Transient tractive rolling contact between elastically dissimilar and multi-layered bodies

Abstract

This paper discusses the tractive rolling contact between dissimilar and multi-layered bodies. Drawn from the Kalker’s theory on the three dimensional rolling contact, the rolling contact in presence of tangential forces and a spinning moment is formulated. In the present paper, the focus is put on the tangential component of the problem. Then, the variational formulation of the contact problem is solved using a Conjugate Gradient Method (CGM) coupled with Fast Fourier Transform (FFT) algorithms for acceleration. The proposed solver allows to solve the tractive rolling contact problem in both transient and steady-state regimes. The multi-layered aspect of the bodies in contact is taken into account through the influence coefficients used for the calculation of the elastic displacements and stresses. Further, a validation of the model is performed by comparison with models from the literature. The transition from the Cattaneo–Mindlin shift to the steady-state regime is analysed, with Kalker’s solution in the validation section for elastically similar bodies, and further in a parametric study for elastically dissimilar bodies. Moreover, the parametric study allows to highlight the effects of various combinations of the tangential loading input on the stick and the slip zones within the contact zone. Finally, the three dimensional stresses are analysed in a multi-layered body.