Gear Types and Selection
Spur, helical, bevel, worm, rack, internal and planetary gears compared: efficiency, noise, thrust and where each is used.
Gear types by shaft arrangement
The first decision is the geometry of the two shafts: parallel, intersecting or crossed. That narrows the choice of gear type before ratio, load and noise are considered.
Spur gears
Spur gears have straight teeth parallel to the axis, and connect parallel shafts. They are the simplest to design and make, the cheapest, the most efficient (98 to 99 percent per mesh) and impose no axial thrust: the only forces are tangential and radial (see Gear Strength and Design Calculations). Their teeth engage along a whole line at once, so they make more noise and vibration at high speed, a hum at the tooth-meshing frequency. A pitch-line speed up to about 20 m/s is typical for commercial spur gears; ground and precision gears run faster.
Helical gears
Helical gears have teeth cut at a helix angle β (15° to 30°). The teeth engage gradually along their length, so more teeth share the load, the action is smoother and quieter and the load capacity is higher than for a spur gear of the same size. The price is an axial thrust Fa = Ft tan β that the bearings must carry, and a slightly lower efficiency (97 to 99 percent). A mating pair has opposite hands (right and left) on parallel shafts. Double-helical (herringbone) gears use two opposite helices so the thrusts cancel.
Worked example: forces on a helical gear
- A helical gear has normal module mn = 2 mm, z = 24 teeth, helix angle β = 20°. The transverse module is mt = mn ÷ cos β = 2.128 mm, so the pitch diameter is d = mt z = 51.1 mm (a straight spur gear with the same module would be 48 mm).
- With a tangential force Ft = 1 000 N: axial Fa = Ft tan β = 1 000 × tan 20° = 364 N, and radial Fr = Ft tan φn ÷ cos β = 387 N.
- The axial force is 36 percent of the tangential force at 20°; at 30° it would be 58 percent. Use thrust bearings (tapered roller or angular-contact: see Bearings and Bearing Selection) and make sure the housing is stiff.
Bevel gears
Bevel gears transmit between shafts that meet at a point (usually 90°). Their pitch surfaces are cones. Straight bevels are the simplest but noisy; spiral and zerol bevels have curved teeth that run smoothly and take more load; hypoid gears are spiral bevels with offset shafts (the standard car rear axle). Bevel gears must be mounted accurately (a movable cone distance and mounting distance), and they produce thrust in both directions. Ratios up to about 6:1 per pair; efficiency 94 to 98 percent.
For a 90° pair with 20 and 40 teeth, the pitch-cone angles are δp = atan(zp ÷ zg) = atan(20 ÷ 40) = 26.6° for the pinion and 63.4° for the gear; the ratio is 2:1.
Worm gears
A worm is a screw that drives a wheel at 90° without intersecting. A single reduction can give 5:1 to 100:1 in a compact, quiet package, and the sliding action can make the drive self-locking: the wheel cannot drive the worm. The cost is sliding friction and heat: the efficiency can be as low as 30 to 50 percent at a high ratio, and the wheel is usually bronze on a hardened steel worm. The ratio is the number of wheel teeth divided by the number of worm starts (threads), not by the worm diameter.
Worked example: efficiency and self-locking of a worm drive
- A single-start worm (z1 = 1) of pitch diameter 40 mm and module 4 mm drives a 40-tooth wheel: the ratio is 40 ÷ 1 = 40:1. The lead is π × 4 × 1 = 12.57 mm, so the lead angle is λ = atan(12.57 ÷ (π × 40)) = 5.7°.
- With a friction coefficient μ = 0.05 the efficiency is η = (cos φn − μ tan λ) ÷ (cos φn + μ cot λ) = 65 percent.
- The drive is self-locking only if μ > cos φn tan λ = 0.094. With μ = 0.05 it is not self-locking: vibration can back-drive it. Do not count on a worm gear as a safety brake (see Braking, Safe Stopping and Troubleshooting).
| Lead angle λ | Efficiency (μ = 0.05) | Self-locking at μ = 0.05? |
|---|---|---|
| 2.0° | 40 percent | Yes |
| 5.0° | 62 percent | No |
| 10.0° | 76 percent | No |
| 20.0° | 86 percent | No |
A small lead angle gives self-locking but low efficiency; a large lead angle (multi-start worms) is efficient but not self-locking.
Rack and pinion
A rack is a gear of infinite radius: a straight bar of teeth that turns the rotation of a pinion into linear travel of π × d per revolution. It is used for long strokes, with a stiff, accurate drive (CNC gantries, lifts, steering). The linear speed is v = π d n ÷ 60 (see Mechanical Transmission).
A 20-tooth pinion of module 2 mm moves the rack 125.7 mm per turn; at 3 000 rpm that is 6.28 m/s. Dual-pinion preloaded drives remove backlash.
Internal, planetary and special gears
- Internal (ring) gears have the teeth on the inside: compact, with a pinion turning the same way. They are the outer member of a planetary set (see Gear Trains, Ratios and Efficiency).
