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

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 preyield 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 gradientbased procedure in minimizing modeling error.