Encyclopedia of Tribology

2013 Edition
| Editors: Q. Jane Wang, Yip-Wah Chung

Hertz Theory: Contact of Spherical Surfaces

  • Q. Jane WangEmail author
  • Dong Zhu
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-92897-5_492



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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  1. J. Boussinesq, Application des Potentiels à l'étude de l'équilibre et du mouvement des solides élastiques, Librairie Scientifique et Technique (Albert Blanchard, Paris, 1885, 1969)Google Scholar
  2. R. Gohar, A. Cameron, Optical measurement of oil film thickness under elasto-hydrodynamic lubrication. Nature 200, 458–459 (1963)CrossRefGoogle Scholar
  3. H. Hertz, On the contact of elastic solids,in Miscellaneous Papers (MacMillan, London 1881/1896)Google Scholar
  4. H. Hertz, On the contact of rigid elastic solids and on hardness, in Miscellaneous Papers (MacMillan, London, 1882/1896)Google Scholar
  5. Y.Z. Hu, D. Zhu, A full numerical solution to the mixed lubrication in point contacts. ASME J. Tribol. 122(1), 1–9 (2000)CrossRefGoogle Scholar
  6. K.L. Johnson, Contact mechanics (Cambridge University Press, Cambridge, UK, 1985, 1996)zbMATHCrossRefGoogle Scholar
  7. M.T. Kirk, Hydrodynamic lubrication of “perspex”. Nature 194, 965–966 (1962)CrossRefGoogle Scholar
  8. Y. Liu, Q. Wang, Y. Hu, W. Wang, D. Zhu, Effects of differential schemes and mesh density on EHL film thickness in point contacts. ASME J. Tribol. 128, 641–653 (2006)CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Center for Surface Engineering and TribologyNorthwestern UniversityEvanstonUSA
  2. 2.State Key Laboratory of Mechanical TransmissionChongqing UniversityChongqingPeople’s Republic of China