圆柱形三自由度超声电机输出性能的仿真设计

摘要

研制了一种基于两个二阶弯振模态和一个一阶纵振模态的圆柱形三自由度超声电机.其定子的长度、直径和质量分别为20 mm,56 mm和130 g;转子直径为25 mm;转子绕X、Y和z-轴的空载转速分别为33、35和66 r·min-1,堵转矩分别为24.8、36.6和30.2 mN·m.根据圆柱形三自由度超声电机的结构和工作原理,建立了它的输出性能仿真数学模型.用有限元方法对定子进行结构动力学分析,得到定子上各驱动点的工作频率和工作振幅,计算驱动点的位移和速度;假设定子和转子是弹性接触的,即定、转子之间的接触点由一系列弹簧相连接,根据定、转子的相对运动和胡克定理,计算出每个接触弹簧的变形和弹性力;计算定、转子之间的摩擦力;进而计算出电机的输出力矩、功率损失和驱动效率.根据所建立的数学模型,用MATLAB软件编制了仿真设计程序,计算出电机的输出性能,并与实验结果进行了比较和分析.实验显示,当输出转矩较小时,仿真结果与实验结果符合良好;随着输出转矩的增加,二者之间的误差逐渐增大,而且实验值小于仿真值.结果表明,实际输出性能的下降是由定、转子之间的打滑造成的.电机输出性能仿真的实现,将为电机的性能预估和优化设计打下理论基础.%A 3-DOF ultrasonic motor with a cylinder type stator and a spherical rotor is developed.The motor can provide 3-DOF rotations around X,Y,and z-axes based on two second order bending modes with orthogonality and a first order longitudinal mode of the stator.The diameter,height and mass of the stator are 20 mm,56 mm,and 130 g,respectively,and the diameter of the rotor is 25 mm.The unloaded rotational speeds of the prototype motor around x,Y,and z-axes are 33,35 and 66 r·min-1 ,respectively.The maximum torques of the prototype motor around x ,y,and z-axes are 24.8,36.6 and 30.2mN·m,respectively.In the present study,a simulated mathematical model of output properties for the motor is established according to its driving principle.Firstly,the amplitude and frequency of the driving points on the stator of the motor are obtained by structural dynamic analysis(FEM)for the stator.Then,the displacement and velocity of the driving points are calculated.It is supposed that the stator contacts with the rotor of the motor in elasticity, which means that a series of contacted points between the stator and the rotor are connected by springs. According to relative motion between the stator and the rotor of the motor, the deformation and elastic force of every spring can be obtained. Furthermore, the friction force between the stator and the rotor of the motor can be deduced. Finally the output torque, power loss and driving efficiency of the motor are calculated.Based on the mathematical model above, a simulated program is developed in MATLAB environment,and the output properties of the motor are simulated by the program. The experimental results indicate that the simulated results of the motor's output properties well accord with the experimental resuits when the output torque of the motor is smaller. However, when the output torque of the motor increases gradually its error gets greater, and the actual values of the output properties are less than the the oretical values. The decrease of the actual output is caused by a slide phenomenon between thestator and the rotor. Experimental results show that the simulation of output properties would provide conditions for estimating the output properties of the motor and optimizing the design in development of USM.