1.Key Laboratory of Conveyance and Equipment of Ministry of Education, East China Jiaotong University, Nanchang 330013, China；
2.State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure, East China Jiaotong University, Nanchang 330013, China)
Abstract：Wheelset’s flexibility, gyroscopic effect, and constraint elasticity are the key to accurately evaluate the vibration characteristics of power wheelset rotor system in high-speed operation environment. To this end, the bending-torsion-axial vibration characteristics of the power wheelset rotor system in a typical high-speed train are systematically studied under wheel-rail contact elastic constraints. First of all, the bending-torsional-axial dynamic equation of power wheelset rotor system is established by the finite element theory of Timoshenko flexible beam rotor. And a linearized wheel-rail contact element which can reflect the contact characteristics between equivalent conical wheel tread and rail is derived by the stiffness influence coefficient method and energy method respectively. Then, the corresponding MATLAB codes are programmed and verified by comparing with the established equivalent ANSYS model. Next, four modal models, namely bending model, bending-torsional model, bending-axial model and bending-torsional-axial model are designed with the self-programming program. And the similarities and differences of vibration characteristics and the influence law of parameters of the four models are discussed in detail. Finally, the possible resonance stability problems of power wheelset rotor system induced by some typical external excitations are also discussed. Results show that: (1) The modal results of bending-torsional-axial model can contain all the results of the other three models, and their modal data is agree well with each other; (2) The constraint elasticity (that is, the support stiffness) of the wheelset is significantly different in the longitudinal and vertical directions due to the consideration of the wheel-rail contact stiffness, so that the first-order and second-order forward-whirling bending modes of wheelset rotor system are delayed to appear in the higher natural frequency domain, and the whirling orbits of the corresponding bending modes are obviously flat; (3) Among the discussed typical external excitations, there are many excitation frequencies which can cause the resonance of the power wheelset rotor system, especially the wheel damage excitation.
[1] Peng B, Iwnicki S, Shackleton P, et al. The influence of wheelset flexibility on polygonal wear of locomotive wheels[J]. Wear, 2019, 432: 102917.
[2] Baeza L, Giner-Navarro J, Thompson D J, et al. Eulerian models of the rotating flexible wheelset for high frequency railway dynamics[J]. Journal of Sound and Vibration, 2019, 449: 300-314.
[3] Ma C, Gao L, Xin T, et al. The dynamic resonance under multiple flexible wheelset-rail interactions and its influence on rail corrugation for high-speed railway[J]. Journal of Sound and Vibration, 2021, 498: 115968.
[4] Wang Z, Cheng Y, Mei G, et al. Torsional vibration analysis of the gear transmission system of high-speed trains with wheel defects[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2020, 234(2): 123-133.
[5] 钟硕乔. 车辆轨道耦合系统中的旋转柔性轮对建模研究[D].西南交通大学,2017.
Zhong Shuo-qiao. Study on modelling of rotating flexible wheelset in vehicle-track dynamic system [D]. Southwest Jiaotong University, 2017.
[6] Kaiser I, Poll G, Voss G, et al. The impact of structural flexibilities of wheelsets and rails on the hunting behaviour of a railway vehicle[J]. Vehicle system dynamics, 2019, 57(4): 564-594.
[7] Morys B. Enlargement of Out-of-Round Wheel Profiles on High Speed trains[J]. Journal of Sound and Vibration, 1999, 227(5): 965-978.
[8] Szolc T. Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model [J].Archive of Applied Mechanics. 1998, 68:30-45.
[9] 徐宁，任尊松，薛蕊，李强. 不同车辆-轨道垂向动力学模型功率流传递特性研究[J]. 铁道学报，2019, 41(05):35-45.
Xu Ning, Ren Zun-song, Xue Rui, Li Qiang. Study on power flow transmission characteristics of different vehicle-track vertical dynamic models [J]. Journal of Railway, 2019, 41 (05): 35-45.
[10] 石俊杰，崔涛，高峰，王铁成. 柔性轮对的轮轨静态接触和车辆动态性能研究[J]. 铁道机车车辆，2020, 40(04):6-12+20.
Shi Jun-jie, Cui Tao, Gao Feng, Wang Tiecheng. Study on wheel-rail static contact and vehicle dynamic performance of flexible wheelsets [J]. Railway rolling stock, 2020, 40 (04): 6-12+20.
