# Multipole Multi-Layered Magnetorheological Brake with Intermediate Slots
## 4 Design Parameters Optimization  
According to the theoretical idea and application requirements, an MPML drum brake was designed. Optimization of the design has been conducted to maximize the torque. As mentioned in Table 2. Parameters like rotor radius, stator radius, and maximum axial width of the brake were fixed due to application constraints. The total shear force in the MR fluid consists of two components: yield force and viscous force. While the viscous force component is influenced by the fluid's default viscosity and speed, the yield force is solely dependent on the magnetic flux. Notably, the viscous force is relatively insensitive to variations in brake design. Therefore, for the purposes of this study, we have maintained a constant rotor speed of 300 rpm. As illustrated in Figure 7, rotor and stator plate thickness (\(t_{p}\)), MR fluid thickness (\(t_{mr}\)), axial slot width (\(t_{s}\)), number of layers, and the stator material are the design variables in this optimization. By using local optimization, the final values of these parameters were found. This optimization has proceeded in several steps: the effect of the plate and MR fluid thickness, the impact of slot width, the selection of the number of MR layers, and choosing the best material for stator and rotor parts. In this design, the possible number of turns for a given design space is 200 T. The maximum current for the chosen winding wire is 3.25 A. Therefore, after considering coil safety aspects, the maximum input supply is 600 AT. The axial slots were placed on the rotor and stator plates to overcome the flux bypassing and bring the maximum possible flux to the outer layers. A 12 mm axial slot width was considered for the initial steps, and then the best probable width was identified in the further steps. In the same way, initially, AISI 1010 material was used for magnetic permeable parts. Then, the design was updated with better material. A three-dimensional (3D) model of the MR brake was created to simulate its behavior under various operating conditions. The 3D model was then imported into COMSOL Multiphysics, a graphical interface platform that enables the simulation of complex physical phenomena. Using COMSOL's intuitive interface, the electromagnetic, magneto-stress, and thermal relations were assigned to the 3D model. This involved defining the material properties, boundary conditions, and physical laws that govern the behavior of the MR brake. Then, the simulations were conducted for the optimization procedure. Firstly, the effect of MR fluid, stator plates, and rotor plate thicknesses on output torque was analyzed. From Figure 8, it is clear that the lesser MR fluid layer thickness gives higher torque. This is due to the lower magnetic permeability of the MR fluid. However, the thinning of the MR layer increases the risk of direct contact with plates. The analysis of the MR fluid layer thickness takes into account the constructional constraints and their interrelationship with the thickness of the rotor and stator plates. Therefore, the least possible thickness, i.e., 0.5, was considered. Figure 9 illustrates that reducing the plate thickness leads to an increase in output torque. This is because magnetic reluctance is directly proportional to the flow length. Consequently, thinner plates are desirable for optimal performance. However, structural \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Initial Values in mm** \\ \hline rotor radius & 56 to 57.5 \\ \hline stator radius & 58 \\ \hline axial width & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fixed parameters of brake. Figure 8: Effect of MR fluid layer thickness on brake torque. Figure 7: Design variables. constraints dictate that the stator and rotor plates cannot be thinner than 1.5 mm. Therefore, we selected 1.5 mm thick rotor and stator plates, accompanied by a 0.5 mm thick MR fluid layer, for further analysis. Secondly, the effect of axial slot width on the final torque was considered.