A theoretical and computational framework for the analysis of thermomechanically coupled transient rolling contact, based on an arbitrary Lagrangian-Eulerian (ALE) kinematical description, is developed. A finite element formulation featuring 2D cylinder-plate rolling contact is implemented. The implementation features penalty-type contact formulations for mechanical and thermal contact. It is noted that the ALE formulation allows for a simplified time description, a compact computational domain and localized mesh refinement. Numerical simulations considering stationary and transient rolling conditions are presented. Highlighted aspects include the influence of variations in thermal contact conductivity, rolling speed and external mechanical load on the contact interface heat flow. The model is shown to give predictions in qualitative agreement with results in the literature. For the velocity range studied, numerical issues such as spurious numerical dissipation/oscillations in the temperature field are noted to have a prominent influence. These phenomena are addressed using a Streamline-Upwind Petrov-Galerkin stabilization scheme together with a bubble function approach.

A theoretical and numerical framework to evaluate rolling contact using an arbitrary Lagrangian-Eulerian (ALE) formulation is established. A finite element formulation is implemented featuring cylinder-plate contact, automated mesh refinement, non-reflecting boundary conditions, and the ability to incorporate surface roughness through user-defined gap functions. Presented examples include rolling contact on a corrugated surface and negotiation of a surface discontinuity. Sensitivity and validation analyses are presented and show the model to be robust and the trends in parametric responses to be reasonable as compared to results in literature. Owing to the ALE formulation, the model can be kept very compact and the computational demands very modest.

A theoretical and computational framework for the analysis of fully transient, thermomechanically coupled, frictional rolling contact based on an arbitrary Lagrangian–Eulerian (ALE) kinematical description is presented. In particular, a computationally efficient methodology for mixed control between the ALE referential velocities and their corresponding driving forces is developed and discussed in depth. Numerical examples involving two-dimensional (2D) cylinder–plate rolling contact are presented, covering a range of transient, thermomechanically coupled rolling contact phenomena, taking place on a broad range of time scales. Here, particular points of emphasis include dynamical effects in the vicinity of the contact region and the time scales on which mechanical and thermal mechanisms operate.

A theoretical and computational framework for the analysis of thermomechanically coupled, frictional, stationary (steady-state) rolling contact based on an Arbitrary Lagrangian-Eulerian (ALE) kinematical description is presented. The finite element method is employed in a numerical implementation featuring two-dimensional cylinder-plate rolling contact, with a contact formulation incorporating mechanical and thermal frictional interaction. The ALE formulation is noted to allow for linearization of the governing equations, localized mesh refinement, a time-independent description of stationary dynamics, velocity-independent contact interface modelling and so on. Numerical simulations show the model to be able to capture, for example, stick/slip behaviour and a range of thermal phenomena, including the effect of convective cooling of the cylinder due to the contact with the plate.