Gear generator and simulator

How to choose the module, the teeth and the backlash

Module: the size of the teeth

The module (m) is the pitch diameter divided by the number of teeth, in millimetres. It sets the size of every tooth, and both gears of a pair must share it. On a 0.4 mm nozzle, 1.5 mm is a good default: the tip of each tooth is wide enough for two perimeter lines. Go down to 1.0 mm only for light loads such as a clock or a dial, and up to 2 or 2.5 mm for gears that carry real torque.

Teeth and ratio

The ratio is the teeth of the driven gear over the teeth of the driving gear. A 12 tooth pinion driving a 36 tooth wheel gives 3:1: the wheel turns three times slower, three times stronger, and the other way round. Keep the smaller gear at 17 teeth or more at a 20 degree pressure angle to avoid undercut (teeth thinned at the root); 12 to 14 teeth work with a profile shift. The generator reports undercut when the pinion is too small.

Backlash: the play between the teeth

Printed teeth come out within about 0.15 mm of the model, so a gear pair with zero backlash binds. The generator starts at 0.25 mm of total play, which suits most printers; a tuned printer runs 0.15 mm, an older printer or PETG 0.3 mm, and planetary sets up to 0.5 mm. Too much backlash makes the output wobble when you reverse.

Face width and bores

A face width of about 8 x module (6 to 12 x m) is a good balance of strength and print time: 12 mm for module 1.5 (the generator starts at 6 mm for a quick test print). For the bore, a smooth printed hole on a smooth shaft slips and creeps under load; use a D or hex shaft with 0.2 mm of clearance, or a heat-set insert with a set screw. A bore too big for its gear is reduced to leave a rim, and the generator says so.

Module and tooth size reference

Printing gears

• Print gears lying flat, with 5 or more walls so the teeth are solid plastic.
• PETG wears less than PLA in gears that run for a long time.
• Chamfer the bottom edge by about 0.5 mm so elephant foot does not lock the teeth.
• Check the pair on the bench before building a whole gearbox around it.

Spur gear formulas

pitch diameter d = m x zoutside diameter = m x (z + 2)root diameter = m x (z - 2.5)centre distance a = m x (z1 + z2) / 2ratio = z2 / z1

Example: module 1.5, 12 and 36 teeth. Pitch diameters 18 and 54 mm, centre distance 1.5 x 48 / 2 = 36 mm, ratio 3:1. The generator places the gears at this distance plus the backlash and phases the teeth so they mesh at rest.

What the motion check does

Most gear tools animate a pair by multiplying the ratio; nothing checks that the teeth actually clear each other while they turn. Here the real solids are turned through a full cycle on our CAD engine and the distance between them is measured at every pose. The line under Play gives the smallest clearance found and where; when teeth touch, it says at which angle, and the gears turn red there. The evidence also lists the centre distance, the ratio from the teeth and the contact ratio (above 1.2 means a tooth pair is always in contact).