Numerical simulation of thermomechanically coupled transient rolling contact - An arbitrary Lagrangian-Eulerian approach

Doktorsavhandling, 2014

Numerical simulation of rolling contact serves as an important complement to laboratory and full-scale testing in the endeavour to further the understanding of related physical mechanisms, e.g. the influence of friction on the rolling motion, the thermomechanical interaction, damage phenomena and related modes of failure. In the development of computational methods for the analysis of rolling contact, a major challenge is to enhance predictive capabilities while keeping computational efforts reasonable. The work presented in this thesis aims to provide a general and versatile theoretical and computational framework for efficient, high-resolution analysis of fully transient, thermomechanically coupled, frictional rolling contact between two deformable bodies. To this end, the pertinent thermomechanically coupled boundary value problem is stated in terms of an Arbitrary Lagrangian--Eulerian (ALE) kinematical description, whereupon a computational framework is developed in the context of the Finite Element (FE) method. Here, the Streamline-Upwind Petrov--Galerkin (SUPG) method is implemented and a quasi Residual-Free Bubble (RFB) method developed in order to address numerical instability issues related to the convective ALE description of the energy balance equation. Other components of the computational model include a support for non-reflecting boundary conditions, irregular surface profiles, and a computationally efficient methodology for mixed control between rolling velocities and corresponding driving forces. In contrast to traditional and still predominant approaches to rolling contact, including semi-analytical methods based on Hertz and Carter theory, the described computational model provides a high geometrical versatility, and accommodates a thermomechanically coupled, fully transient analysis, including inertial effects. The ALE description is noted to allow for, among other things, a highly localized mesh refinement, linearization of the thermomechanical response, a compact computational domain and velocity-independent contact interface modelling. Numerical simulations are presented, covering a range of transient, thermomechanical rolling contact phenomena. These show the model to be able to capture e.g. fully transient stick/slip behaviour, negotiation of strongly non-smooth surface profiles, and a range of thermomechanical phenomena, including frictional heat generation and the effect of convective cooling of the rolling body due to the contact with the foundation. Numerical results are as far as possible validated toward analytical solutions.