盆架状压电宏微平面作动器半解析性理论建模

Semi-Analytical Theoretical Modeling of Basin Type Piezoelectric Macro-Micro Planar Actuator

为丰富宏微平面运动装置形式,该文提出了盆架状压电作动器。设定盆架状结构的一阶面内对称弯振模态和二阶反对称纵振模态为工作模态,利用粘附于盆架状作动器表面的压电陶瓷激发工作模态振动,迫使驱动足同时沿xOz、yOz面做椭圆轨迹行进以推动移动体。根据传递阵力学原理,构造作动器各单元的振动传递方程,在确定各单元间连接与传递条件及作动器压电边界条件基础上,建立了作动器的半解析性机电耦合传递矩阵模型,编制了模型的解算程序。建立作动器的多目标优化数学模型,求得其优化结构尺寸。为印证半解析理论模型,还构建了作动器的机电耦合有限元数值模型。传递阵模型与数值模型解得的作动器工作模态频率差分别为177 Hz和191 Hz,求取驱动足在x、y、z向的振幅分别为2.95μm、3.27μm、1.37μm及3.12μm、3.61μm、1.82μm,表明了半解析模型的有效性。结果表明,该文提出的结构设计与驱动原理相结合的作动器分析方式,为优化压电作动器性能开启了新思路。

To enrich the structure of macro-micro planar motion device,a basin type piezoelectric actuator was proposed in this paper.The 1 st order in-plane symmetric bending vibration mode and 2 nd order antisymmetric longitudinal vibration mode of the basin type structure were set as the working modes,and the piezoelectric ceramics adhered to the surface of the basin type actuator is used to excite the working modes vibration,forcing the driving feet to travel elliptically along the xOz and yOz planes simultaneously to push the moving bode.According to principle of transfer matrix mechanics,the vibration transfer equation of each element of the actuator is constructed,and by determining transfer conditions between the connecting elements and the piezoelectric boundary,a semi-analytical electromechanical coupling transfer matrix model of the actuator is established,and the solution program of the model was compiled.A multi-objective optimization mathematical model of the actuator was established to obtain its optimal sizes.To validate the semi-analytical model,a finite element model(FEM)of the actuator was also established.The working modal frequency differences obtained from the semi-analytical model and FEM model were 177 Hz and 191 Hz,respectively,and the driving foot’s vibration amplitude along x,y and z directions were 2.95μm,3.27μm,1.37μm and 3.12μm,3.61μm and 1.82μm,respectively,which validated the effectiveness of the semi analytical model.The results indicate that the proposed actuator analysis method combining structural design with driving principles opens up a new idea for optimizing the performance of piezoelectric actuators.