复合型超声马达纵向振动建模

针对采用一维理论模型在研究复合型超声马达振动特性时分析结果出现误差的情况,设计一种新型双定子复合型超声马达;利用马达的对称性建立了定子纵向振动分析物理模型;将定子纵向与横向振动的动能同时引入Hamilton方程,推导了考虑马达横向振动效应的定子纵向振动分析微分方程与动力边界条件;运用Maple软件对定子运动微分方程进行求解,获得了定子纵向振动固有频率;采用有限元模型与一维理论模型时定子的纵向振动固有频率进行对比计算,并对马达原型机的固有频率进行测定.研究结果表明:所建模型比一维理论模型具有更高的分析精度;分析结果与实验值及有限元计算值吻合.

Modeling of longitudinal vibration of hybrid ultrasonic motor

One-dimensional model will lead to analytical error when the vibration characters of hybrid ultrasonic motor are considered. A new type of hybrid ultrasonic motor with 2 stators was developed. Considering the symmetrical properties of this motor, a physical model for longitudinal vibration analysis of the stator was established. By introducing the kinetic energy of the vibrations in longitudinal and transversal directions into the Hamilton equation, the differential ~equation for longitudinal vibration analysis and the dynamical boundary conditions were deduced, in which the transversal vibration effect was considered. The Maple software was used to solve these differential equations and the eigenfrequency of longitudinal vibration for the stator was obtained. For the purpose of comparison with the refined theoretical model, a finite element model and a one-~dimensional model were used to compute the eignefrequency of longitudinal vibration. Furthermore, the eignefrequency of this motor prototype was measured in the experiment. The research results show that the theoretical model proposed has much higher accuracy than one-~dimensional model. The analytical results agree well with the experimental results and the calculted results obtained by the finite element method.