Turning and Boring on a Lathe Chapter 4

Turning and Boring on a Lathe
Online Reprint Chapter 4

This a complete book, published in 1914, divided into chapters on how to use a metal lathe, covering all turning and boring operations.

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Turning and Boring

by Franklin D. Jones

Published by Industrial Press 1914

A special treatise for machinists students in industrial and engineering schools, and apprentices on turning and boring methods including modern practice with engine lathes, vertical, and horizontal boring machines.

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CHAPTER IV

THREAD CUTTING IN THE LATHE

When threads are cut in the lathe a tool t is used (see Fig. 2), having a point corresponding to the shape of the thread, and the carriage is moved along the bed a certain distance for each revolution of the work (the distance depending on the number of threads to the inch being cut) by the lead-screw S which is rotated by gears a, b and c, which receive their motion from the spindle. As the amount that the carriage travels per revolution of the work, and, consequently, the number of threads per inch that is cut, depends on the size of the gears a and c (called change gears) the latter have to be changed for cutting different threads. The proper change gears to use for cutting a given number of threads to the inch is ordinarily determined by referring to a table or “index plate” I which shows what the size of gears a and c should be, or the number of teeth each should have, for cutting any given number of threads per inch.

Selecting the Change Gears for Thread Cutting.—Suppose a V-thread is to be cut on the end of the bolt B, Fig. 2, having a diameter of 1¹/₄ inch and seven threads per inch of length, as shown at A in Fig. 1, which is the standard number of threads per inch for that diameter. First the change gears to use are found on plate I which is shown enlarged in Fig. 3. This plate has three columns: The first contains different numbers of threads to the inch, the second the size gear to place on the “spindle” or “stud” at a (Fig. 2) for different threads, and the third the size of gear c for the lead-screw. As the thread selected as an example has 7 threads per inch, gear a should have 48 teeth, this being the number given in the second column opposite figure 7 in the first. By referring to the last column, we find that the lead-screw gear should have 84 teeth. These gears are selected from an assortment provided with the lathe and they are placed on the spindle and lead-screw, respectively.

Intermediate gear b does not need to be changed as it is simply an “idler” for connecting gears a and c. Gear b is mounted on a swinging yoke Y so that it can be adjusted to mesh properly with different gear combinations; after this adjustment is made, the lathe is geared for cutting 7 threads to the inch. (The change gears of many modern lathes are so arranged that different combinations are obtained by simply shifting a lever. A lathe having this quick-change gear mechanism is described in the latter part of this chapter.) The work B is placed between the centers just as it would be for turning, with the end to be threaded turned to a diameter of 1¹/₄ inch, which is the outside diameter of the thread.

The Thread Tool.—The form of tool used for cutting a V-thread is shown at A, Fig. 4. The end is ground V-shaped and to an angle of 60 degrees, which corresponds to the angle of a standard V-thread. The front or flank, f of the tool is ground back at an angle to provide clearance, but the top is left flat or without slope. As it is very important to grind the end to exactly 60 degrees, a gage G is used, having 60-degree notches to which the tool-point is fitted. The tool is clamped in the toolpost as shown in the plan view, Fig. 2, square with the work, so that both sides of the thread will be cut to the same angle with the axis of the work. A very convenient way to set a thread tool square is illustrated at B, Fig. 1. The thread gage is placed against the part to be threaded, as shown, and the tool is adjusted until the angular sides of the point bear evenly in the 60-degree notch of the gage. The top of the tool point should be at the same height as the lathe centers, as otherwise the angle of the thread will not be correct.

Cutting the Thread.—The lathe is now ready for cutting the thread. This is done by taking several cuts, as indicated at A, B, C and D in Fig. 5, the tool being fed in a little farther for each successive cut until the thread is finished. When these cuts are being taken, the carriage is moved along the bed, as previously explained, by the lead-screw S, Fig. 2. The carriage is engaged with the lead-screw by turning lever u which causes the halves of a split nut to close around the screw. The way a lathe is handled when cutting a thread is as follows: After the lathe is started, the carriage is moved until the tool-point is slightly beyond the right end of the work, and the tool is fed in far enough to take the first cut which, ordinarily, would be about ¹/₁₆ inch deep. The carriage is then engaged with the lead-screw, by operating lever u, and the tool moves to the left (in this case ¹/₇ inch for each revolution of the work) and cuts a winding groove as at A, Fig. 5. When the tool has traveled as far as the thread is wanted, it is withdrawn by a quick turn of cross-slide handle e, and the carriage is returned to the starting point for another cut. The tool is then fed in a little farther and a second cut is taken as at B, Fig. 5, and this operation is repeated as at C and D until a “full” thread is cut or until the top of the thread is sharp. The thread is then tested for size but before referring to this part of the work, the way the carriage is returned to the starting point after each cut should be explained.

When the tool is withdrawn at the end of the first cut, if the carriage is disengaged from the lead-screw and returned by hand, the tool may or may not follow the first cut when the carriage is again engaged with the lead-screw. If the number of threads to the inch being cut is a multiple of the number on the lead-screw S, then the carriage can be returned by hand and engaged with the lead-screw at random and the tool will follow the first cut. For example, if the lead-screw has six threads per inch, and 6, 12, 18 or any number of threads is being cut that is a multiple of six, the carriage can be engaged at any time and the tool will always follow the original cut. This is not the case, however, when the number of threads being cut is not a multiple of the number on the lead-screw.

One method of bringing the carriage back to the starting point, when cutting threads which are not multiples, is to reverse the lathe (by shifting the overhead driving belts) in order to bring the tool back to the starting point without disengaging the carriage; in this way the tool is kept in the same relation to the work, and the carriage is not disengaged from the lead-screw until the thread is finished. This is a good method when cutting short threads having a length of say two or three inches; but when they are longer, and especially when the diameter is comparatively large (which means a slower speed), it is rather slow as considerable time is wasted while the tool is moving back to its starting point. This is due to the fact that the carriage is moved slowly by the lead-screw, but when disengaged, it can be traversed quickly by turning handle d, Fig. 2.

A method of returning the carriage by hand when the number of threads being cut is not a multiple of the number on the lead-screw is as follows: The tool is moved a little beyond the right end of the work and the carriage or split nut is engaged with the lead-screw. The lathe is then turned forward by hand to take up any lost motion, and a line is made on the lathe bed showing the position of the carriage. The positions of the spindle and lead-screw are also marked by chalking a tooth on both the spindle and lead-screw gears, which happens to be opposite a corner or other point on the bed. After a cut is taken, the carriage is returned by hand to the original starting point as shown by the line on the bed, and is again engaged when the chalk marks show that the spindle and lead-screw are in their original position; the tool will then follow the first cut. If the body of the tailstock is moved against the bridge of the carriage before starting the first cut, the carriage can be located for each following cut by moving it back against the tailstock, and it will not be necessary to have a line on the bed.

