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.
Fig. 29. (A) Lathe with Simple Gearing for Thread Cutting.
(B) Compound Geared Lathe
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:
| threads per inch of lead-screw | teeth in gear on spindle stud | |
| ———————————— | = | ———————————— |
| threads per inch to be cut | teeth in gear on lead-screw |