A nonlinear transient model for magnetorheological damper response for a time varying field controllable yield shear stress

A nonlinear transient model for the prediction of damper force based on the flow of magnetorheological (MR) fluid through the channel of a semi-active MR damper has been presented which has a potential for its application in the design of adaptive control policies for such dampers. In this work, a transient analytical fluid dynamics model is developed by using a combination of Laplace and Weber transform and Duhamel's superposition of velocity boundary condition. The solution of the system of nonlinear simultaneous equations, obtained by applying conservation of volumetric flux with nonlinear effects of fluid compressibility and gas spring, zero velocity gradient across the plug and force equilibrium of Bingham plastic plug flow through the annular channel. This method is shown to generate direct and inverse model of an MR device. The temporal variation of yield shear stress corresponding to the change in field excitation has been taken into account by using Fourier series. The model has been validated by testing a commercial MR damper on a test rig for sinusoidal velocity signals for constant field excitation current and constant velocity signals with square wave field excitation current. A useful outcome of the damper tests with constant velocity driving signal and square wave field excitation is that it can be used to measure the sum of non-controllable components of the damper force. The model predictions agree with the experiments within 13.5% error. The benchmarking and comparison with phenomenological/hysteresis models shows that such models can predict response for low-frequency current excitation and in the limited range for damper velocity variations. The phenomenological models are not suitable for high-speed MR damper applications.