## 3 Modeling and Methods
### Developed Model  
Modeling was conducted using the finite element method (FEM) in a 3D model using Ansys: Maxwell 3D software. The 3D design of the braking system was performed by using the 3D SolidWorks modeling software of SolidWorks, and the produced 3D modeling data were then exported to Maxwell 3D. Table 1 shows the basic specifications of the developed braking system, including the materials and geometry. Throughout the numerical calculation and experimental test, the air gap and disc thickness are fixed at 0.5 and 4 mm.  
Table 2 shows the parameters that are evaluated in this study, including the number of coil windings, the number of electromagnets, and the electrical current. These parameters are considered to significantly influence the generated magnetic field intensity. During the numerical calculation, the heat generated during braking is ignored. The disk brake is used as a rotor, while the electromagnet is adopted as the source of magnetic fields for the braking system. In order to validate the model, a validation test is initially conducted, and its results are explained in Section 4.  
Figure 2 shows the basic designs of the used disk and coil core during the validation test and numerical calculation. These designs are based on the general designs of a motorcycle disk brake. The disk brake uses non-ferrous material, which has a good performance as an ECB disk. The size of the coil core is also adjusted based on the size of the vehicle brake caliper; therefore, it can be applied to motorcycles. The design of the ECB uses different brackets from the conventional brake caliper. Therefore, if the conventional brake operates, the conventional brake does not affect the ECB parameter performance in terms of the position and the air gap.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Unit** & **Value** \\ \hline Pole shoe length & mm & 30 \\ Pole shoe width & mm & 12.5 \\ The total length of the coil core & mm & 248 \\ Distance of pole shoe to disk center & mm & 83.5 \\ Air gap & mm & 0.5 \\ Disk thickness & mm & 4 \\ Relative permeability of aluminum & - & 1.000022 \\ Relative permeability of steel & - & 400 \\ Conductivity of aluminum & \(\Omega\)m & \(2.06\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic specifications of the developed compact ECB system, including material and geometry.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Unit** & **Values** \\ \hline Number of coil winding & - & 360, 540, 720 \\ Number of magnet & - & 1, 2, 4 \\ Electrical current & A & 20, 25, 30, 35, 40 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluated parameters during the modeling and numerical calculation.  
Figure 2: Designs of the used **(a)** disk and **(b)** magnet.  
The numerical calculation was carried out with the objective of obtaining the data in the form of braking torque produced by the ECB under different evaluated parameters. The data are used to determine the characteristics of the variables toward the optimum design of the brake. Before conducting the analysis, the clarification of the required braking conditions and the calculation of the required braking torque were conducted. The braking conditions were determined as the braking required to reduce the speed of a vehicle with a weight of 100 kg (assumed as motorcycle) and two wheels from 17 to 5.6 m/s, in a deceleration distance of 50 m. In addition, the disc has a diameter of 120 mm [24]. From this braking condition, it is clarified that the required torque to reduce the speed from 17 to 5.6 m/s is 52.1 Nm.