基于有限元的高速列车车轮多边形磨耗成因分析

研究了中国高速列车车轮多边形磨耗的形成原因，考虑轮对的旋转惯量，建立了高速列车轮对-轨道-盘式制动系统有限元模型. 基于轮轨系统摩擦自激振动的理论，采用有限元复特征值分析法研究了高速列车制动时轮对-轨道-盘式制动系统的稳定性. 研究了饱和的轮轨蠕滑力和盘式制动系统摩擦力耦合作用对车轮多边形磨耗的影响，并调查了轮轨-轨道-盘式制动系统的参数敏感性. 数值模拟结果表明:在饱和的轮轨蠕滑力和盘式制动器摩擦力耦合作用下，轮轨系统的摩擦自激振动导致高速列车车轮多边形磨耗的产生，其导致的21~22阶和23~24阶车轮多边形磨耗占主导地位，这与中国高速列车高阶车轮多边形磨耗最为符合. 饱和的轮轨蠕滑力主要影响较低阶车轮多边形磨耗，盘式制动器摩擦力主要影响较高阶车轮多边形磨耗. 制动压力为13 kN时，车轮多边形磨耗形成的几率最小，发展速度最慢. 过高或者过低的垂向悬挂力均不利于抑制车轮多边形磨耗. 垂向悬挂力为75 kN时，车轮多边形磨耗形成的可能性最小，发展速度最慢. 

Formation of Polygonalization of the High-Speed Train Wheels Based on the Finite Element Method

