Investigation of Magnitude and Position of Maximum von Mises Stress in The Cylindrical Contact Problems

In the analysis of contact mechanics problems, determination of stress field in mechanical elements is essential. Between the stress components the von Mises stress is more important, because it is used in the investigation of yield criteria and fatigue fracture of elements. The aim of this study is to present formulas for determining the magnitude and position of maximum von Mises stress. For this purpose, the effect of various material properties, element geometries and loading conditions on these two parameters are investigated. By applying Hertzian contact stress and von Mises relations, the magnitude and position of maximum von Mises stress are determined. The von Mises stress is assumed to be a function of material properties, geometry of the element and loading conditions and finally two formulas are presented for the calculation of the magnitude and position of maximum von Mises stress. The results of these presented formulas are in close agreement with the literature. The error is less than 1% for depth prediction and less than 6% for stress value prediction, which confirms the accuracy of the presented formulas