Nondimensional Analysis of Electrorheological and Magnetorheological Dampers Using a Herschel-Bulkley Constitutive Model

Quasisteady modeling of linear stroke flow mode magnetorheological (MR) and electrorheological (ER) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the yield stress of the fluid, τ_y, is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a preyield condition where the local shear stress is less than the yield stress, τ < τ_y, or (2) a postyield condition, where the local shear stress is greater than the yield stress, τ > τ_y, so that the material flows with a constant postyield viscosity. The objective of this paper is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits postyield shear thinning or thickening behavior, that is, the postyield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results—velocity profile, shear stress profile, and damping coefficient—are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.