Indicator or Chasing Dial for Catching Threads.—On some lathes there is an indicator for “catching threads,” as this is called in shop language. This is a simple device attached to the carriage and consists of a graduated dial D and a worm-wheel W (see Figs. 2 and 6) which meshes with the lead-screw, so that the dial is revolved by the lead-screw when the carriage is stationary, and when the carriage is moved by the screw, the dial remains stationary. The indicator is used by engaging the carriage when one of the graduation lines is opposite the arrow mark; after a cut is taken the carriage is returned by hand and when one of the graduation lines again moves opposite the arrow, the half-nuts are thrown into mesh, as before, and this is repeated for each successive cut, thus causing the tool to always come right with the thread. If the number of threads per inch is even, engagement can be made when any line is opposite the arrow, but for odd numbers such as 3, 7, 9, 11, etc., one of the four long or numbered lines must be used. Of course, if the thread being cut is a multiple of the number on the lead-screw, engagement can be made at any time, as previously mentioned.

Principle of the Thread Indicator.—The principle upon which the thread indicator operates is as follows: The number of teeth in worm-wheel W is some multiple of the number of threads per inch of the lead-screw, and the number of teeth in the worm-wheel, divided by the pitch of the screw, equals the number of graduations on the dial. For example, if the lead-screw has six threads per inch, the worm-wheel could have twenty-four teeth, in which case the dial would have four divisions, each representing an inch of carriage travel, and by sub-dividing the dial into eighths (as shown) each line would correspond to ¹/₂ inch of travel. The dial, therefore, would enable the carriage to be engaged with the lead-screw at points equal to a travel of one-half inch. To illustrate the advantage of this suppose ten threads per inch are being cut and (with the lathe stationary) the carriage is disengaged and moved ¹/₆ inch or one thread on the lead-screw; the tool point will also have moved ¹/₆ inch, but it will not be opposite the next thread groove in the work as the pitch is ¹/₁₀ inch. If the carriage is moved another thread on the lead-screw, or ²/₆ inch, the tool will still be out of line with the thread on the work, but when it has moved three threads, or ¹/₂ inch, the tool will then coincide with the original cut because it has passed over exactly five threads. This would be true for any number of threads per inch that is divisible by 2. If the thread being cut had nine threads per inch or any other odd number, the tool would only coincide with the thread at points 1 inch apart. Therefore, the carriage can only be engaged when one of the four graduations representing an inch of travel is opposite the arrow, when cutting odd threads; whereas even numbers can be “caught” by using any one of the eight lines.

This indicator can also be used for “catching” fractional threads. As an illustration, suppose 11¹/₂ threads per inch are to be cut, and the carriage is engaged for the first cut when graduation line 1 is opposite the arrow; engagement would then be made for each successive cut, when either line 1 or 3 were opposite the arrow, or in other words at spaces equal to a carriage movement of 2 inches. As the use of the indicator when cutting fractional threads is liable to result in error, it is better to keep the half-nuts in engagement and return the carriage by reversing the lathe.

Replacing Sharpened Thread Tool.—If it is necessary to sharpen the thread tool before the thread is finished, it should be reset square with the work by testing with the thread gage as at B, Fig. 1. The carriage is then engaged with the lead-screw and the lathe is turned forward to bring the tool opposite the partly finished thread and also to take up any backlash or lost motion in the gears or half-nut. If the tool-point is not in line with the thread groove previously cut, it can be shifted sidewise by feeding the compound rest E in or out, provided the latter is set in an angular position as shown in the plan view, Fig. 2.

If the thread tool is ground flat on the top as at A, Fig. 4, it is not a good tool for removing metal rapidly as neither of its two cutting edges has any slope. In order to give each cutting edge a backward slope, it would be necessary to grind the top surface hollow or concave, which would be impracticable. When a course thread is to be cut, a tool shaped as at B can be used to advantage for rough turning the thread groove, which is afterward finished to the correct depth and angle by tool A. This roughing tool is ground with a backward slope from the point and the latter is rounded to make it stronger.

Use of Compound Rest for Thread Cutting.—Another form of thread tool is shown at A, Fig. 7, which is very good for cutting V-threads especially of coarse pitch. When this tool is used, the compound rest E is set to an angle of 30 degrees, as shown, and it is fed in for the successive cuts by handle w in the direction indicated by the arrow. It will be seen that the point a of the tool moves at an angle of 60 degrees with the axis of the work, thus forming one side of the thread, and the cutting edge a—b, which can be set as shown at B, forms the opposite side and does all the cutting. As this edge is given a backward slope, as shown, it cuts easily and enables threading operations to be performed quickly. Threads cut in this way are often finished by taking a light cut with a regular thread tool. The cutting edge a—b is ground to an angle of 60 degrees (or slightly less, if anything) with the side, as shown by sketch A.

When cutting threads in steel or wrought iron, some sort of lubricant is usually applied to the tool to preserve the cutting end and give a smooth finish to the thread. Lard oil or a mixture of equal parts of lard oil and paraffin oil are often used for this purpose. If the thread is small, the lubricant may be applied from an ordinary oil can, but when cutting comparatively large threads, it is better to have a stream of oil constantly playing upon the tool-point. This constant flow may be obtained by mounting a can having a spout leading to the tool, on a bracket at the rear of the carriage.

Threads Commonly Used.—Three forms of threads or screws which are in common use are shown in Fig. 8; these are the V-thread (A), the U. S. standard (B), and the square thread (C). The shapes of these threads are shown by the sectioned parts. The V-thread has straight sides which incline at an angle of 60 degrees with each other and at the same angle with the axis of the screw. The U. S. standard thread is similar to the V-thread except that the top of the thread and bottom of the groove is left flat, as shown, and the width of these flats is made equal to ¹/₈ of the pitch. The square thread is square in section, the width a, depth b and space c being all equal. All of these threads are right-hand, which means that the grooves wind around to the right so that a nut will have to be turned toward the right to enter it on the thread. A left-hand thread winds in the other direction, as shown at D, and a nut is screwed on by turning it to the left.

