Short notes on gear standardisation

(a) Module and diametral pitch

• Module $m = d/z$ (mm): pitch circle diameter divided by number of teeth. It is the metric size of the tooth. Gears must have the same module to mesh. Standard modules (ISO/IS) include 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12 mm.
• Diametral pitch $P = z/d$ (teeth per inch) in the inch system, with $P = 25.4/m$.
• Circular pitch $p_c = \pi m = \pi d/z$.

(b) Standard tooth systems

• Gears from the same system and module are interchangeable.
• The 20 degree system has a stronger tooth (thicker at the root) and a smaller $z_{min}$ (18) than the 14.5 degree system (32).
• Stub teeth are stronger and avoid undercutting but have a smaller contact ratio.

(c) Undercutting

When a gear is cut with a hobbing cutter or rack cutter and the number of teeth is below $z_{min}$, the cutter tip removes part of the tooth root below the base circle. The tooth becomes thin at the root and weak, and the useful involute is shortened.

Remedies: use a larger pressure angle (20 or 25 degrees), stub teeth, or profile shifting (the cutter is moved outward by $xm$ so that the tooth gets a thicker root).

The minimum number of teeth to avoid undercutting for a rack cutter is $z_{min} = 2/\sin^2\phi$.