throw away those that are turned very much undersize. If blanks are only slightly undersize, they can be cut by making allowance for the error in setting for depth of teeth, and the resultant gears will run satisfactorily, though not perfectly.
Secure Blank on Arbor. The next important step is to see that the work arbor runs true and that the blank does not spring it when ​forced or tightened. A good method of holding blanks is on arbors, such as our milling machine cutter arbors, that have a taper shank to fit the index spindle; the outer end of the arbor being supported by the foot-stock centre. Another way of holding blanks is by means of a shank arbor with expanding bushing, such as our gear cutting machine "work arbors." A nut is located on the arbor at each end of the bushing, one nut forcing the bushing up on the arbor and holding the blank, while the other pushes the bushing off the taper and releases the gear when finished.
If a common arbor and dog are used, care should be taken that the tail of the dog is fastened between the set screws provided on the spiral head, so there will be no backlash between the index spindle and work; also see that the dog does not spring the arbor when it is clamped.
Set Knee for Depth of Cut. The depth of cut is regulated by the height of the knee of the machine. To make this setting, the knee is brought up until the cutter just touches the blank. Then the blank is moved out from under the cutter and the knee is raised the number of thousandths of an inch required for the depth of tooth, which can be ascertained from the tables on pages 321 to 324, or by dividing the constant 2.157 by the diametral pitch.
When raising the knee, use the graduated dial on the vertical hand feed screw for a guide to get the required depth, but be sure to take out any backlash that may exist before making an adjustment.
Testing for Correct Depth. To make certain that the depth of groove cut is correct and the size of teeth accurate, cut two grooves into the face of the blank far enough so that the full form of the tooth is produced, and then measure the resultant tooth at the pitch line for thickness and the depth of the tooth to the pitch line. The correct thicknesses of spur gear teeth of different pitches at the pitch line are given in the tables on pages 321 to 324, or can be found by dividing the constant 1.57 by the diametral pitch.
By cutting only part way across the face of the blank the trial grooves can be quickly made and measured. If, on the other hand, the grooves are cut across the full width of the face, there is liability, under some conditions, of more stock being taken from these grooves when the actual cutting is commenced and the cutter is allowed to pass through the same grooves a second time, thus making these grooves too deep.
Chordal Thickness of Gear Teeth. When accurate measurements of gear teeth are required, it is necessary to work to the chordal ​ Fig. 61 figures, t" = thickness of tooth and s" = distance from chord t" to top of tooth (See Fig. 61).
These dimensions vary from the standard dimensions of tooth parts shown on pages 321 to 324. The fewer the number of teeth in the gear, the greater the variation.
The Table of Chordal Thickness t" and Distances from Chord to top of Tooth s" on page 325 gives these dimensions for gears of 1 diametral pitch. To obtain t" and s" for any diametral pitch, divide the figures given in the table opposite the required number of teeth, by the required diametral pitch.
Example: Find t" and s" for a gear 5 diametral pitch, 23 teeth.
1.5696 ÷ 5 = .3139 = t".
1.0268 ÷ 5 = .2054 = s".
To obtain t" and s" for any circular pitch, multiply the figures given in the table opposite the required number of teeth, by the addendum s (taking 5 from the Table of Tooth Parts, pages 321 and 322).
Example: Find t" and s" for a 3/4" circular pitch gear, 15 teeth.
Fig. 62 1.5679 X .2387 = .3743 = t". 1.0411 X .2387 = .2485 = s".
If number of teeth required is not shown in table, take the nearest number of teeth.
An accurate and convenient tool for taking the measurements of gear teeth is shown in Fig. 62. With this gear tooth vernier, the distance from the top of the teeth to the pitch line, and thickness at the pitch line, can be accurately determined. ​Another tool, Vernier Caliper, No. 573, by use of which the bottom diameter of the teeth may be accurately measured to determine the depth of grooves, is shown in Fig. 63.
The depth of grooves may be ascertained when there are an even number of teeth by cutting two grooves opposite each other on the circumference of the blank and calipering the diameter from the bottom of the grooves, then computing the depth. When the number of teeth is uneven cut one groove and caliper the diameter from the bottom of the groove to the opposite side of the blank. In this last case be sure that the blank is of the correct diameter and runs true, otherwise the measurement will not be correct, unless allowance is made for these points.
