# Power Dissipation and Wear Modeling in Wheel-Rail Contact
## 1 Introduction  
The contact occurring when a wheel moves over a rail is characterized by high stress in the contact patch, creep distribution as well as the friction phenomenon. It can lead to the gradual wear of surfaces and the deterioration of wheel and rail operational conditions [1]. The rolling contact fatigue phenomenon is frequently observed in rolling contact. This phenomenon, caused by a high alternating stress field in the contact area, leads to material removal driven by crack propagation. This phenomenon also accounts for wheel squeal noise [2]. This unpleasant noise, occurring mainly due to lateral creepage, is troublesome in densely populated areas. The wear phenomenon is described as the gradual removal or deformation of material from the surface of a solid body subjected to physical or chemical factors [1, 3, 4]. This phenomenon may be generated by corrosion, repeated cyclical rubbing between two surfaces or different chemical factors. It involves different physical processes from nano- to macro-scale dependent on many parameters. Wear and rolling contact fatigue may lead to the appearance of worn material debris in the gap between the bodies in contact or cracks on the contacting surfaces. It leads to an update or change in the position and shape ofthe surfaces in contact. For the surfaces of wheels and rails in contact, the update in the longitudinal or transversal directions is especially visible. The update of surfaces in contact due to wear makes the numerical modeling of this phenomenon very difficult. One way to reduce these numerical challenges is to much better understand the metallurgical aspects of the wear phenomenon. Such investigations are performed in many laboratories [5]. The ultrafast friction energy dissipation models at nano-scale, including the dynamics of excited electrons and phonons, are reviewed in [3]. Although many different wear laws are formulated in the literature or used in industry, they can be divided into two groups [1; 4; 6]. The first approach to formulating the wear law is based on the equations relating normal loads and the amount of worn material. The other approach consists of evaluating the volume of the worn material as proportional to the energy or power dissipated due to friction forces at the contact interface. Both approaches can be also considered either as global or local wear laws. The global form of the wear law leads to the estimation of the volume of the worn material based on the calculation of global forces and creepage along the contact interface [7]. In the local form of the wear law, its impact on contacting surfaces results from the friction coefficient, tangential force and sliding velocity along the contact zone. Local and global approaches to wear estimation also have different impacts on its computational modeling. The calculation of wear according to the local wear law directly provides the wear depth along the contact zone. However, this approach is usually characterized by a higher computational cost than calculation based on the global wear law. On the other hand, global wear law calculation requires an additional computational effort to redistribute the total volume of the worn material along the contact patch at each time step. The wear evolution process of wheels and rails is a slow, strong, nonlinear phenomenon. From experimental or numerical tests [1; 8; 9; 10], it follows that this process depends on many variables, including operating conditions, initial profiles, contact and friction conditions, stresses and their distribution, temperature, materials or surface properties and parameters. The sensitivity of sliding velocity and contact pressure with respect to the friction coefficient is experimentally investigated in [11], where a series of pin-on-disc tribometer experiments is realized. Since these factors are changing during the wheel movement, the friction coefficient as well as friction energy are changing.