# A Study on the Pantograph Slide Wear Model Based on Energy Dissipation
## 1 Introduction  
The pantograph slide and the catenary wire form a typical sliding electrical contact friction pair, which provides the necessary energy for the stable operation of electric locomotives through sliding contact. Compared to the pantograph slide, the catenary wire, as a power transmission line, has higher hardness and is difficult to replace, requiring a longer service life. Therefore, the current-carrying wear between the pantograph and catenary system is mainly borne by the pantograph slide [1]. Under sliding electrical contact conditions, the wear mechanism of the pantograph slide is complex, involving both mechanical and electrical wear, as well as the coupling effects between them. The interaction of these two types of wear accelerates the overall degradation [2]. As a consumable friction pair, if the pantograph slide is worn beyond its limit without timely replacement, it will affect the safety of train operations [3,4]. Therefore, developing a friction and wear model for the pantograph slide is of significant theoretical and practical value inpredicting the lifespan of the friction pair and guiding the friction design of the pantograph-catenary system. In recent years, scholars both domestically and internationally have made significant contributions to the modeling of pantograph slide wear. Based on the relevant literature, there are currently two main approaches to predicting the wear of the pantograph slide and catenary wire. One approach is to calculate the correlation coefficients between various influencing factors and wear and derive a fitting formula for wear. For example, [PERSON] et al. [5] studied the wear of the pantograph slide under different current, speed, and fluctuating load conditions and developed a regression prediction model for the wear of the pantograph slide. [PERSON] et al. [6] investigated the effects of the catenary contact pressure, contact current, sliding speed, and operating time on the wear of pure carbon pantograph slides, using partial least squares regression to establish a wear prediction model, and analyzed the influence of each parameter on wear. [PERSON] et al. [7] established a support vector regression-based model to predict the wear trends of subway pantograph slides, enabling the prediction of wear based on the operational mileage. [PERSON] et al. [8] developed a wear prediction model for the pantograph slide by analyzing the variation in wear with the operational temperature under different parameters, incorporating the effect of the temperature. The second approach is to analyze the wear evolution and mechanisms under various influencing factors and derive a mathematical wear model. For example, [PERSON] et al. [9] considered both mechanical and electrical wear, as well as the coupling wear between them, and used the Archard wear model to establish a mathematical expression for the wear rate. [PERSON] et al. [10] proposed a heuristic wear model for the pantograph slide and catenary wire, which can be used in conjunction with a numerical model of the pantograph-catenary interaction to predict wear over long periods. Some scholars have established related wear prediction models based on the wear mechanisms proposed by [PERSON] and [PERSON] [11]. For example, [PERSON] et al. [12] proposed an adaptive wear prediction method through pantograph-catenary coupling dynamic simulations combined with experimental data. [PERSON] et al. [13], based on the [PERSON] and [PERSON] theory, established a wear prediction model for the pantograph slide and catenary wire by combining actual maintenance data from subway lines. However, in most of the models established through the aforementioned methods, the influence of the friction coefficient on wear is not considered.