Numerical Analysis of Outer-Rotor Synchronous Motors for In-Wheel E-Bikes: Impact of Number of Windings, Slot, and Permanent Magnet Shapes

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.

1. Introduction

1.1. Research Background and Motivation

Mobility is a concept that combines technologies, such as autonomous driving and artificial intelligence, with machines that are utilized for transportation, such as automobiles. Personal mobility is defined as the next-generation personal means of transportation and is powered by electric-based bicycles (e-bikes), wheels, and kickboards. In the future transportation sector, personal mobility is expected to be useful in various aspects, and it is currently being utilized for short-range transportation in cities. Recently, the demand for environmentally friendly transportation has increased owing to concerns regarding environmental pollution, traffic jams, and government regulations on carbon emissions. Among these, extensive studies on e-bikes, which can replace existing means of transportation, are underway, owing to the rapid increase in users [1].

The driving torque of an electric bicycle is generated by the combination of the torque from the rider’s pedaling and the torque produced by the electric motor. For this purpose, a combination of permanent-magnet-type BLDC motors and lithium-ion or lithium-polymer batteries is primarily used. The key performance indicators of an electric bicycle include power and mileage per charge, which are determined by the battery and performance of the electric motor. Because the energy capacity of an e-bike’s battery is limited, the efficiency 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.

Hong-seok Ko 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].

Z. Arifind 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].

Mohd Izat Bin Zainuddin 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, Verbek 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]. Sung-Mam Cho 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]. Mi-Jung Kim 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].

In particular, as an example of a previous study on motor structure and in-wheel systems, Seong-Hwan Bang et al. developed three distinct design types by varying the number and configuration of permanent magnets. Their findings indicated that an increase in the number of permanent magnets was associated with enhanced performance [8]. Jeong-Min Kim investigated the potential for enhancing the efficiency of electric vehicles by integrating in-line and in-wheel motors [9]. Md Sariful Islam et al. examined the impact of asymmetric winding on V-shaped permanent magnets. Their findings revealed a notable reduction in conductor losses, enhanced efficiency, and an elevated continuous peak [10]. Alexandru-Ionel Constantin et al. utilized Altair FluxMotor and concluded that numerical analysis is more suitable for different rotor topologies (V and ∇ shapes) designed for electric buses [11]. Mustafa Yaseen Bdewi et al. employed an optimization method to enhance the magnet span, slot width, and slot opening of an outrunner PMSM. This approach was undertaken with the objective of improving torque density performance and maintaining low torque ripple over a wide range of current densities [12].

Also, Muhammed Muhsin Coşdu et al. used a multiobjective differential evolutionary optimization algorithm (MODE) on an external rotor PMSM hub motor for the “Efficiency Challenge” competition to determine its lightweight potential [13]. Christian A. Rivera et al. found that the application of banana-shaped magnets can improve motor performance for the same magnet weight [14]. Keun-Young Yoon et al. proposed a novel flared-ferrite IPM model as an alternative to the conventional spoke-ferrite IPM model. Their findings revealed a 0.9% increase in efficiency and a 66.2% reduction in torque ripple [15]. Di Tan et al. observed that electromagnetic properties influence the temperature distribution of the motor through iron core loss, winding loss, and PM loss. Among these factors, winding loss represents the most significant heat source. The resistivity of stator silicon steel and winding copper was identified as the primary factor influencing the electromagnetic properties of temperature [16].

Extensive research has been conducted on altering the number of poles in motor rotors to enhance performance. However, studies focusing on hollow-structured outer-rotor in-wheel motors, resembling e-bike wheels, have been limited.

1.2. Research Purpose

This study aims to develop a hubless in-wheel e-bike by analyzing the characteristics of a hubless in-wheel motor, where the outer rotor directly drives the tire rim. Due to the larger overall size of these motors compared to conventional motors, it is imperative to optimize the size and amount of permanent magnets and the number of windings. This study employed numerical analysis to explore efficient models by varying the length and thickness of the magnets and the number of windings. A hubless e-bike features an in-wheel structure with a motor embedded in a hollow wheel after the hub has been removed, as shown in Figure 1. A planetary gear was installed to increase torque and achieve the target of 75 Nm at the tires. The sun gear of a planetary gear is a multi-stage structure in which the sun gear protrudes in the axial direction of the rotor and meshes with a centrally located gear. The pinion gear meshes with the inner gear of the tire. The derailleur is connected to a chain that meshes with the chain and is powered by the pedals.

