A Kinetostatic and Dynamic Modeling Method of Piezo-Actuated Compliant Mechanisms Based on Dynamic Stiffness Matrix Method

Piezoelectric actuator is a critical component of piezo-actuated compliant mechanisms, especially for the precision positioning stage. To design and optimize a stage with high bandwidth and proper motion range, it is necessary to establish a kinetostatic and dynamic model for the piezo-stack widely used in nano-positioning stage. Based on piezoelectric vibration theory and dynamic stiffness method, a new modeling method for compliant mechanisms actuated by piezo-stack has been proposed in this work. The planar dynamic stiffness matrices of the piezo-plate, the piezo-stack, and the piezoelectric actuator with insulating plates are deduced by considering PEA as several beam components with external forces equivalent to piezo-actuated forces. To verify the proposed modeling method, the dynamic models of piezoelectric actuator and two piezo-actuated compliant mechanisms are deduced based on the proposed method and validated by the finite element method.