Longitudinal vibrations modeling of a piezoelectric actuator used in forming process

Experimental results in the field of forming processes have shown that forming loads are significantly reduced when applying vibrations to the die. Piezoelectric actuators are well suited for this purpose because large forces and small amplitudes of vibrations are typically required in such processes. The main objective of the models proposed in this study is to describe the dynamical behavior of piezoelectric stack actuators using the 33-effect which can be used in the frame of a mechanical design. Two models of piezoelectric actuators are proposed: the first using an analytical solution and the second using a finite element approach. Both models are based on the Hamilton's principle to establish the equation of motion. The analytical approach uses the modal decomposition method to solve them and establish the transfer functions model between the inputs and the outputs of the system, however it is limited. The finite element approach provides a state space model which can be included in simulations integrating the forming process model. Both models are implemented using Matlab software. The comparisons of the results of finite element model (FEM) with those of the analytical model (AM) are presented in time and frequency domains and show a good agreement between the two models. The results obtained are also compared with other previous works.