The subject of interpretation in this study is the motor setup before the installation of the planetary gear. A flowchart of the research process applied in this study is shown in Figure 2.

2. Research Method

2.1. Base Model

Prior to the implementation of numerical analysis, a model of a motor with an outer-rotor structure was investigated and utilized as a reference for the development of the model. Figure 3 illustrates the inner frame functioning as a stator, while the outer frame, which is secured to the rim where the tire is mounted, acts as an external PMSM rotor due to the hubless in-wheel motor structure. To maintain the air gap between the stator and rotor, the rotor is radially supported by sixteen urethane bearings (eight on each side of the wheel motor). The average vertical load on each bearing is approximately 13.4 kg, based on a rear wheel load of 80 kg.

The rotor and stator have large diameters; thus, a number of poles and slots were de-signed, as shown in Figure 4. The hubless in-wheel motor has no brush and requires less maintenance, has excellent speed–torque characteristics, and is designed with a PMSM structure without loss in a wide operating area.

Table 1. Basic specifications.

Factor	Unit	Value
Target wheel torque	Nm	75
Voltage	V	36
Current	A	14
Target motor torque	Nm	20
Slot	ea	72
Pole	ea	42
Winding diameter	mm	1.2
Winding number	ea	21, 23, 25
Rotor out	mm	403
Rotor in	mm	374
Stator out	mm	372
Stator in	mm	280

shows the basic specifications of the hubless in-wheel motor used in the numerical analysis model in this study. The target tire wheel torque was 75 Nm, the target motor torque was 20 Nm, the number of slots was 72, the number of poles was 42, and the rectangular permanent magnet was arranged in the shape of an SPM. The winding was circular, with a diameter of 1.2 mm. The front and rear wheels of a typical e-bike are the same size, and the stator and rotor sizes of the motor are designed to range from 12 inches to 26 inches. The outermost diameter of the outer rotor was 403 mm and the inner diameter was 374 mm. The outermost and innermost diameters of the stator were 372 mm and 280 mm, respectively. The applied voltage and current were 36 V and 14 A, respectively. In this motor model, the side of the motor is attached to the rim, and the axial faces are exposed externally.

Considering these structural characteristics and the advantageous heat dissipation of an outer-rotor motor, the design omits the need for additional housing and cooling systems, thereby enhancing manufacturability and design flexibility. The utilization of outer-rotation motors is advantageous in that they employ a greater number of permanent magnets and exhibit a more favorable power output than that of inner-rotation motors.

2.2. Motor Modeling Based on the Altair Program

2.2.1. Analytic Model Features

Altair Flux Motor software (2020) was used to perform numerical analysis to determine the performance and optimization conditions of the target object. Altair FluxMotor is a commercial software program designed for motor analysis, capable of predicting performance based on specific target variables [17]. To conduct numerical analysis of the motor, the final model was developed by entering key dimensions, including the type of external diameter, and stator and rotor materials. Further, detailed properties such as the characteristics of the permanent magnets, slot openings, slot widths, and windings were specified.

The shape and size of permanent magnets, as well as the configuration of coils, are essential factors in generating the electromagnetic fields that interact within the motor. Therefore, increasing the size of these variables generally enhances the maximum torque and output of the motor, including those of hubless motors. However, the electromagnetic forces produced by permanent magnets and coils can exacerbate negative outcomes such as cogging torque and torque ripple depending on variables such as the number and arrangement of slots and magnets as well as slot openings. Therefore, the influence of the number of turns per coil, slot opening, and the length and width of permanent magnets on the performance of the motor was investigated by setting them as variables.

Subsequently, other parameters, such as input power, rotor speed, load, and time, were kept fixed for the numerical analysis. The shape of the motor developed by applying the values in Table 1, which is an outer-rotor type with permanent magnets located on the outside as the rotor and slots arranged on the inside as the stator, is shown in Figure 5.

