Gears are classified by how their shafts are arranged: parallel shafts use spur, helical, double-helical (herringbone), internal gears and rack and pinion; intersecting shafts use bevel gears (straight, spiral, zerol, mitre); and shafts that neither meet nor run parallel use worm, hypoid and crossed helical gears. Parallel and bevel gears transmit power at about 98-99.5% efficiency per mesh, while a worm drive can be anywhere from about 30% to 90%, the price of its very large single-stage reduction.
This page is the overview of gear types. Why meshing teeth give a constant speed ratio, and why the involute profile is used, is explained on our law of gearing page; gear trains, including epicyclic trains, are on the gear trains page.
Gear terminology you need first
- Pitch circle: the imaginary circle on which two meshing gears roll without slipping. Its diameter d is the pitch diameter, and the speed ratio of a pair is d2/d1 = z2/z1 (ratio of tooth numbers).
- Module (m): pitch diameter divided by number of teeth, m = d/z, in mm. It sets the tooth size; two gears must have the same module to mesh. A 40-tooth gear of module 2 has d = 80 mm.
- Circular pitch: p = πm, the distance from one tooth to the next along the pitch circle.
- Addendum and dedendum: the tooth height above and below the pitch circle; for standard full-depth teeth, 1m and 1.25m.
- Pressure angle: the angle between the line of action and the tangent to the pitch circles. 20° is the usual standard today; 14.5° is found on older gears.
- Helix angle (β): for helical gears, the angle of the teeth to the gear axis.
How are gears classified?
| Shaft arrangement | Gear types | Contact |
|---|---|---|
| Parallel shafts | Spur, helical, double-helical (herringbone), internal, rack and pinion | Mostly rolling |
| Intersecting shafts | Straight bevel, spiral bevel, zerol bevel, mitre | Mostly rolling |
| Non-parallel, non-intersecting shafts | Worm and worm wheel, hypoid, crossed helical (screw) | Rolling plus considerable sliding |
The sliding in the third group is why those gears run hotter, need better lubricants and are less efficient.
Gears for parallel shafts
Spur gears
Straight teeth cut parallel to the axis. They are the simplest and cheapest to make, carry no axial thrust and are very efficient. Because each tooth engages across its whole width at once, they are noisy at high speed. Uses: machine tools, clocks, washing machines, gear pumps, low-speed gearboxes, reverse gear in many car gearboxes.
Helical gears
The teeth are cut at a helix angle (typically around 15-30°), so contact starts at one end of a tooth and spreads gradually across it. More teeth share the load, so helical gears run quieter and carry more load than spur gears of the same size. The drawback is an axial thrust that the bearings must take (worked example below). Uses: car gearboxes (the constant-mesh gears in a synchromesh gearbox), industrial speed reducers, turbines, compressors.
Double-helical and herringbone gears
Two helical gears of opposite hand side by side on one gear (with a gap between them in double-helical; meeting in a V in herringbone). The two axial thrusts cancel, so large helix angles and heavy loads are possible without thrust bearings. Uses: marine reduction gears, steel rolling mills, large turbine gearboxes, heavy compressors.
Internal gears
Teeth cut on the inside of a ring. An internal gear and its pinion turn in the same direction, give a compact drive, and have more teeth in contact. Uses: the ring gear of planetary (epicyclic) gearboxes in automatic transmissions, wind turbines and hub motors.
Rack and pinion
A rack is a gear of infinite radius, a straight bar with teeth. A pinion rolling along it turns rotation into straight-line motion (distance moved per revolution = π × pinion pitch diameter). Uses: car steering (see steering geometry), CNC machine axes, lathe carriages, sliding gates, rack railways.
Gears for intersecting shafts: bevel gears
Bevel gears are cut on cones, and the shafts usually meet at 90°.
- Straight bevel: straight teeth pointing to the cone apex. Simple, but noisy at speed. Used in hand drills, differentials of older and smaller vehicles, and slow drives.
- Spiral bevel: curved, oblique teeth that engage gradually, so they are smoother and stronger. Used in vehicle drives, helicopter transmissions and machine tools. They produce axial thrust that changes direction with rotation.
- Zerol bevel: curved teeth with zero spiral angle; smoother than straight bevel but with thrust like straight bevel.
- Mitre gears: a pair of bevel gears with equal numbers of teeth (1:1 ratio) and shafts at 90°, used only to change direction.
