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Research Papers

Mathematical Modeling, Analysis, and Design of Magnetorheological (MR) Dampers

[+] Author and Article Information
Weng Wai Chooi

Dynamics and Aeroelasticity Research Group, School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M60 1QD, UK

S. Olutunde Oyadiji1

Dynamics and Aeroelasticity Research Group, School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M60 1QD, UKs.o.oyadiji@manchester.ac.uk

1

Corresponding author.

J. Vib. Acoust 131(6), 061002 (Oct 27, 2009) (10 pages) doi:10.1115/1.3142884 History: Received January 12, 2008; Revised January 26, 2009; Published October 27, 2009

Most magnetorheological (MR) fluid dampers are designed as fixed-pole valve mode devices, where the MR fluid is forced to flow through a magnetically active annular gap. This forced flow generates the damping force, which can be continuously regulated by controlling the strength of the applied magnetic field. Because the size of the annular gap is usually very small relative to the radii of the annulus, the flow of the MR fluid through this annulus is usually approximated by the flow of fluid through two infinitely wide parallel plates. This approximation, which is widely used in designing and modeling of MR dampers, is satisfactory for many engineering purposes. However, the model does not represent accurately the physical processes and, therefore, expressions that correctly describe the physical behavior are highly desirable. In this paper, a mathematical model based on the flow of MR fluids through an annular gap is developed. Central to the model is the solution for the flow of any fluid model with a yield stress (of which MR fluid is an example) through the annular gap inside the damper. The physical parameters of a MR damper designed and fabricated at the University of Manchester are used to evaluate the performance of the damper and to compare with the corresponding predictions of the parallel plate model. Simulation results incorporating the effects of fluid compressibility are presented, and it is shown that this model can describe the major characteristics of such a device—nonlinear, asymmetric, and hysteretic behaviors—successfully.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic and pictorial view of the MR damper

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Figure 2

Velocity profile for the flow of any fluid with a yield stress in a concentric annulus and notations used for the derivation of a general solution for this type of flow

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Figure 3

Experimental result of a typical MR fluid tested at the University of Manchester using an especially designed viscometer (27) showing the relationship between shear stress and strain rate. The nonlinearity, which merits the use of the Herschel–Bulkley rheological model over the linear Bingham model, is especially apparent at low shear strain rates.

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Figure 4

Simulation results for the annulus flow of a Herschel–Buckley fluid. For the purpose of comparison, the parallel-plate approximations are also shown. The fluid has the following properties: τY=2.1 kPa, m=1.1, R=200 mm, and σ=0.6. (a) Flow rate Q versus pressure drop ΔP for various values of ηHB, (b) the plug boundaries a and b as a function of the pressure drop ΔP, and (c) a typical velocity profile of this flow for a pressure drop of 7.5×104 Pa.

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Figure 5

Flow between stationary, flat, and parallel plates

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Figure 6

Error in the parallel-plate approximation technique expressed in terms of percentage relative to the exact solution found using annulus flow solutions

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Figure 7

The effect of the Herschel–Buckley consistency index ηHB on the parallel-plate approximation technique. The errors are evaluated for R=50 mm.

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Figure 8

The effect of the fluid yield stress τY for different values of σ on the accuracy of the parallel-plate approximation technique. The errors are evaluated for R=50 mm, mean velocity=3 m/s, ηHB=1 Pa s, and m=1.1.

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