Electrorheological Dampers, Part I: Analysis and Design

Abstract

Electrorheological (ER) materials are suspensions of specialized, micron-sized particles in nonconducting oils. When electric fields are applied to ER materials, they exhibit dramatic changes (within milli-seconds) in material properties. Pre-yield, yielding, and post-yield mechanisms are all influenced by the electric field. Namely, an applied electric field dramatically increases the stiffness and energy dissipation properties of these materials. A previously known cubic equation which describes the flow of fluids with a yield stress through a rectangular duct can be applied to annular flow, provided that certain conditions on the material properties are satisfied. An analytic solution and a uniform approximation to the solution, for the rectangular duct Poiseuille flow case is presented. A numerical method is required to solve the flow in annular geometries. The approximation for rectangular ducts is extended to deal with the annular duct case.

Large-scale MR fluid dampers: modeling and dynamic performance considerations

“…Phillips [43] developed a set of nondimensional variables and a corresponding quintic equation to determine the pressure gradient of the flow through a parallel duct. This approach was utilized by Gavin et al [4] and Makris et al [6] in their studies. Wereley and Li [51] developed a similar parallel-plate model utilizing a different set of nondimensional variables.…”

“…In this case, Eq. (3) can be reduced to (4) The solution of Eq. (4) is (5) where is equal to a constant which can be evaluated by the boundary conditions.…”

“…In this section, following a procedure similar to that utilized by Gavin et al [4], a quasistatic axisymmetric model is derived based on the Navier-Stokes equation to predict the damper's force-velocity behavior. The pressure gradient then can be solved numerically.…”

“…Because most of MR dampers incorporate a cylindrical geometry, an axisymmetric model is necessary to precisely describe their quasi-static behavior. Gavin et al [4] and Kamath et al [52] each developed an axisymmetric model. Kamath et al assumed constant yield stress in the annular gap.…”

“…For simplicity, it is assumed to follow an inverse power law [4] (27) where C and n are empirical material constants. A comparison between the parallel-plate and axisymmetric models for is made for the nominal design parameters of the full-scale MR damper shown in Table 1.…”