###### Abstract  
This study investigates the design an electric motor propelling hubless wheel mounted on an electric bicycle (e-bike) by numerical analysis. The motor is part of an in-wheel system that uses a permanent magnet synchronous motor (PMSM) to drive the hubless wheel. This paper presents an optimized PMSM design and compares various torque-related parameters, such as cogging torque, cogging torque total harmonic distortion (THD), and ripple torque. The comparison is based on a motor design that examines the effect of different factors, including the number of windings, slot openings, permanent magnet span, and magnet thickness. The motor was modeled and analyzed with variations in the number of windings (21, 23, 25), slot openings (2.4 mm, 3.0 mm, 3.6 mm), permanent magnet span (23 mm, 25 mm, 27 mm), and permanent magnet thickness (3.5 mm, 4.0 mm, 4.5 mm). Our findings suggest that increasing the permanent magnet's thickness leads to a higher magnetic flux density. Additionally, when the permanent magnet span exceeds 25 mm, there is a sharp increase in cogging torque THD. Based on these results, a slot opening of 3.0 mm and the use of 25 windings are considered suitable for a hubless e-bike. e-bike; hubless wheel; permanent magnet synchronous motor; personal mobility +
Footnote †: journal: Applied  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON] Numerical Analysis of Outer-Rotor Dynamical Analysis of Outer-Rotor Synchronous Motors for In-Wheel E-Bikes: Impact of Number of Number of Windings, Slot, and Permanent Magnet Magnet Magnet Magnet Magnet Shapes. **Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON] Numerical Analysis of Outer-Rotor-Numerical Analysis of Outer-Rotor Dynamical Analysis of Outerefficiency of the motor is important. In addition, to achieve benefits in terms of weight and cost, a design that minimizes the use of permanent magnets within the rotor is required. This approach necessitates the engineering design to maintain performance while reducing material usage. [PERSON] et al. theoretically analyzed the cogging torque of a motor using a permanent magnet. Based on their study, cogging torque occurs when the pore is not constant, owing to the influence of components such as slots in motors that utilize permanent magnets. Cogging torque is generated by the force required to return to a stable position and is not related to loads; however, it is only related to the shape of the pore and permanent magnets, and causes noise, vibration, and a change in rotational speed [2]. [PERSON] et al. changed the parameters of slot depth and width in an existing BLDC surface permanent magnet (SPM) outer-rotor motor and compared the basic design with the Halbach array design by utilizing two and three magnets [3]. [PERSON] et al. experimented with a dual external rotor layer machine that amplified the magnetic flux constituting the magnetic flux density to determine the torque density of the motor. The proposed design reduced the space of the magnet and created a high magnetic flux density [4]. As a comparative study between the outer and inner rotors of electric motors in electric personal mobility devices, [PERSON] et al. confirmed that motors with an outer-rotor configuration exhibit superior heat dissipation capabilities compared to those with an inner-rotor design. Furthermore, their study demonstrated that outer-rotor-type motors deliver higher nominal torque, outperforming inner-rotor-type motors in this regard [5]. [PERSON] et al. identified the advantages and characteristics of BLDC electric motors and demonstrated that they can be fully utilized in electric bicycles due to their superior speed-torque characteristics compared to general DC motors [6]. [PERSON] et al. demonstrated the efficacy of the V-type in electric scooters. They found that, despite the use of the same amount of permanent magnets in the IPMSM, the length of the permanent magnet in the V-type was longer than in the bar type. This resulted in a higher reverse electromotive force and torque level [7].