Multiple Threads.—Threads, in addition to being right-and left-handed, are single, as at A, B, C and D, double, as at E, and triple, as at F, and for certain purposes quadruple threads or those of a higher multiple are employed. A double thread is different from a single thread in that it has two grooves, starting diametrically opposite, whereas a triple thread has three grooves cut as shown at F. The object of these multiple threads is to obtain an increase in lead without weakening the screw. For example, the threads shown at C and E have the same pitch p but the lead l of the double-threaded screw is twice that of the one with a single thread so that a nut would advance twice as far in one revolution, which is often a very desirable feature. To obtain the same lead with a single thread, the pitch would have to be double, thus giving a much coarser thread, which would weaken the screw, unless its diameter were increased. (The lead is the distance l that one thread advances in a single turn, or the distance that a nut would advance in one turn, and it should not be confused with the pitch p, which is the distance between the centers of adjacent threads. Obviously the lead and pitch of a single thread are the same.)

Cutting a U. S. Standard Thread.—The method of cutting a U. S. standard thread is the same as described for a V-thread, so far as handling the lathe is concerned. The thread tool must correspond, of course, to the shape of a U. S. standard thread. This tool is first ground to an angle of 60 degrees, as it would be for cutting a V-thread, and then the point is made flat as shown in Fig. 9. As will be recalled, the width of this flat should be equal to ¹/₈ of the pitch. By using a gage like the one shown at G, the tool can easily be ground for any pitch, as the notches around the periphery of the gage are marked for different pitches and the tool-point is fitted into the notch corresponding to the pitch wanted. If such a gage is not available, the width of the flat at the point can be tested by using, as a gage, a U. S. standard tap of the same pitch as the thread to be cut.

When cutting the thread, the tool is set square with the blank, and a number of successive cuts are taken, the tool being fed in until the width w of the flat at the top of the thread is equal to the width at the bottom. The thread will then be the right size provided the outside diameter D is correct and the tool is of the correct form. As it would be difficult to measure the width of this flat accurately, the thread can be tested by screwing a standard nut over it if a standard thread is being cut. If it is being fitted to a tapped hole, the tap itself is a very convenient gage to use, the method being to caliper the tap and then compare its size with the work.

A good method of cutting a U. S. standard thread to a given size is as follows: First turn the outside of the blank accurately to diameter D, and then turn a small part of the end to diameter r of the thread at the root. The finishing cut for the thread is then taken with the tool point set to just graze diameter r. If ordinary calipers were set to diameter r and measurements taken in the thread groove, the size would be incorrect owing to the angularity of the groove, which makes it necessary to hold the calipers at an angle when measuring. To determine the root diameter divide 1.299 by the number of threads per inch and subtract the quotient from the outside diameter. Expressing this rule as a formula,

in which D equals outside diameter; N, the number of threads per inch; and r, the root diameter. The number 1.299 is a constant that is always used.

Cutting a Left-hand Thread.—The only difference between cutting left-hand and right-hand threads in the lathe is in the movement of the tool with relation to the work. When cutting a right-hand thread, the tool moves from right to left, but this movement is reversed for left-hand threads because the thread winds around in the opposite direction. To make the carriage travel from left to right, the lead-screw is rotated backwards by means of reversing gears a and b (Fig. 10) located in the headstock. Either of these gears can be engaged with the spindle gear by changing the position of lever R. When gear a is in engagement, as shown, the drive from the spindle to gear c is through gears a and b, but when lever R is raised thus shifting b into mesh, the drive is direct and the direction of rotation is reversed. The thread is cut by starting the tool at a, Fig. 8, instead of at the end.

Cutting a Square Thread.—The form of tool used for cutting a square thread is shown in Fig. 11. The width w is made equal to one-half the pitch of the thread to be cut and the end E is at an angle with the shank, which corresponds to the inclination x—y of the threads. This angle A depends upon the diameter of the screw and the lead of the thread; it can be determined graphically by drawing a line a—b equal in length to the circumference of the screw to be cut, and a line b—c, at right angles, equal in length to the lead of the thread. The angle α between lines a—b and a—c will be the required angle A. (See end view of thread tool). It is not necessary to have this angle accurate, ordinarily, as it is simply to prevent the tool from binding against the sides of the thread. The end of a square thread tool is shown in section to the right, to illustrate its position with relation to the threads. The sides e and e₁ are ground to slope inward, as shown, to provide additional clearance.

When cutting multiple threads, which, owing to their increased lead, incline considerably with the axis of the screw, the angles for each side of the tool can be determined independently as follows: Draw line a—b equal in length to the circumference of the thread, as before, to obtain the required angle f of the rear or following side e₁; the angle l of the opposite or leading side is found by making a—b equal to the circumference at the root of the thread. The tool illustrated is for cutting right-hand threads; if it were intended for a left-hand thread, the end, of course, would incline in the opposite direction. The square thread is cut so that the depth d is equal to the width. When threading a nut for a square thread screw, it is the usual practice to use a tool having a width slightly greater than one-half the pitch, to provide clearance for the screw, and the width of a tool for threading square-thread taps to be used for tapping nuts is made slightly less than one-half the pitch.

Cutting Multiple Threads.—When a multiple thread is to be cut, such as a double or triple thread, the lathe is geared with reference to the number of single threads to the inch. For example, the lead of the double thread, shown at B, Fig. 12, is one-half inch, or twice the pitch, and the number of single threads to the inch equals 1 ÷ ¹/₂ = 2. Therefore, the lathe is geared for cutting two threads per inch. The first cut is taken just as though a single thread were being cut, leaving the work as shown at A. When this cut is finished the work is turned one-half a revolution (for a double thread) without disturbing the position of the lead-screw or carriage, which brings the tool midway between the grooves of the single thread as indicated by dotted lines. The second groove is then cut, producing a double thread as shown at B. In the case of a triple thread, the work would be indexed one-third of a revolution after turning the first groove, and then another third revolution to locate the tool for cutting the last groove. Similarly, for a quadruple thread, it would be turned one-quarter revolution after cutting each successive groove or thread.

There are different methods of indexing the work when cutting multiple threads, in order to locate the tool in the proper position for cutting another thread groove. Some machinists, when cutting a double thread, simply remove the work from the lathe and turn it one-half a revolution by placing the tail of the driving dog in the opposite slot of the faceplate. This is a very simple method, but if the slots are not directly opposite or 180 degrees apart, the last thread will not be central with the first. Another and better method is to disengage the idler gear from the gear on the stud, turn the spindle and work one-half, or one-third, of a revolution, as the case might be, and then connect the gears. For example, if the stud gear had 96 teeth, the tooth meshing with the idler gear would be marked with chalk, the gears disengaged, and the spindle turned until the chalked tooth had made the required part of a revolution, which could be determined by counting the teeth. When this method is used, the number of teeth in the stud gear must be evenly divisible by two if a double thread is being cut, or by three for a triple thread, etc. If the stud is not geared to the spindle so that each makes the same number of revolutions, the ratio of the gearing must be considered.

