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Hydrodynamic Lubrication

# Modeling of Magnetorheological Fluids by the Discrete Element Method

[+] Author and Article Information
Mickaël Kargulewicz, Ivan Iordanoff

Arts et Métiers ParisTech,  Institut de Méchanique et Ingénierie - Bordeaux (UMR 5295), Esplanade des Arts et Métiers, 33405, Talence Cedex, France

Victor Marrero

Department of Mechanical, Aerospace, and Nuclear Engineering,  Rensselaer Polytechnic Institute, Troy, NY 12180-3590

John Tichy1

Department of Mechanical, Aerospace, and Nuclear Engineering,  Rensselaer Polytechnic Institute, Troy, NY 12180-3590tichyj@rpi.edu

1

Corresponding author.

J. Tribol 134(3), 031706 (Jun 27, 2012) (9 pages) doi:10.1115/1.4006021 History: Received April 20, 2011; Revised December 20, 2011; Published June 26, 2012; Online June 27, 2012

## Abstract

Magnetorheological (MR) fluids are fluids whose properties vary in response to an applied magnetic field. Such fluids are typically composed of microscopic iron particles ($~1-20μm$ diameter, $20-40%$ by volume) suspended in a carrier fluid such as mineral oil or water. MR fluids are increasingly proposed for use in various mechanical system applications, many of which fall in the domain of tribology, such as smart dampers and clutches, prosthetic articulations, and controllable polishing fluids. The goal of this study is to present an overview of the topic to the tribology audience, and to develop an MR fluid model from the microscopic point of view using the discrete element method (DEM), with a long range objective to better optimize and understand MR fluid behavior in such tribological applications. As in most DEM studies, inter-particle forces are determined by a force-displacement law and trajectories are calculated using Newton’s second law. In this study, particle magnetization and magnetic interactions between particles have been added to the discrete element code. The global behavior of the MR fluid can be analyzed by examining the time evolution of the ensemble of particles. Microscopically, the known behavior is observed: particles align themselves with the external magnetic field. Macroscopically, averaging over a number of particles and a significant time interval, effective viscosity increases significantly when an external magnetic field is applied. These preliminary results would appear to establish that the DEM is a promising method to study MR fluids at the microscopic and macroscopic scales as an aid to tribological design.

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## Figures

Figure 1

Particles in MR fluid. (a) upper left: no magnetic field, no shear - random distribution; (b) upper right: field applied - magnetization of particles, interparticle forces; (c) middle left: field applied, formation of chains; (d) middle right: shear applied, chains deform; (e) lower left: chains rupture in shear; (f) lower right: field removed, particles move with shear.

Figure 2

Schematic of the Bingham Model, yield stress varies with magnetization

Figure 3

Domain of the simulations

Figure 4

Typical magnetization curve of a ferro magnetic material

Figure 5

Magnetization curve used in present model

Figure 6

Alignment of a column of particles in the MR fluid - applied magnetic field with no shear; evolution with time shown from left to right

Figure 7

Shearing of a column of particles in the MR fluid - applied magnetic field; evolution with time shown from left to right

Figure 8

Shearing of a column of particles in the MR fluid with applied magnetic field

Figure 9

Simulation results: typical shear stress evolution with time - the behavior of moving averages

Figure 10

Simulation results: shear stress versus shear rate - the ‘off’ condition (no applied magnetic field) is the lower curve, the ‘on’ condition (applied external magnetic field) is the upper curve

Figure 11

Simulation results: ratio of ‘on’ shear stress to ‘off’ shear stress versus Mason number

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