Two-dimensional dynamics of a quasi-static legged piezoelectric actuator

Piezoelectric actuators are becoming a viable alternative to electrodrives in terms of size, speed and stall force characteristics. In this paper, a novel dynamic model of a contemporary linear piezoelectric actuator is presented. The model is based on physically meaningful parameters and macroscopically measured data for the fully assembled state. The model describes the frictional interaction between multiple piezoelectric legs and a ceramic rod. It consists of two orthogonal dynamics which are coupled together by means of preload and frictional forces. Linearity of the model is maintained through most of the modelling stages with a clear indication of nonlinear effects due to hysteresis, friction and impact dynamics of the legs. Unknown model parameters are estimated within a global optimization procedure and bounds on parameter values are indicated. The model presented explains the linear drive frequency/velocity as well as the nonlinear load force/velocity characteristics of the actuator within its full operational range. The insights gained throughout the modelling process indicate the possibilities of design improvements. Moreover, the model can be used to explain the resonance phenomena limiting the range of actuator operation and is used to anticipate an alternative drive strategy.