Nondimensional Herschel-Bulkley analysis of magnetorheological and electrorheological dampers

Quasisteady modeling of linear stroke flow mode magnetorheological (MR) (or 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 variable yield stress of the fluid, tau(y), is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a pre-yield condition where the local shear stress is less than the yield stress, tau < tau(y), or (2) a post-yield condition, where the local shear stress is greater than the yield stress, tau > tau(y), so that the material flows with a constant post-yield viscosity. The objective of this study is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits post-yield shear thinning or thickening behavior, that is, the post-yield 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, pre-yield thickness, 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.