A Unifying Perspective on the Quasi-steady Analysis of Magnetorheological Dampers

Abstract

A magnetorheological (MR) fluid, modeled as a Bingham plastic (BP) material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscometric measurements, such a BP model is an idealization to physical MR 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 when the shear stress is less than the transition stress, and (2) assume a power law fluid (i.e., strain rate dependent viscosity) when the shear stress is greater than the transition stress. Assuming a power law fluid in postyield allows the model to account for shear thinning behavior exhibited by MR fluids at higher strain rates. Such an idealization for MR fluid constitutive behavior is called an viscous-power law model, or a Herschel—Bulkley (HB) model with preyield viscosity. This study develops a quasi-steady analysis for such a constitutive MR fluid behavior applied to an MR flow mode damper. Closed form solutions are developed 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). For the given fluid properties and flow mode damper geometry, the fluid velocity profile and gradient, and the relationship of the damper force and piston velocity are analyzed. In addition, specializations to existing models, such as the HB, biviscous, and BP models, are shown to be easily captured by this model when physical constraints (idealizations) are placed on the rheological behavior of the MR fluid.