Indexing. Indexing gear blanks is essentially the same as indexing any other work, and the instructions in Chapter IV are complete on this subject; therefore it is unnecessary to make any additional remarks here upon this point.
Fig. 63
Cutting Two or More Gears Simultaneously. If the holes in the blanks are straight, and the hubs do not project beyond the face, a number of blanks may be fastened together on a gang arbor and several gears cut at a time. Care should be taken, however, if this is done, to see that the sides of the blanks are exactly parallel, otherwise when the arbor nut is clamped, the blanks will spring the arbor, causing it to run out and making it impossible to produce accurate gears.
Cutting Bevel Gears. The teeth of bevel gears constantly change in pitch from their large to small end, and for this reason it is impossible to cut gears whose tooth curves are theoretically correct, with rotary cutters having fixed curves, such as those used for cutting these gears on a milling machine. The cutter employed must be of a curve that will make the correct form at the large end of the tooth, hence it will necessarily leave the curve too straight at the small end. It is, therefore, the practice to cut the teeth as nearly correct as possible, ​ Fig. 64 and then finish the gears by hand, filing the small ends of the teeth to get the correct curve.
Pitch of Bevel Gear. The pitch of a bevel gear is always considered as that at the largest end of the teeth.
Data Required to Cut Bevel Gears with Rotary Cutter. Pitch and number of teeth in each gear.
The whole depth of tooth spaces at both large and small ends of teeth.
The thickness of teeth at both ends.
The height of teeth above the pitch line at both ends.
The cutting angle; the angle to set spiral head on milling machine, and the proper cutter or cutters.
Scratch Depth Line on Blank. Before placing the blank on machine, measure the length of face, angles and outside diameter of blank, and, if all dimensions are correct, place the blank on the arbor and fasten it securely in place ; then scratch the whole depth of space at large end with a depth of gear tooth gauge similar to that shown in Fig. 64.
Selection of Cutter for Bevel Gears. The length of teeth or face on bevel gears is not ordinarily more than one-third the apex distance, Ab, Fig. 65, and cutters usually carried in stock are suitable for this face. If the face is longer than one-third the apex distance, special thin cutters must be made.
Fig. 65 Rule for Selecting Cutter. Measure the back cone radius a b for the gear, or b c for the pinion. This is equal to the radius of a spur gear, the number of teeth in which would determine the cutter to use. Hence twice a b times the diametral pitch equals the number of teeth for which the cutter should be selected for the gear. Looking in the list given on page 149, the proper number for the cutter can be found.
Thus, let the back cone radius a b be 4" and the diametral pitch be 8. ​Twice four is 8, and 8 x 8 is 64, from which it can be seen that the cutter must be of Shape No. 2, as 64 is between 55 and 134, the range covered by a No. 2 cutter.
The number of teeth for which the cutter should be selected can also be found by the following formula:
$\tan \propto ={\frac {Na}{Nb}}$
No. of teeth to select cutter for gear $={\frac {Na}{\cos \propto }}$
No. of teeth to select cutter for pinion $={\frac {Nb}{\sin \propto }}$
If the gears are mitres or are alike, only one cutter is needed; if one gear is larger than the other, two may be needed.
Setting Cutter out of Centre. As the cutter cannot be any thicker than the width of space at small end of teeth, it is necessary to set it out of centre and rotate the blank to make the spaces of the right width at the large end of the teeth.
The amount to set cutter out of centre can be calculated with the table on page 326 and the following formula:
Set-over = Tc/2 - factor from table/P
P = diametral pitch of gear to be cut.
Tc = thickness of cutter used, measured at pitch line.
Given as a rule, this would read: Find the factor in the table corresponding to the number of the cutter used and to the ratio of apex distance to width of face; divide this factor by the diametral pitch and subtract the quotient from half of the thickness of the cutter at the pitch line.
As an illustration of the use of this table in obtaining the set-over, take the following example: A bevel gear of 24 teeth, 6 pitch, 30 degrees pitch cone angle and 1 1/4" face. These dimensions call for a No. 4 cutter and an apex distance of 4 inches.