Setting Tool When Cutting Multiple Threads.—Another method, which can sometimes be used for setting the tool after cutting the first groove of a multiple thread, is to disengage the lock-nuts from the lead-screw (while the spindle is stationary) and move the carriage back whatever distance is required to locate the tool in the proper position for taking the second cut. Evidently this distance must not only locate the tool in the right place, but be such that the lock-nuts can be re-engaged with the lead-screw. Beginning with a simple illustration, suppose a double thread is being cut having a lead of 1 inch. After the first thread groove is cut, the tool can be set in a central position for taking the second cut, by simply moving the carriage back ¹/₂ inch (one-half the lead), or ¹/₂ inch plus the lead or any multiple of the lead. If the length of the threaded part were 5 inches, the tool would be moved back far enough to clear the end of the work, or say ¹/₂ + 5 = 5¹/₂ inches. In order to disengage the lock-nuts and re-engage them after moving the carriage 5¹/₂ inches (or any distance equal, in this case, to one-half plus a whole number), the lead-screw must have an even number of threads per inch.

Assume that a double thread is being cut having 1¹/₄ single threads per inch. The lead then would equal 1 ÷ 1¹/₄ = 0.8 inch, and if the carriage is moved back 0.8 ÷ 2 = 0.4 inch, the tool will be properly located for the second cut; but the lock-nuts could not be re-engaged unless the lead-screw had ten threads per inch, which is finer than the pitch found on the lead-screws of ordinary engine lathes. However, if the movement were 0.4 + 0.8 × 2 = 2 inches, the lock-nuts could be re-engaged regardless of the number of threads per inch on the lead-screw. The rule then, is as follows:

Divide the lead of the thread by 2 for a double thread, 3 for a triple thread, 4 for a quadruple thread, etc., thus obtaining the pitch; then add the pitch to any multiple of the lead, which will give a movement, in inches, that will enable the lock-nuts to be re-engaged with the lead-screw.

Whenever the number obtained by this rule is a whole number, obviously, the movement can be obtained with a lead-screw of any pitch. If the number is fractional, the number of threads per inch on the lead-screw must be divisible by the denominator of the fraction.

To illustrate the application of the foregoing rule, suppose a quadruple thread is to be cut having 1¹/₂ single threads per inch (which would be the number the lathe would be geared to cut). Then the lead of the thread = 1 ÷ 1¹/₂ = 0.6666 inch and the pitch = 0.6666 ÷ 4 = 0.1666 inch; adding the pitch to twice the lead we have 0.1666 + 2 × 0.6666 = 1.499 inch. Hence, if the carriage is moved 1¹/₂ inch (which will require a lead-screw having an even number of threads per inch), the tool will be located accurately enough for practical purposes. When the tool is set in this way, if it does not clear the end of the part being threaded, the lathe can be turned backward to place the tool in the proper position.

The foregoing rule, as applied to triple threads or those of a higher number, does not always give the only distance that the carriage can be moved. To illustrate, in the preceding example the carriage movement could be equal to 0.499, or what is practically one-half inch, instead of 1¹/₂ inch, and the tool would be properly located. The rule, however, has the merit of simplicity and can be used in most cases.

Special faceplates are sometimes used for multiple thread cutting, that enable work to be easily and accurately indexed. One of these is illustrated in Fig. 13; it consists of two parts Aand B, part A being free to rotate in relation to B when bolts C are loosened. The driving pin for the lathe dog is attached to plate A. When one groove of a multiple thread is finished, bolts C are loosened and plate A is turned around an amount corresponding to the type of thread being cut. The periphery of plate A is graduated in degrees, as shown, and for a double thread it would be turned one-half revolution or 180 degrees, for a triple thread, 120 degrees, etc. This is a very good arrangement where multiple thread cutting is done frequently.

Taper Threading.—When a taper thread is to be cut, the tool should be set square with axis a—a as at A, Fig. 14, and not by the tapering surface as at B. If there is a cylindrical part, the tool can be set as indicated by the dotted lines. All taper threads should be cut by the use of taper attachments. If the tailstock is set over to get the required taper, and an ordinary bent-tail dog is used for driving, the curve of the thread will not be true, or in other words the thread will not advance at a uniform rate; this is referred to by machinists as a “drunken thread.” This error in the thread is due to the angularity between the driving dog and the faceplate, which causes the work to be rotated at a varying velocity. The pitch of a taper thread that is cut with the tailstock set over will also be slightly finer than the pitch for which the lathe is geared. The amount of these errors depends upon the angle of the taper and the distance that the center must be offset.

Internal Threading.—Internal threading, or cutting threads in holes, is an operation performed on work held in the chuck or on a faceplate, as for boring. The tool used is similar to a boring tool except that the working end is shaped to conform to the thread to be cut. The method of procedure, when cutting an internal thread, is similar to that for outside work, as far as handling the lathe is concerned. The hole to be threaded is first bored to the root diameter D, Fig. 15, of the screw that is to fit into it. The tool-point (of a tool for a U. S. standard or V-thread) is then set square by holding a gage G against the true side of the work and adjusting the point to fit the notch in the gage as shown. The view to the right shows the tool taking the first cut.

Very often the size of a threaded hole can be tested by using as a gage the threaded part that is to fit into it. When making such a test, the tool is, of course, moved back out of the way. It is rather difficult to cut an accurate thread in a small hole, especially when the hole is quite deep, owing to the flexibility of the tool; for this reason threads are sometimes cut slightly under size with the tool, after which a tap with its shank end held straight by the tailstock center is run through the hole. In such a case, the tap should be calipered and the thread made just small enough with the tool to give the tap a light cut. Small square-threaded holes are often finished in this way, and if a number of pieces are to be threaded, the use of a tap makes the holes uniform in size.

Stop for Thread Tools.—When cutting a thread, it is rather difficult to feed in the tool just the right amount for each successive cut, because the tool is moved in before it feeds up to the work. A stop is sometimes used for threading which overcomes this difficulty. This stop consists of a screw S, Fig. 16, which enters the tool slide and passes through a block B clamped in front of the slide. The hole in the block through which the stop-screw passes is not threaded, but is large enough to permit the screw to move freely. When cutting a thread, the tool is set for the first cut and the screw is adjusted until the head is against the fixed block. After taking the first cut, the stop-screw is backed out, say one-half revolution, which allows the tool to be fed in far enough for a second cut. If this cut is about right for depth, the screw is again turned about one-half revolution for the next cut and this is continued for each successive cut until the thread is finished. By using a stop of this kind, there is no danger of feeding the tool in too far as is often done when the tool is set by guess. If this form of stop is used for internal threading, the screw, instead of passing through the fixed block, is placed in the slide so that the end or head will come against the stop B. This change is made because the tool is fed outward when cutting an internal thread.

