磁-流-固多场耦合下空气静压主轴动力学建模及振动响应分析OA
Dynamic Modeling and Vibration Response Analysis of Aerostatic Spindle Under Magnetic-fluid-structure Multi-field Coupling
为了厘清空气静压主轴多物理场耦合机理,建立了电磁场、流体场及固体场互相耦合作用下的空气静压主轴模型.首先,提出一种永磁同步电机不平衡磁拉力(Unbalance magnetic pull,UMP)的计算方法,通过构建磁隙磁通密度解析模型,得到不同电机极对数下的 UMP 计算结果.随后,通过求解雷诺方程,得到前/后空气径向轴承的刚度、阻尼系数;通过切片法,得到电机对应处的不平衡磁力/力矩,分别将其耦合到对应转子 Timoshenko 梁单元上,建立磁-流-固多场耦合的空气静压主轴模型,并通过与有限元仿真软件的对比验证模型的正确性.在不平衡质量力作用下,采用 Newmark-β方法求解主轴动力学运动方程,对主轴的振动特性进行分析.结果表明:定转速(5×104 r/min)时,不平衡磁力/力矩随时间正弦波动,波动周期为主轴转动周期;磁隙厚度在时域上随周向角度和时间的变化而波动,在频域上不受周向角度影响;在有 UMP 情况下的主轴振动响应较大;变转速(1×104～1×105 r/min)时,电机转子处振动响应在9.5×104 r/min 处与主轴达到1 阶(1 506 Hz)和2 阶(1 642 Hz)固有频率的叠加谐共振,幅值最大;磁隙厚度在 9×104 r/min 处与主轴达到 1 阶共振;不平衡磁力/力矩与电机转子处振动响应规律一致.
In order to clarify the multi-physical coupling mechanism of aerostatic spindle,the aerostatic spindle model under the interaction of electromagnetic field,fluid field and solid field was established.Firstly,a calculation method of unbalance magnetic pull(UMP)in permanent magnet synchronous motor is proposed.By constructing an analytical model of magnetic gap flux density,UMP calculation results under different motor poles are obtained.Then,the stiffness and damping coefficient of the front/rear air radial bearing are obtained by solving Reynolds equation.The unbalanced magnetic force/torque at the corresponding position of the motor was obtained by using the slice method and coupled to the Timoshenko beam element of the corresponding rotor respectively.A magnetic-fluid-solid multi-field coupling aerostatic spindle model was established.The correctness of the model was verified by comparing with that via finite element simulation software.Under the action of unbalanced mass force,Newmark-β method is used to solve the dynamic equation of the spindle,and the dynamic characteristics of the spindle are analyzed.The results show that the unbalance magnetic force/torque fluctuates sinusoidal with time at a constant speed(5×104 r/min),and the fluctuation period is the rotation period of the spindle.The magnetic gap thickness fluctuates with the change of circumferential angle and time in the time domain,but is not affected by the circumferential angle in the frequency domain.The vibration response of the spindle with UMP is greater than that without UMP.When the speed changes(1×104-1×105 r/min),the vibration response at the rotor of the motor reaches the superimposed harmonic resonance of the first order(1 506 Hz)and second order(1 642 Hz)natural frequency with the main shaft at 9.5×104 r/min,and the amplitude is the largest.The magnetic gap thickness reaches a first-order resonance with the main shaft at 9×104 r/min.The unbalanced magnetic pull/torque is consistent with the vibration response at the motor rotor.
冯鑫;史江海;曹宏瑞;沈黎
西安交通大学 装备运行安全保障与智能监控国家地方联合工程研究中心,西安 710049||西安交通大学 机械工程学院,西安 710049西安交通大学 装备运行安全保障与智能监控国家地方联合工程研究中心,西安 710049||西安交通大学 机械工程学院,西安 710049西安交通大学 装备运行安全保障与智能监控国家地方联合工程研究中心,西安 710049||西安交通大学 机械工程学院,西安 710049西安交通大学 机械工程学院,西安 710049
机械制造
磁-流-固多场耦合不平衡磁力/力矩空气静压主轴切片法振动响应
magnetic-fluid-structure multi-field couplingunbalanced magnetic pull/momentaerostatic spindleslice methodvibration response
《机械科学与技术》 2026 (5)
749-760,12
国家自然科学基金项目(52205125)
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