In order to get the factor from the table, the ratio of apex distance with length of face must be known. This ratio is 4/1.25 = 3.2/1, or about 3 1/4/1. The factor in the table for this ratio with a No. 4 cutter is 0.280. Next, measure the cutter at the pitch line. To do this, refer to the regular "Table of Tooth Parts" on pages 323 and 324, and get the depth of space below pitch line s + f. This depth of space below pitch line can also be found by dividing 1.157 by the diametral ​pitch. In the case of 6 pitch s + f = 0.1928 inch. The thickness of the cutter at the pitch line is then found to be 0.1745 inch. This dimension will vary with different cutters, and will vary in the same cutter as it is ground away, since formed bevel gear cutters are commonly provided with side relief. Substituting these values in the formula, the following result is obtained:
Set-over = 0.1745/2 - 0.280/6 = 0.0406 inch, which is the required dimension.
After selecting a cutter and determining how much to set it out of centre, proceed as follows:
Set the cutter central with the spiral head or universal index head spindle, as the machine may be equipped.
Set the head to the proper cutting angle.
Set the index head for the number of teeth to be cut, placing the sector on the straight row of holes that are numbered to start with.
Set the dial on the cross feed screw to the zero line.
Scratch the depth of both the large and small end of the tooth to be cut in the blank.
Index and cut two or three grooves or centre cuts to conform to the lines in depth.
Set the cutter out of centre the trial distance, according to the formula on the previous page, by moving the saddle and noting adjustment on the cross feed screw dial.
Rotate the gear in the opposite direction from that in which the table is moved off centre (Fig. 66), until the side of the cutter nearest the centre line of the gear will cut the entire surfaces of the approaching sides of the teeth.
After making one or more cuts in accordance with this setting, move the table the same distance on the opposite side of the centre and rotate the gear in the opposite direction from that in which the table is moved until the cutter just touches the side of a tooth at the small end and cuts the entire surface of this side the same as the other.
Cut one or more spaces and measure the teeth at both large and small ends, either with a gear tooth vernier or with gauges made from thin pieces of metal and having a slot cut to give the correct depth and width at the pitch line.
Fig. 66
The adjustment of the cutter and the rotating of the blank are shown in Fig. 66, which shows the setting, so that the right side of cutter will trim the left side of tooth and widen the large end of the space. The table has been moved to the right and the blank brought to the position shown, by rotating it in the direction of the arrow; the first out of centre cut was taken when the cutter was set on the other side of the centre.
After determining the proper amount to set cutter out of centre, the teeth can be finished, without making a central cut, by cutting round the blank with the cutter set out of centre, first on one side and then on the other.
To prevent the teeth being too thin at either end, it is important, after cutting once around the blank with cutter out of centre, to give careful attention to the rotative adjustment of the gear blank, when setting the cutter for trimming the opposite sides of the teeth. If by measurement, both ends are a little too thick, but proportionately right, rotate the gear blank and make trial cuts until one tooth is of the correct thickness at both ends. The cutting can then be continued until the gear is finished. Teeth of incorrect thickness may be more objectionable than a slight variation in depth.
The finished spaces, or teeth, as already mentioned, are of the correct form at the larger ends, and the teeth are of the correct thickness their entire length, but the tops of the teeth at the small ends are not rounded over enough. It is, therefore, generally necessary to file the faces of the teeth slightly above the pitch line at the small ends, as indicated by the dotted lines F F, Fig. 67. In filing the teeth, they should not be reduced any in thickness at or below the pitch line.
When cutting cast iron gears coarser than five diametral pitch, it is best to make one central cut entirely around the blank before attempting to find the correct setting of the cutter or rotation of the blank for correct thickness of teeth; and it is generally advantageous to take a central cut on nearly all bevel gears of steel. ​Cutting Spiral Gears. In Chapter IV, we have gone into the subject of cutting spirals thoroughly, and, inasmuch as spiral gears are essentially cylinders having a succession of spiral grooves evenly spaced on their periphery, many of the points we have treated apply equally well to cutting them.
An important point in cutting these gears is the selection of the proper cutters to use. It is impossible to give in concise form any set of rules for doing this that will be readily understood, and anyone who desires to cut spiral gears, should make a far more complete study of the subject of spiral gearing than we can possibly give in this book. It is treated upon in our "Practical Treatise on Gearing," and "Formulas in Gearing," both of which books are extremely useful to the practical workman.
