Coupled dynamic modeling of piezo-actuated compliant mechanisms subjected to external loads
Mingxiang Ling, Xianmin Zhang
Abstract
Piezoelectrically actuated compliant mechanisms are key techniques in designing micro/nano manipulators, precision positioning stages/grippers and many other mechanical instruments. By considering the coupling relationship among piezoelectric actuator, compliant mechanisms and their external loads, a new modeling methodology in Laplace domain is proposed to capture the coupling dynamic characteristics of such a complex system. The coupled dynamic model of piezo-actuated compliant mechanisms subjected to mass-spring-damper loads with an accessorial force is analytically derived in the form of transfer function based on the concept of two-port dynamic stiffness model and control theory. The coupled dynamic model is further transformed into a generalized control block diagram in a unified form. As an application case, the static and dynamic performances of a typical flexure-based precision manipulator actuated by amplified piezoelectric stacks are analyzed with the presented model. It is demonstrated, both numerically and experimentally, that the proposed approach is accurate and straightforward for solving the coupled dynamic modeling issue in piezo-actuated compliant mechanisms subjected to external loads, and would be general enough for a wide class of applications involving multi-domain dynamic problems.