The hysteresis behavior of a linear stroke magnetorheological damper is characterized for sinusoidal displacement excitation at 2.0 Hz (nominal). First, we characterize the linearized MR damper behavior using equivalent viscous damping and complex stiffness. Four different nonlinear modeling perspectives are then discussed for purposes of system identification procedures, including: (1) nonlinear Bingham plastic model, (2) nonlinear biviscous model, (3) nonlinear hysteretic biviscous model, and (4) nonlinear viscoelastic-plastic model. The first three nonlinear models are piecewise continuous in velocity. The fourth model is piecewise smooth in velocity. By adding progressively more model parameters with which to better represent pre-yield damper behavior, the force vs. velocity hysteresis model is substantially improved. Of the three nonlinear piecewise continuous models, the nonlinear hysteretic biviscous model provides the best representation of force vs. velocity hysteresis. The nonlinear viscoelastic plastic model is superior for purposes of simulation to the hysteretic biviscous model because it is piecewise smooth in velocity, with a smooth transition from pre-yield to post-yield behaviors. The nonlinear models represent the force vs. displacement hysteresis behavior nearly equally well, although the nonlinear viscoelastic-plastic is quantifiably superior. Thus, any of the nonlinear damper models could be used equally successfully if only a prediction of energy dissipation or damping were of interest.
Nomenclature
ER Electrorheological MR Magnetorheological NBP Nonlinear Bingham-Plasticis primarily manifested as a substantial increase in the dynamic yield stress of the fluid, while the viscosity remains relatively constant [1]. When compared to ER fluids, MR fluids have superior properties, including an order of magnitude higher yield stress, typically 50-100 kPa, and a much wider operational temperature range, typically -40 to 150 degrees C. High payoff may result by applying these materials in dampers for aerospace systems such as the lag mode damper for stability augmentation of helicopter rotor systems [2, 3], dampers for landing gear to enhance crashworthiness [4,5], and shock and vibration isolation mounts for avionics packages.This article presents a systematic procedure with which to analyze the hysteresis behavior of MR dampers. Because the rheological behavior of ER fluids is qualitatively similar to that of MR fluids [6], these results can also be extended to ER dampers.