Design, modelling and testing of magnetorheological (MR) dampers using analytical flow solutions

The most widely used configuration of MR dampers incorporates an annular gap through which the magnetically active MR fluid is forced to flow. The damping force, which is also known as the restoring force and opposes the applied external force, is produced by the movement of the MR fluid through this annular gap. The design of this annular gap usually utilises an approximation that represents this assembly as a flow of fluids between two infinitely wide parallel plates. This assumption has been found to be fairly accurate and sufficient for engineering design purposes, especially when the size of the annular gap is small relative to the mean radius of the annulus, which is usually the case for MR dampers. However, it is still important to have expressions that represent the physical processes exactly. In this paper, the general solutions are derived and the corresponding methodology for representing exactly the flow of fluids with a yield stress through annuli is given. Computational fluid dynamics simulations were also carried out to validate the general expressions presented. The general expression is applicable to any models of fluids with a yield stress. An example of the application of the general analytical expressions using the Herschel–Buckley model is given, and the limitations of the parallel-plate approximation is illustrated for configurations whereby the size of the annular gap relative to the mean radius is large. A mathematical model for a double-tube MR damper fabricated at the University of Manchester, UK is developed based on the annular solution and on the compressibility of MR fluid inside the chambers. It is shown that the modelling procedure represents the MR damper satisfactorily.