2.2.2. Magnet Setting

In this study, a surface-mounted permanent magnet synchronous motor (PMSM) was used. This type of motor is characterized by a relatively low output, reduced vibration, and a simpler manufacturing process compared to an interior permanent magnet synchronous motor (IPMSM). For the magnetic structure, a ring type was designed using FluxMotor, as depicted in Figure 6. In this context, “TM” represents magnet thickness, while “WM” denotes magnet span. For the magnet, we used REF.HF_220_270 from the Fluxmotor library and REF.M330_35A as an iron core, as shown in Figure 7.

2.2.3. Slot Setting

Stator design affects output power, as a synchronous motor generates torque through the interaction between the magnetic fields created by the coil current and the magnet. When designing a motor to meet a specific target output, the area and number of slots must be taken into account. Figure 8 shows the slot shapes used in this analysis. WS1 and WS2 indicate the slot widths, while W0 refers to the slot opening.

2.2.4. Winding Setting

Winding arrangements also determine the output power of the motor. The arrangement of the winding, such as the shape of the connection, coil pitch, and number of parallel circuits, can be set in the winding menu of FluxMotor. As shown in Figure 9, the winding method can be set within the FluxMotor software and the type of connection can be selected as a Y or delta connection. Coil pitch refers to the distance between two coils, which is called full-pitch winding provided the pitch of the coil is equal to the extreme pitch. The Y-connection method was used and the number of parallel circuits was 2 in this study. The coil shape used is of the circular type.

2.2.5. Thermal Setting

Considering that conventional hub motors typically operate with winding temperatures ranging from 120 to 180 °C and magnet temperatures below 100 to 160 °C, it is worth noting that the thermal setting plays a crucial role in motor performance. However, the motor under study here is of the hubless type, featuring a hollow center that allows for direct cooling by external air. So, the temperatures of motor components such as windings, winding ends, and magnets were maintained at 100 and 120 °C, as shown in

Table 2. Thermal settings used in Altair FluxMotor.

Factor	Unit	Value
Straight part winding temperature	°C	120
C.S. end winding temperature	°C	120
O.C.S. end winding temperature	°C	120
Magnet temperature, Tmag	°C	100

.

3. Numerical Analysis Conditions

The variables used in the numerical analysis are shown in

Table 3. Variables used in numerical analysis.

Factor	Unit	Value
Turns per coil	ea	21, 23, 25
Slot opening	mm	2.4, 3.0, 3.6
Magnet span	mm	23, 25, 27
Magnet thicknesses	mm	3.5, 4.0, 4.5

. The analysis included three configurations of windings, three slot opening sizes, three permanent magnet spans, and three permanent magnet thicknesses. Detailed descriptions of Models (1), (2), and (3) used in the numerical analysis are provided below.

The power applied to the numerical analysis is a sine wave, Max. Line-Line voltage, rms 36 V, Max line current, rms 13.888 A.

(1)

Analysis model of turns per coil and slot openings

The model used to analyze the effect of the number of windings and slot openings is shown in Figure 10. This system was modeled with variables set to reflect windings of 21, 23, and 25 turns. The permanent magnet’s thickness was fixed at 3.5 mm, with a span of 23 mm. Slot shape optimization is crucial for comparing performance with different numbers of windings. As the number of windings increases, slot width also increases to accommodate the additional coil space. This necessitates maintaining a consistent fill factor. The slot width, determined by the values WS1 and WS2, had a fill factor set at 53.4%, a value influenced by manufacturing costs. The slot openings, representing 200% to 300% of the coil diameter for ease of manufacturing, ranged from 2.4 mm to 3.6 mm. The cross-section of a copper wire is circular.

(2)

Analysis model of various magnet thicknesses

To analyze the effect of the span and thickness of the permanent magnet, the magnet span and thickness were changed from 23 mm to 27 mm and 3.5 mm to 4.5 mm, respectively, as shown in

Table 4. Analysis model of various magnet spans.

Span (mm)	23	25	27

and

Table 5. Analysis model of various magnet thicknesses.

Thickness (mm)	3.5	4.0	4.5

.

