Modeling and TF-BPNN inverse modeling of a magnetorheological damper

Rail vehicles equipped with secondary semi-active suspension can effectively improve ride quality. Magnetorheological (MR) dampers are widely used as actuators in semi-active suspensions due to their advantages such as rapid response and wide adjustment range. However, their complex nonlinear characteristics pose challenges for research and application. This paper studies modeling of a MR damper and its inverse models. For MR damper modeling, a physical model is developed that incorporates both the shear-thinning effect and viscoelastic characteristics of MR fluids by integrating the bi-plastic Bingham model and the Maxwell model. The proposed model provides greater physical interpretability and a more accurate characterization of the mechanical behavior than a widely used improved Bouc-Wen hysteresis model. This performance is validated by Hardware-in-the-loop (HIL) tests on a 3-DOF rail vehicle lateral model. The proposed model outperformed an improved Bouc-Wen model, with a lower overall RMSE (55.7 N vs 103.1 N) and a smaller average amplitude error under small-amplitude vibration conditions in the 17–18 Hz range (7.5% vs 27%). For the MR damper inverse model, a Transfer function - Back Propagation Neural Network (TF-BPNN) model was proposed to track the desired force required by semi-active control strategies. The TF component compensates for the force response lag behind the current, and the BPNN models the nonlinear relationship between force and current. HIL test results demonstrated that the TF-BPNN achieves higher R 2 values (0.857, 0.856, and 0.861 at 20°C, 31°C, and 45°C, respectively) than the Look-up table method (0.709, 0.751, and 0.786 at the same temperatures) within the critical low-frequency sway range of 1.5-2 Hz. The proposed model demonstrates high tracking accuracy and insensitivity to temperature. The validity of the developed models was experimentally verified using HIL tests, confirming their strong potential for both simulation and experimental applications.