Non-dimensional analysis for effective design of semi-active electrorheological damping control systems

Abstract

This paper presents a non-dimensional analysis for e ective design of semi-active electrorheological ( ER) damping control systems. The non-dimensional equations consist of the Bingham number, the non-dimensional damping force, the dynamic range and the non-dimensional geometric parameter. After showing the e ectiveness of the proposed analysis scheme through a comparative examination of predictions and measured values of the non-dimensional damping force, sequential steps for the ER damper design have been developed. A ow mode type ER damper, considering control performance of a semi-active quarter-car system, has been designed on the basis of the proposed non-dimensional design steps. To assess the e ectiveness of the proposed non-dimensional design methodology, the eld-dependent damping forces of an ER damper have been experimentally evaluated and compared with those obtained from the non-dimensional analysis.

Physical modeling and experimental verification of magneto-rheological damper under medium and high frequency excitation

“…Although this model does not regard the post-yield shear thinning and thickening effects at high shear rates, which was observed experimentally, the accuracy of Bingham model-based tools is acceptable. 26–28 Remarkable contributions have been made by this model to depict the MRD output characteristics, shown as where τ0 and η, the key parameters in picturing the flow behavior of MRF, refer to the field-induced yield stress and the fluid viscosity, respectively. du/dy refers to the velocity gradient.…”

Nondimensional characterization of flow-mode magnetorheological/electrorheological fluid dampers

“…The same procedure that is used with the Bingham model, for example, can be applied to the cubic formula of Phillips (1969). The formula provides the relationship between the pressure gradient and the volume flow rate, and it has been basis of research and design studies over the years (Gavin et al, 1996;Hong et al, 2003). The closed-form solution for the equation was first obtained by Gavin et al (1996) in the following form…”

“…Omitting the effects results in under/overprediction of damping force (or torque) in smart devices as highlighted by Jolly et al (1999) and Yang (2001). However, the accuracy of Bingham model-based tools is acceptable, and they have formed basis of various research efforts to describe the MR/ER hardware behavior (Gavin et al, 1996;Hong et al, 2003Hong et al, , 2008Peel et al, 1996;Stanway et al, 1996). The authors recognized that meaningful results would be obtained with significantly less effort through nondimensional groups involving all key (geometric and material) variables.…”

“…Using the same parameters, Gavin et al (1996) documented a closed-form formula for pressure gradient in a smart damper and studied the impact of the nondimensional parameters on the device dynamic range. Later, Hong et al (2003) found his solution useful as a basis for effective design scheme of semi-active ER dampers. In the studies of a long-stroke flow-mode ER damper, both Peel et al (1996) and Stanway et al (1996) utilized a novel nondimensional group involving known quantities, namely, the friction coefficient, C f , the Reynolds number, Re, and the Hedstrom number, He.…”

“…In analyses that followed, Wereley et al (2004) applied the approach to the study of a secondary flow path in ER valves (bypass) and extended it with the pre-yield-to-post-yield viscosity ratio of a biviscous material model. Based on the nondimensional set of parameters, a design scheme was proposed and its effectiveness demonstrated for flow-mode and mixedmode ER and MR dampers (Browne et al, 2011;Hong et al, 2003Hong et al, , 2005, respectively. Subsequently, using the Herschel-Bulkley model, Wereley (2003) applied the same nondimensional scheme to study shear thickening/thinning scenarios, and Hong et al ( 2008) extended it for a generic Herschel-Bulkley model with pre-yield viscosity and nonzero yield stress.…”