The hysteresis behavior of a linear stroke magnetorheological damper is characterized for sinusoidal displacement excitation at 2.0 Hz (nominal). Four different modeling perspectives are discussed for purposes of system identification procedures, including: (1) equivalent viscous damping, (2) nonlinear Bingham plastic model, (3) nonlinear biviscous model, and (4) nonlinear hysteretic biviscous model. By progressively adding model parameters with which to better represent pre-yield damper behavior, the force vs. velocity hysteresis model is substantially improved. The three nonlinear models represent the force vs. displacement hysteresis behavior nearly equally well. Thus, any of the three nonlinear damper models could be used equally successfully if only a prediction of energy dissipation or damping were of interest. The nonlinear hysteretic biviscous model provides the best representation of force vs. velocity hysteresis of the four models examined here.

Electrorheological-(ER-) fluid-based dashpot dampers have smart capabilities because ER fluids undergo large changes in yield stress as electric field is applied. Our objective is the development and experimental validation of quasi-steady dashpot damper models, based on an idealized nonlinear Bingham plastic shear flow mechanism, for purposes of preliminary design and performance predictions. The data required for the Bingham plastic model is normally supplied by ER fluid suppliers, that is, plastic viscosity and dynamic yield stress as a function of applied field, as determined from a shear stress versus shear strain rate diagram. As force is applied to the dashpot damper, the ER fluid flows through an annulus between the concentric inner and outer electrodes. The idealized Bingham plastic shear flow mechanism predicts that three annular flow regions develop as a function of the local shear stress. In the central pre-yield or plug region, the local shear stress is less than the dynamic yield stress, so that the plug behaves like a rigid solid. The remaining two annular regions, adjacent to the electrodes, are in the post-yield condition and correspond to the shear stress exceeding the dynamic yield stress, so that the material flows. Equivalent viscous damping performance of an ER fluid dashpot damper is strongly coupled with the plug behavior. For a constant force, as the applied field increases, so does the plug thickness and equivalent viscous damping. For a constant applied field, as the force increases, the plug thickness and equivalent viscous damping both decrease. The passive and active or field-dependent damping behavior of an ER-fluid-based dashpot damper can be designed for a specific application using these quasi-steady Bingham plastic models.

A nonlinear dynamic model is presented that characterizes electrorheological material behavior in terms of its shear stress versus shear strain behavior. The ER fluid model is essentially a nonlinear combination of linear shear flow mechanisms. These linear shear flow mechanisms, a three-parameter viscoelastic fluid element and a viscous fluid element, are used to describe shear flow behavior in the pre-yield and the post-yield regimes, respectively. In order to capture the material behavior in the transition through the yield point, a nonlinear combination of these linear shear flow mechanisms is used. The model, which relates the shear strain input to the shear stress output, is represented by a simple network that consists of two parallel linear mechanisms whose outputs are combined using nonlinear weighting functions. The weighting functions are dependent on the strain rate in the material. A system identification technique is developed to estimate the model parameters from experimental data, which consists of shear stress versus shear strain hysteresis loops at different levels of electric field. The results of this system identification approach indicate that the model parameters are smooth monotonic functions of the electric field. The experimental hysteresis loops are reconstructed using the estimated model parameters and the results show that the model accurately predicts material response. It is shown that the Coulomb friction-like behavior at high field strengths, which is characteristic of ER fluids, can be captured by this nonlinear mechanism-based model.

~en,rh Assf. Assoc;ecir~liut A p e d Gessow Rofu,rrnfr Cerlfer Lor{/ C o r~~o r n f i o~~ fle/>flrf~~tee,~f ofAero.r/~<~cc Engir~eerirzg Tlzo,rcns Lord Research Center. U~ri~,ersif~' of Mnr)'lo,cd 110 Lod Drive College Park. MD 20742 C a r : NC 27511Magnetorheological fluid dampers are attractive candidates for augmentation oflag mode damping in helicopter rotors, where additional damping is required lo avert instabilities only during specific flight conditions. Magnetorheological (MR) fluids change properties dran~alically with application of a magnetic field. This active damping component presents an advantage over passive elastnmeric and fluid-elastomeric dampers. An extensive comparative study of fluid-elastomeric and MR dampers is presented. The study was conducted with four (a pair each) 116th Froude scale dampers. The MR dampers were tested with the magnetic field turned off (OFF condition) and with the magnetic field turned on (ON condition). The dampers were tested individually and in pairs, under different preloads, and under single and dual frequency excitation conditinns. The fluid-elastomeric and MR (OFF) damper hehavior was linear, while the MR (ON) hehavior was nonlinear with the sliffness and damping varying with the displacement amplitude. Under dual frequency conditions, the MR dampers (ON condition) showed a significant degradation in damping and stiffness as the dual frequency excitation was increased. The MR (OFF) damperssho~ved n o change in properlies. The fluid-elastonieric dampers showed a mild degradation in stiffness and damping under dual frequency excitation conditions. The MR (ON) damper hysleresis was modeled using a nonlincar viscoelaslic-plastic model. The model captures the nonlinear behavior accurately. Using the single frequency parameters, the dual frequency hysteresis hehavior was predicted, and it correlales well wilh experimental data.

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.

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