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

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.