# Simulation of Electromagnetic Generator as Biomechanical Energy Harvester
## 2 Electromagnetic Generator Modelling
### Air Gap Thickness of the Generator  
The air gap thickness between the stator and rotor needs to be determined in order to obtain the desired performance of the generator. Equation (1) shows the air gap thickness influence on the magnetic flux density in the air gap region:  
\[\Phi=\text{MMF}\times(\mu_{\text{m}}\text{A}/\text{dm}) \tag{1}\]  
where \(\Phi\) is the flux in the air gap, \(\mu_{\text{m}}\) is the permeability of the magnetic material, A is the cross-sectional area, and \(\text{dm}\) is air gap thickness. To determine the optimum air gap thickness of the generator design, the electromagnetic force reaction on the stator iron was evaluated by varying the air gap thickness between the permanent magnet and the stator iron for multiple magnet sizes as shown in Table 2 and stator designs which are square edge and T shape. Figure 5 shows the electromagnetic force strength towards the stator. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline S & Number of slots \\ P & Number of poles \\ R\({}_{1}\) & Inner radius of the rotor \\ R\({}_{2}\) & Permanent magnet surface radius \\ \(\Theta\) & Overall diameter \\ \(\alpha\) & Permanent magnet sector angle \\ \(\text{dm}\) & Air gap thickness \\ \(\beta\) & Slot opening angle \\ \(\delta\) & Slot pitch angle \\ \(\beta/\delta\) & Slot opening to slot pitch ratio \\ L & Thickness \\ d & Coil wire diameter \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters associated with the generator design. Figure 4: One sector of electromagnetic generator assembly. The electromagnetic force strength towards the stator iron is highly influenced by the dimension of the magnet, magnetic properties, and air gap thickness. The electromagnetic force strength has been investigated for the square edge stator by varying the magnet sizes and air gap thickness as shown in Table 2.  
The highest force reaction happens when the magnet is placed at a distance of 0.5 mm from stator iron. The electromagnetic force versus air gap thickness by magnet sizes has been plotted as shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Magnet Size (mm) (Thickness \(\times\)** & & & & & & & & & \\
**Outer Arc Length \(\times\) Inner** & & & & & & & & & \\
**Arc Length)** & & & & & & & & & & \\ \hline
**Label** & **Dimension** & **0.5** & **1.0** & **1.5** & **2.0** & **2.5** & **3.0** & **3.5** & **4.0** & \\ \hline Magnet A & 2.0 \(\times\) 5.38 \(\times\) 4.39 & 3.931 & 1.314 & 0.402 & 0.173 & 0.081 & 0.042 & 0.025 & 0.015 \\ Magnet B & 2.5 \(\times\) 5.62 \(\times\) 4.39 & 6.831 & 1.387 & 0.426 & 0.225 & 0.099 & 0.054 & 0.035 & 0.020 \\ Magnet C & 3.0 \(\times\) 5.86 \(\times\) 4.39 & 6.339 & 1.452 & 0.460 & 0.236 & 0.116 & 0.061 & 0.041 & 0.026 \\ Magnet D & 2.0 \(\times\) 6.14 \(\times\) 5.03 & 6.449 & 1.390 & 0.462 & 0.241 & 0.122 & 0.065 & 0.040 & 0.025 \\ Magnet E & 2.5 \(\times\) 6.42 \(\times\) 5.03 & 8.580 & 1.454 & 0.516 & 0.261 & 0.133 & 0.078 & 0.050 & 0.035 \\ Magnet F & 3.0 \(\times\) 6.70 \(\times\) 5.03 & 6.985 & 1.550 & 0.568 & 0.285 & 0.147 & 0.091 & 0.056 & 0.038 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Electromagnetic force by magnet dimensions for square edge stator. Figure 5: Electromagnetic force strength. (**a**) Square edge stator. (**b**) T shape stator. Figure 6: Electromagnetic force reaction due to air gap thickness by magnet size. Because the generator is intended to be fitted into an energy-harvesting mechanism that will be worn at the hip or thigh and will be driven by leg motion, it must be designed to have minimal or zero impact on the normal gait cycle of the user. Based on Table 2, the electromagnetic force is significantly high at the 0.5 mm air gap thickness which ranges between 3.931 N and 8.58 N, and this will require a huge effort from the user to actuate the generator.