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A gear is a toothed wheel that passes rotation to another gear without slipping. Two meshing gears act like two rollers pressed together, except that the teeth stop them sliding, so the speed ratio is exact and they can carry large torques. Gears change speed, change torque, change the direction of rotation and change the axis of rotation. Almost every machine with a motor has some.
How a gear pair works
When two gears mesh, their pitch circles roll on each other without slipping, touching at the pitch point. The surface speed at the pitch circle is the same on both gears. Because the smaller gear has fewer teeth, it has to turn faster to keep up, and the two gears always turn in opposite directions.
The teeth are shaped as involute curves so that the contact point slides smoothly along a straight line of action as the teeth roll through mesh. The result is a constant speed ratio, with no jerk, even if the centre distance is slightly off.
Gear ratio, speed and torque
| Symbol | Meaning | Unit |
|---|---|---|
| Gear ratio | none | |
| Number of teeth on the driver and the driven gear | none | |
| Speeds | rev/min | |
| Pitch circle diameters | mm | |
| Input and output torque | N·m | |
| Mesh efficiency (about 0.98–0.99 for a spur or helical pair) | none |
A ratio above 1 reduces speed and increases torque. Power stays the same apart from small losses: .
For a gear train of several pairs, multiply the ratios: a 3 : 1 stage followed by a 4 : 1 stage gives 12 : 1. Idler gears between two gears change the direction but not the ratio.
The terms on a gear drawing
| Term | Meaning | Formula (standard spur gear) |
|---|---|---|
| Module, | Tooth size in mm; meshing gears must have the same module | |
| Pitch diameter, | Diameter of the pitch circle | |
| Addendum | Height of the tooth above the pitch circle | |
| Dedendum | Depth below the pitch circle | |
| Tip diameter | Outside diameter of the blank | |
| Pressure angle | Angle of the line of action; standard is 20° | — |
| Centre distance, | Distance between the shafts |
Inch-based gears use diametral pitch (teeth per inch of pitch diameter) instead of module. A standard 20° spur gear needs at least about 17 teeth to avoid undercutting at the root; in practice pinions of 12–16 teeth are used with a profile shift.
Types of gears
| Type | Shafts | Features | Typical uses |
|---|---|---|---|
| Spur | Parallel | Straight teeth; simple and efficient; noisy at high speed | Gearboxes, pumps, clocks, machine tools |
| Helical | Parallel | Angled teeth engage gradually: quieter and stronger, but create axial thrust | Car gearboxes, industrial reducers |
| Double helical (herringbone) | Parallel | Two opposite helices cancel the thrust | Large, heavily loaded drives |
| Bevel | Intersecting, usually 90° | Cone-shaped; straight or spiral teeth | Differentials, hand drills, right-angle drives |
| Worm and wheel | Crossed, 90° | High ratio in one stage (10 : 1 to 100 : 1); often self-locking; lower efficiency | Hoists, gates, conveyors, tuning pegs |
| Rack and pinion | Rotation to straight line | Converts rotation to linear motion | Steering, CNC axes, sliding gates |
| Planetary (epicyclic) | Coaxial | Sun, planets and ring share the load; high ratio in a small space | Automatic gearboxes, robot joints, wind turbines |
Worked example: a single-stage reducer
A 5 kW motor running at 1450 rev/min drives a 20-tooth pinion of module 2 mm, which meshes with a 60-tooth gear. Find the output speed and torque, the pitch diameters, the centre distance and the force on the teeth. Take the mesh efficiency as 98 %.
Step 1: ratio and output speed.
Step 2: torques.
Step 3: geometry.
Step 4: tangential force on the teeth.
The tooth force is what sizes the gear: it sets the bending stress at the tooth root and the contact stress on the tooth flanks, which are checked against the material’s strength using ISO 6336 or AGMA 2101. It also loads the shafts and bearings, which is the subject of the bearings and shafts guide.
Modelling gears in CAD
Most CAD packages generate standard involute gears from the module, tooth count, pressure angle and face width, or insert them from a toolbox library. For the drawing, gears are usually shown simplified (tip and pitch circles, no individual teeth) with a gear data table: module, number of teeth, pressure angle, helix angle, profile shift, pitch diameter, accuracy grade and the mating gear’s part number.
Key points
- Meshing gears roll on their pitch circles; the ratio is the tooth ratio, and they turn in opposite directions.
- Reducing speed multiplies torque by the same ratio, less a small loss per mesh.
- Pitch diameter = module × teeth; centre distance = module × (z₁ + z₂) / 2.
- Spur for simplicity, helical for quiet strength, bevel for right angles, worm for high ratios, planetary for compact high ratios.