Gears for non-parallel, non-intersecting shafts
Worm and worm wheel
A worm (a screw with one or more threads, or “starts”) drives a worm wheel at 90°. One turn of a single-start worm advances the wheel by one tooth, so the ratio is:
Ratio = number of teeth on the wheel / number of starts on the worm
This gives reductions of about 5:1 to 100:1 in a single, compact, quiet stage. The teeth slide heavily, so efficiency is much lower than for other gears: KHK’s gear reference gives 30-90% for worm gears. With a small lead angle the drive becomes self-locking: the wheel cannot drive the worm backwards. The usual pairing is a hardened steel worm with a phosphor bronze wheel. Uses: lifts and hoists, conveyor drives, gate openers, tuning pegs on guitars, steering boxes of older vehicles, indexing heads.
Hypoid gears
Like spiral bevel gears, but the pinion axis is offset below (or above) the wheel axis. The offset allows a larger, stronger pinion and, in rear-wheel-drive cars, a lower propeller shaft and floor. The extra sliding means lower efficiency than spiral bevel and a need for extreme-pressure (hypoid) gear oil. Uses: final drive (crown wheel and pinion) of rear-wheel-drive cars, trucks and buses, feeding the differential.
Crossed helical (screw) gears
Two helical gears on non-parallel shafts, touching at a point rather than along a line. They carry light loads only. KHK gives 70-95% efficiency for screw gears. Uses: distributor and oil-pump drives in older engines, speedometer drives, light instrument drives.
Comparison table: types of gears
Efficiency ranges for parallel, intersecting, screw and worm gears are from KHK’s gear technical reference (per mesh, excluding bearing and lubricant losses). Ratio, noise and the hypoid efficiency are typical figures, not limits.
| Gear type | Shafts | Efficiency per mesh | Typical ratio per stage | Noise | Axial thrust | Typical use |
|---|---|---|---|---|---|---|
| Spur | Parallel | 98-99.5% | Up to about 5-6:1 | Highest of the parallel types | None | Machine tools, pumps, reverse gears |
| Helical | Parallel | 98-99.5% | Up to about 6-10:1 | Low | Yes (Ft tan β) | Car gearboxes, industrial reducers |
| Double helical / herringbone | Parallel | 98-99.5% | Up to about 10:1 | Low | Cancels out | Marine, rolling mills, turbines |
| Internal | Parallel | 98-99.5% | Compact in planetary sets | Low | None (spur) or yes (helical) | Epicyclic gearboxes |
| Rack and pinion | Rotary to linear | 98-99.5% | Not applicable | Moderate | None (straight teeth) | Steering, CNC axes |
| Straight bevel | Intersecting | 98-99% | Up to about 3-5:1 | High at speed | Yes | Hand drills, slow right-angle drives |
| Spiral / zerol bevel | Intersecting | 98-99% | Up to about 5-6:1 | Low | Yes | Vehicle drives, helicopters |
| Hypoid | Offset, non-intersecting | Typically about 90-95% | About 3-10:1 | Low | Yes | Car and truck final drives |
| Crossed helical | Non-parallel, non-intersecting | 70-95% | Low ratios | Low | Yes | Light instrument and pump drives |
| Worm | Non-parallel, non-intersecting (90°) | 30-90% | About 5-100:1 | Very low | Large, on the worm | Hoists, conveyors, gate drives |
Worked example 1: compound gear train, output speed and torque
A 5 kW, 1440 rpm motor drives a two-stage spur reducer. Stage 1: a 20-tooth pinion drives a 60-tooth gear. Stage 2: an 18-tooth pinion on the same shaft drives a 54-tooth gear. Take 98% efficiency per stage.
- Overall ratio = (60/20) × (54/18) = 3 × 3 = 9
- Output speed = 1440 / 9 = 160 rpm
- Input torque = P / ω = 5000 / (2π × 1440 / 60) = 5000 / 150.8 = 33.2 N·m
- Ideal output torque = 33.16 × 9 = 298.4 N·m
- Actual output torque = 298.4 × 0.98 × 0.98 = 286.6 N·m
Check with power: output power = 5000 × 0.9604 = 4802 W; output ω = 2π × 160 / 60 = 16.76 rad/s; torque = 4802 / 16.76 = 286.6 N·m. Speed goes down by the ratio and torque goes up by the ratio, less the losses. Try other trains with the gear ratio calculator.
Worked example 2: axial thrust on a helical gear
A helical pinion of 80 mm pitch diameter transmits 100 N·m. Helix angle β = 20°, normal pressure angle αn = 20°.
