Design, Fabrication and Characterization of an Optimal Magnetorheological (Mr) Damper for Prosthetic Knee Application

Abstract

A transfemoral amputation is the removal of lower limb above the knee joint in the thigh, through the femur bone. The design of any device which can make a transfemoral amputee’s gait similar to a normal gait is a challenging problem. An even more challenging task is to make the prosthetic leg adapt to variable walking speeds, terrains and intents. Magnetorheological (MR) fluids with their magnetic field controllable rheological properties, along with their fast response have been applied to design prosthetic knee devices capable of assisting a transfemoral amputee in replicating a near-normal gait. In this study, various design configurations based on MR fluids are explored for their suitability in prosthetic knee domain and an optimal design is selected among them. The device should be capable enough of producing the required knee braking torque sufficient for normal human walking and a low off-state resistance with a least possible mass, which forms a design optimization problem. The optimal design of any device configuration based on MR fluid involves coupling a mechanical design and an electromagnetic design. The mechanical design is based on the application of fluid constitutive models on the problem geometry. Equivalent magnetic methods (EMM) and finite element magnetostatics (FEM) are the two methods used in the electromagnetic design process. The former results in producing significant errors in magnetic field variables, whereas the latter requires a large computational time and effort. In this study, a combined magnetostatics approach is proposed which can address the various shortcomings associated with the available optimization methodologies. The proposed algorithm is compared with frequently used optimization methodologies based on FEM, EMM as well as neural network based data-driven methods. A statistical comparison of hypervolume indicator revealed that the proposed methodology produces similar design points compared to optimization based on FEM method and also substantially reduces the computational time. Although there exists only one commercially available design based on MR fluid, many alternative knee design configurations have been studied by various researchers. However, not all the previously studied design configurations are optimally iii designed specific to prosthetic knee applications. In this study, four design configurations based on MR fluids are selected based on intuition and also from models based on literature. The design configurations namely waveform arc boundary MR brake, multi-pole MR brake, twin rod MR damper and rotary vane MR damper are considered for a preliminary design process. The commercially available multi-plate MR brake has been extensively studied in the literature and thus is avoided from optimal design, although it is used in comparative studies at a later stage in this work. Among the chosen design configurations, twin rod MR damper and rotary vane MR damper are selected based on the criteria of producing normal human knee braking torque adequately. The multi-pole MR brake is found to produce a braking torque of 14 Nm, which is insufficient for normal human walking and thus is rejected for further testing. Although the waveform arc boundary MR brake is capable of producing the required braking torque, the design has limitations similar to that of commercially available multi-plate MR brakes and thus is also rejected for further testing. A prototype of the other two dampers is fabricated with random dimensions so as to obtain a few insights into the working nature of the device. Later, optimal design of selected design configurations is performed using the developed optimization methodology. The twin rod MR damper is characterized on a linear dynamic testing machine using harmonic excitations of varying amplitudes, frequencies and currents. This device configuration is capable of producing a damping force of 1020 N (equivalent to 40.8 Nm at 40 mm force moment arm) at a current of 1 A and also has a mass of 0.71 kg. An equivalent test setup to characterize the rotary vane MR damper is developed. This device configuration is found to produce a damping torque of 33 Nm at a current of 1A and has a mass of 1.1 kg. Based on the experimental findings and a comparison of the dampers with the available commercial model and models based on literature, the twin rod MR damper is selected as the optimal design configuration for prosthetic knee application. Finally, the twin rod MR damper is mathematically modelled using Bouc-Wen model with the model parameters evaluated by minimizing the error norms for time, displacement and velocity between the experimental and the model-generated results using a multi-objective genetic algorithm optimization. In the process, two different iv experimental data sets are used, one for mathematical modeling and the other for assessing the accuracy of the fit model. Also, an inverse model based on the forward damper model is proposed and validated later. This model predicts the current directly and avoids the necessity of solving any quadratic equation, which is otherwise required in the case of inverse models based on the modified Bouc-Wen model. The dynamic model of a single axis two segmental prosthetic knee is coupled with the forward Bouc-Wen model, the inverse model and a proportional derivative (PD) plus controlled torque (CT) controller to realize a complete semi-active prosthetic knee model. The parameters of PD plus CT controller are tuned to minimize the error between the desired and the controller-estimated torques. A closed loop control study is performed for the swing phase of the gait cycle. The results from the dynamic analysis predict that the damper is suitable for reproducing knee angle trajectories similar to those of normal gait and thus can be applied for prosthetic knee applications. Further, it was observed that the shank reaches full knee extension at the end of the swing phase with terminal velocity small enough to be handled by an extension stop.