# Design of a 120 W Electromagnetic Shock Absorber for Motorcycle Applications
## 3 Modeling and Parametric Study of EHSA
### Parametric Geometry Study  
To better understand the effects of various factors on the performance of machines, the individual sensitivity analysis of machine geometrical parameters in this EHSA is investigated in this section. As stated in Equations (8) and (12), the power is proportional to the square of magnetic flux density in the radial direction \(B_{r}\), and to the effective volume of the coil \(V_{coil}=LA_{w}\). As a result, there are two ways to increase the power generated by an EHSA. Increasing the magnetic flux density inside the air gap is one option. The alternative option is to increase the effective volume of the coil \(V_{coil}\), which is equivalent to shortening the inner stator radius \(R_{is}\), as shown in Figure 4. The stator radius ratio \(K_{r}\) is given by:  
\[K_{r}=\frac{R_{is}}{R_{os}} \tag{13}\]  
where \(R_{is}\) and \(R_{os}\) is the inner and outer stator radius. In addition, since the PM is the source of the magnetomotive force that determines the magnetic loading of the motor, the shape of PM, e.g., the thickness and the length of PM are also the key parameters of the EHSA. Therefore, the magnet width and thickness of axial PM, \(w_{am}\) and \(t_{am}\), which are represented by the ratio \(K_{w\_pm}\) and \(K_{t\_pm}\), should be investigated. The magnet width ratio \(K_{w\_pm}\) is the ratio of the width of one axial PM \(w_{am}\)  
Figure 4: Design parameter of EHSA with the stator outer radius \(R_{os}\) and stator yoke thickness \(t_{sy}\) is fixed. and the pole pitch, which was fixed at 30 mm. The magnet thickness ratio \(K_{t\_pm}\) is defined as the ratio between the axial magnet thickness \(t_{am}\) and the thickness of a mover \(t_{om}\):  
\[K_{w\_pm}=\frac{w_{am}}{w_{am}+w_{rm}} \tag{14}\]  
\[K_{t\_pm}=\frac{t_{am}}{t_{om}} \tag{15}\]  
Finally, due to the high relative permeability of the iron spacer attached to radial PM, it will increase the magnetic flux density in the air gap. However, it means decreasing the thickness of radial PM, which will reduce the magnet volume, reduce the magnetic strength and the magnetic flux density in the airgap can be reduced. The effect of thickness of the iron spacer \(t_{sp}\) will be studied by the iron spacer thickness ratio \(K_{sp}\), which is defined as  
\[K_{sp}=\frac{t_{sp}}{t_{am}} \tag{16}\]  
It should be noted that when one of the four geometrical parameters varies during the parametric analysis, the others are fixed. Hence, the interaction effects of these parameters are neglected. Table 2 shows the lower and upper parametric values and constants in each study. Figure 5 shows the magnetic flux density in the radial direction \(|B_{r}|\) and average output power \(P_{out}\) with design parameters. We see that \(|B_{r}|\) always decreases with the decrease of the inner stator radius \(R_{is}\), which corresponds to an increase in the coil volume. It should be noted that the value of \(|B_{r}|\) in Figure 5 is the root-mean-square (RMS) of the radial magnetic flux density along the air gap at time t = 0 s.  
In addition, Figure 6 illustrates the effect of the design parameters on the output power of the EHSA, which is obtained by the integration of the instant power. The output power values of each parametric case are normalized using the values of the initial design. According to Figure 6, the maximum output power at the design parameter stator radius ratio \(K_{r}\), magnet thickness ratio \(K_{t\_pm}\), magnet width ratio \(K_{w\_pm}\), and iron spacer thickness ratio \(K_{sp}\) is 0.64, 0.52, 0.25, and 0.4, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Parameter** & **Lower** & **Upper** & **Constant** \\ \hline
1 & \(K_{r}\) & 0.2 & 0.7 & \(K_{t\_pm}=0.7\), \(K_{w\_pm}=0.3\), \(K_{sp}=0.3\) \\
2 & \(K_{t\_pm}\) & 0.2 & 0.8 & \(K_{r}=0.6\), \(K_{w\_pm}=0.3\), \(K_{sp}=0.3\) \\
3 & \(K_{w\_pm}\) & 0.2 & 0.8 & \(K_{t\_pm}=0.7\), \(K_{r}=0.6\), \(K_{sp}=0.3\) \\
4 & \(K_{sp}\) & 0.2 & 0.8 & \(K_{t\_pm}=0.7\), \(K_{w\_pm}=0.3\), \(K_{r}=0.6\) \\ \hline \hline \end{tabular}
\end{table}