Rheological Parameter Estimation for a Ferrous Nanoparticle-based Magnetorheological Fluid using Genetic Algorithms

Abstract

This study examines identification of rheological parameters for a constitutive model characterizing the rheological behavior of a ferrous nanoparticle-based magnetorheological (MR) fluid. Particle size is nominally 28 nm and the MR fluid has a weight fraction of 27.5% Fe. A constant shear rate rheometer is used to measure flow curves (shear stress vs. shear rate), as a function of applied magnetic field, of an MR suspension of nanometer-sized iron particles in hydraulic oil. The MR fluid is characterized using both Bingham-plastic (BP) and Herschel-Bulkley (HB) constitutive models. These models have two regimes that can be characterized by a field-dependent yield stress: pre-yield implies that the local shear stress is less than the yield stress, and post-yield implies that the local shear stress is greater than the yield stress. Both models of MR fluid behavior assume that the MR fluid is rigid in the pre-yield regime. However, the post-yield behavior is different. The BP model assumes that the post-yield increase in shear stress is proportional to shear rate. However, the HB model assumes that the post-yield increase in shear stress is proportional to a power law of shear rate. Identification of the model parameters is complicated by model non-linearities, as well as variance in experimental data. The rheological parameters of the BP and HB models are identified using both a gradient-based least mean square minimization procedure, as well as a genetic algorithm (GA). The HB model is shown to represent better, the rheological behavior of the ferrous nanoparticle-based MR fluid. Also, the GA performs better than the gradient-based procedure in minimizing modeling error.