## 5 Conclusions  
This study examined the performance characteristics of an outer-rotor in-wheel motor mounted on a hubless e-bike using numerical analysis with Altair FluxMotor. The analysis focused on optimizing electric motor characteristics to improve the mileage per charge, performance, and efficiency of the hubless e-bike. The numerical analysis model was based on a PMSM structure, with variables including the number of windings, slot opening, and span and thickness of the permanent magnet. The comparative analysis explored how these variables impacted motor performance. The numerical analysis yielded the following results under the given conditions: the number of windings was set at 21, 23, and 25; slot openings at 2.4 mm, 3.0 mm, and 3.6 mm; magnet spans at 23 mm, 25 mm, and 27 mm; and magnet thicknesses at 3.5 mm, 4.0 mm, and 4.5 mm. 1. Based on the analysis of the number of windings and slot opening size, we found that maximum torque, maximum ripple torque, power, and efficiency are influenced by both winding number and slot opening size, with winding number having a greater impact except on maximum ripple torque. When the number of windings increased from 21 to 25, maximum torque improved by up to 18.91%, while the range of maximum torque rotation decreased by up to 38.1%. Additionally, as slot opening size increased from 2.4 mm to 3.6 mm, maximum ripple torque decreased by up to 44.0%. However, maximum cogging torque and the THD of cogging torque were barely affected by changes in winding number, maintaining maximum and minimum values of 0.00295 Nm and 2.81%, respectively, when the slot opening was 3.0 mm. Therefore, to maximize torque while minimizing cogging torque, a model with 25 windings and a 3.0 mm slot opening is ideal;
2. From the analysis of the permanent magnet's span and thickness, increasing the thickness of permanent magnets results in a greater increase in maximum torque and a smaller decrease in maximum torque rotation range compared to increasing the span. When the thickness increases from 3.5 mm to 4.5 mm, maximum torque increases by up to 6.33%, and the maximum torque rotation range decreases by less than 2.10%. However, when the span increases from 23 mm to 27 mm, these values are 3.60% and 2.59%, respectively. With a span increase from 23 mm to 27 mm, there is a decrease in maximum cogging torque by up to 17.6%. However, the THD of cogging torque and maximum torque ripple increase substantially by 241% and 165.5%, respectively, especially with a span increase from 23 mm to 25 mm, where the THD of cogging torque increases notably. Therefore, for efficient torque improvement, the model with a span of 23 mm and a thickness of 4.5 mm is suitable. The effects of the number of poles, the number of windings, and the thickness of the permanent magnet on the motor were investigated, and the developed analytical model was found to be suitable for the hubless e-bike through comparative analysis. These results are expected to improve the performance and efficiency of the hubless e-bike. Moving forward, the results of this simulation study are intended for experimental validation in collaboration with Korea Mobility. Methodology, J.L. and I.C. ; software, I.C., C.J. and J.H. ; validation, J.L. and I.C. ; formal analysis, J.H., C.J., I.C. and J.L. ; investigation, J.H., C.J., I.C. and J.L. ; data curation, J.L. ; writing--original draft preparation, J.H., C.J. and I.C. ; writing--review and editing, J.L. and I.C. ; visualization, J.H. and C.J. ; supervision, J.L. ; project administration, J.L. and I.C. ; funding acquisition, I.C. All authors have read and agreed to the published version of the manuscript. This research was funded by 2023 R&D Korea Mobility Co., Ltd., Republic of Korea. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. **Acknowledgments:** We thank Spur Co. for their assistance with this study.