Modeling and dynamic response of variable mass system of maglev turning electric spindle - Cao, Zheng; Kang, Huimin; Liu, Houcai; Duan, Lianghui; Ouyang, Zhihai; Zhou, Yue; Jiang, Guan; Li, Wang (Nonlinear dynamics, 2023)
Accurately predicting the dynamic response of the maglev turning electric spindle is the key requirement for ensuring cutting stability and realizing the active control of the magnetic bearing. The previous research usually does not consider the influence of the variable mass effect, which leads to the control accuracy of the magnetic bearing not reaching the expected effect. Aiming at the problem that the cross-sectional area, moment of inertia and mass of the shaft will change in real time due to the removal of the workpiece material during the turning process of the maglev electric spindle. Based on the Rayleigh continuous beam vibration theory, considering the three-dimensional moving cutting force of turning processing, the reverse thrust caused by chip loss, and the time-varying electromagnetic force caused by the change in vibration, using the hypothetical mode method and with the help of Lagrange equations, the variable mass system model of the maglev turning electric spindle is established, then the Runge–Kuta method is used for numerical calculation and MATLAB is used for simulation. The simulation results show that the rotor-active magnetic bearing-workpiece system model established in this paper is more accurate in predicting the dynamic response. The dynamic response is characterized by quasi-periodic vibration, and the influence of the first four modes cannot be ignored. At the same time, the cutting force caused by the axial movement and the reverse thrust caused by the time-varying mass together determine the overshoot of the unbalanced response and the severity of the vibration. In addition, the time-varying mass makes the natural frequency of the system no longer constant, but varies with the workpiece mass.