The Acme Standard Thread.—The Acme thread is often used, at the present time, in place of a square thread. The angle between the sides of the Acme thread is 29 degrees (see Fig. 21) and the depth is made equal to one-half the pitch plus 0.010 inch to provide clearance and insure a bearing upon the sides. The thread tool is ordinarily ground to fit a gage having notches representing different pitches. An improved form of Acme thread gage is shown in Fig. 17. The tool point is first ground to the correct angle by fitting it to the 29-degree notch in the end of the gage, as at A. The end is then ground to the proper width for the pitch to be cut, by testing it, as at B. The numbers opposite the shallow notches for gaging the width represent the number of threads per inch. With this particular gage, the tool can be set square by placing edge D against the turned surface to be threaded, and adjusting the tool until the end is in line with the gage, as at C. By placing the tool in this position, the angle between the side and the end can also be tested.

In case it should be necessary to measure the end width of an Acme thread tool, for a pitch not on the regular gage, this can be done by using a vernier gear-tooth caliper, as indicated in Fig. 18. If we assume that the caliper jaws bear on the sides of the tool at a distance A from the top, equal to ¹/₄ inch, then the width of the tool point equals the caliper reading (as shown by the horizontal scale) minus 0.1293 inch. For example, if the caliper reading was 0.315 inch, the width at the point would equal 0.315 - 0.1293 = 0.1857 inch, assuming that the sides were ground to the standard angle of 29 degrees. The constant to be subtracted from the caliper reading equals 2 A tan 14° 30' or, in this case, 2 × 0.25 × 0.2586 = 0.1293.

The Whitworth Thread.—The Whitworth (or British Standard Whitworth) thread, which is used principally in Great Britain, has an included angle of 55 degrees, and the threads are rounded at the top and at the root, as shown in Fig. 23. The shape of the tool used for cutting this thread is also shown in this illustration. The end is rounded to form the fillet at the root of the thread, and the round corners on the sides give the top of the thread the required curvature. Every pitch requires a different tool, and the cutting end is given the curved form by milling or hobbing. The hob used for this purpose is accurately threaded to correspond with the pitch for which the tool is required, and then it is fluted to form cutting edges, and is hardened. The hob is then used like a milling cutter for forming the end of the thread tool. The tool is sharpened by grinding on the top. The method of cutting a Whitworth thread is, of course, similar to that followed for a U. S. standard or V-thread, in that the tool is set square with the unthreaded blank and at the same height as the lathe centers, in order to secure a thread of the proper form. Care should be taken to turn the blank to the right diameter so that the top of the thread will be fully rounded when the screw is the required size.

Worm Threads.—The standard worm thread has an angle of 29 degrees between the sides, the same as an Acme thread, but the depth of a worm thread and the width of the flat at the top and bottom differ from the Acme standard, as will be seen by comparing Figs. 21 and 24. The whole depth of the thread equals the linear pitch multiplied by 0.6866, and the width of the thread tool at the end equals the linear pitch multiplied by 0.31. Gages notched for threads of different pitch are ordinarily used when grinding worm thread tools.

When it is necessary to cut multiple-threaded worms of large lead in an ordinary lathe, difficulty is sometimes experienced because the lead-screw must be geared to run much faster than the spindle, thus imposing excessive strains on the gearing. This difficulty is sometimes overcome by mounting a belt pulley on the lead-screw, beside the change gear, and connecting it to the countershaft by a belt; the spindle is then driven through the change gearing from the lead-screw, instead of vice versa.

Coarse Threading Attachment.—To avoid the difficulties connected with cutting threads of large lead, some lathes are equipped with a coarse screw-cutting attachment. The arrangement of this attachment, as made by the Bradford Machine Tool Co., is as follows: On the usual reversing shaft, and inside of the headstock, there is a sliding double gear, so arranged as to be engaged with either the usual gear on the spindle, or with a small pinion at the end of the cone. The gears are so proportioned that the ratio of the two engagements is as 10 to 1; that is, when engaged with the cone gear (the back-gears being thrown in) the mating gear will make ten revolutions to one of the spindle, so that when the lathe is ordinarily geared to cut one thread per inch, it will, when driven by the cone pinion, cut one thread in ten inches. This construction dispenses with the extra strain on the reverse gears due to moving the carriage at the rapid rate that would be necessary for such a large lead, when not using an attachment. These attachments are not only extensively used for the cutting of coarse screws but for cutting oil grooves on cylindrical parts.

When cutting a thread of large lead or “steep pitch,” the top of the thread tool should be ground so that it is at right angles to the thread; then the thread groove will be cut to the same width as the tool.

Testing the Size of a Thread.—When the thread tool has been fed in far enough to form a complete thread, the screw is then tested for size. If we assume that a bolt is being threaded for a standard nut, it would be removed from the lathe and the test made by screwing a nut on the end. If the thread were too large, the nut might screw on very tightly or not at all; in either case, the work would again be placed in the lathe and a light cut taken over it to reduce the thread to the proper size. When replacing a threaded part between the centers, it should be put back in the original position, that is, with the “tail” of the driving dog in the same slot of the faceplate it previously occupied.

As it is difficult to tell just when a thread is cut to the exact size, special thread calipers having wedge-shaped ends are sometimes used for measuring the diameter of a V-thread or a U. S. standard thread, at the bottom of the grooves or the root diameter, as shown at A in Fig. 25. These calipers can be set from a tap corresponding to the size of the thread being cut, or from a previously threaded piece of the right size.

The Thread Micrometer.—Another form of caliper for testing threads is shown at B. This is one of the micrometer type and is intended for very accurate work. The spindle of this micrometer has a conical end and the “anvil” is V-shaped, and these ends bear on the sides of the thread or the surfaces which form the bearing when the screw is inserted in a nut or threaded hole. The cone-shaped point is slightly rounded so that it will not bear in the bottom of the thread. There is also sufficient clearance at the bottom of the V-shaped anvil to prevent it from bearing on top of the thread. The diameter as indicated by this micrometer is the “pitch diameter” of the thread and is equal to the outside diameter minus the depth of one thread. This depth may be determined as follows:

The movable point measures all pitches, but the fixed anvil is limited in its capacity, for if made large enough to measure a thread of, say, ¹/₄-inch pitch, it would be too wide at the top to measure a thread of ¹/₂₄-inch pitch, hence each caliper is limited in the range of threads that the anvil can measure. When measuring the “angle diameter” of a thread, the micrometer should be passed back and forth across the thread, in order to make sure that the largest dimension or the actual diameter is being measured. If the micrometer is placed over what seems to be the center of the screw and the reading is taken by simply adjusting in the anvil or point against the thread, without moving the micrometer back and forth across it, an incorrect reading may be obtained.

