Geometry optimization of MR valves constrained in a specific volume using the finite element method

This paper presents the geometric optimal design of magnetorheological (MR) valves in order to improve valve performance, such as pressure drop. The optimization problem is to find the optimal geometric dimensions of MR valves constrained in a specific volume. After describing the configuration of MR valves, their pressure drops are investigated on the basis of the Bingham model of an MR fluid. Then, the valve ratio, which is an objective function., is derived by considering the field-dependent (controllable) and viscous (uncontrollable) pressure drops of the MR valves. Subsequently, the optimization procedure using a golden-section algorithm and a local quadratic fitting technique is constructed via a commercial finite element method (FEM) parametric design language. From the constructed optimization tool, optimal solutions of the MR valves, which are constrained in a specific cylindrical volume defined by its radius and height, are calculated and compared with analytical ones. In addition, several different types of MR valves are optimized in the same specific volume and results are presented.