Quasi-Steady Herschel-Bulkley Analysis of Magnetorheological Dampers With Preyield Viscosity

A magnetorheological (MR) fluid, modeled as a Bingham-plastic material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscometric measurements, such a Bingham-plastic model is an idealization to physical magnetorheological behavior, albeit a useful one. A better approximation involves modifying both the preyield and postyield constitutive behavior as follows: (1) assume a high viscosity preyield behavior over a low shear rate range below the yield stress, and (2) assume a power law fluid (i.e., variable viscosity) above the yield stress that accounts for the shear thinning behavior exhibited by MR fluids above the yield stress. Such an idealization to the MR fluid’s constitutive behavior is called a viscous-power law model, or a Herschel-Bulkley model with preyield viscosity. This study develops analytical quasi-steady analysis for such a constitutive MR fluid behavior applied to a flow mode MR damper. Closed form solutions for the fluid velocity, as well as key performance metrics such as damping capacity and dynamic range (ratio of field on to field off force). Also, specializations to existing models such as the Herschel-Bulkley, the Biviscous, and the Bingham-plastic models, are shown to be easily captured by this model when physical constraints (idealizations) are placed on the rheological behavior of the MR fluid.