[11] 廖小康，易彩，张议，陈滋利，林建辉. 车轮柔性化对高铁轴箱轴承振动特性分析[J/OL]. 铁道科学与工程学报，2022:1-12.
Liao Xiao-kang, Yi Cai, Zhang Yi, Chen Zi-li, Lin Jian-hui. Analysis of wheel flexibility on vibration characteristics of high-speed railway axle box bearing [J/OL]. Journal of Railway Science and Engineering, 2022:1-12.
[12] Liu P, Liu H, Wu Q. Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models[J]. Shock and Vibration, 2021:9973421.
[13] 杨柳. 基于机车传动系统动力学模型的故障机理与诊断方法研究[D]. 北京交通大学，2019.
Yang Liu. Research on fault mechanism and diagnosis method based on locomotive transmission system dynamic model [D]. Beijing Jiaotong University, 2019.
[14] 王滋昊，王美令，马思群. 基于有限单元法轮对-车轴系统动力学特性研究[J]. 大连交通大学学报，2021, 42(01):25-29+35.
Wang Zi-hao, Wang Mei-ling, Ma Si-qun. Study on dynamic characteristics of wheelset-axle system based on finite element method [J]. Journal of Dalian Jiaotong University, 2021, 42 (01): 25-29+35.
[15] Al-Maliki H, Meierhofer A, Trummer G, et al. A new approach for modelling mild and severe wear in wheel-rail contacts[J]. Wear, 2021, 476: 203761.
[16] 肖乾，蒋吴曦，李超，王丹红，罗志翔. 接触刚度对高速列车轮轨接触动力学时变特性的影响及其机制[J]. 润滑与密封，2019, 44(11):79-84.
Xiao Qian, Jiang Wu-xi, Li Chao, Wang Dan-hong, Luo Zhi-xiang. Effect of contact stiffness on time-varying characteristics of wheel-rail contact dynamics of high-speed train and its mechanism [J]. Lubrication and sealing, 2019, 44 (11): 79-84.
[17] 杨柳,李强,杨绍普,王久健,顾晓辉.机车传动系统振动分析[J].机械工程学报,2018,54(12):102-108.
Yang Liu, Li Qiang, Yang Shao-pu, Wang Jiu-jian, Gu Xiao-hui. Vibration analysis of locomotive transmission system [J]. Journal of Mechanical Engineering, 2018. 54 (12): 102-108.
[18] 周生通，曹涛影，朱经纬，祁强，周新建. 动车牵引电机转子的弯扭振动特性研究[J]. 铁道学报，2021, 43(02):52-60.
Zhou Sheng-tong, Cao Tao-ying, Zhu Jing-wei, Qi Qiang, Zhou Xin-jian. Study on bending and torsional vibration characteristics of traction motor rotor of bullet train [J]. Journal of Railways, 2021, 43 (02): 52-60.
[19] 林腾蛟，郭松龄，赵子瑞，魏静. 裂纹故障对斜齿轮时变啮合刚度及振动响应的影响分析[J]. 振动与冲击，2019, 38(16):29-36+63.
Lin Teng-jiao, Guo Song-ling, Zhao Zi-rui, Wei Jing. Analysis of the influence of crack fault on time-varying meshing stiffness and vibration response of helical gear [J]. Vibration and shock, 2019, 38 (16): 29-36+63.
[20] 朱彬. 高速列车车轮多边形磨耗机理研究[D]. 西南交通大学，2021.
Zhu Bin. Study on polygonal wear mechanism of high-speed train wheels [D]. Southwest Jiaotong University, 2021.
[21] 李辉，蔡卫星，韩宁，马力. 高速动车组列车轴箱轴承振动监测与故障分析[J]. 动力系统与控制，2020, 9(1):40-49.
Li Hui, Cai Wei-xing, Han Ning, Ma Li. Vibration monitoring and fault analysis of axle box bearing of high speed EMU train [J]. Power Systems and Control, 2020, 9 (1): 40-49.
[22] 杨光，任尊松，袁雨青. 车轮扁疤伤损对高速列车轮对动力学性能影响[J]. 北京交通大学学报，2018, 42(03):103-111.
Yang Guang, Ren Zun-song, Yuan Yu-qing. Effect of wheel flat scar damage on dynamic performance of high-speed train wheelset [J]. Journal of Beijing Jiaotong University, 2018, 42 (03): 103-111.