One point that it is well to remember is that in calculating spirals, the angle should be figured as that at the pitch line of the teeth, and not that on the surface or periphery of a gear.
Spirals of any angle to 45 ° can be cut on all of our universal milling machines with the cutter mounted in the regular way, and the swivel table swung to the proper angle, while those of an angle up to 55° with the axis, can be cut in some of our universal machines. If, however, the required angle is greater than that to which the table can be set, a vertical spindle milling attachment is required, and the adjustment for the cutting angle is then done with the attachment.
Fig. 68
To Set Cutter Central. It is essential that the cutter be set central with the work centres, and it may be done as follows: First, set the table, or attachment, in case the latter is used, to the correct cutting angle. Take a trial piece, Fig. 68, which is simply a cylindrical piece with centre holes in the ends, and mount it on the work centres, dogging it to the spiral head spindle. Draw, or scratch the line B C on the side of the arbor at the exact height of the work centres, and then revolve the arbor one-quarter of a turn by means of the index crank; that is, bring the mark B C exactly on the top of the piece. Now, start the machine and raise the knee until a gash is cut on the top of the piece. This gash shows the position of the cutter,' and if a and ​b are equal, the cutter is centred with the trial piece, which will, of course, bring it central with the work.
The same method is employed when using a vertical spindle milling attachment, except the scratched line is left at the side of the piece where it is at the exact height of the centres. The gash is then cut and examined as described above.
Test Settings and Index Gears. Before cutting a blank, it is well to raise the knee until the cutter will just make a slight trace on the work to see if the lead obtained by the change gears is correct. If the material in the gear blank is expensive, it is sometimes advisable to make a cast iron blank to experiment with before cutting into the expensive material.
Fastening Blanks. Spiral gears are more liable to slip in cutting than spur gears. Small blanks may be dogged to the spindle, but the dog must be far enough from the blank so that it will not interfere with the cutter. For blanks that are more than three or four inches in diameter, it is better to use a taper shank arbor held directly in the spindle; and for still heavier work, the arbor may be drawn into the spindle with a threaded rod.
Cutting Teeth. In cutting the teeth, either the cutter should be stopped after cutting each groove and positioned so that the teeth will not scrape the sides and bottom of the groove, the table being returned by hand; or the knee should be dropped so that cutter will clear the groove just cut, and then run the table back to the starting point. Most mechanics prefer to stop the machine, for in dropping the knee, there is more liability of error, as the depth of cut has to be set for each groove, and this also takes more time than it does to stop the machine.
Cutting a Spur Gear, Using the Spiral Head
Cutting a spur gear on a milling machine is a comparatively simple operation, as can be seen from the illustration. No special rigging whatsoever is required. The blank in this case is fastened on an ordinary lathe arbor mounted on the centres and dogged to the spiral head spindle.
Cutting a Large Spur Gear, Using Gear Gutting Attachment
This operation shows the use of the gear cutting attachment described in Chapter V. The gear being cut is too large to be accommodated by the spiral head centres without using raising blocks, and then the results are not as satisfactory as can be gained by using this attachment.
Gashing Teeth in Worm Wheel
Finishing a worm wheel on a milling machine requires two separate operations. First, the operation of gashing the teeth, shown above, is performed; and then the teeth are hobbed, as shown in the illustration on page 164.
Hobbing Teeth in Worm Wheel
The work is set up practically the same as in the operation of gashing the teeth, only the dog on the arbor is removed and the swivel table is set at zero. The worm wheel revolves freely on the centres, being rotated by the hob.
The wheel can be hobbed to the right depth by using a steel rule at the back of the knee to measure a distance equal to the centre distance of the worm and wheel from a line marked "Centre," on the vertical slide to the top of the knee. This line on the vertical slide indicates the position of the top of the knee when the index centres are at the same height as the centre of the machine spindle.
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Cutting Teeth in Bevel Gear
The illustration on this page shows a milling machine set up for cutting the teeth of a bevel gear.
The gear is held in place by a split bushing that is expanded in the hole. The spiral head is elevated to the proper cutting angle and the table is fed longitudinally from left to right.
Cutting Teeth in Spiral Gear
The machine is shown, in the illustration above, set in position to cut a left-hand spiral gear of 45° angle.
