## 3 Influence of Stator Configuration on Thrust Force
### Influence of Design Parameters on Thrust Force  
The design parameters of stator core--such as stator height, slot height, and slot width--were parameterized, but the slot area was kept constant. The thrust force was computed using FEA. The  
Figure 4: Thrust forces of initial LOA over the stroke range. \(b_{1}\) is not as identical to \(b_{2}\), which was produced by the comparative design given above. For this reason, the shape of the stator tooth is unparalleled. Part of slot leakage flux passes through the slot region to form a loop and chains across some of the coils; another part traverses the slot opening to form a loop and chains across all the coils. In this way, the flux that passes through the top of the tooth region was slightly less pronounced than that of the slot root region. When the paralleled tooth was used, the tooth root region became saturated much more easily than the area surrounding the top of the tooth. The design scheme of unparalleled teeth was used because it may reduce the flux density of the tooth root region and correspondingly decrease the iron loss caused by the stator core, thus increasing actuator efficiency. Figure 11 shows the variations of thrust force and its fluctuation with lateral tooth tip width \(b_{3}\). As shown, the thrust force had a monotonically decreasing property with \(b_{3}\). The thrust force fluctuation reached a minimum as \(b_{3}\) approached 7 mm. For this reason, \(b_{3}\) was set to 7 mm. Figure 12 shows the variations in thrust force and its fluctuations with stator lateral width \(b_{e}\). As shown, the thrust force displayed no obvious variation as \(b_{e}\) increased and its fluctuation varied by 4.8%. Fluctuation was minimum at a \(b_{e}\) of 0 mm. Hence, \(b_{e}\) has been chosen to be 0 mm, which is equivalent to the structure of two C-cored actuators with \(\tau_{p}\) being 32 mm combined together without additional top width of stator core. Figure 13 shows the variations in thrust force and its fluctuation with \(b_{m0}\). As shown, \(b_{m0}\) had little impact on the thrust force and prominently influenced its fluctuation. The thrust force increases slowly with gradual increasing \(b_{m0}\) and its fluctuation first increased slowly and then decreased rapidly. The thrust force and its fluctuation ceased to show visible variations as \(b_{m0}\) approached 11 mm. The lateral magnet width \(b_{m0}\) was set to \(\approx\)15 mm. Figure 11: Variations in thrust force and its fluctuation with \(b_{3}\). Figure 12: Variations in thrust force and its fluctuation with \(b_{e}\). ### Influence of Design Parameters on Thrust Force  
The optimal combination of design parameters was found, and the final slot (slot A) size is given in Table 2. Another commonly used slot (slot B) with the paralleled tooth is also given for comparison. The thrust forces also changed with stroke range. As the position varied between \(-1.0\) mm and \(1.0\) mm. The average thrust force of LOA with slot A and slot B was 370.3 N and 327.2 N, respectively, and the thrust force ripple was 1.6% and 5%, respectively as shown in Figure 14. The average thrust force of LOA with slot A was increased 13.2% more than in slot B, and the thrust force ripple was 68% lower. The thrust force density of LOA with slot A increased to 115,700 N/m\({}^{2}\). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Items**} & \multicolumn{2}{c}{**Value**} \\ \cline{2-3}  & **Slot A** & **Slot B** \\ \hline Slot open width \(b_{0}\) (mm) & 5 & 3 \\ Slot top width \(b_{1}\) (mm) & 19 & 19.5 \\ Slot bottom width \(b_{2}\) (mm) & 14.1 & 19.5 \\ Lateral tooth tip width \(b_{3}\) (mm) & 7 & 7 \\ Lateral tooth width \(b_{e}\) (mm) & 0 & 0 \\ Lateral magnet width \(b_{m0}\) (mm) & 15 & 15 \\ Tooth tip height \(h_{0}\) (mm) & 2 & 2 \\ Tooth top height \(h_{1}\) (mm) & 13 & 6 \\ Tooth bottom height \(h_{2}\) (mm) & 48.55 & 45.76 \\ Lateral shoulder height \(h_{3}\) (mm) & 9 & 9 \\ Stator height \(h_{s}\) (mm) & 72 & 61.9 \\ \hline \hline \end{tabular}
\end{table}