Approximating Annular Duct Flow in ER/MR Dampers Using a Rectangular Duct

In general, ER/MR dampers have a cylindrical cross-section, for reasons of simplicity of design and maximum strength of the damper. Usually the ER/MR effect is activated by applying field across an annular valve. However, for simplicity of the analysis and design, a rectangular duct flow model is usually adopted. This paper compares analytical solutions of the rectangular and annular duct model under the assumption of uniform field across the valve gap. To compare errors between annular and rectangular duct models, a formulation for the error in the case of Bingham plastic material will be derived for flow mode dampers. This paper focuses on the errors of shear stress, velocity profile and equivalent viscous damping coefficient arising from the approximation of an annular duct as a rectangular duct. The impact of the small gap assumption, that is, the valve gap, d, is much smaller than the annular radius, R₁, is thoroughly investigated. We conclude that the approximate rectangular duct model can accurately describe the annular valve behavior as long as d/R₁ ≪ 1.