4. Result and Discussion

4.1. Results of Numerical Analysis of Models by Number of Windings and Slot Opening Size

As shown in

Table 6. Numerical data of 21-turns-per-coil model.

Item	Unit	Value
winding	No. turns	21
slot opening	mm	2.4	3	3.6
maximum torque	Nm	16.36	16.24	16.09
maximum torque rotation range	rpm	152.1	157.6	162.3
maximum cogging torque	peak-peak, Nm	0.01134	0.00295	0.00775
THD of cogging torque	%	0.978	2.81	1.03
maximum torque ripple	peak-peak, Nm	0.1064	0.0649	0.0595
maximum flux density	T	0.460	0.458	0.452
power	W	261	268	273
efficiency	%	33.5	34.1	34.5

,

Table 7. Numerical data of 23-turns-per-coil model.

Item	Unit	Value
winding	No. turns	23
slot opening	mm	2.4	3	3.6
maximum torque	Nm	17.91	17.78	17.62
maximum torque rotation range	rpm	119.9	124.3	128.1
maximum cogging torque	peak-peak, Nm	0.0113	0.00295	0.00774
THD of cogging torque	%	0.978	2.82	1.03
maximum torque ripple	peak-peak, Nm	0.1175	0.0741	0.0665
maximum flux density	T	0.490	0.497	0.492
power	W	225	231	236
efficiency	%	28.5	29.1	29.5

and

Table 8. Numerical data of 25-turns-per-coil model.

Item	Unit	Value
winding	No. turns	25
slot opening	mm	2.4	3	3.6
maximum torque	Nm	19.45	19.31	19.13
maximum torque rotation range	rpm	94.1	97.6	100.5
maximum cogging torque	peak-peak, Nm	0.01130	0.00296	0.00773
THD of cogging torque	%	0.978	2.80	1.03
maximum torque ripple	peak-peak, Nm	0.1288	0.0838	0.0740
maximum flux density	T	0.515	0.512	0.510
power	W	191.7	197.3	201
efficiency	%	23.9	24.4	24.8

, a numerical analysis was conducted to determine the impact of the number of windings and slot opening size. Magnet thickness was set at 3.5 mm, and the length of the magnet was 23 mm.

Figure 11 shows the mechanical output under different winding and slot opening conditions. As the number of windings increased, the maximum torque also increased, but it decreased with a larger slot opening. Conversely, the range of rotation for maximum torque showed the opposite trend. When the number of windings increased from 21 to 25, the maximum torque went up by as much as 18.9%, while the range of maximum torque rotation decreased by up to 38.1%. On the other hand, when the slot opening expanded from 2.4 mm to 3.6 mm, the maximum torque decreased by up to 1.66%, while the range of maximum torque rotation grew by as much as 6.78%.

Figure 12 illustrates the variation in cogging torque. The solid line represents a 21 turns, the dashed line a 23 turns, and the dotted line a 25 turns model. The maximum cogging torque and the THD of cogging torque were hardly influenced by changes in the number of turns per coil but were significantly affected by slot opening. When the slot opening was 3.0 mm, the maximum cogging torque reached approximately 0.00295 Nm, while the THD of cogging torque peaked at 2.81%. This effect is likely due to the reduction in the slot opening area that interacts most closely with the permanent magnet.

Figure 13 demonstrates the variation in torque ripple. The solid line represents a 21 turns, the dashed line a 23 turns, and the dotted line a 25 turns model. The maximum torque ripple increased with an increase in winding number but decreased with an increase in slot opening. When the number of turns per coil increased from 21 to 25, the maximum torque ripple increased by up to 29.1%, while increasing the slot opening from 2.4 mm to 3.6 mm resulted in a maximum decrease of 44.0%. This is because the concentration of the induced electromotive force generated in the winding inside the slot weakens as the slot opening increases.

Figure 14 shows that mechanical power decreases as the number of windings in-creases, but increases as the slot opening widens. When the windings increase from 21 to 25, mechanical power decreases by as much as 26.4%. In contrast, when the slot opening is widened from 2.4 mm to 3.6 mm, mechanical power increases by up to 5.03%.

