Characterizing the electric field- and rate-dependent hysteresis of piezoelectric ceramics shear motion with the Bouc-Wen model

Piezoelectric technology is widely used in the field of precision drives. However, when piezoelectric actuators are employed at high voltages and high frequencies, their hysteresis can greatly affect the accuracy of such systems. The Bouc-Wen model has typically been used by researchers to characterise the hysteresis of piezoelectric materials. Besides, to extract the parameters of this model from experimental data, particle swarm optimization (PSO) is often employed. However, the majority of such studies only considers hysteresis as a function of the electric field strength and not as a function of actuation frequency. In addition, most of such existing reports have focused on longitudinal type piezo actuators. In this context, the research presented here complements this body of knowledge by demonstrating the application of the PSO algorithm for determining the parameters of the Bouc-Wen model when hysteresis depends not only on the electric field but also on the rate of the driving signal and when applied on a shear-type piezoelectric actuator. The obtained experimental data showed that with the increase of electric field strength, both the piezoelectric coefficient and hysteresis value increased significantly, and that with the increase of frequency, the piezoelectric coefficient decreased, while the hysteresis value changed slightly. The variations of the Bouc-Wen model parameters with the electric field and frequency were identified and then used to predict the shear motion trajectory of the piezoelectric stack. It was found that in the identified range of electric field and frequency, the predicted error rate of the hysteresis loop amplitude was less than 16.5% with a minimum value of 0.1%, and the error rate of the hysteresis loop width was less than 14.5% with a minimum value of 2.7%. Based on the identified electric field- and rate-dependent Bouc-Wen model, a novel finite element (FE) model was also proposed to analyse the effect of electrical and mechanical coupling on the piezoelectric movement.