Gear Tooth Contact Stress (Surface Durability)

Gear pitting - the Hertzian surface-durability stress, which often governs before root bending does.

Run the calculator

Example

You enter

You get

Checked against published worked examples from: McGraw-Hill.

Details, formula, and sources

Scopesigma_c = Cp sqrt(Wt / (F dp I)), with elastic coefficient Cp (about 2300 sqrt-psi for steel on steel), pinion pitch diameter dp = Np/Pd, face width F, and the AGMA geometry factor I = (cos phi sin phi / 2) mG/(mG+1) for an external spur mesh, mG = Ng/Np. The same 500 lb, 8-pitch, 1.5 in, 20-tooth pinion that runs 7,800 psi in bending sees about 76,500 psi in contact -- ten times higher, which is why pitting governs. Static value only: the AGMA 2001 Ko/Kv/Ks/Km/Cf factors are 1 and the allowable is the material's. Companion to the root bending check; AGMA 2001 and the gear maker govern.

Formula or tablesigma_c = Cp sqrt(Wt / (F dp I)); dp = Np/Pd; I = (cos phi sin phi / 2) mG/(mG+1), mG = Ng/Np (external spur); Cp about 2300 sqrt-psi steel on steel.

Source and editionHertzian gear contact stress for surface durability (J. O. Buckingham; Shigley, Mechanical Engineering Design) with the AGMA surface-durability geometry factor I, by name.

Free accessThe Hertzian contact-stress form and the external-spur geometry factor are standard published gear-durability theory (public domain / Shigley / Machinery's Handbook).

What governsEstimate. AHJ and licensed professional govern.

API field namestransmitted_load_lb, diametral_pitch_1_in, pinion_teeth, gear_teeth, face_width_in, pressure_angle_deg, elastic_coefficient_cp, contact_stress_psi, geometry_factor_I

Related tools