Dynamic Characteristics and Performance Assessment of Improved Suspension Frame System
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摘要:
为了增大高温超导钉扎磁悬浮列车的悬浮力和提升安全性，提出了抱轨式改进型悬浮架系统，首先，采用等效处理方法计算了高温超导块材阵列和永磁轨道之间的悬浮力，并利用悬浮力实验装置测量两者的悬浮力，实验验证了等效处理方法的正确性；其次，基于等效处理方法得到改进型悬浮架系统的悬浮力，利用悬浮力和悬浮间隙的关系建立了单个改进型悬浮架本体在轨道不平顺简谐激励下的动力学模型，进一步基于线性微分方程理论推导得到简谐激励下的幅频方程；最后，研究了运行速度和阻尼对稳态振幅的影响，得到阻尼在最高运行速度下应取的范围. 研究结果表明：在质量、刚度、轨道不平顺波长和幅值一定的情况下，稳态振幅的大小取决于运行速度和阻尼，且稳态振幅随着运行速度的增大而增大，随着阻尼的减小而增大；以磁悬浮安全性指标为约束，在最高运行速度600 km/h情况下阻尼应大于6905 Ns/m.
Abstract:In order to improve the levitation force and enhance the safety of high-temperature superconducting pinned maglev trains, an improved rail-holding suspension frame system was proposed. Firstly, the levitation force between high-temperature superconductor arrays and permanent magnet guideways was calculated based on the equivalent processing method. The levitation forces of high-temperature superconductor arrays and permanent magnet guideways were also measured by the levitation force test device, which validated the equivalent processing method experimentally. Then, the levitation force of the improved suspension frame system was obtained based on the equivalent processing method. According to the relationship between levitation force and levitation gap, the dynamic model of a single improved suspension frame was set up under track irregularity harmonic excitation. The amplitude-frequency equation was derived by linear differential equation theory. Lastly, the influence of running velocity and damping on the steady-state amplitude was investigated. The feasible domain of damping under the maximum running velocity was obtained. The results show that the steady-state amplitude is dependent on the running velocity and damping under a certain mass, stiffness, and track irregularity wave length and amplitude. In addition, the steady-state amplitude increases as the running velocity improves, or as the damping decreases. With the maglev safety index as the constraint, the damping should be more than 6 905 Ns/m under the maximum running velocity of 600 km/h.
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图 2 包含已有悬浮架系统的高温超导钉扎磁悬浮列车主要组成
Figure 2. Components of high-temperature superconducting pinned maglev train with current suspension frame system
图 3 包含改进型悬浮架系统的高温超导钉扎磁悬浮列车主要组成
Figure 3. Components of high-temperature superconducting pinned maglev train with improved suspension frame system
图 7 永磁轨道尺寸和磁化方向
Figure 7. Size and magnetization direction of permanent magnet guideway
图 10 大永磁轨道和标准高温超导块材阵列的悬浮力
Figure 10. Levitation force between large permanent magnet guideway and standard high-temperature superconductor array
图 11 改进型悬浮架系统和已有悬浮架系统的悬浮力对比关系
Figure 11. Comparison between levitation forces of improved suspension frame system and current suspension frame system
图 12 改进型悬浮架系统的垂向力学模型
Figure 12. Vertical force model of improved suspension frame system
图 13 数值解和解析解的幅频响应对比结果
Figure 13. Comparison of numerical and analytical amplitude-frequency responses
图 14 稳态振幅与阻尼和运行速度的关系
Figure 14. Relationship between steady-state amplitude and damping and running velocity
图 15 临界速度和阻尼系数的关系
Figure 15. Relationship between critical velocity and damping coefficient
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