Multi-stage hysteresis modelling of magnetorheological dampers and experimental verification.

• A multi-stage hysteresis (MSH) model is proposed for magnetorheological dampers. • Steady-state and transient finite element methods are combined. • An equivalent weighted mean magnetic field hypothesis is proposed and validated. • The MSH model effectively predicts the behaviour of magnetorheological dampers. • The MSH model has a smooth transition in different stages. An accurate theoretical model is the basis for the structural design and parameter optimisation of magnetorheological dampers (MRDs). Owing to the inability of existing models to accurately describe the motion characteristics of MRDs in the entire region, a multi-stage hysteresis (MSH) model for low-frequency conditions was proposed. The MSH model comprised a magnetic chain model and Bi-Viscous model to describe the characteristics of the pre-yield and yield flow stages, respectively. The local loss and inertia effect were considered in the MSH model. Steady-state and transient finite element methods were combined to analyse the magnetic field distribution during MRD motion, and an equivalent weighted mean magnetic field hypothesis was proposed to reduce the quantisation error and time consumption. The experimental results demonstrate the prediction effectiveness of the MSH model. Moreover, the quantitative evaluation parameters of the flow and hysteresis regions were obtained and the variation trend of the MRD main design indices with the magnetic circuit parameters was analysed. The obtained velocity distribution parameters indicate a smooth transition of the stages in the MSH model from a qualitative perspective. The mixed mode incorporates the physical properties of the shear and flow modes, but cannot simply be regarded as a linear superposition of these two modes. [Display omitted] [ABSTRACT FROM AUTHOR]