Gears

Gear terminology

The pinion (p) is the smaller gear in a meshing gearset and the wheel (w) is the larger.

The circular pitch, p is the spacing of gear teeth measured around the pitch circle.

i.e. circular pitch, p = pi D / T

Since it is impractical to specify the circular pitch as a precise measure of tooth size (because pi is used), in the SI system the module, m is used for specifying tooth size. The module is the ratio of pitch diameter to number of teeth.

i.e. metric module, m = D_p / T_p = D_w / T_w

For gears in mesh,

Centre distance, C = (D_w + D_p) / 2
Tangential velocity, v = pi D_p n_p/ 60 000 =pi D_w n_w / 60 000
Gear reduction, R = T_w / T_p = n_w / n_p = d_w / d_p
Overall reduction (compound gear trains), R = R1 R2 R3 . . .

The involute tooth profile is most common in general use because the profile has many important advantages: -

The tooth geometry is fully defined by reference to a simple straight sided rack; this enables cutters to be produced accurately and cheaply.
All gears are generated from a given rack (regardless of diameter and number of teeth) and so will intermesh correctly.
Any variation in centre distance (due to shaft deflection and manufacturing tolerances) will not affect uniform motion.
The weakening of gears with small numbers of teeth by undercutting may be reduced by modification enabling standard cutters to be used at adjusted machine settings.

See the adjacent diagram for definitions of other terms. The involute tooth profile is generated about the Base Circle Diameter. Meshing gear teeth will be in contact along the Contact (or Pressure) Line which passes through the Pitch Point. The angle subtended by this line and the common tangent between meshing gears is called the Pressure Angle and in the British Standard system of gears an angle of 20^o is used.