The gear is mounted in the same manner as in several previous operations, but instead of remaining stationary as the table advances, it is rotated by means of the required change gears to give the correct lead to the teeth. The table is fed longitudinally from left to right.
A right-hand spiral gear of the same angle may be cut in the same manner by setting the table to 45° the other side of zero and leaving put the intermediate or reverse gear.
Cutting Spiral Teeth in Milling Cutter
This operation shows the arrangement for cutting teeth in a right-hand spiral milling cutter.
The work is 6 inches long and 3 inches in diameter, and an angular cutter 3 inches in diameter is employed. An angle of 11 1/4° is desired, and the saddle is accordingly set to that angle and the head is geared to give a lead of 48".
The work is mounted on an arbor that is dogged to the spiral head spindle, and care is taken that there is no lost motion between the spindle and work.
Gashing a Hob
While this is not strictly a gear cutting operation, it is set up and performed in practically the same manner, the principal difference being in the shape of cutter used. Many hobs are gashed spirally, and this is done in a similar way to cutting the teeth in a spiral gear. In this operation, the cut is heavy and it is advisable to use arm braces, so that a coarser feed can be employed and the work done more quickly.
The table is fed longitudinally from left to right. Oil is used on the cutter and is collected and strained in the pan below the work. An oil pump equipment can be used to good advantage on such jobs.
Cutting Teeth in Spiral Gear, Using Compound Vertical Spindle Milling Attachment
This operation shows the use of a compound vertical spindle milling attachment in cutting a spiral gear.
It will be noticed that where this attachment is used, the swivel table is set at zero and the angle of the spiral obtained by swinging the head of the attachment. The cutting is also done on the side, instead of the top of the gear.
In cutting left-hand spirals, the cutter would be at the back of the blank, the head of the attachment swung to the other side of zero, and an intermediate gear would be introduced in the train to reverse the direction of rotation.
Cutting a Short Lead Spiral Gear, Using a Vertical Spindle Milling Attachment
When the table cannot be swung to the required angle, a vertical spindle attachment may be used. The attachment is swung 90° up from zero, and the required angle of the spiral is then obtained by the swivel table.
Where the lead is as short as that above, it is better to employ the special attachment shown in Chapter V, for the ratio of gearing of the spiral head is such that severe stresses are brought to bear upon it in feeding the work. If, however, the job is set up as above, it is necessary to feed the work by hand.
Milling Rack Teeth in Cylindrical Shaft
Sometimes it is required to mill a few rack teeth in a cylindrical shaft or plunger, and where a rack cutting attachment is at hand, this can be readily done. If one is not convenient, however, the work can be done in the manner shown above.
The shaft is supported on a parallel and clamped in a vise, and the teeth are indexed by means of the graduated dial on the cross feed screw.
Before indexing, care should be taken to remove backlash from the screw.
Cutting Teeth in Rack, Using Rack Cutting and Indexing Attachments
The method of cutting a steel rack, using the rack cutting and indexing attachments described in Chapter V, is clearly shown in this illustration.
The rack is fastened in the vise of the attachment, and the teeth are indexed by the indexing attachment.
The automatic transverse table feed is used and the direction of cut is from the back of the rack toward the front, that is, against the direction in which the cutter rotates. Oil is used as a lubricant.
Cutting a Worm Thread, Using Rack Cutting Attachment
Another use of the rack cutting attachment on a universal milling machine is illustrated in this operation. It is especially serviceable for cutting short lead spiral gears, when the angle is such that they cannot be cut on the milling machine in the usual way. An advantage of the rack cutting attachment over the vertical spindle milling attachment for this purpose is that the work of smaller diameter can be accomodated, or a smaller cutter can be used.
Cutting Blade Grooves in Bodies of Inserted Tooth Cutters
Nine of these steel cutter bodies are placed together on an arbor and clamped solidly by a nut at the end. The arbor is then driven into the spiral head spindle and the foot-stock is put in place. To give the proper rake to the front of the blades, the saddle is set so that the cutter does not come directly over the spiral head and foot-stock centres. As the number of grooves cut is 20, indexing can be conveniently accomplished with any index plate.
Sections of Milling Machine Departments in Our Works,
Constant Speed Drive Plain Milling Machine