In recent decades, the high-speed railway in China has developed rapidly, and its operating mileage and speed rank first in the world. The high-speed railway traffic and transportation have greatly facilitated the travel of people and goods transport. However, serious wheel tread damage also comes with the increase of high-speed train operation speed and the expansion of operation scale. Wheel polygonalization is one of the most prominent tread damage problems at present. Wheel polygonalization will cause strong vibration of the vehicle-track system and annoying noise emission, which poses a potential threat to the safety of high-speed train operation and deteriorates the operation quality of the trains. High-order polygonal wear (14~24 order) is dominant on the wheel treads of high-speed trains in China, whose causes of formation are still unclear. When the train runs at high speed, the vibration caused by the high-order polygonal wear is particularly severe, which seriously affects the operation safety of high-speed trains and limits the further improvement of train speed. Therefore, it is very urgent to reveal the causes of high-order wheel polygonal wear and develop effective control measures.　Considering the periodicity of wheel polygonal wear on wheel tread, it is most likely to be caused by some form of vibration. As an important vibration form of the wheel-rail system, frictional self-excited vibration may be a potential cause of wheel polygonal wear. When the frictional self-excited vibration of the wheelset-track system occurs, the wheel-rail normal contact force will oscillate, leading to the fluctuation of the wheel/rail friction power, which may eventually lead to the formation of wheel polygonal wear. The frictional self-excited vibration of the wheelset-track system may be induced by the saturated creep force between the wheel and rail or the friction between the brake disc and brake pad. When the high-speed train is braked by the disc brake system, the creepage between the wheel and rail will increases significantly, and the creep force between the wheel and rail is likely to be saturated. In that case, the coupling effect of the saturated creep force and the friction of the disc brake system must be considered when studying the relationship between the frictional self-excited vibration of the wheelset-track system and the formation of wheel polygonal wear. In this paper, the coupling influence of the saturated creep force between the wheel and rail and the friction of the disc brake system on polygonal wear of high-speed train wheels was studied based on the theory of frictional self-excited vibration. A finite element of wheelset-track-disc brake system of high-speed train was established. The complex eigenvalue analysis based on the finite element method was performed to investigate the stability of the wheelset-track-disc brake system when the high-speed train was braked by the disc brake system on a straight track. The frequency distribution and corresponding mode shapes of the frictional self-excited vibration of the wheelset-track-disc brake system were analyzed to clarify the relationship between the frictional self-excited vibration of this system and the formation of wheel polygonal wear. A new generation mechanism of wheel polygonal wear has been found, which can be used to explain the high-order polygonal wear on the wheels of high-speed trains in China. The influence of the vehicle speed, braking pressure and vertical suspension force on wheel polygonal wear were studied to develop measures to restrain wheel polygonal wear.　The results showed that the friction-induced vibration of the wheelset-track-disc brake system occurred when the saturated creep force was coupled with the friction of the disc brake system. The vibration frequencies were 203.0, 422.0, 422.2, 592.2, 679.2 and 784.3 Hz. The vibrations at these frequencies may cause wheel polygonal wear of 7~8, 14~15, 20~21, 23~24 and 27~28 order, respectively. The 20~21 and 23~24 order wheel polygonal wear caused by the vibrations at 679.2 Hz and 592.2 Hz were dominant, which was consistent with that the 20~24 order polygonal wear was the most significant in Chinese high-speed trains. The vehicle speed had obvious influence on wheel polygonalization. When the speed was 250 km/h, the frequencies of the dominant unstable vibrations were 578 Hz and 800 Hz, which may cause 23~24 order and 33~34 order wheel polygonal wear. When the speed was 350 km/h, the frequencies of the dominant unstable vibrations were 578 Hz and 748 Hz, which may cause wheel polygonal wear of 17~18 order and 22~23 order, respectively. The braking pressure had obvious influence on wheel polygonalization. When the braking pressure were 7.5, 13 and 15 kN, the frequencies of the dominant unstable vibrations falled in 650~700 Hz, these unstable vibrations led to the 22~24 order polygonal wear. When the braking pressure was 10 kN, the frequency of the dominant unstable vibration was about 159 Hz, which caused the 5~6 order polygonal wear. When the braking pressure increased to 21 kN, the unstable vibration at 546.4 Hz was dominant, which led to the 18-19 order polygonal wear. The vertical suspension force also obviously affected the wheel polygonal wear. The frequency and the real part of the dominant unstable vibration changed obviously with the change of the vertical suspension force. When the vertical suspension force was 50 kN and 90 kN, the frequencies of the dominant unstable vibrations were about 758.9 Hz and 786.2 Hz, respectively. The 26~28 order wheel polygonal wear can be generated. When the vertical suspension was 75 kN, the frequency was about 679.2 Hz, the 20~21 order wheel polygonal wear can be generated. According to the results of numerical simulation, the following conclusions can be drawn. 　When the high-speed train was braked by the disc brake system, the wheel/rail creep force was easy to be saturated. The friction-induced vibration of the wheelset-track-disc brake system was excited by the saturated creep force and the friction of the disc brake system. The frequencies of the dominant unstable vibrations falled in 590~680 Hz. The unstable vibrations at these frequencies were the main cause of the 20~24 order polygonal wear in Chinese high-speed trains. Both the saturated ceep force and the friction of the disc brake system had an important influence on the friction-induced vibration of this system. The saturated creep force mainly led to lower frequency vibration, leading to the formation of lower-order wheel polygonal wear. However, the friction of the disc brake system mainly led to higher frequency vibration, leading to higher-order wheel polygonal wear. Due to the inertia of the wheelset, the frictional self-excited vibration of the wheelset-track-disc brake system led to wheel polygonal wear of different orders. Therefore, when studying the wheel polygonal wear, the effect of the wheelset inertia can’t be ignored. Both the braking pressure and the vertical suspension force had obvious influence on the wheel polygonal wear. Different braking pressure led to wheel polygonal wear of different orders. When the braking pressure was 13 kN, the possibility of occurrence of the friction-induced vibration of the wheelset-track-disc brake system was the lowest, and the development rate of the wheel polygonal wear was the slowest. Too high or too low vertical suspension increased the possibility of occurrence of the friction-induced vibration of the wheelset-track-disc brake system. When the vertical suspension force was 75 kN, the possibility of occurrence of the wheel polygonal wear was the least and the development rate of the wheel polygonal wear was the slowest.