# Power Dissipation and Wear Modeling in Wheel-Rail Contact
## 1 Introduction
The thermo-elasto-plastic rolling contact problems are considered in papers [27; 28]. The two-dimensional problem in [28] is solved using the generalized Newton method. Contact stress distributions are provided and discussed. In paper [27], a three-dimensional problem is solved using the LS-DYNA programming environment. Recently, new wear models motivated by classical Archard's law and combined with a universal kriging technique have been formulated and numerically tested in papers [29; 30; 31]. Especially in paper [29], the wear coefficient is considered as a random variable. The wear rate is estimated as a segment with minimal and maximal values rather than as single deterministic value. This approach is applicable in damage analysis by providing a relatively accurate wear distribution along the contact interface. This paper deals with the estimation of power dissipation due to friction and the simulation of the wear propagation process in wheel-rail contact problems. The friction is governed by the Coulomb model [14]. Moreover, heat flow due to friction is also taken into account [14; 21]. We focus on power dissipation modeling rather than stresses as in [28]. This work develops a new approach to numerically estimate power dissipation and wear modeling in wheel-rail contact problems and provides new insights into the research of these problems. The elasto-plastic deformation of rail material is assumed. Wear estimation is based on the combined power dissipation and Archard models rather than the Archard model only. The simulation of the discretized contact problem is based on the generalized Newton method [30] rather than the Fastsim or Contact software methods [32]. The update finite element mesh algorithm related to the worn material volume rather than the general-type algorithm is used. Based on numerical results, a few conclusions are formulated. Contact patches obtained for an elasto-plastic case are characterized by longer zones and lower stress intensity than in the elastic case. For relatively small increases in temperature, the contact patches are slightly longer than for the plasto-elastic model. The power dissipated as well as the wear rate are strongly dependent on the friction coefficient, i.e., they increase when the friction coefficient increases. This paper has the following structure. Section 2 is concerned with the formulation and details of the elasto-plastic and thermal material models. Next, the rolling contact problem is presented. This problem is provided in the form of the system of two nonstationary coupled elasto-plastic and conductive equations with nonpenetration, friction and heat flow boundary conditions. The energy dissipated due to friction and the wear of rail in both the global and local forms are evaluated. In Section 3, the wear evaluation algorithm and its implementation details are described. The operator splitting method is used to numerically solve the coupled thermo-mechanical contact problem. A semi-smooth Newton method [32] is used to numerically solve this mechanical subproblem. In Section 4, numerical results including the distribution of the friction dissipated power, temperatures in the contact area, the change in the location and the geometry of the contact interface due to wear are provided.