Study on Effective Estimation of Parameters of the Herschel-Bulkley Fluid Model for Magnetorheological Fluid

Abstract

Abstract Among different rheological models for Magnetorheological (MR) fluids, Herschel-Bulkley (H-B) fluid model is the most suitable model in explaining the characterization results. The current study presents an effective way for estimating parameters of the H-B model by considering the post-yield low shear rate data to high shear rate data where the shear-thinning effect takes place; this is termed as effective H-B model. For the comparison purpose, the linear Bingham Plastic (BP) model is fitted by projecting high shear rate data onto the y-axis and another H-B model is fitted using all characterization data. To determine the damping forces, formulation for the flow of MR fluid inside the MR valve is presented. The estimated damping forces resulting from the H-B model, BP model and effective H-B model are then compared for different magnetic fields. It was found that the H-B model overestimates the damping forces and, on the other hand, the inability of the BP model in explaining the shear-thinning effects at high shear rates lead to overestimation of damping forces and it becomes more pronounced at high piston velocities. This study may provide guidance for estimating parameters of the H-B model for accurate prediction of damping forces in the design-phase.