IDB-GER-035
Gears · module · ratio · strength · quality
Gear design basics
The gear vocabulary and the numbers behind it — types, the module and pitch geometry, ratio and torque, tooth strength, quality and backlash, and the failure modes.
Abstract
Gears transmit rotation and multiply (or divide) torque between shafts. The design starts with geometry — the module sets tooth size and centre distance, the tooth counts set the ratio — then checks tooth strength (bending and surface durability) and chooses a quality grade and lubrication.
Section 1 covers gear types and terms. Section 2 is geometry and the module. Section 3 is ratio, speed and torque. Section 4 is tooth strength and sizing. Section 5 is quality, backlash and lubrication. Section 6 is selection and failure modes.
1.Gear types and terms
The shaft arrangement (parallel, intersecting, skew) and the ratio largely pick the type:
| Type | Shaft axes | Ratio / stage | Efficiency | Notes |
|---|---|---|---|---|
| Spur | parallel | up to ~6–8 | 98–99% | Simplest, cheapest; noisier at speed |
| Helical | parallel (or crossed) | ~6–10 | 97–98% | Quiet, smooth; produces axial thrust |
| Bevel | intersecting (usually 90°) | ~1–5 | 97–98% | Right-angle drives |
| Worm | non-intersecting 90° | 5–100 | 50–90% | Very high ratio, compact, can self-lock |
| Rack & pinion | rotary ↔ linear | — | ~98% | Converts to linear motion |
| Planetary | coaxial | 3–10 / stage | high | High torque density, compact |
2.Geometry and the module
Everything keys off the module m and tooth count z:
- Pitch diameter
d = m · z - Centre distance
a = (z₁ + z₂) · m / 2(for external gears at standard centres) - Addendum
= m, dedendum= 1.25 m, so outside diameter= m(z + 2) - Standard pressure angle 20°; standard addendum proportions per ISO 53 / DIN 867.
Pick a standard module (…1, 1.25, 1.5, 2, 2.5, 3, 4, 5…) for available cutters and stock gears, then set tooth counts for the ratio and centre distance. Keep the pinion above the minimum tooth count (≈17 at 20° for no undercut, fewer with profile shift).
3.Ratio, speed and torque
- Ratio
i = z₂ / z₁ = n₁ / n₂the pinion (small) drives the gear (large) to reduce speed and multiply torque. - Torque scales with ratio and efficiency:
T₂ ≈ T₁ · i · η. - Pitch-line velocity
v = π · d · nsets noise, lubrication and quality needs (faster → quieter helical, higher quality, oil). - Keep per-stage ratio sensible (≈≤6–8 for spur/helical); cascade stages or use planetary/worm for big reductions.
4.Tooth strength and sizing
Two independent checks — size for the worse of them:
- Bending (tooth root): the classic Lewis equation and its modern form (ISO 6336 / AGMA 2001) check the root doesn't fatigue. Bending capacity rises with module, face width and material strength.
- Surface durability (pitting): Hertzian contact stress at the tooth flank must stay below the material's contact limit, or the flanks pit. Surface-hardened teeth resist this far better.
Practical levers: increase module (bigger teeth), face width (8–12 × module typical), or material/heat-treat. Materials run from acetal/nylon (light, quiet, low load) through through-hardened steel to case-hardened steel (≈58–62 HRC) for high power density. Pair with the Fatigue primer and Hertz contact references.
5.Quality, backlash and lubrication
- Quality grade (ISO 1328 / AGMA) sets tolerance on tooth form and spacinghigher grade = quieter, smoother, costlier. Match grade to pitch-line velocity and noise spec.
- Backlash is designed-in clearance; too little binds and overheats, too much adds noise and lost motion. Set it via tooth thinning or centre distance.
- Lubrication by speed: grease for slow/intermittent, splash oil for moderate, forced/jet oil for high speed. Worm gears need EP oil (high sliding); check yellow-metal compatibility.
6.Selection and failure modes
| Failure | Cause | Fix |
|---|---|---|
| Pitting (surface fatigue) | contact stress too high | harder/case-hardened flanks, larger gears, better lube |
| Tooth bending fatigue | root stress too high | bigger module, wider face, stronger material, root fillet |
| Scoring / scuffing | lube film breakdown (speed/load/heat) | EP oil, lower temp, better finish |
| Abrasive wear | contamination, poor lube | filtration, sealing, correct lubricant |
| Excess noise / whine | low quality, backlash, misalignment | helical teeth, higher quality, alignment |
Selection checklist: shaft arrangement → type · required ratio (single vs multi-stage) · input torque/speed → module + tooth counts + face width · check bending and contact (size for the worse) · pick material/heat-treat · set quality grade, backlash and lubrication for the pitch-line velocity.