Gear Pitting Analysis

Pitting is one of the failure modes of gears.

The surface durability of a gear is given by the Hertz contact equation:

$${\sigma }_c=-C_p{\left[\frac{K_v{W}_t}{F\cos \varphi }\left(\frac{1}{r_1}+\frac{1}{r_2}\right)\right]}^{1/2}$$

where $C_p$ is called the elastic coefficient and is defined by

$$C_p=\left[\frac{1}{\pi \left(\frac{1-v_P^2}{E_P}+\frac{1-v_G^2}{E_G}\right)}\right]$$

and $r_1$ and $r_2$ are defined by

$$r_1=\frac{d_P\sin \varphi }{2},r_2=\frac{d_G\sin \varphi }{2}$$

This ${\sigma }_C$ is compared against $S_c$ (surface strength), which is often parametrized by $H_B$ (Brinell hardness), e.g.

$$S_c=2.76H_B-70\text{ MPa}\text{or}0.4H_B-10\text{ kpsi}$$

for steel at $10^8$ cycles.

Example