Optimal Design of Magnetorheological Valve Using the Coupling of FE Magnetic Analysis and MOGA Optimization for Prosthetic Ankle

Background: Magnetorheological (MR) fluid has recently been used in a variety of applications, including vibration control, prostheses, and tactile devices. A magnetic field is used to control the rheological properties of the MR fluid (MRF), allowing for a high pressure drop, high shear stress, and reversibility of these features. The modifiability imparts smartness to the material, and recent studies have investigated their behavior extensively. Purpose: The present work involves the design of an MR fluid-based actuator to function as an ankle in a prosthetic foot. Methods: The initial design constraint of the MR valve and stroke length of the MR damper have been identified based on anthropometric constraints and biomechanical requirements of below-knee amputees (BKA). Second, magnetostatic analysis has been performed to solve an approximated parametric magnetic model (PMM) based on linear electromagnetic systems. Finally, finite element magnetostatic (FEMS) analysis was conducted to understand the magnetic flux density (MFD) of the MR fluid and the pressure drop was modeled and obtained using the Bingham model. Next, optimization of the damper was done. For this, the optimization goal functions were to (a) maximize damping force and (b) minimize the mass of the damper valve (by minimizing the volume of the damper and MR fluid), hence minimizing the weight of the prosthetic ankle. The geometric dimensions of the MR valve are optimized using an integration of a multi-objective genetic algorithm (MOGA) in MATLAB and FEMS in ANSYS APDL software. MOGA chooses values for design variables that are constrained within the specified bounds, and they are coupled by the FEMS analysis; this routine is automated and repeated for all possible values within the specified bounds. Results: It was observed that the results of MFD computed from PMM are valid for low ranges of current; however, it over-estimates MFD beyond 0.5 A. Furthermore, optimal solutions obtained are plotted on a Pareto front, which satisfies the objective function of maximizing the damping force and minimizing the weight of the damper. The optimization findings show trade-offs between damping force and damper mass. Conclusions: The optimized outcomes show enhancements in the cost function as compared to the unoptimized values. The proposed methodology integrating FEMS and MOGA shows promise and can be extended to other applications of MR dampers as well.