Mathematical modelling of magneto-hydrodynamic dampers with time-varying fluid properties

The fluid dynamics of dampers is investigated for the case where the damping fluid flows through passages in which a magnetic field is applied. This is a specific case of a new and promising field of applications that has emerged through the design of devices that take advantage of some properties of the so-called electrorheological fluids and magnetorheological fluids (ERF and MRF). These fluids are created when a base fluid is seed with very small dielectric or iron particles, so that it reacts to electric or magnetic fields by developing some non-Newtonian characteristics, most prominently a yield stress, viscosity change, and also viscoelasticity. These fluid properties can be controlled through control of the electric or magnetic fields' strength. In this paper, a typical damping load is modeled and related to the required flow of a MRF inside the damper. To this end the fluid is modeled as a Bingham fluid with time-varying yield-stress. The analysis here developed makes it possible to determine the magnetic field variation necessary in order to achieve a specific displacement of the damper's piston. The flow equations are analytically solved for any time-history of the dimensionless fluid's yield-stress. Main results are some simplified relationships that correlate damping load and magnetic field time-variations. These results aim at providing analytical tools that may facilitate dampers' design.