The Hertzian contact theory is approximated according to a concept by Tanaka (2001, “A New Calculation Method of Hertz Elliptical Contact Pressure,” ASME J. Tribol., 123, pp. 887–889) yielding simple analytical expressions for the elliptical semi-axes, the maximum contact pressure, the mutual approach and the contact spring constant. Several configurations are compared using the exact Hertz theory and the current approximation. The results agree within technical accuracy.
Approximate Analytical Model for Hertzian Elliptical Wheel/Rail or Wheel/Crossing Contact Problems
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Fischer, F. D., and Wiest, M. (August 1, 2008). "Approximate Analytical Model for Hertzian Elliptical Wheel/Rail or Wheel/Crossing Contact Problems." ASME. J. Tribol. October 2008; 130(4): 044501. https://doi.org/10.1115/1.2958074
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