Finite element analysis of transient thermomechanical rolling contact using an efficient arbitrary Lagrangian–Eulerian description

Abstract

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.

Finite element modelling of frictional thermomechanical rolling/sliding contact using an arbitrary Lagrangian–Eulerian formulation

“…For a more detailed derivation, see Draganis et al 8 In terms of the ALE description, the momentum balance equation takes the form ( denotes the dyadic (open) product)…”

“…8 Further,qN is the intrinsic (physical) heat flux, and the subscript P represents prescribed quantities.…”

“…In the present section, the ALE-formulation of the thermomechanically coupled boundary value problem -assuming isotropic, homogeneous and thermoelastic materials -is presented. For a more detailed derivation, see Draganis et al 8 In terms of the ALE description, the momentum balance equation takes the form ( denotes the dyadic (open) product)…”

“…By contrast, various numerical problems have been found to have a prominent influence for the discretized energy balance equation, even for very modest rolling speeds. 8 The numerical problems are manifested as node-to-node oscillations in the plate domain and oscillations together with energy dissipation in the cylinder domain. In order to address these problems, two numerical stabilization methods are employed: The Streamline-Upwind Petrov-Galerkin (SUPG) method 10,16 is used for the plate domain, and a quasi Residual-Free Bubble (RFB) approach 17,18 -a variant of the scheme presented in Brezzi et al 19 -is used for the cylinder domain.…”

“…The current paper builds on previously published developments 7,8 in order to present a finite element framework for the analysis of frictional, thermomechanically coupled rolling/sliding contact, based on an Arbitrary Lagrangian-Eulerian (ALE) kinematical description. [9][10][11] This approach leads to a more complicated boundary value problem, but also allows for highly localized mesh refinement, a more compact computational domain, linearization of the governing equations, a time-independent description of stationary rolling/sliding contact and velocity-independent contact interface modelling.…”