On MR Differential with Limited Slip

Design of a magnetorheological (MR) sports car differential is presented in this paper, with the aim of the total mass reduction and the torque maintenance. The torque output is controlled by adjusting the applied magnetic field. The nominal output torque of the differential is derived by using Bingham plastic constitutive model; the choice of the materials occurs to minimize the thickness of the circuit, but preliminary sizing based on electromagnetic theory does not lead to satisfactory results. Electromagnetic finite element analysis (FEA) is performed to estimate the effective distribution of the magnetic field. The shear stress distribution in MR Fluid is theoretically predicted using the distribution of magnetic flux density evaluated by FEA. An optimization process is applied to obtain the desired performance in terms of mass and torque; first stage optimization allows finding the best geometry of the magnetic circuit to provide the required torque. Furthermore the optimization of the shape of the reel box is carried out, in order to reduce the mass of the differential, and the vehicle mass in consequence, with satisfactory results. The conclusion is done that magnetorheological differential can be used as low efficiency differential even in the absence of magnetic field, reducing the likelihood of skidding of one of the two wheels of the same axle.