Contact Stresses

stresses arising from the mechanical interaction of solid deformable bodies in their areas of contact and in the vicinity of such areas—for example, during compression of bodies that are touching. A knowledge of contact stresses is important in calculating the strength of bearings, gear and worm drives, ball and cylindrical rollers, and cam mechanisms.

Contact stresses decrease rapidly with increasing distance from the area of contact. The distribution of contact stresses over the area of contact (see Figure 1) and in its vicinity is nonuniform and is characterized by large gradients. The maximum tangential stresses ℸ_max, which to a large extent determine the strength of compressed bodies (for example, in the compression of spheres or intersecting cylinders), arise at a certain depth (point A) beneath the area of contact. The stress state in the immediate vicinity of this area is close to hydrostatic compression, for which tangential stresses are known to be absent.

Figure 1. Stress distribution upon compression of spherical bodies: ( P ) compressive force, ( R₁ ,) and (R₂) radii of the spheres, ( p₀ ) maximum stress in the center of the area of contact S, (p) stress at distance r from the center of the area of contact, (a) radius of area of contact, (A) point of maximum stress