Rapid-convergence iterative method for Hertzian point contact theory

Point contact theory between two bodies with constant curvature was built by H. Hertz. His theory is now widely known as "Hertzian contact theory" and it is widely applied to the calculation of the stiffness of ball bearings and CVJs. Calculation of the theory, however, has some difficulties: numerical calculation of the complete elliptic integrals and convergence calculation for ellipticity parameter are required. Some fitting equations have been already suggested to resolve the difficulties. They are convenient for hand calculation, but they are too rough to calculate with the latest high-spec computers. So more accurate algorithm for Hertzian contact theory is required. In this paper, rapid-convergence iterative method is suggested for computing the theoretical solution of Hertzian contact theory. The method can be programmed simply and converge rapidly because the method is based on "self-convergence algorithm" which is also suggested in this paper. As 10-digit accurate values can be get by 3 iterations, the method is fast enough to apply to dynamic simulations, in which point contact has to be evaluated very frequently.

Abstract licence: CC BY-NC-ND

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