An electromechanical dynamic stiffness matrix of piezoelectric stacks for systematic design of micro/nano motion actuators

Abstract

Piezoelectric stacks have proved to be effective for micro/nano motion actuators with large blocking forces. A critical problem is to build their electro-mechanical model for systematic design of statics and dynamics including piezoelectric hysteresis and elasto-kinematics of compliant mechanisms. To ease this issue, this paper proposes a new electro-mechanical dynamic stiffness matrix of piezoelectric stacks to enable a systematic analysis. Positive and inverse piezoelectric effects are included into the dynamic stiffness matrix of Timoshenko beams in the form of Taylor’s series with a clear definition of physical parameters. Consequently, the Jacobian matrix, input/output stiffness, natural frequencies, frequency-domain spectrums of mechanical displacement and electrical impedance as well as the time-domain response of piezoelectric hysteresis can be fully obtained with a single modeling process. Particularly, the time-domain response in the presence of piezoelectric rate-dependent hysteresis and dynamic resonance behaviors of compliant mechanisms is captured in a parameter-insightful way but not the manner in Hammerstein hysteresis model with a black-box transfer function. Experiments on a proof-of-concept prototype of precision positioning stage verify the easy operation and satisfying prediction accuracy of the presented approach.