If standard threaded reference gages are available, the size of the thread being cut can be tested by comparing it with the gage. Micrometers having small spherical measuring ends (see sketch A, Fig. 26) are sometimes used for this purpose. The ball points are small enough to bear against the sides of the thread and the diameter, as compared with the reference gage, can be determined with great accuracy.

Three-wire System of Measuring Threads.—A method of measuring threads by using an ordinary micrometer and three wires of equal diameter is illustrated at B and C, Fig. 26. Two wires are placed between the threads on one side and one on the opposite side of the screw. The dimension M over the wires is then measured with an ordinary micrometer. When the thread is cut to a standard size, the dimension M for different threads is as follows:

In these formulas, d = standard outside diameter of screw; m = measurement over wires; w = diameter of wires; p = pitch of thread = 1 ÷ number of threads per inch.

To illustrate the use of the formula for the U. S. standard thread, let us assume that a screw having 6 threads per inch (¹/₆-inch pitch) is to be cut to a diameter of 1¹/₂ inch, and that wires 0.140 inch diameter are to be used in conjunction with a micrometer for measurement. Then the micrometer reading m should be

If the micrometer reading were 1.670 inch, it would indicate that the pitch diameter of the screw was too large, the error being equal to difference between 1.667 and the actual reading.

Rivett-Dock Threading Tool.—A special form of thread tool, which overcomes a number of disadvantages common to an ordinary single-point thread tool, is shown in Fig. 27. This tool has a circular-shaped cutter C, having ten teeth around its circumference, which, beginning with tooth No. 1, gradually increase in height, cutter No. 2 being higher than No. 1, etc. This cutter is mounted on a slide S, that is fitted to the frame F, and can be moved in or out by lever L. The hub of this lever has an eccentric stud which moves slide S and locks it when in the forward or cutting position. The action of the lever in moving the slide engages the cutter with pawl P, thus rotating the cutter one tooth at a time and presenting a different tooth to the work for each movement of the lever. When the slide is moved forward, the heel or underside of the tooth which is in the working position rests on a stop that takes the thrust of the cut.

When the tool is in use, it is mounted on the tool-block of the lathe as shown in the illustration. The cutter is set for height by placing a tooth in the working position and setting the top level with the lathe center. The cutter is also set square with the work by using an ordinary square, and it is tilted slightly from the vertical to correspond with the angle of the thread to be cut, by adjusting frame F. At first a light cut is taken with lever L moved forward and tooth No. 1 on the stop. After this cut is completed, the lever is reversed which rotates the cutter one tooth, and the return movement places tooth No. 2 in the working position. This operation is repeated until the tenth tooth finishes the thread. It is often necessary, when using a single-point thread tool, to re-sharpen it before taking the finishing cut, but with a circular tool this is not necessary, for by using the different teeth successively, the last tooth, which only takes finishing cuts, is kept in good condition.

Cutting Screws to Compensate for Shrinkage.—Some tool steels are liable to shrink more or less when they are hardened; consequently if a very accurate hardened screw is required, it is sometimes cut so that the pitch is slightly greater than standard, to compensate for the shrinkage due to the hardening operation. As the amount of contraction incident to hardening is very little, it is not practicable to use change gears that will give the exact pitch required. A well-known method of obtaining this increase of pitch is by the use of a taper attachment.

For example, suppose a tap having 8 threads per inch is to be threaded, and, owing to the contraction of the steel, the pitch must be 0.12502 inch instead of 0.125 inch. The lathe is geared to cut 8 threads per inch or 0.125 inch pitch, and then the taper attachment is set to an angle a, Fig. 28, the cosine of which equals 0.125÷0.12502; that is, the cosine of angle a equals the pitch required after hardening, divided by the pitch necessary to compensate for shrinkage. The angle is then found by referring to a table of cosines. The tap blank is also set to the same angle a by adjusting the tailstock center, thus locating the axis of the work parallel with the slide of the taper attachment. When the carriage moves a distance x, the tool point will have moved a greater distance y along the work, the difference between x and y depending upon angle a; hence the tool will cut a thread of slightly greater pitch than the lathe is geared to cut.

To illustrate by using the preceding example, cosine of angle a = 0.125÷0.12502 = 0.99984. By referring to a table of cosines, we find that 0.99984 is the cosine of 1 degree, approximately; hence, the taper attachment slide and the work should be set to this angle. (The angle a in Fig. 28 has been exaggerated in order to more clearly illustrate the principle.)

As is well known, it is objectionable to cut a thread with the tailstock center offset, because the work is not rotated at a uniform velocity, owing to the fact that the driving dog is at an angle with the faceplate. For a small angle such as 1 degree, however, the error resulting from this cause would be very small.

If a thread having a pitch slightly less than standard is needed to fit a threaded part which has contracted in hardening, the taper attachment can also be used provided the lathe is equipped with special gears to cut a little less than the required pitch. Suppose a screw having a pitch of 0.198 inch is required to fit the thread of a nut the pitch of which has been reduced from 0.200 inch to 0.198 inch. If gears having 83 and 84 teeth are available, these can be inserted in a compound train, so as to reduce the 0.200 inch pitch that would be obtained with the regular gearing, to ⁸³/₈₄ of 0.200 or 0.19762 inch. This pitch, which is less than the 0.198 inch pitch required, is then increased by using the taper attachment as previously described. (This method was described by Mr. G. H. Gardner in Machinery, February, 1914.)

Calculating Change Gears for Thread Cutting.—As previously mentioned, the change gears for cutting threads of various pitches are shown by a table or “index plate” attached to the lathe. The proper gears to be used can be calculated, but the use of the table saves time and tends to avoid mistakes. Every machinist, however, should know how to determine the size of gears used for cutting any number of threads to the inch. Before referring to any rules, let us first consider why a lathe cuts a certain number of threads to the inch and how this number is changed by the use of different gears.

