Thread cutting on lathe and change gears

Thread cutting on a lathe

The spindle and the lead screw are connected through a train of change gears so that, for each revolution of the job, the carriage moves through one pitch of the thread.

1. Set a low spindle speed and set the change gears (or the quick-change gear box) for the required pitch.
2. Fit a 60° V thread tool ground to the thread profile, and set it at centre height and square to the job using the thread (centre) gauge.
3. Engage the half-nut on the lead screw. For later passes, re-engage at the correct point using the thread-chasing dial; where the dial cannot be used (as here, since 6/1.75 is not a whole number), keep the half-nut engaged and reverse the spindle to bring the tool back.
4. Cut several passes, increasing the depth with the compound slide set at 29° (so the cutting is mainly on the leading flank). Withdraw the tool with the cross slide at the end of each pass and return the carriage to the start.
5. Check the thread with a gauge or nut.

Change gear calculation

The train ratio is the ratio of job rotation to lead-screw rotation:

$$\frac{N_{spindle}}{N_{leadscrew}} = \frac{p_{lead\ screw}}{p_{thread}} \quad\Rightarrow\quad \frac{\text{Driver}}{\text{Driven}} = \frac{p_{thread}}{p_{lead\ screw}}$$ $$\frac{\text{Driver}}{\text{Driven}} = \frac{1.75}{6} = \frac{7}{24} = 0.2917$$

Simple train: multiply the numerator and denominator by 5:

$$\frac{7}{24} = \frac{35}{120}$$

Both gears are in the set (20 to 120 teeth). So a 35-tooth driver on the spindle (stud) drives a 120-tooth gear on the lead screw, through an idler gear of any size, which only fills the gap and keeps the direction correct.

 spindle gear 35 --> idler --> 120 lead screw gear
       (driver)                  (driven)

Compound train (alternative):

$$\frac{7}{24} = \frac{7}{8}\times\frac{1}{3} = \frac{35}{40}\times\frac{20}{60}$$

Check: $\frac{35}{40}\times\frac{20}{60} = 0.875 \times 0.3333 = 0.2917 = \frac{1.75}{6}$.

Here the 35 driver meshes with a 40, and a 20 on the same shaft as the 40 drives the 60 on the lead screw.

Answer: simple train - driver 35 teeth, driven 120 teeth (with an idler); or compound train - drivers 35 and 20, driven 40 and 60.