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Nondimensional analysis of semi-active electrorheological and magnetorheological dampers using approximate parallel plate models

We develop nonlinear quasi-steady electrorheological (ER) and magnetorheological (MR) damper models using an idealized Bingham plastic shear flow mechanism. Dampers with cylindrical geometry are investigated, where damping forces are developed in an annular bypass via Couette (shear mode), Poiseuille (flow mode) flow, or combined Couette and Poiseiulle flow (mixed mode). Models are based on parallel plate or rectangular duct geometry, and are compared to our prior 1D axisymmetric models. Three nondimensional groups are introduced for damper analysis, namely, the Bingham number, , the nondimensional plug thickness, , and the area coefficient defined as the ratio of the piston head area, , to the cross-sectional area of the annular bypass, . The approximate parallel plate analysis compares well with the 1D axisymmetric analysis when the Bingham number is small, or , or the nondimensional plug thickness is small, . Damper performance is characterized in terms of the damping coefficient, which is the ratio of the equivalent viscous damping constant, , to the Newtonian viscous damping constant, C. In shear mode, the damping coefficient is a linear function of the Bingham number. In flow mode, the damping coefficient is a function of the nondimensional plug thickness only. For the mixed mode damper, the damping coefficient reduces to that for the flow mode case when the area coefficient is large. The quasi-steady damping coefficient versus nondimensional plug thickness diagram is experimentally validated using measured 10 Hz hysteresis cycles for a electrorheological mixed mode damper.