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Hertz Theory: Contact of Cylindrical Surfaces, Fig. The orthogonal principal radii of curvature at a contact location are generally R 1x and R 1y for body 1 and R 2x and R 2y for body 2, but for the line contact, one for each body in the same orientation is infinite, such as R 1y and R 2y , as shown in Fig. 2.

Hertz showed that the contact stress that develops as two curved surfaces come in contact and deform under the imposed loads depends upon the normal contact force, the radii of curvature of both bodies as well as the modulus of elasticity of both bodies.

Hertz's theory considers the contact of two bodies with curved surfaces under force W. There is a theoretical point or line contact between the rolling elements and races. But due to elastic deformation, the contact area between two curved bodies in point contact has an elliptical shape.

Conformal contacts fit into each other with a high degree of geometrical conformity so that the load is carried over a large area. Non-conformal contacts have surfaces that do not conform to each other. In these contacts the load is carried by a small area.

Hertz theory assumes that surfaces are continuous and nonconforming, strains are small, each solid can be considered as an elastic half-space, and surfaces are frictionless. Under these assumptions, only normal pressure acts between two bodies due to Hertz contact producing normal displacements of the surfaces.

Practical examples include contact of a wheel and a rail, valve cams and tappets, in rolling bearings and mating gear teeth. High contact stresses may lead to failures such as cracks, pits and flaking in the surface material.

A conforming contact is one in which the two bodies touch at multiple points before any deformation takes place (i.e., they just "fit together"). A non-conforming contact is one in which the shapes of the bodies are dissimilar enough that, under zero load, they only touch at a point (or possibly along a line).

Hertz theory assumes that surfaces are continuous and nonconforming, strains are small, each solid can be considered as an elastic half-space, and surfaces are frictionless. Under these assumptions, only normal pressure acts between two bodies due to Hertz contact producing normal displacements of the surfaces.