Dynamic Characteristic Analysis of a Toothed Electromagnetic Spring Based on the Improved Bouc-Wen Model

Electromagnetic spring active isolators have attracted extensive attention in recent years. The standard Bouc-Wen model is widely used to describe hysteretic behavior but cannot accurately describe asymmetric behavior. The standard Bouc-Wen model is improved to better describe the dynamic characteristic of a toothed electromagnetic spring. The hysteresis model of toothed electromagnetic spring is established by adding mass, damping, and asymmetric correction terms with direction. Subsequently, the particle swarm optimization algorithm is used to identify the parameters of the established model, and the results are compared with those obtained from the experiment. The results show that the current has a significant impact on the dynamic curve. When the current increases from 0.5 A to 2.0 A, the electromagnetic force sharply increases from 49 N to 534 N. Under different excitations and currents, the residual points predicted by the model proposed in this work fall basically in the horizontal band region of -20-20 N (for an applied current of 1.0 A) and -40-80 N (for an application of 4.5 mm/s). Furthermore, the maximum relative error of the model is 12.75%. The R² of the model is higher than 0.98 and the highest value is 0.9993, proving the accuracy of the established model.