Modeling of a walking piezo actuator

Piezoelectric actuators are often used in positioning devices that require (sub)nanometer resolution. In this paper, we develop an electro-mechanical dynamic model of a walking piezo actuator. The derived model structure can be used for the dynamic modeling of bimorph piezo motors in general. Furthermore, the physical nature enables the model to be used in design optimizations to derive new motors with different properties and for a dynamic analysis to investigate the maximum allowable driving frequency in relation to the dynamic effects of the motor. The walking piezo actuator contains four legs, each with two electrically separated piezo stacks. The legs are modeled as a connection of coupled mass-spring-damper systems. Using a Lagrange approach, the nonlinear system dynamics are derived. The variation in the system dynamics is assessed using linearization around different equilibrium positions. Also a static linearized approximation is derived, which describes the static relation between the supply voltages and the tip trajectories of the legs. The dynamic analysis shows that the motor can be modeled sufficiently accurate using a connection of six lumped mass-spring-damper systems. The variation in system dynamics appears to be most significant in the movement perpendicular to the leg orientation. Experiments show that the static linearized model accurately describes the tip trajectories of the legs for both sinusoidal and asymmetric waveforms.