Analytical model and finite element analysis of piezoelectric displacement amplification mechanism

Kinematic and dynamic modeling of piezoelectric displacement amplifying mechanisms was researched. The static analytical models(such as displacement amplifying ratio) for a bridge type compliant displacement amplifying mechanism was derived based on the law of conservation of energy and elastic beam theory. Then, an analytical model of natural frequency was also built by employing the Lagrange equation. The finite element analysis was used for verification of the feasibility and superiority of proposed analytical models and for comparison with several typical mathematical models deduced by other authors. The results show that the proposed theoretical formula of the displacement amplification ratio has the highest accuracy, because it considers both the translational and rotational stiffnesses of the mechanism during modeling and abandons the approximate geometric relationship between input and output displacements of the bridge-type compliant mechanism. Moreover, the discrepancy between the theoretical formula of natural frequency in this paper and the finite element calculation results is kept within 5%. The modeling method and corresponding theoretical formulas of the displacement amplification ratio and natural frequency proposed in this paper provides a useful and accurate reference for optimal designing and manufacturing of satisfactory structures of bridge-type displacement amplification mechanisms. © 2016, Science Press. All right reserved.