Hertz Theory: Contact of Spherical Surfaces
Contact of bodies occurs in all interfaces transmitting force or motion, or both. The Hertzian contact (Hertz 1881, 1882) is referred to the frictionless contact between two bodies. Spherical contact is a special case of the Hertz contact, which is between two spheres, or between a sphere and the surface of a half space. This type of contact is also called the point contact because theoretically the contact spot is a “point” before load application; the contact spot becomes a “circular area” once the bodies are deformed under loading, giving it another name, the circular contact. In general, if the elements in contact have three-dimensional shapes, such as balls in a rolling-element bearing shown in Fig. 1, the contact can be simplified into the interaction between two ellipsoidal bodies determined with the orthogonal principal radii of curvature at...
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