# Simulation Study of Thermal-Mechanical Coupling Fretting Wear of Ti-6 Al-4V Alloy
## 1 Introduction  
Fretting is the vibratory motion of two contacting objects under the action of a small relative displacement. Frictional behavior accompanying fretting can lead to material damage, including fretting wear and fretting fatigue [1; 2; 3]. Friction and plastic deformation during fretting wear generate energy and dissipate it in the contact area, leading to temperature rise [4; 5]. Temperature affects the mechanical and thermal properties of a material, including its Young's modulus, yield limit, density, specific heat, and thermal conductivity among others. These material characteristics significantly affect fretting wear, seriously jeopardizing the dependability of the mechanical power system's contact parts [6]. Therefore, the influence of the temperature rise of the contact surface needs to be considered in the fretting wear simulation study. For wear problems, the most common wear models include the Archard wear model [7] and the energy dissipation wear model [8]. The Archard wear model is a simplified model related to normal stress, relative slip, and material hardness. It is frequently employed in finite element simulation analysis [9; 10]. The Archard model, however, is unable to account for the impact of debris and rough surface microtopography. The Archard wear model is consequently updated and improved on a regular basis. A finite element model consideringthe effect of a third body (wear debris) on refetting wear in partial slip states was developed by [PERSON] et al. [11]. It demonstrates that the presence of the third body can tremendously affect the fretting wear rate. Two-dimensional models of adhesive wear and abrasive wear on rough surfaces were established by [PERSON] et al. [12] based on fractal theory. They studied the wear of the steel spool valve and discussed the significant effect of the three-body layer on surface damage. [PERSON] et al. [6] extended the 2D model to 3D to analyze the fretting wear process on rough surfaces, and the accuracy of the model is progressed by the neural network algorithm. However, the Archard wear model is only applicable when the friction coefficient is constant [13; 14]. The energy dissipation wear model has also been widely used in recent years because it is not affected by the friction coefficient. Electrical contact durability under fretting wear was studied by [PERSON] et al. [15] using an energy dissipation model. The failure of electromagnetic induction is then examined. A spherical/spherical lateral contact model involving the contact angle was developed by [PERSON] et al. [16] based on the energy dissipation model. The influence of contact angle and different load conditions on fretting wear is obtained through this model. There is a strong interaction between fretting wear behavior and temperature [17], but none of the above studies consider temperature. Numerical methods are widely used in the prediction of temperature distribution due to the difficulty in measuring the temperature in the contact zone under fretting. The finite element model of the fractal rough contact surface was established by [PERSON] et al. [18] to study the temperature rise distribution in the fretting contact. The variation of the wear profile was considered by [PERSON] et al. [5] to study the effect of wear on the temperature field of the fretting contact. [PERSON] et al. [19] studied the thermal response of Ti-6 Al-4V alloy fretting sliding by integrating the factors of wear, roughness, and plastic dissipation and obtained the influence law of surface roughness and plastic dissipation on temperature rise. Although wear effects were taken into account, the study of the temperature rise distribution on the contact surfaces was the main objective of these works. Meanwhile, the Archard wear model, which cannot be used in situations where the friction coefficient varies, was employed in these studies. The Archard wear model is not appropriate for wear studies that take temperature into account because temperature changes affect the friction coefficient [20; 21].