As the carriage C and the tool are moved by the lead-screw S (see Fig. 2), which is geared to the spindle, the number of threads to the inch that are cut depends, in every case, upon the number of turns the work makes while the lead-screw is moving the carriage one inch. If the lead-screw has six threads per inch, it will make six revolutions while the carriage and the thread tool travel one inch along the piece to be threaded. Now if the change gears a and c (see also sketch A, Fig. 29) are so proportioned that the spindle makes the same number of revolutions as the lead-screw, in a given time, it is evident that the tool will cut six threads per inch. If the spindle revolved twice as fast as the lead-screw, it would make twelve turns while the tool moved one inch, and, consequently, twelve threads per inch would be cut; but to get this difference in speeds it is necessary to use a combination of gearing that will cause the lead-screw to revolve once while the lathe spindle and work make two revolutions.

Suppose that nine threads to the inch are to be cut and the lead-screw has six threads per inch. In this case the work must make nine revolutions while the lead-screw makes six and causes the carriage and thread tool to move one inch, or in other words, one revolution of the lead-screw corresponds to one and one-half revolution of the spindle; therefore, if the lead-screw gear c has 36 teeth, the gear a on the spindle stud should have 24 teeth. The spindle will then revolve one and one-half times faster than the lead-screw, provided the stud rotates at the same rate of speed as the main lathe spindle. The number of teeth in the change gears that is required for a certain pitch can be found by multiplying the number of threads per inch of the lead-screw, and the number of threads per inch to be cut, by the same trial multiplier. The formula which expresses the relation between threads per inch of lead-screw, threads per inch to be cut, and the number of teeth in the change gears, is as follows:

Applying this to the example given, we have 6÷9 = 24÷36. The values of 36 and 24 are obtained by multiplying 6 and 9, respectively, by 4, which, of course, does not change the proportion. Any other number could be used as a multiplier, and if gears having 24 and 36 teeth were not available, this might be necessary. For example, if there were no gears of this size, some other multiplier as 5 or 6 might be used.

Suppose the number of teeth in the change gears supplied with the lathe are 24, 28, 32, 36, etc., increasing by four teeth up to 100, and assume that the lead-screw has 6 threads per inch and that 10 threads per inch are to be cut. Then,

By multiplying both numerator and denominator by 4, we obtain two available gears having 24 and 40 teeth, respectively. The 24-tooth gear goes on the spindle stud and, the 40-tooth gear on the lead-screw. The number of teeth in the intermediate or “idler” gear b, which connects the stud and lead-screw gears, is not considered as it does not affect the ratios between gears a and c, but is used simply to transmit motion from one gear to the other.

We have assumed in the foregoing that the spindle stud (on which gear a is mounted) and the main spindle of the lathe are geared in the ratio of one to one and make the same number of revolutions. In some lathes, however, these two members do not rotate at the same speed, so that if equal gears were placed on the lead-screw and spindle stud, the spindle would not make the same number of revolutions as the lead-screw. In that case if the actual number of threads per inch in the lead-screw were used when calculating the change gears, the result would be incorrect; hence, to avoid mistakes, the following general rule should be used as it gives the correct result, regardless of the ratios of the gears which connect the spindle and spindle stud:

Rule.—First find the number of threads per inch that is cut when gears of the same size are placed on the lead-screw and spindle, either by actual trial or by referring to the index plate. Then place this number as the numerator of a fraction and the number of threads per inch to be cut, as the denominator; multiply both numerator and denominator by some trial number, until numbers are obtained which correspond to numbers of teeth in gears that are available. The product of the trial number and the numerator (or “lathe screw constant”) represents the gear a for the spindle stud, and the product of the trial number and the denominator, the gear for the lead-screw.

Lathes with Compound Gearing.—When gearing is arranged as shown at A, Fig. 29, it is referred to as simple gearing, but sometimes it is necessary to introduce two gears between the stud and screw as at B, which is termed compound gearing. The method of figuring compound gearing is practically the same as that for simple gearing. To find the change gears used in compound gearing, place the “screw constant” obtained by the foregoing rule, as the numerator, and the number of threads per inch to be cut as the denominator of a fraction; resolve both numerator and denominator into two factors each, and multiply each “pair” of factors by the same number, until values are obtained representing numbers of teeth in available change gears. (One factor in the numerator and one in the denominator make a “pair” of factors.)

Suppose the lathe cuts 6 threads per inch when gears of equal size are used, and that the number of teeth in the gears available are 30, 35, 40 and so on, increasing by 5 up to 100. If 24 threads per inch are to be cut, the screw constant 6 is placed in the numerator and 24 in the denominator. The numerator and denominator are then divided into factors and each pair of factors is multiplied by the same number to find the gears, thus:

The last four numbers indicate the gears which should be used. The upper two having 40 and 30 teeth are the driving gears and the lower two having 80 and 60 teeth are the driven gears. The driving gears are gear a on the spindle stud and gear c on the intermediate stud, meshing with the lead-screw gear, and the driven gears are gears b and d. It makes no difference which of the driving gears is placed on the spindle stud, or which of the driven is placed on the lead-screw.

Fractional Threads.—Sometimes the lead of a thread is given as a fraction of an inch instead of stating the number of threads per inch. For example, a thread may be required to be cut, having ³/₈-inch lead. The expression “³/₈-inch lead” should first be transformed to “number of threads per inch.” The number of threads per inch (the thread being single) equals:

To find the change gears to cut 2²/₃ threads per inch in a lathe having a screw constant of 8 and change gears varying from 24 to 100 teeth, increasing by 4, proceed as follows:

As another illustration, suppose we are to cut 1³/₄ thread per inch on a lathe having a screw constant of 8, and that the gears have 24, 28, 32, 36, 40 teeth, etc., increasing by four up to one hundred. Following the rule:

The gears having 72 and 64 teeth are the driving gears, and those with 36 and 28 teeth are the driven gears.

Change Gears for Metric Pitches.—When screws are cut in accordance with the metric system, it is the usual practice to give the lead of the thread in millimeters, instead of the number of threads per unit of measurement. To find the change gears for cutting metric threads, when using a lathe having an English lead-screw, first determine the number of threads per inch corresponding to the given lead in millimeters. Suppose a thread of 3 millimeters lead is to be cut in a lathe having an English lead-screw and a screw constant of 6. As there are 25.4 millimeters per inch, the number of threads per inch will equal 25.4 ÷ 3. Place the screw constant as the numerator, and the number of threads per inch to be cut as the denominator:

The numerator and denominator of this fractional expression of the change-gear ratio are next multiplied by some trial number to determine the size of the gears. The first whole number by which 25.4 can be multiplied so as to get a whole number as the result is 5. Thus, 25.4 × 5 = 127; hence, one gear having 127 teeth is always used when cutting metric threads with an English lead-screw. The other gear required in this case has 90 teeth. Thus:

Therefore, the following rule can be used to find the change gears for cutting metric pitches with an English lead-screw:

Rule.—Place the lathe screw constant multiplied by the lead of the required thread in millimeters multiplied by 5, as the numerator of the fraction, and 127 as the denominator. The product of the numbers in the numerator equals the number of teeth for the spindle-stud gear, and 127 is the number of teeth for the lead-screw gear.

