Motion Decoupling and Dynamic Response of Permanent Magnet Maglev Bogie
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摘要:
针对永磁磁浮“红轨”列车转向架在悬浮与导向性能上的不足，提出一种新型转向架方案并开展动力学研究. 首先，采用有限元法分析Halbach阵列磁场与磁力特性，明确永磁侧偏对导向性能及运动解耦对稳定悬浮的影响机制；其次，详细阐述新型转向架结构设计，构建车辆系统动力学模型，重点研究车辆直线运行及通过R50小半径曲线时转向架关键部件的动力学响应；最后，探究横向轮自由间隙与刚度对转向架冲击振动的影响. 研究结果表明：当横向轮自由间隙设为0，刚度值设为6 × 106 N/m时，转向架冲击振动得到有效抑制；车辆过曲线时，转向架在永磁侧偏力作用下，以横向轮紧贴曲线内侧来平衡离心力，与传统轨道车辆动力学特性明显不同；在运行速度≤60 km/h工况下，空载（AW0）状态时车辆的横向与垂向平稳性指标均优于超载（AW3）状态，且两者平稳性指标均控制在2.5以内.
Abstract:To address levitation and guidance performance deficiencies in permanent magnet maglev “Red Rail” train bogies, an innovative bogie scheme was proposed, and dynamic analyses were performed. First, the finite element method was used to analyze the Halbach array’s magnetic field and force characteristics and clarify the influence of lateral offset of the permanent magnet on guidance performance and that of motion decoupling on stable levitation. Next, the innovative bogie’s structural design was detailed, and a vehicle system dynamics model was built to investigate the dynamic responses of key bogie components during straight-line operation and passing through a 50-m radius curve (R50). Finally, the impact of free gaps and stiffness of lateral wheels on bogie impact vibration was explored. The results show that when the free gap of lateral wheels is 0, and the stiffness is 6 × 106 N/m, bogie impact vibration is effectively suppressed. When the train passes through a curve, the bogie balances centrifugal force by keeping lateral wheels in close contact with the inner curve side under the lateral offset force of a permanent magnet, which is distinct from traditional rail vehicle dynamics. When the speed is no more than 60 km/h, the lateral and vertical ride quality indices of no-load (AW0) vehicles outperform those in overload (AW3), with both indices controlled below 2.5.
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Key words:
- permanent magnet /
- bogie /
- magnetic levitation /
- lateral offset of permanent magnet /
- dynamic response
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图 2 Halbach永磁阵列结构及有限元模型
Figure 2. Structure of Halbach permanent magnet array and its finite element model
图 4 悬浮力、横向力随悬浮间隙与侧偏量变化
Figure 4. Variation of levitation force and lateral force with levitation gap and lateral offset
图 5 单点等比例Halbach阵列磁力测试平台
Figure 5. Magnetic force testing platform of single-point equal-proportion Halbach array
图 6 单点等比例磁体磁力测试结果
Figure 6. Magnetic force testing results of single-point equal-proportion magnet
图 8 无侧偏/有侧偏时悬浮力拟合曲线
Figure 8. Fitting curves of levitation force without/with lateral offset
图 10 转向架直线运行的动力学响应结果
Figure 10. Dynamic response results of bogie during straight-line operation
图 11 不同横向轮自由间隙下直线运行动力学响应结果
Figure 11. Dynamic response results of bogie during straight-line operation under different free gaps of lateral wheel
图 12 零自由间隙下具有二级刚度的横向轮模型
Figure 12. Lateral wheel model with secondary stiffness under zero free gap
图 13 不同横向轮自由间隙下直线运行动力学响应结果
Figure 13. Dynamic response results of bogie during straight-line operation under different free gaps of lateral wheel
图 14 通过R50曲线时车载磁体力矩平衡及横向力平衡示意
Figure 14. Balance of on-board magnetic force torque and lateral force when passing through R50 curve
图 15 转向架通过R50曲线时的动力学响应结果
Figure 15. Dynamic response results of bogie when passing through R50 curve
图 16 轿厢后端横向与垂向平稳性指标
Figure 16. Transverse and vertical ride comfort index at rear of train carriage
表 1 轮胎式与2种永磁磁浮转向架技术对比
Table 1. Technical comparison among tire-type and two types of permanent magnet maglev bogies
类型 承载 导向/抗侧滚 牵引 制动 轮胎式 充气轮胎 横向轮与稳定轮 旋转电机 电制动与机械制动 兴国线 永磁副 导向/稳定轮 直线电机 电制动与机械制动 本文研究 永磁副 横向轮与姿态轮 直线电机 机械制动 
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表 2 钕铁硼N45 和 N52M永磁材料参数
Table 2. Parameters of NdFeB N45 and N52M permanent magnet materials
牌号 矫顽力/（kA•m−1） 相对磁导率 剩余磁感应强度/T N45 955.20 1.14 1.37 N52M 1114.40 1.04 1.46
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表 3 不同悬浮间隙下永磁磁浮系统的垂向刚度
Table 3. Vertical stiffness of permanent magnet maglev system with different levitation gaps
悬浮间
隙/mm单点载
荷/kN响应主
频/Hz悬浮刚度/
（MN·m−1）20.1 5.5 3.6 0.28 16.4 6.8 3.9 0.42 13.9 8.2 4.4 0.62 12.0 9.6 4.6 0.83 11.4 10.1 5.0 1.02 8.7 13.7 5.5 1.66
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表 5 AW0状态不同侧偏量下悬浮间隙、侧偏力及修正系数
Table 5. Levitation gap, lateral offset force, and correction coefficient under different lateral offsets in AW0 condition
侧偏量/mm 悬浮间隙/mm 侧偏力/N 修正系数/% 0 22.81 0 100.00 −5 21.86 2988.4 96.15 −10 19.60 7222.4 86.05 −15 15.51 14201.4 70.45 −20 8.09 27106.5 49.40
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表 6 AW3状态不同侧偏量下悬浮间隙、侧偏力及修正系数
Table 6. Levitation gap, lateral offset force, and correction coefficient under different lateral offsets in AW3 condition
侧偏量/mm 悬浮间隙/mm 侧偏力/N 修正系数/% 0 16.74 0 100.00 −5 15.78 4659.2 96.15 −10 13.52 10564.1 86.05 −15 9.44 19213.9 70.45 −17 7.05 24008.7 62.67 −18 5.63 26829.5 58.45 −19 4.16 29848.3 54.01 −20 2.03 33764.7 49.40
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