- Planetary (epicyclic) gearboxes share the load between several planets for a high torque density: the standard servo gearhead.
- Harmonic (strain-wave) and cycloidal gears give very high ratios with almost no backlash: robot joints.
- Face (crown) gears, crossed-helical (screw) gears and hypoid gears serve special arrangements; crossed helicals are for light loads only (point contact).
- Non-circular gears, Geneva wheels and ratchets make variable-speed and indexing motions.
- Plastic and 3D-printed gears work for light loads and prototypes (see the materials below).
Comparing the types
| Type | Shafts | Typical ratio per stage | Efficiency | Noise | Axial thrust |
|---|---|---|---|---|---|
| Spur | Parallel | 1:1 to 6:1 | 98 to 99 % | Highest | None |
| Helical | Parallel (or crossed) | 1:1 to 10:1 | 97 to 99 % | Low | Yes: tan β × Ft |
| Bevel (straight) | Intersecting | 1:1 to 4:1 | 94 to 98 % | High | Yes |
| Bevel (spiral, hypoid) | Intersecting or offset | 1:1 to 10:1 | 90 to 98 % | Low | Yes |
| Worm | Crossed at 90° | 5:1 to 100:1 | 30 to 90 % | Very low | Large on the worm |
| Planetary | Coaxial | 3:1 to 10:1 per stage | 95 to 98 % | Low to moderate | Only with helical teeth |
| Rack and pinion | Linear | π d per turn | 95 to 98 % | Moderate | None |
Materials and manufacture
| Material | Use | Notes |
|---|---|---|
| Case-hardened steel (16MnCr5, 8620) | High-power, compact gears | Hard surface (58 to 62 HRC) with a tough core; ground for precision |
| Through-hardened steel (4140, 42CrMo4) | Medium loads | Quenched and tempered; moderate surface hardness |
| Cast iron | Large, low-speed gears; damping | Good wear and noise damping; lower strength |
| Bronze | Worm wheels, bushings | Low friction against a steel worm; limited strength |
| Sintered metal | Mass-produced small gears | Cheap in volume; lower strength |
| Nylon, acetal (POM), PEEK | Light loads, quiet, no lubricant | Low weight; creep and moisture absorption (see Material Properties) |
| 3D-printed (nylon, resin) | Prototypes, low-load maker gears | Lower accuracy and strength; oversize the face width and module |
Gears are made by hobbing, shaping, milling (see CNC Machining), broaching, forging, molding or sintering, then often heat-treated and ground or honed. The accuracy class (AGMA 5 to 15, ISO 1328 grades 1 to 12) sets the noise and the allowable speed.
How to select a gear type
| If you need… | Choose | Why |
|---|---|---|
| A simple, cheap drive between parallel shafts | Spur | Easiest and most efficient; no thrust |
| Quiet, high-speed or high-load parallel shafts | Helical | Gradual engagement; accept the thrust |
| A right-angle drive with moderate ratio | Bevel (spiral for speed) | Intersecting shafts |
| A large ratio in a small space; right angle | Worm | Compact, quiet; mind efficiency and heat |
| High torque in a coaxial package | Planetary | Shares the load between planets |
| No backlash and a huge ratio | Harmonic or cycloidal | Robotics |
| A long linear stroke | Rack and pinion | Unlimited length; see the preloading options |
Related
- Gears and Power Transmission: the overview of this guide.
- Gear Basics and Terminology and Gear Strength and Design Calculations: geometry and strength.
- Gear Trains, Ratios and Efficiency: combining gears and choosing tooth counts.
- Lubrication, Wear and Gear Failures: lubrication needs by gear type (worm gears need special oil).
- Gear Ratio, Torque and Speed Generator.
FAQ
Why do helical gears make less noise than spur gears?
A helical tooth engages gradually, line by line, rather than along its whole length at once, so the load changes smoothly and more teeth are in contact. The result is a lower mesh vibration and a higher load capacity.
Can a worm drive be used as a brake?
Only if it is truly self-locking (a small lead angle with friction above cos φ × tan λ), and even then vibration and wear can back-drive it. Use a proper brake for anything that could injure.
What is the best gear for a robot joint?
Low-backlash, high-ratio, compact types: harmonic drives, cycloidal drives or precision planetary gearheads.
Do helical gears need special bearings?
They need bearings that carry axial thrust: tapered roller, angular-contact ball or a thrust bearing, and a housing stiff enough to hold the shafts against the thrust.
References
- Shigley, J. E. and Mischke, C. R., Mechanical Engineering Design, McGraw-Hill: helical, bevel and worm gears.
- AGMA 2001-D04 (spur and helical), AGMA 2003 (bevel), AGMA 6034 (worm); ISO 6336 (calculation of load capacity).
- Dudley, D. W., Handbook of Practical Gear Design, CRC Press; Machinery’s Handbook, gearing section.
Last reviewed: October 2026. Efficiencies and ratios are typical ranges; use the manufacturer’s catalog for real gearboxes.