Nondimensional characterization of flow-mode magnetorheological/electrorheological fluid dampers

Magnetorheological/electrorheological dampers are complex devices and involve a large set of important material and geometric variable with mutual interactions between them. As such, reliable predictions of the damping force level in these devices are difficult to achieve. However, meaningful results can be obtained with significantly less effort through nondimensional parameters involving all key variables. Therefore, the goal of this study was to propose a robust set of nondimensional parameters for the purpose of modeling of magnetorheological/electrorheological dampers (and other flow-mode devices) as well as the characterization of data from experiments with magnetorheological/electrorheological devices. The proposed scheme employs five parameters characterizing the contribution of flow inertia, viscosity, and yield stress, as well as shear thinning/thickening effects to the damping force output of magnetorheological/electrorheological valves. It is the result of analysis of several constitutive models of non-Newtonian fluid models (Bingham plastic model, biviscous model, biplastic Bingham model, and Herschel–Bulkley model). Specifically, the goal was to derive analytical (exact) formulae for pressure gradient of all examined models excluding the Herschel–Bulkley model. In the Herschel–Bulkley model, the nondimensional relationship between pressure gradient and flow rate is given in a power-law form, and the analytical (exact) solution cannot be obtained. Prior art included analytical (exact) solutions for the Bingham plastic model only. In the most generic form, the expressions can be useful for designing magnetorheological/electrorheological flow-mode devices. Exemplary calculations of the damping force output are presented in this article for a custom single-gap magnetorheological piston. The piston contains a semi-bypass feature in the annulus to allow for low-breakaway forces at near-zero piston velocity inputs. The steady-state calculations are presented for two exemplary damper units, and the model is validated against experimental data. Finally, the expressions allow one to easily characterize flow data into separate regimes of damper operation by means of the proposed scheme.