QUASI-STEADY AXISYMMETRIC BINGHAM-PLASTIC MODEL OF MAGNETORHEOLOGICAL FLOW DAMPER BEHAVIOR Jin-Hyeong Yoo and Norman M. Wereley Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA E-mail:jhyoo@eng.umd.edu, wereley@umd.edu ABSTRACT A typical magnetorheological (MR) flow mode damper consists of a piston attached to a shaft that travels in a tightly fitting hydraulic cylinder. The piston motion makes fluid flow through an annular valve in the MR damper. An electro-magnet applies magnetic field to the MR fluid as it flows through the MR valve, and changes its yield stress. An MR fluid, modeled as a Bingham-plastic material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Although the analysis of such an annular MR valve is well understood, a closed form solution for the damping capacity of a damper using such an MR valve has proven to be elusive. Closed form solutions for the velocity and shear stress profile across the annular gap are well known. However, the location of the plug must be computed numerically. As a result, closed form solutions for the dynamic range (ratio of field on to field off damper force) cannot be derived. Instead of this conventional theoretic procedure, an approximated closed form solution for a dampers dynamic range, damping capacity and other key performance metrics is derived. And the approximated solution is used to validate a rectangular duct simplified analysis of MR valves for small gap condition. These approximated equations are derived, and the approximation error is also provided. INTRODUCTION Magnetorheological (MR) fluids are suspensions of soft magnetic particles, such as iron or cobalt, in a carrier fluid [1- 3]. The benefits of such fluids are that the yield stress of the fluid can be varied through exposure to a magnetic field. MR fluids have been used in numerous types of smart actuation systems, such as dampers, clutches and isolators [4, 5]. Especially, the MR fluids are achieving success as hydraulic fluids in damping applications for military, civil and automotive systems. The performance of the MR damper is based on the MR valve design. Most of the MR valve has a circular cross-section to construct an annular duct model because of its simple design and higher strength of the damper structure. The circular cross- section also has an advantage of simple magnetic circuit construction. As a result, MR valves are physically realized as an annular duct. To fully account for the annular geometry of MR valves, several investigations have studied Poiseuille flow of Bingham plastic materials [6] through an annular duct. In some studies, a rectangular duct was used to approximate annular duct geometry [7,10]. Usually, the MR devices are designed using rectangular duct approximations [8] to exploit simple performance analyses. This study focuses on determining analytical expressions for damper performance using an idealized Bingham plastic model. Dampers with cylindrical geometry are investigated, where damping forces are developed in an annular bypass via Poiseuille flow. Although the analysis of such an annular MR valve is well understood [9], a closed form solution for the damping capacity of a damper using such an MR valve has proven to be elusive. In this study, an approximate closed form solution for a damper’s dynamic range, damping capacity and other key performance metrics is derived by making linear and quadratic approximations to the solution of plug location. The quadratic equation is proven to have very small error and it could be used as an analytical solution for the case where annular gap is small relative to piston radius. The approximate solution is utilized to verify rectangular duct analysis of MR valves. We will show that the approximate equivalent viscous damping coefficient (C eq /C) for the annular duct reduces to that for the rectangular duct when the small gap assumption, d/R 1 <<1, is applied. NOMENCLATURE d Electrode gap ∆p Pressure drop along electrodes r Radial coordinate measured from shaft axis u(r) Velocity distribution in electrode gap v 0 Piston head or shaft velocity A Piston head area Bi Bingham number C N Viscous damping (Newtonian) C eq Equivalent viscous damping (Bingham plastic) 1 Copyright © 2005 by ASME Proceedings of IMECE2005 2005 ASME International Mechanical Engineering Congress and Exposition November 5-11, 2005, Orlando, Florida USA IMECE2005-82592 Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/27/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use