The rule for finding the gears to be used on the spindle and lead-screw is: Multiply the number of threads on the lead-screw and the number of threads to be cut, by the same number; the products will equal the numbers of teeth on the gears to be used.

Suppose the lead-screw has four threads per inch, and ten threads per inch are to be cut. Multiply both numbers by any convenient number, such as 6. Then the gears should have 24 teeth and 60 teeth.

Let

a

=

Number of threads per inch on the lead-screw

b

=

Number of threads per inch to be cut

c

=

Any convenient number

Then aXc

=

Number of teeth of gear on stud

bXc

=

Number of teeth of gear on lead-screw

If the gears thus found are not at hand, multiply by some other number. Thus, suppose gears of 60 and 24 teeth were not available; multiply 4 and 10 by any other number that would give the number of teeth of the gears at hand.

Another way to find the gears is to remember that the number of threads to be cut is to the number on the lead-screw as the number of teeth on the screw gear is to the number of teeth on the stud gear.

Examples For Practice

1. The lead-screw has a pitch of \ inch. What is the ratio of gears to be used to cut a screw with 9 threads to the inch? If one gear has 24 teeth, how many should the other have?

Ans.

l:2 1/4

54 teeth

2. The lead-screw has a pitch of 1/4 inch. What is the ratio of gears to be used to cut a screw with 16 threads to the inch?

Ans. 1:4

3. The lead-screw has a pitch of 1/3 inch. What is the ratio of gears to be used to cut a screw with 12 threads to the inch?

Ans. 1:4

In these cases the actual number of teeth on the gears to be used is obtained by multiplying the ratio by some common multiple. Thus, in Example I, multiplying by 10 gives 40 teeth for the stud gear, and 90 for the screw gear

Fig. 164. Simple Lathe Gearing

Fig. 164. Simple Lathe Gearing.

Fig. 165. Compound Lathe Gearing

Fig. 165. Compound Lathe Gearing.

In Example 2, multiplying by 20 gives 20 teeth for the stud, and 80 for the screw gear; and the same result is obtained by using the same multiple for Example 3.

Every screw-cutting lathe is provided with a set of change gears from which selections can be made. In order to facilitate the choice of the gears to be used, a gear table, often cast in raised letters is screwed to the front piece of the headstock. This table shows the gears to be used for cutting such threads as may be listed in the table.