球形行波型超声波电机的驱动数学模型

球形行波型超声波电机可以实现球面轨迹的运动,但是目前其设计仍处于经验阶段。该文从球形行波型超声波电机的原理与基本结构出发,利用坐标变换关系得到转子运动时定、转子接触面上接触力的分布情况,分析了行波定子与球转子接触点的摩擦驱动力和摩擦阻力。根据运动稳定时球转子的力和力矩平衡及行波定子的轴向力平衡关系,得到球形行波型超声波电机的驱动数学模型。通过仿真分析了结构参数和行波定子特性的影响,初步验证了上述模型。

The Driving Mathematic Model of Spherical Traveling-wave Type Ultrasonic Motor

Spherical traveling type ultrasonic motor can move at spherical traces.But until now its design only depends on experience and its mechanics can't be explained clearly.The principle and basic structure of three degree-of-freedom traveling type ultrasonic motor are presented in this paper.Then through coordinate conversion the distribution of the force on the contact area can be got when the rotor rotates.So the motor's driving and friction force can be calculated on the contact area of stator and rotor.Also the driving and frictional torque can be derived at the contact point of stator and rotor.By solving the equation of rotation force balance and torque balance and axis force balance of stator when the rotor stabilize the motor's math model can be got.Finally through simulation the motor's structure parameter and stator velocity are analyzed and the model can be verified preliminarily.