## 1 Introduction  
The good quality of current collection performed by the pantograph is an important factor in ensuring the stable operation of high-speed trains. Research on the uplift characteristics of pantographs under crosswind conditions has been advanced through significant contributions from scientists worldwide. [PERSON], [PERSON] [1] laid the groundwork by identifying the increased uplift forces caused by crosswinds, leading to further investigations using wind tunnel models by [PERSON], [PERSON] et al. [2]. [PERSON] et al. [3] focused on the role of individual components but did not as comprehensively explore the variations in aerodynamic lift across different components. In this study, this is extended by showing that the bow collector experiences the most significant uplift, while the upper frame experiences negative lift, an observation that was not detailed in the previous literature. [PERSON] et al. [4] provided wind tunnel studies on crosswind effects but did not capture this non-linear behavior. In this study, their experimental work is developed by using advanced numerical simulations (DES) to show how aerodynamic lift behaves at extreme wind angles and speeds, offering new insights that were not previously reported. [PERSON] et al. [5] previously identified the importance of the pantograph head; in this study, this is expanded by detailing how crosswind angles affect different components, offering more precise guidance for optimizing pantograph design. European researchers have since focused on integrating aerodynamic analyses with overall train stability and control, contributing to the development of robust pantograph designs that maintain reliable contact with the catenary under varying wind conditions [6]. Meanwhile, American scientists have emphasized advanced CFD modeling and experimental studies, which have deepened the understanding of complex airflow patterns and dynamic responses of pantographs [7]. These global efforts have collectively improved the safety and efficiency of high-speed rail systems, although challenges remain, particularly in addressing extreme crosswind conditions as train speeds continue to rise. In this study, we seek to build on these global contributions by offering a comprehensive analysis of pantograph uplift under crosswind conditions, aiming to enhance the overall understanding and mitigation strategies. The contact force of the bow net includes two parts, the static lift force and the aerodynamic lift force generated by the pantograph, collectively referred to as the dynamic contact force of the bow net. The static lift force is generally around 70 N, typically not exceeding 90 N [8; 9; 10]. During high-speed operation, the contact pressure between the bow net and the pantograph is the sum of the static lift force and the aerodynamic lift force generated by the pantograph, known as the dynamic contact force of the bow net. During the sliding contact between the pantograph and the contact line, if the dynamic contact force is too small, the contact resistance increases, leading to phenomena such as the pantograph lifting and arcing during operation [11]. Conversely, if the contact pressure is too high, local grooves may be formed on the sliding block, resulting in serious accidents such as the contact wire bouncing and pantograph scraping. Therefore, it is necessary to ensure a reasonable aerodynamic lift force for the pantograph during operation, which requires the pantograph itself to have good aerodynamic characteristics [12; 13]. A large amount of research has been conducted based on the dynamics of the bow net, but there is relatively little research on the impact of aerodynamic forces on the contact force of the bow net, especially without considering the change in aerodynamic effects of the pantograph under crosswind conditions [14; 15; 16]. Furthermore, as the train speed increases, the impact of aerodynamic forces cannot be ignored. Combined with the effect of crosswind, the law of aerodynamic lift force of the pantograph also changes.