Optimum Structural Design of Active Magnetic Bearing Based on RBF Approximation Model
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摘要:
主动磁悬浮轴承（active magnetic bearing，AMB）-转子系统中，转子质量分布上的不平衡引起不平衡振动，为提高系统的稳定性、减小转子在一阶弯曲临界转速处的不平衡振动，建立了考虑不平衡力和不平衡磁拉力的磁悬浮柔性转子机电一体化模型，并结合径向基（radial basis function，RBF）神经网络算法，得到转子振幅关于磁悬浮轴承结构参数的近似模型；以振幅最小为目标，通过参数灵敏度分析和多岛遗传算法（multi-island genetic algorithm，MIGA）对磁悬浮轴承进行结构优化设计. 数值仿真结果表明：在一定范围内增大磁悬浮轴承的偏置电流、磁极面积、线圈匝数，减少单边气隙能够增大系统阻尼，可以降低一阶弯曲临界转速处的不平衡振动幅值，优化后不平衡振幅较优化前减少近50%.
Abstract:In active magnetic bearing (AMB)-rotor system, the unbalance vibration of system is caused by the uneven mass distribution with respect to the axis. In order to improve the system stability and reduce the unbalance vibration of the rotor at first-order bending critical speed, the mechatronic model of AMB-flexible rotor system considering unbalanced force and unbalanced magnetic pull is established, and combined with the radial basis function (RBF) neural network algorithm, an approximation model of rotor vibration amplitude related to the structure parameters of AMB is obtained. Combined with parametric sensitivity analysis and multi-island genetic algorithm (MIGA), the structural parameters are optimizied with the goal of minimizing the amplitude of rotor vibration. Numerical simulation results show that increasing bias current, area of magnetic poles, number of turns and decreasing air gap within a certain range can increase the system damping, and can reduce unbalanced amplitude at the first-order bending critical speed. The unbalance amplitude is reduced by nearly 50% than before.
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图 4 实验和理论模型自由频响对比
Figure 4. Comparison between experimental and theoretic frequency response
图 7 8极径向磁悬浮轴承结构和x方向电磁力示意
Figure 7. Diagram of 8-poles radial AMB structure and electromagnetic force generated by radial AMB in x direction
图 9 加入不平衡力和不平衡磁拉力的闭环系统
Figure 9. Closed-loop system both with unbalanced force and unbalance magnetic pull
图 13 转子一阶弯曲临界转速处响应
Figure 13. Displacement response of rotor at first-order bending critical speed
图 14 近似模型及优化流程
Figure 14. Flow diagram for establishment of approximation model and structure optimization
图 17 结构参数对不平衡响应的影响
Figure 17. Influence of structural parameters on the unbalanced response
图 19 优化前后转子一阶弯曲临界转速处轴心轨迹数值仿真对比
Figure 19. Comparison between shaft centerline orbit before and after optimization
表 1 径向磁悬浮轴承结构参数
Table 1. Structural parameters of radial AMB
参数 值 单个磁极线圈/匝 75 磁极面积/m2 4.05 × 10−4 偏置电流/A 2 气隙/mm 0.25 
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表 2 结构参数范围
Table 2. Range of structural parameters
取值 A/mm2 I0/A C0/μm N/匝 标准值 405 2.0 250 75 最小值 350 1.8 200 65 最大值 450 2.8 300 85
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表 3 参数优化结果
Table 3. Parameter optimization results
项目 A/mm2 I0/A C0/μm N/匝 优化前 405 2.0 250 75 优化后 380 2.1 200 85
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