WIT Press

Non-Hertzian Rolling Contact Stress Analysis


Free (open access)








700 kb

Paper DOI



WIT Press


C. H. Liu & W.-E. Hsu


In a previous study the three-dimensional rolling contact problem under Hertzian pressure has been dealt with. Two new initial guesses for the Newton-Raphson method were proposed, which always lead to convergent solutions for tangential stresses. However, non-Hertzian contact often appears in moderately used contact elements. The present study extends the previous study to cases with non-Hertzian contact. In particular the counter-formal case is treated. In this case the contact region can still be bounded by a plane, although the contact pressure is not Hertzian. The previous numerical algorithm is used to treat counter-formal contacts, and convergent results can always be obtained. Keywords: rolling contact, rail and wheel contact, non-Hertzian contact, computational stress analysis. 1 Introduction Rolling contact occurs in many mechanical pairs, such as gear and pinion, cam and follower, wheel and rail, and also in ball to ball contacts in bearings. Many analytical as well as numerical techniques have been suggested to solve for rolling contact stresses. Basically these techniques can be grouped into the following three categories: the integral equation method [1–5], the method based on variational principles [6,7], and the mixed method [8–10] that makes use of both of the two preceding methods. Among the various techniques based upon integral equations, the numerical procedure developed by Liu and Paul [5] may determine tangential contact stress distribution for elastically similar bodies in rolling contact. Their iterative procedure showed fast convergence for cases with small spins, but might fail to converge for cases with even moderate values of spin. In a previous study by Liu and Hsu [11], Liu and Paul’s numerical scheme was improved by using two new initial guesses, so that it might also converge


rolling contact, rail and wheel contact, non-Hertzian contact, computational stress analysis.