- Tangential force Ft = 2T / d = 2 × 100 / 0.080 = 2500 N
- Axial thrust Fa = Ft tan β = 2500 × tan 20° = 2500 × 0.364 = 910 N
- Radial force Fr = Ft tan αn / cos β = 2500 × 0.364 / 0.940 = 968 N
So over a third of the tangential force appears as end thrust, which is why helical gear shafts need taper roller or angular contact bearings. A double-helical gear with two opposite 20° halves would cancel the 910 N internally.
Worked example 3: worm ratio, efficiency and self-locking
A worm with 2 starts drives a 40-tooth worm wheel from a 1440 rpm motor. Worm pitch diameter = 50 mm, axial module = 4 mm.
- Ratio = 40 / 2 = 20; wheel speed = 1440 / 20 = 72 rpm
- Lead = starts × π × m = 2 × π × 4 = 25.13 mm
- Lead angle: tan λ = lead / (π × d) = 25.13 / 157.08 = 0.160, so λ = 9.09°
Using the simplified screw-thread formula (ignoring pressure angle), efficiency with the worm driving is η = tan λ / tan(λ + φ), where φ = tan-1 μ is the friction angle. Take μ = 0.05 (an assumed, well-lubricated value): φ = 2.86°.
- η = 0.160 / tan(11.95°) = 0.160 / 0.212 = about 76%
- λ (9.09°) is greater than φ (2.86°), so the drive is not self-locking: a load on the wheel can turn the worm backwards.
Now use a single-start worm (ratio 40, lead 12.57 mm, tan λ = 0.080, λ = 4.57°) in poorer conditions, μ = 0.10 (φ = 5.71°):
- η = 0.080 / tan(10.28°) = 0.080 / 0.181 = about 44%
- λ (4.57°) is less than φ (5.71°), so the drive is self-locking.
A self-locking worm always has an efficiency below 50%, which is the cost of the “free brake”. Do not rely on self-locking alone for lifting safety, though: vibration can make a nominally self-locking worm creep, so hoists still fit a brake.
Gear materials
- Case-hardened alloy steels (carburised grades such as 20MnCr5 and 16MnCr5): hard, wear-resistant surface with a tough core; standard for vehicle gearboxes and heavy reducers.
- Through-hardened and medium-carbon steels: general industrial gears.
- Cast iron: large, slow, quiet gears; good damping and wear.
- Phosphor bronze: worm wheels, because it slides well against a hardened steel worm.
- Plastics (nylon, acetal): quiet, light, need no lubrication; used in appliances, printers and toys at light loads.
- Sintered powder metal: cheap, accurate mass-produced small gears.
How to choose a gear type
| Need | Choose |
|---|---|
| Parallel shafts, low cost, low speed | Spur |
| Parallel shafts, high speed or quiet running | Helical |
| Parallel shafts, very high power, no thrust bearings | Double helical / herringbone |
| Compact, coaxial, high ratio | Planetary set with internal gear |
| Rotation to straight-line motion | Rack and pinion |
| Right angle, shafts meet | Bevel (spiral for speed and load) |
| Right angle, large ratio in one stage, or must not back-drive | Worm |
| Right angle with offset, high load (vehicle axle) | Hypoid |
| Light-duty skew drive | Crossed helical |
For planetary gear sets in automatic transmissions and for theory of machines lectures, see NPTEL – Engineering Courses.
FAQs
What are the main types of gears?
Spur, helical, double-helical (herringbone), internal and rack and pinion for parallel shafts; straight, spiral and zerol bevel for intersecting shafts; and worm, hypoid and crossed helical gears for shafts that are neither parallel nor intersecting.
Which type of gear is most efficient?
Spur, helical and other parallel-shaft gears, at about 98-99.5% per mesh, followed closely by bevel gears at about 98-99%. Worm gears are the least efficient, at about 30-90%.
Why are helical gears quieter than spur gears?
Helical teeth engage gradually from one end to the other, and more teeth are in contact at once, so the load changes smoothly. Spur teeth engage across the full width at once, which causes impact and noise at speed.
How do you calculate the ratio of a worm gear?
Divide the number of teeth on the worm wheel by the number of starts on the worm. A 40-tooth wheel with a 2-start worm gives a 20:1 ratio.
What is a self-locking worm gear?
A worm drive whose lead angle is smaller than the friction angle, so the wheel cannot drive the worm backwards. Its efficiency is below 50%.