Theoretical calculation of the instantaneous friction-induced energy losses in arbitrarily excited axisymmetric mechanical contact systems. (February 2019) - Truyaert, Kevin; Aleshin, Vladislav; Van Den Abeele, Koen; Delrue, Steven
Abstract: In this paper, we present the theoretical formula for calculating a friction-induced energy loss in a mechanical contact system consisting of two convex axisymmetric bodies subject to arbitrarily varying oblique loading. Non-flat contact geometry engenders a particular regime, partial slip, in which weakly compressed areas of the contact zone slip, while strongly compressed ones stick. Mechanical energy is transformed into heat only in the slip area in which two field characteristics should be calculated: the local infinitesimal slip distance distribution and shear stress. Their product equals the spatial distribution of the energy loss or heat source density, while the integration over the slip zone produces the global energy loss. The energetic characteristics are obtained in a general situation. In the proposed method, energy losses can be calculated at any time during a loading protocol, in the general case of an arbitrary load expressed in terms of normal and tangential displacements. This is a step forward in comparison to more traditional approaches in contact mechanics allowing to calculate the energy loss per period in the case where the contact is excited by a single periodic input. In this work, the loading is limited to two dimensions: one normal and one tangential. Therefore, the tangential loading is colinear with the tangential displacement. All required contact characteristics, including displacement and stress distributions, are provided by the semi-analytical Method of Memory Diagrams (MMD) that has initially been developed to obtain memory-dependent solutions to the problem of frictional contact between axisymmetric profiles and has later been generalized for rough surfaces. Correspondingly, the proposed solution is exact for axisymmetric bodies and is approximately valid in the case of rough surfaces for which the energy loss per unit nominal area is calculated. The obtained theoretical results for energy dissipation are compared to analytical and numerical calculations for periodic and non-periodic loading situations, illustrating the potential of this method in realistic contact settings.