Conformal contact: corrections and new results

There has been a mistake in the work presented in the paper Solving conformal wheel-rail rolling contact problems' [Vollebregt E, Segal A. Solving conformal wheel-rail rolling contact problems. Veh Syst Dyn. 2014;52(suppl. 1):455-468] on conformal contact analysis. This concerns the reference results for the Hertzian/planar test-case. The effective lateral radius' was computed twice higher than it should be. This makes the Hertzian ellipse appear wider and shorter than in the corrected results. Furthermore, the effect of contact angle on the effective curvature was omitted in both the Hertzian and conformal test cases. Finally, it has been argued that there could be an error in our formulas for the creep calculation. In that case, however, the formulation proves to be right if interpreted properly, and is easier to understand than that of the earlier references. This paper presents the corrections and their effects on the results. The normal problem appears to be affected the most: the size and shape of the contact area, total force and maximum pressure. The corrections reduce the influence of conformality compared to the planar contact approach, in correspondence with findings of Blanco-Lorenzo etal. [On the influence of conformity on wheel-rail rolling contact mechanics. Tribol Int. 2016;103:647-667]. The tangential problem is affected also, through the traction bound . There the same conclusions hold as before, when looking at other, closer conformal contact situations.