Magnetic force characteristics and dynamics simulation of permanent magnet suspension system based on inclined suspension surface
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摘要:
提出了一种结构简洁的倾斜悬浮面侧滑抑制方案，该方案通过被动结构设计，利用重力分力与附加横向力实现侧滑抑制，无需增加复杂主动控制组件，工程可实现性强；研究过程中，基于等效磁荷法推导了倾斜悬浮面下悬浮力与横向力计算模型；采用N45H小尺寸永磁体建立了3D磁场有限元分析(FEA)模型并通过台架试验进行验证；构建了车载与轨道均为5块永磁体横向布置Halbach阵列的全尺寸FEA模型；结合单节车辆多体动力学模型，在直线60 km·h-1、小半径曲线20 km·h-1工况下开展了仿真分析。研究结果表明：磁力特性分析下，悬浮面倾斜对悬浮力影响微弱，最大变化幅度低于±1 kN，对横向力提升作用显著，10°倾斜时最大横向力较0°增加153%；直线工况下9.5°倾斜使永磁副悬浮力波动降低约19.59%，导向轮接触稳定性提升，横向偏移量显著降低；曲线通过时，悬浮力幅值及波动减小，横向力幅值及波动有所提升，车辆横向定位精度优化，有效抑制侧滑现象。本文明确了倾斜悬浮面的调控规律与工程设计区间，为永磁悬浮交通系统的结构优化、参数匹配及工程应用提供理论依据与数据支撑。
Abstract:A concise structural scheme of sideslip suppression was proposed for an inclined suspension surface. By adopting a passive structural design, the scheme realized sideslip suppression by virtue of gravity component force and additional lateral force, with no additional complex active control components required and high engineering feasibility. In the research, the calculation models of suspension force and lateral force for the inclined suspension surface were derived based on the equivalent magnetic charge method. A 3D magnetic field finite element analysis (FEA) model was established with small-size N45H permanent magnets and verified by bench tests. A full-scale FEA model was constructed, in which five transversely arranged Halbach arrays of permanent magnets were deployed on both the vehicle and track sides. Combined with the multi-body dynamics model of a single vehicle, simulation analyses were carried out under the straight-line condition of 60 km·h-1 and the small-radius curve condition of 20 km·h-1. Research results show that after the magnetic force characteristics analysis, the inclination of the suspension surface has a weak influence on suspension force, with a maximum variation amplitude lower than ±1 kN, and produces a significant promotion effect on lateral force. The maximum lateral force at an inclination angle of 10° increases by 153% compared with that at 0°. Under the straight-line condition, the inclination angle of 9.5° reduces the fluctuation of suspension force of permanent magnet pairs by approximately 19.59%, improves the contact stability of guide wheels, and significantly reduces the lateral offset. During curve passing, the amplitude and fluctuation of suspension force decrease, while the amplitude and fluctuation of lateral force increase slightly. The lateral positioning accuracy of vehicles is optimized, and the sideslip is effectively suppressed. The regulation law and engineering design interval of inclined suspension surfaces are clarified, providing theoretical basis and data support for the structural optimization, parameter matching, and engineering application of permanent magnet suspension transportation systems.
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图 5 不同倾斜角度下悬浮力结果对比
Figure 5. Comparison of suspension force results at different inclined angles
图 8 α=0°时转动参数对磁力的影响
Figure 8. Influence of rotational parameters on magnetic force when α=0°
图 9 α=10°时转动参数对磁力的影响
Figure 9. Influence of rotational parameters on magnetic force when α=10°
图 13 一位悬浮架永磁副悬浮力与横向力
Figure 13. Suspension force and lateral force of permanent magnet pair on one-chassis bogie
图 16 一位悬浮架永磁副悬浮力与横向力
Figure 16. Suspension force and lateral force of permanent magnet pair on one-chassis bogie
图 17 一位悬浮架导向轮横向力及相对轨道偏移量
Figure 17. Lateral force and relative track offset of one-chassis bogie guide wheel
表 1 N45H材料参数
Table 1. N45H material parameters
材料参数 数值 剩余磁感应强度/T 1.35 矫顽力/(kA·m-1) 890 磁化强度/(kA·m-1) 978.8 相对磁导率 1.22 
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表 2 动力学参数
Table 2. Dynamics parameters
参数 参数值 满载质量/kg 16 700 中间件质量/kg 1 017.5 单侧磁浮架质量/kg 600 中间件转动惯量/(kg·m2) 600/600/80 单侧磁浮架转动惯量/(kg·m2) 60/300/300 摆臂转动惯量/(kg·m2) 20/10/20 导向轮径向刚度/(N·m-1) 1.2×107 直线电机长(m)×宽(m)×厚(m)廓形尺寸 2.12×0.49×0.10 磁轴距/mm 900 轨距/mm 880
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表 3 永磁副磁力
Table 3. Magnetic force of permanent magnet pair
角度/(°) 名称 统计值/kN 峰值 均值 标准差 0.0 悬浮力 27.84/17.56 21.19 2.19 横向力 12.96/-12.14 2.41 4.82 9.5 悬浮力 23.57/17.90 19.35 1.04 横向力 15.63/-3.09 6.74 3.88
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表 4 导向轮横向力
Table 4. Lateral force of guide wheels
角度/(°) 名称 统计值/kN 峰值 均值 标准差 0.0 右前轮 0/-11.57 -1.83 2.51 左前轮 16.85/0 2.74 3.22 9.5 右前轮 0.08/-0.41 0.04 0.08 左前轮 18.18/0.31 4.45 3.95
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