How a lathe change-gear ratio sets thread pitch
The carriage advances one leadscrew pitch for each leadscrew revolution. If gear A on the spindle drives gear B on the leadscrew, leadscrew revolutions per spindle revolution are A ÷ B. A compound train multiplies two stages: (A ÷ B) × (C ÷ D), with B and C fixed to the same stud. Therefore actual thread pitch equals leadscrew pitch × train ratio.
The solver converts metric pitches and imperial TPI to millimetres per revolution before comparing them. An 8 TPI leadscrew advances 3.175 mm per turn; cutting a 1.5 mm pitch needs a ratio of 1.5 ÷ 3.175 = 60 ÷ 127. A physical 60T driver and 127T driven gear therefore make that mathematical conversion exactly.
What 2, 3, and 4 gears mean here
A 2-gear result is one external mesh. A 3-gear result places a freely rotating idler between the driver and driven gear: the idler changes rotation direction and physical placement but cancels out of the numeric ratio. A 4-gear compound has two real ratios and requires two separate gears on the intermediate stud. Repeated sizes are allowed only when your inventory contains enough physical copies.
Actual lathes use different studs, bushings, spacers, transposing gears, quadrant slots, quick-change gearbox settings, and tumbler-reverse arrangements. The solver has no model-specific geometry, so it cannot confirm that tooth counts mesh, clear the cover, align, produce the intended hand, or match a gearbox chart.
Reading pitch error and cumulative drift
Parts can appear acceptable over a few threads while drifting out of phase over a long engagement. Error is shown in parts per million and percent; cumulative drift is the difference between actual and target axial travel after the number of spindle turns needed for the entered target length. Positive drift means the produced pitch is longer; negative drift means it is shorter.
An “exact” result means exact ratio arithmetic at the displayed target—not guaranteed cutting accuracy. Leadscrew pitch error, backlash, gear error, tool geometry, deflection, thermal effects, and setup remain outside the calculation.
Shop verification checklist
- Confirm the leadscrew specification and every physical gear tooth count.
- Compare the proposed topology with the lathe manual and any quick-change gearbox or transposing position.
- Check studs, bores, keys, spacers, center distances, banjo travel, cover clearance, backlash, and rotation direction by hand with power isolated.
- Set the correct thread angle, tool, compound/feed method, and engagement procedure for the machine.
- Make a low-speed scratch pass, stop, and verify pitch and handedness with an appropriate gauge before committing to the part.
Frequently asked questions
Why does the idler tooth count not affect pitch?
In a simple train, the first mesh contributes A ÷ I and the second I ÷ B. Multiplying cancels I, leaving A ÷ B. The idler still matters for direction, spacing, clearance, and physical availability.
Does a 127T gear always solve metric threading?
It provides the exact 25.4 mm-per-inch conversion factor when arranged in the correct ratio, but the other gears, leadscrew, gearbox settings, and available mounting geometry still determine the thread you can produce.
Can I trust the top result without a test cut?
No. It is only the closest arithmetic ratio from the inventory and topology entered. Always verify the machine-specific setup and make a scratch/test cut.