How Do Gears Work? Trading Speed for Force With Teeth

When two meshing gears turn, the same teeth pass the contact point, so if the driving gear has twenty teeth and the driven gear has sixty, the driven gear turns once for every three turns of the driver. That is a gear ratio of three to one, and the driven shaft turns at a third of the speed. Because the arrangement cannot create energy, and power is torque multiplied by rotational speed, dividing the speed by three multiplies the torque by three, less whatever is lost to friction, which in a well-made spur gear pair is only a percent or two. This is the entire point of a gearbox: an engine or motor produces its useful power over a narrow range of speeds, and the load rarely wants that speed, so gearing converts what the source produces into what the load needs. A bicycle in a low gear turns the wheel slowly for a given pedal speed and multiplies the rider's force at the road, which is why a hill becomes climbable and why the bicycle then moves slowly.

A tooth cannot be any convenient shape, because a badly shaped one delivers jerky motion: the driven gear would speed up and slow down within each tooth engagement, producing vibration, noise and rapid wear. The requirement, called conjugate action, is that the shape delivers a constant velocity ratio throughout the contact. The near-universal solution is the involute curve, the path traced by the end of a taut string unwound from a circle. Involute teeth have several properties that made them dominate: the ratio stays constant even if the two gears are not positioned at exactly the correct centre distance, which makes manufacturing and assembly tolerances manageable; the force between teeth always acts along one fixed line, so bearing loads are steady; and all gears of the same tooth size, the module, mesh correctly with each other regardless of diameter, which makes gears interchangeable and lets them be cut with a single standard tool by hobbing.

Different geometries solve different problems of shaft arrangement, load and noise:

• •Spur gears, with teeth parallel to the axis, the simplest and most efficient, but noisy because each tooth engages along its whole width at once
• •Helical gears, with teeth cut at an angle so contact begins at one corner and sweeps across, which is much quieter and stronger but generates a sideways thrust the bearings must absorb, removed by using a double helical or herringbone form
• •Bevel gears, cone-shaped for transmitting motion between intersecting shafts, usually at a right angle, with spiral bevel and hypoid variants used in vehicle axles
• •Worm gears, a screw driving a wheel, giving a very large reduction in one stage and usually unable to be driven backwards, which makes them self-locking and useful for hoists
• •Rack and pinion, a gear meshing with a straight toothed bar, converting rotation into linear motion, as in steering
• •Planetary or epicyclic sets, with planet gears orbiting a central sun inside a ring gear, which are compact, share load across several teeth at once and can give different ratios by holding different members, which is how automatic transmissions work

Gears fail in identifiable ways and designing them is mostly about avoiding those modes. Bending fatigue breaks a tooth at its root, and is countered by larger teeth, better root fillets and stronger material. Pitting and spalling occur where the contact stress between tooth surfaces exceeds what the material tolerates, progressively removing metal from the working flank, which is why gear teeth are commonly case hardened to give a hard surface over a tough core. Scuffing happens when the lubricant film breaks down under high load and speed and the surfaces weld and tear microscopically. Lubrication is therefore not optional but part of the design, with the oil both separating surfaces and carrying heat away. Backlash, the small clearance between teeth, is deliberately provided to allow for thermal expansion and lubricant, and is a problem only where positioning accuracy matters, where anti-backlash arrangements are used. Noise comes chiefly from transmission error, the tiny departure from perfectly constant velocity caused by manufacturing deviation and by teeth deflecting under load, which is why high-quality gears are profile modified to be slightly not-involute so that they become involute once loaded.

Meshing teeth fix the speed ratio between two shafts by tooth count alone, and since power is conserved, dividing the speed multiplies the torque. Teeth use the involute curve because it keeps the ratio constant, tolerates imprecise centre distance, keeps the tooth force on a fixed line and makes gears of the same tooth size interchangeable. Spur, helical, bevel, worm, rack and planetary arrangements solve different shaft and load problems, and the limits are tooth bending fatigue, surface pitting and lubricant breakdown.