DESIGN, FABRICATION AND MODELLING OF A MINIATURE PIEZOELECTRIC BIMORPH ACTUATOR

Abstract

The motoring behavior of cubic piezoelectric ceramics is discussed and two motor modes are defined. Four basic configurations of piezoelectric actuators are presented. They are: extender structure, bimorph structure, monomorph structure, and stack structure. Their perfonnances are compared and the bimorph structure is selected for design analysis and prototyping. A piezoelectric bimorph actuator is designed and fabricated. The actuator consists of two bimorph pairs, one moving plate, two guides and one base. On each side of the moving plate, there 1s one bimorph pair installed. The center of one beam in each bimorph pair is fixed to the wall of the base and the center of the other beam in this bimorph pair is fixed to the moving plate. The two bimorph pairs are so electrically energized that one expands while the other contracts. The moving plate is thus driven from one side to the other side. Higher displacement output can be achieved by installing more bimorph pairs in series on each side of the moving plate and high stiffness and high force output can be achieved by more bimorph pairs in parallel on each side of the moving plate. The actuator was fabricated with the piezoelectric bimorph G-1195 from PJEZO SYSTEM INC. To set up a dynamic model of the piezoelectric bimorph actuator, the mechanics of the piezoelectric bimorph beam is discussed. First, bending of the piezoelectric bimorph beam subjected to both an applied electric field and an external force are considered and the total energy stored in this beam is derived. The total energy stored in the piezoelectric bimorph beam comprises energy due to the electric field, energy due to the external force and energy due to the coupling of both the applied electric field and the external force. From the stored energy we obtain the displacement of the mid-point of a simply supported piezoelectric bimorph beam subjected to both the applied electric field and external force. The nonlinear dynamic model is derived which takes into account the hysteretic behavior by introducing a nonlinear state variable into the piezoelectric exciting force. To evaluate the performance of the piezoelectric bimorph actuator developed and to determine the parameters of its dynamic model, experiments are designed and carried out. The experiments include displacement test, step response test and frequency response test. The displacement test shows the displacement output capability and the hysteresis that exists. When 100 volts sinusoidal voltage is applied to it, it generates displacement output ranging from about -90 to +90 microns. The step response test shows that the step response of the actuator looks like a lightly damped second order system and the frequency response test shows that the frequency response of the actuator also looks like a second order system with a low resonant frequency. Finally, the parameters of the established model are determined. They include the effective stiffness, the effective piezoelectric strain coefficient, the damping coefficient and the parameters ?, ? and ?. The effective stiffness and the effective piezoelectric strain coefficient can be obtained directly from the expressions derived. The effective mass can be computed from an energy method analysis. And the damping coefficient can be determined from the step response or the frequency response. The parameters ?, ? and ? are determined by a nonlinear filter system identification method. Simulations of the established dynamic model with the determined parameters are also done and the simulated results closely match to the experimental results. This model can be used in a control system with a piezoelectric bimorph actuator to improve the tracking accuracy.