五自由度全永磁轴承系统的稳定悬浮特性分析

Stable Levitation Performance Analysis of Five Degrees of Freedom All Permanent Magnetic Bearing System

为探讨永磁悬浮轴承系统的稳定悬浮特性,从轴承刚度角度对五自由度全永磁轴承系统的稳定悬浮特性进行了分析。采用等效磁荷理论建立永磁轴承的承载力、承载力矩和刚度的数学表达式,并利用蒙特卡洛法对表达式中存在的四重积分进行求解。探究转子在受迫进动情况下以及受到外力矩干扰时继续保持稳定旋转所需要的最低临界转速。基于轴向永磁轴承与径向永磁轴承的结构,提出一种六磁环五自由度全永磁轴承系统结构模型,对全永磁轴承的转子系统承受轴向和径向外载荷的承载力、力矩和承载刚度进行分析,得出轴向可以承受外载荷而径向无法承受外载荷,即静态下轴向可以稳定悬浮、径向不能稳定悬浮,符合Earnshaw定理。利用刚性转子的陀螺惯性力矩来承受全永磁轴承系统的不平衡力矩和外力矩,从而保持转子定轴自稳定悬浮,并对系统稳定悬浮特性进行计算,结果表明转子在超过最低临界转速后是可以实现动态稳定悬浮的,具有一定的工程应用价值。

To investigate the stable levitation performance of permanent magnetic bearings system, the stable levitation performance of the five-DOF permanent magnetic bearing （PMB） system is analyzed from the perspective of bearing stiffness. The analysis formulas of PMB’ s loading capacity, torque and stiffness are established based on the equivalent magnetic charge theory, then use Monte Carlo method to solve the quadruple integral formula to get the result of the force, moment and stiffness. The minimum critical speed for rotor in the case of forced precession and in the situation of external torque is explored. Puts forward a six circular magnetic rings and five DOF all permanent magnetic bearing structure model based on the structure of radial and axial magnetic bearings, the carrying capacity, moment and stiffness of five-DOF PMB system are analyzed, this shows that the model can withstand stably axial load and cannot bear radial load under the static, this is consistent with the Earnshaw-theorem. Finally, using the levitation performance of rigid rotor gyro inertial torque to withstand the imbalance torque of the all permanent magnetic bearing system and external torque. Thereby maintaining the stable fixed-axis rotation. The calculation results of stable levitation performance for the system shows that the rotor in all permanent magnetic bearing can be dynamic stable suspension after its speed over the minimum critical speed and has a certain value for engineering application.