Question

Hertzian Contact streess

A ball and socket joint used at the end of an automotive rocker arm has a hardened steel spherical surface 20 mm in diameter fitting in a hard–bronze alloy spherical seat 20.2 mm in diameter. Determine the maximum contact stress resulting from a load of 2,000 N.

The hardened steel rocker arm material properties:

Poisson’s ratio ?steel = 0.3, modulus of elasticity Esteel = 207 GPa

The hard–bronze alloy spherical seat material properties:

Poisson’s ratio ?bronze = 0.33, modulus of elasticity Ebronze = 110 GPa

Assumptions:

• The contacting surfaces are smooth and continuous

• The radii of curvature are large compared to the dimensions of the contact area

• The compressive yield stress of the weaker material is not exceeded

Briefly discuss the implications for maximum contact stress if the diameters of the rocker arm’s spherical surface and the spherical seat were equal.

Answer 1