This work aims to establish the mathematical model with the high effectiveness in predicting the damping force of an MR damper with nonmagnetized passages in piston. The pressure drops due to viscous loss, MR effect, and the minor losses at the inlet and outlet of passages are considered in the mathematical model. The widely reported Bingham model is adopted to describe the mechanical property of MR fluid. The mechanical behaviours of the MR damper are experimentally evaluated under different excitations and current. The yield stress of MR fluid with respect to the current applied to piston coil is obtained by finite element analysis in Ansoft Maxwell 14.0. The proposed model is validated by comparing the simulated damping characteristics with the measured data under various currents applied to the piston coil. The simulated results are also compared with those obtained from the mathematical model without the pressure drop due to the minor losses at the inlet and outlet of passages. The comparisons show that the proposed mathematical model can yield more accurate predictions of damping force. This indicates that the pressure drop due to the minor losses is significant and nonnegligible. The nonlinearity of force-velocity characteristics is discussed. In order to quantitatively explain the necessity of taking the minor losses into account for modelling the MR damper, the proportion of pressure drop due to the minor losses to the total pressure drop is investigated and discussed. Pressure drops due to the minor losses and viscous loss are also investigated and discussed. At last, the proposed mathematical model is used to analyse the working principle of nonmagnetized passages.
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