Transient effect modelling of magnetorheological fluid–based damper at low speed and its comparison with the existing magnetorheological damper models

This article presents a transient model of a magnetorheological damper, which takes into account the effect of Duhamel’s superposition of the variation of magnetorheological damper piston velocity with time. The magnetorheological fluid flow channel studied in this work is in the shape of an annular gap between the piston and the bore of the cylinder of the magnetorheological damper. The model was derived using a Bingham plastic model for shear stress versus shear rate behaviour of the magnetorheological fluid by applying the combination of Laplace and Weber transforms to the Navier–Stokes equations for obtaining the analytical solutions of the velocity in the sheared regions in a given cross section of an annular magnetorheological fluid flow channel. The solution is further modified to include the effect of time variation of piston velocity by using Duhamel’s superposition integral. The equations of the velocity profiles have been used to obtain the equations of mass flow rate balance, velocity compatibility for the plug flow boundaries and equilibrium of forces acting on the plug. The set of non-linear algebraic equations has been solved by Newton–Raphson’s method. The proposed model has been validated by comparison with the experimental results.