动力吸振器下高温超导磁悬浮列车振动特性研究

Research on Vibration Characteristics of High-Temperature Superconducting Maglev Trains with Dynamic Vibration Absorbers

摘要

高温超导磁悬浮列车高速走行时由于直线电机牵引时法向力激扰会导致列车悬浮间隙发生变化，当悬浮间隙超过安全标准时，严重威胁行车安全。为了防止列车高速走行振动超限，拟采用动力吸振的方法抑制列车的振动，开展动力吸振器下高温超导磁悬浮列车振动特性研究。首先，利用力学特性有限元方法得到磁悬浮列车的悬浮力数据，拟合悬浮力和重力合力的经验公式。之后，建立磁悬浮列车在直线电机牵引时法向力瞬态激扰下的垂向动力学模型，利用谐波平衡法推导悬浮架振幅、附加质量块振幅稳态响应的近似解析解，分析动力吸振器刚度及阻尼系数对悬浮架振幅的影响规律。研究结果表明：随着线性刚度 k₂ 的增大，悬浮架的振幅逐渐减小，附加质量块 m₂ 的振幅逐渐增大；随着阻尼参数 c₂ 的增大，悬浮架振幅小幅减小，附加质量块的振幅逐渐增大。在保证振幅最小的条件下，得到了刚度与阻尼在一定范围内最优参数组合；相比于无减振措施，采用动力吸振器大幅减小了悬浮架的振幅。该研究成果为保障和提升磁悬浮列车行车安全提供一种减振方法。

Abstract

During high-speed operation，the high-temperature superconducting magnetic levitation（maglev）train may experience variations in the levitation gap due to normal force disturbances from the linear motor traction，which can seriously threaten operational safety when the levitation gap exceeds safety standards.To prevent excessive vibration of the train during high-speed operation，a dynamic vibration absorber was proposed to suppress the vibration of the train，and a study on the vibration characteristics of the high-temperature superconducting maglev train with dynamic vibration absorber was conducted.First，the finite element method for mechanical characteristics was used to obtain the levitation force data of the maglev train，and an empirical formula for the combined force of levitation force and gravity was established.Subsequently，a vertical dynamic model of the maglev train under transient normal excitation from the linear motor traction was developed.The harmonic balance method was employed to derive approximate analytical solutions for the steady-state responses of the levitation frame amplitude and additional mass block amplitude.The influence of the stiffness and damping parameter of dynamic vibration absorber on the levitation frame amplitude was analyzed.The research results show that as the linear stiffness k₂ increases，the amplitude of the levitation frame gradually decreases，while the amplitude of the additional mass block m₂ gradually increases.As the damping parameter c₂ gradually increases，the amplitude of the levitation frame slightly decreases，and the amplitude of the additional mass block gradually increases.Under the condition of minimizing the amplitude，the optimal combination of stiffness and damping parameters within a certain range is obtained.Compared to the scenario without vibration reduction measures，the use of the dynamic vibration absorber significantly reduces the amplitude of the levitation frame.The findings of this study provide a vibration reduction method for ensuring and improving the operational safety of maglev trains.

关键词

磁悬浮列车 / 动力吸振器 / 谐波平衡法 / 振幅

Key words

maglev train / dynamic vibration absorber / harmonic balance method / vibration ampli- tude

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基金资助

石家庄铁道大学2025年大学生创新创业训练计划项目(S202510107092)