A new design optimization methodology for the optimal design of a single-coil annular magnetorheological valve constrained in a specific volume inside a magnetorheological damper has been presented in this article. The methodology combines the finite element model, with the design of experiments and response surface techniques in order to develop approximate response surface functions for the magnetic field intensity across the activation length of a magnetorheological valve orifice with respect to identified design variables. The accuracy of the developed response surface functions over the entire design space has been verified. The developed analytical response functions have then been used in Bingham plastic model, which is based on the steady behavior of a magnetorheological fluid in order to derive the field-dependent performance functions of the magnetorheological damper, which can be effectively used in the design optimization problems. The design optimization problem has been formulated for single- and multiobjective performance functions using sequential quadratic programming technique and the genetic algorithm to find the global optimum geometrical parameters of the magnetorheological valve. Finally, a proportional–integral–derivative controller has been designed to evaluate the closed-loop performance of the optimally designed magnetorheological valve confined in a magnetorheological damper used in a quarter-car suspension model.

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The primary purpose of this paper is to establish a new methodology to optimal design of single-coil annular MR valves constrained in a specific volume in typical flow-mode MR dampers. Operating principles of MR valve and its configurations are described and then governing mechanical equations are derived by assuming quasi-static Bingham plasticity model. Magnetic flux density and Magnetic Field intensity across the ducts are obtained by high fidelity finite element model constructed in ANSYS parametrically. The finite element model of the MR valve is then effectively used to construct an approximate response function using design of experiments and response surface method. It has been shown that the developed approximate response function can accurately estimate the magnetic flux density and magnetic field intensity over the entire design space efficiently and accurately. The derived approximate functions for magnetic field are then used to formulate the damping force with respect to design variables analytically which, in turn, can be effectively used in design optimization problem. The optimization problem has been formulated using gradient based nonlinear mathematical programming technique based on Sequential Quadratic Programming technique and also stochastic optimization technique based on the Genetic Algorithm to find optimal geometrical parameters of the MR valve in order to maximize the damping force under given constrained volume. NomenclatureA p = piston cross-sectional area A s = piston shaft cross-sectional area B = magnetic flux density d = valve orifice gap d h = valve housing thickness F d = Total damping force H = magnetic field intensity L = valve length P a = accumulator pressure R = valve radius t = pole length = piston velocity w = coil width τ y = yield stress in MR fluid