Kinetostatic Modeling of Piezoelectric Displacement Amplifiers Based on Matrix Displacement Method

Displacement amplification ratio and input stiffness modeling of three types of piezoelectric displacement amplifiers (PDAs) were investigated in this paper. The main feature is that we further improved the accuracy of matrix displacement model (MDM) by setting a node on both input and output points, and simplified modeling process of the MDM by utilizing axial symmetry of PDAs. Firstly, we deduced the stiffness matrix of the flexure element based on the general flexure hinge’s compliance formulas. Then, we established the MDM of a PDA by discretizing a displacement amplifier into flexure elements and assembling element stiffness matrices. The finite element method was employed to verify the superiority of presented model and to compare with typical analytical models and conventional MDMs. The results show that the presented model of both the displacement amplification ratio and input stiffness has better accuracy on the whole, thanks to consider deformation of both the input and output points during modeling and abandons considering input and output ends as a lumped mass.