SPUR GEARS (GEOMETRY, LEWIS BENDING)

Spur gear geometry is set by the module m (or diametral pitch P_d in inch units), number of teeth N, and pressure angle (commonly 20°). Pitch diameter d = m·N. Contact ratio measures how many tooth pairs share the load at any instant; 1.4-1.8 is typical. The Lewis bending equation estimates root stress: σ = W_t / (F·m·Y) where Y is the Lewis form factor based on tooth count. Modern AGMA design adds geometry, dynamic, and surface-condition factors.

• d = m · N
• i = N₂ / N₁
• C = (d₁ + d₂) / 2
• σ = W_t / (F · m · Y) (Lewis)
• m_c = (Z_a + Z_r) / p_b (contact ratio)

References & StandardsAGMA 2001, ISO 6336, ANSI B6.1

Size gears for any rotational power transmission: gearbox, automotive transaxle, robot joint, conveyor drive. Start with required ratio and center distance, then iterate on module to satisfy bending and contact-stress allowables. Pinion is typically critical (smaller, higher tooth-load cycles). Verify backlash, undercut for pinions with low tooth count, and lubrication for pitting resistance.