二维微动工作台分析及其优化设计方法

ANALYSIS AND OPTIMUM DESIGN OF 2-DOF MICRO-POSITIONING STAGE

设计了一种压电陶瓷驱动的二维微动工作台,采用结构力学理论建立了工作台的简化模型,并推导出工作台沿x、y方向刚度计算表达式。将工作台简化为2自由度弹簧一质点系统,得出其前二阶固有频率计算表达式。通过微动工作台固有频率及沿x、y方向刚度的试验测试,验证了解析法和有限元法用于微动工作台设计分析的可行性。采用有限元法,研究了微动工作台的直角平板柔性铰链特征参数对微动工作台性能的影响。有限元分析结果表明:当平板柔性铰链长度较小或铰链宽度较大时,其刚度、频率及驱动力较高,然而铰链根部应力集中也较严重。通过改变柔性铰链的特征参数,可达到控制和优化工作台固有频率、输出位移、应力分布及驱动力响应的目的,并提出一种优化设计微动工作台柔性铰链的简易方法。

A two-degree-of-freedom （2-DOF） micro-positioning stage driven by piezoelectric actuator （PZT） is developed and the simplified modeling of the micro-positioning stage is discussed. The x and y direction stiffness of the micro-positioning stage is deduced according to the theory of structural mechanics. After simplifying the micro-positioning stage as a 2-DOF spring-mass system, two resonant frequencies of the micro-positioning stage are derived. The comparative results of the theory, finite element analysis （FEA） and experiments show the accuracy of theory model and the validity of FEA. FEA on static and dynamic behavior of the micro-positioning stage is performed and FEA indicates that the stiffness, the natural frequency and the driving force will increase and the maximum stress of the stage will also increase, as the hinge length decreases or the hinge width increases. Modification of dimensions enables us to control and optimize natural frequency, displacement, stresses, and force to be applied to the hinges to achieve the desired response of the micro-positioning system. Finally, a simple optimum design procedure is developed by which the proper dimensions of the micro-positioning stage can be found.