Non-dimensional analysis of an unsteady flow in a magnetorheological damper

Theoretical modeling is often applied to study magnetorheological dampers (MRDs) with dimensional and non-dimensional analyses. In contrast to dimensional models, non-dimensional analyses can eliminate the influence of dimensionality and reduce the number of redundant parameters to simplify theoretical modeling and provide more universal applicability. However, most previous non-dimensional analyses have been based on quasi-steady flows that cannot reflect the transient response of an MRD because of the key assumption that the fluid velocity changes instantaneously. This study presents an investigation of the transient response of an MRD using a non-dimensional analysis approach based on an unsteady model. We focus on the step response of the MRD with a step excitation of the piston speed, while the magnetic field is kept constant. For a comprehensive analysis, a set of dimensionless parameters are defined, including a non-dimensional coordinate, a non-dimensional time parameter, the Bingham number, a non-dimensional pre-yield thickness, a damping coefficient, and a hydraulic amplification ratio. The relationships between these dimensionless numbers are analyzed. An unusual “concave area” is found in the velocity profile instead of a simple rigid flow during the transient process under a magnetic field. However, when the non-dimensional time is 0.4, the delayed concave area disappears, and the rigid area fluid velocity reaches 98% of its stable value.