If the lathe has a metric pitch lead-screw, and a screw having a given number of threads per inch is to be cut, first find the “metric screw constant” of the lathe or the lead of thread in millimeters that would be cut with change gears of equal size on the lead-screw and spindle stud; then the method of determining the change gears is simply the reverse of the one already explained for cutting a metric thread with an English lead-screw.

Rule.—To find the change gears for cutting English threads with a metric lead-screw, place 127 in the numerator and the threads per inch to be cut, multiplied by the metric screw constant multiplied by 5, in the denominator; 127 is the number of teeth on the spindle-stud gear and the product of the numbers in the denominator equals the number of teeth in the lead-screw gear.

Quick Change-gear Type of Lathe.—A type of lathe that is much used at the present time is shown in Fig. 30. This is known as the quick change-gear type, because it has a system of gearing which makes it unnecessary to remove the change gears and replace them with different sizes for cutting threads of various pitches. Changes of feed are also obtained by the same mechanism, but the feeding movement is transmitted to the carriage by the rod R, whereas the screw S₁ is used for screw cutting. As previously explained, the idea of using the screw exclusively for threading is to prevent it from being worn excessively, as it would be if continually used in place of rod R, for feeding the carriage when turning.

The general construction of this quick change gear mechanism and the way the changes are made for cutting threads of different pitch, will be explained in connection with Figs. 30, 31 and 32, which are marked with the same reference letters for corresponding parts. Referring to Fig. 30, the movement is transmitted from gear s on the spindle stud through idler gear I, which can be moved sidewise to mesh with either of the three gears a, b or c, Fig. 31. This cone of three gears engages gears d, e and f, any one of which can be locked with shaft T (Fig. 32) by changing the position of knob K. On shaft T there is a gear S which can be moved along the shaft by hand lever L and, owing to the spline or key t, both the sliding gear and shaft rotate together. Shaft T, carrying gears d, e and f and the sliding gear S, is mounted in a yoke Y, which can be turned about shaft N, thus making it possible to lower sliding gear S into mesh with any one of a cone of eight gears C, Fig. 31. The shaft on which the eight gears are mounted has at the end a small gear m meshing with gear n on the feed-rod, and the latter, in turn, drives the lead-screw, unless gear o is shifted to the right out of engagement, which is its position except when cutting threads.

With this mechanism, eight changes for different threads or feeds are obtained by simply placing gear S into mesh with the various sized gears in cone C. As the speed of shaft T depends on which of the three gears d, e and f are locked to it, the eight changes are tripled by changing the position of knob K, making twenty-four. Now by shifting idler gear I, three speed changes may be obtained for gears a, b and c, which rotate together, so that the twenty-four changes are also tripled, giving a total of seventy-two variations without removing any gears, and if a different sized gear s were placed on the spindle stud, an entirely different range could be obtained, but such a change would rarely be necessary. As shown in Fig. 30, there are eight hardened steel buttons B, or one for each gear of the cone C, placed at different heights in the casing. When lever L is shifted sidewise to change the position of sliding gear S, it is lowered onto one of these buttons (which enters a pocket on the under side) and in this way gear S is brought into proper mesh with any gear of the cone C. To shift lever L, the handle is pulled outward against the tension of spring r (Fig. 32), which disengages latch l and enables the lever to be lifted clear of the button; yoke Y is then raised or lowered, as the case may be, and lever L with the sliding gear is shifted laterally to the required position.

The position of lever L and knob K for cutting threads of different pitches is shown by an index plate or table attached to the lathe and arranged as shown in Fig. 33. The upper section a of this table shows the different numbers of threads to the inch that can be obtained when idler gear I is in the position shown by the diagram A. Section b gives the changes when the idler gear is moved, as shown at B, and, similarly, section c gives the changes for position C of the idler. The horizontal row of figures from 1 to 8 below the word “stops” represents the eight positions for lever L, which has a plate p (Fig. 30) just beneath it with corresponding numbers, and the column to the left shows whether knob K should be out, in a central position, or in.

In order to find what the position of lever L and knob K should be for cutting any given number of threads to the inch, find what “stop” number is directly above the number of threads to be cut, which will indicate the location of lever L, and also what position should be occupied by knob K, as shown in the column to the left. For example, suppose the lathe is to be geared for cutting eight threads to the inch. By referring to section a we see that lever L should be in position 4 and knob K in the center, provided the idler gear I were in position A, as it would be ordinarily, because all standard numbers of threads per inch (U. S. standard) from ¹/₄ inch up to and including 4 inches in diameter can be cut with the idler gear in that position. As another illustration, suppose we want to cut twenty-eight threads per inch. This is listed in section c, which shows that lever L must be placed in position 3 with knob K pushed in and the idler gear shifted to the left as at C.

The simplicity of this method as compared with the time-consuming operation of removing and changing gears is apparent. The diagram D to the right shows an arrangement of gearing for cutting nineteen threads per inch. A 20-tooth gear is placed on the spindle stud (in place of the regular one having 16 teeth) and one with 95 teeth on the lead-screw, thus driving the latter direct as with ordinary change gears. Of course it will be understood that the arrangement of a quick change-gear mechanism varies somewhat on lathes of different make.

threads per inch of lead-screw		teeth in gear on spindle stud
————————————	=	————————————
threads per inch to be cut		teeth in gear on lead-screw

6		2 × 3		(2 × 20) × (3 × 10)		40 × 30
—	=	———	=	————————	=	———
24		4 × 6		(4 × 20) × (6 × 10)		80 × 60

8		2 × 4		(2 × 36) × (4 × 24)		72 × 96
—	=	———	=	—————————	=	————
2²/₃		1 × 2²/₃		(1 × 36) × (2²/₃ × 24)		36 × 64

8		2 × 4		(2 × 36) × (4 × 16)		72 × 64
—	=	———	=	—————————	=	————
1³/₄		1 × 1³/₄		(1 × 36) × (1³/₄ × 16)		36 × 28

6			25.4		6 × 3
————	=	6 ÷	——	=	——
25.4			3		25.4
——
3