A Finite Element Study of the Deformations, Forces, Stress Formations, and Energy Losses in Sliding Cylindrical Contacts

This work presents the results of a Finite Element Analysis (FEA) used to simulate two-dimensional (2D) frictionless sliding between two interfering elasto-plastic cylinders. The materials for the cylinders are both modeled as elastic-perfectly plastic and follow the von Mises yield criterion. The FEA results in trends in the deformation, reaction forces, stresses, and net energy loss as a function of sliding distance. All these results are found to be related to the magnitude of vertical interference. In addition, equations representing the pattern followed by the residual deformation for each of these interference cases are shown. Contour plots of the von Mises stresses are also presented to show the formation and distribution of stresses with increasing plastic deformation as sliding progresses. This work shows that for the plastic loading cases the ratio of the vertical force to the horizontal reaction force is not zero at the point where the cylinders are perfectly aligned about the vertical axis. This work also presents empirical equations that relate the net energy loss due to sliding under an elasto-plastic deformation as a function of the sliding distance. In addition, a “load ratio” of the horizontal reaction force to the vertical one is defined. Although this is analogous to the common definition of the coefficient of friction between sliding surfaces, it just contains the effect of energy loss in plasticity. The values of the contact half-width are obtained for different vertical interferences as sliding progresses.