A new hysteresis model for magneto–rheological dampers based on Magic Formula

This paper investigates a novel model based on the Magic Formula and the Pan’s model to effectively predict the inherent nonlinear hysteresis behavior of magneto–rheological (MR) dampers. In the proposed model, the hysteresis element is employed from the Magic Formula and Pan’s model, and two new independent horizontal shift parameters, which are separated from one original parameter of the Pan’s model, are added. Each of them characterizes an offset with respect to the origin for each branch of hysteresis curves, providing more flexibility and effectiveness for simulating curves with high asymmetry. In addition, a parameter to further control the sharpness of hysteresis curves in the backward region of damping force–velocity is proposed, which is useful to simulate the behavior of MR dampers in rather extreme operating cases. A case study is performed on a prototype MR damper for washing machines, in which the model incorporates applied current and excitation frequency as variables to make it more adaptable to a wide range of working conditions. For comparison, performance of three hysteresis models, including the Spencer’s model, the Pan’s model and the proposed model, are analyzed and evaluated. The research results show that, as compared with the others, the proposed model can not only predict the nonlinear hysteresis behavior of MR dampers more precisely, but is also more compatible with different operating excitations, and the clearer meanings of the model parameters make them easier to study and identify.