Quasi-Steady Herschel-Bulkley Analysis of Electroand Magneto-Rheological Flow Mode Dampers

Abstract

Electrorheological (ER) and magnetorheological (MR) fluid-based dampers are typically analyzed using Bingham-plastic shear flow analysis under quasi-steady fully developed flow conditions. An alternative perspective, supported by measurements reported in the literature, is to allow for post-yield shear thinning and shear thickening. A Herschel-Bulkley constitutive shear flow relationship can be used to account for such post-yield shear thinning or thickening behavior. Depending on the value of the flow behavior index number, varying degrees of post-yield shear thickening or thinning behavior can be analyzed. A nominal ER bypass damper is considered. Damping forces are analyzed by approximating the annular geometry of the ER/MR valve by parallel plates. The impact of the flow behavior index on the shear stress vs. shear rate behavior and velocity profile are also examined numerically as a function of applied electric field. Analytical damping predictions are compared using the nonlinear Bingham-plastic and Herschel-Bulkley analyses.