Analyzing quarter car model with Magneto-Rheological (MR) damper using equivalent damping and Magic formula models

Abstract

Mathematical modelling of Magneto-Rheological (MR) damper has been an intriguing field of research ever since the invention of the device itself. An accurate model of MR damper results in development of an efficient controller for a semi-active system with MR damper. Hence, a number of models have been put forward to accurately predict the MR damper behavior. One of these models is Magic formula model. Based on the famous Magic formula used in tire force calculation, this model can be used for representing the peak damper force vs damper piston velocity amplitude graph. This model was later modified to capture the force displacement diagram of MR damper. The former model is denoted as Magic Formula Model-1 (MFM-1) and the latter one is denoted as Magic Formula Model-2 (MFM-2) here onwards. In the current study a commercial MR damper has been tested for various piston velocities and currents. The equivalent damping coefficient is then calculated for the tested conditions. The equivalent damping coefficients are used for analyzing a quarter car model. Two quarter car models with MR damper are simulated, one uses MFM-1 for MR damper and the other uses MFM-2. All the quarter car models are subjected to single pulse input and the sprung mass response is measured in terms of displacement. The RMS error between the response of quarter car model with equivalent damping and quarter car models with MR damper is used to determine the performance of each mathematical model. The study revealed that MFM-1 represents the MR damper behavior more accurate than that of MFM-2. © 2019 Elsevier Ltd.