Mechanical efficiency decreases as the number of windings increases, but improves as the slot opening widens. When the number of windings increases from 21 to 25, mechanical efficiency drops by up to 28.5%. However, when the slot opening is increased from 2.4 mm to 3.6 mm, mechanical efficiency rises by a maximum of 3.78%. It can be observed that as the number of windings increases, both the motor’s output and efficiency decrease linearly. This decrease is likely due to the interaction between torque ripple and permanent magnets caused by an increase in the induced electromotive force.

4.2. Analysis Results by Magnet Span and Thickness

As shown in

Table 9. Numerical data of 23 mm span model.

Item	Unit	Value
span	mm	23
thickness	mm	3.5	4	4.5
maximum torque	Nm	19.31	19.98	20.5
maximum torque rotation range	rpm	97.6	96.5	95.7
maximum cogging torque	peak-peak, Nm	0.00296	0.00306	0.00308
THD of cogging torque	%	2.80	2.77	2.86
maximum torque ripple	peak-peak, Nm	0.0838	0.0843	0.0819
maximum flux density	T	0.512	0.528	0.540
power	W	197.3	202	206
efficiency	%	24.4	24.9	25.2

,

Table 10. Numerical data of 25 mm span model.

Item	Unit	Value
span	mm	25
thickness	mm	3.5	4	4.5
maximum torque	Nm	19.77	20.5	21.0
maximum torque rotation range	rpm	96.0	94.9	94.0
maximum cogging torque	peak-peak, Nm	0.001390	0.001440	0.001460
THD of cogging torque	%	7.52	7.88	8.32
maximum torque ripple	peak-peak, Nm	0.1669	0.1647	0.1663
maximum flux density	T	0.518	0.534	0.546
power	W	198.8	203	207
efficiency	%	24.6	25.0	25.3

and

Table 11. Numerical data of 27 mm span model.

Item	Unit	Value
span	mm	27
thickness	mm	3.5	4	4.5
maximum torque	Nm	19.99	20.7	21.3
maximum torque rotation range	rpm	95.2	94.1	93.2
maximum cogging torque	peak-peak, Nm	0.00251	0.00258	0.00254
THD of cogging torque	%	8.76	9.22	9.75
maximum torque ripple	peak-peak, Nm	0.223	0.219	0.215
maximum flux density	T	0.520	0.536	0.549
power	W	199.3	204	207
efficiency	%	24.6	25.1	25.4

, numerical analysis was conducted to assess the impact of the span and thickness of the permanent magnet. The number of windings was set to 25, and slot opening size was set to 3.0 mm.

Figure 15 shows the mechanical output under the various magnet span and thickness conditions. The solid line represents a 23 mm span, the dashed line a 25 mm, and the dotted line a 27 mm span model. Maximum torque increased with a rise in magnet span and thickness, while the range of maximum torque rotation decreased. When the span increased from 23 mm to 27 mm, maximum torque increased by up to 3.59%, but the range of maximum torque rotation decreased by up to 2.59%. Likewise, when the thickness increased from 3.5 mm to 4.5 mm, maximum torque increased by up to 6.33%, while the range of maximum torque rotation decreased by up to 2.10%.

Figure 16 illustrates the variation in cogging torque. The solid line represents a 23 mm span, the dashed line a 25 mm, and the dotted line a 27 mm model. When the thickness increases from 3.5 mm to 4.5 mm, maximum cogging torque increases by up to 5.47%, and the THD of cogging torque increases by up to 11.4%. When the magnet span increases, the maximum cogging torque decreases by up to 17.6%, while the THD of cogging torque increases by up to 241%. Particularly, when the span increases from 25 mm to 27 mm, the THD of cogging torque increases by a maximum of 17.20%. However, when the span increases from 23 mm to 25 mm, there is a significant increase of up to 223.8% in the THD of cogging torque.

Figure 17 demonstrates the variation in torque ripple. The solid line represents a 23 mm span, the dashed line a 25 mm, and the dotted line a 27 mm model. When the span increases from 23 mm to 27 mm, the maximum torque ripple increases by up to 165.5%. However, when the thickness increases from 3.5 mm to 4.5 mm for spans of 23 mm and 27 mm, the maximum torque ripple decreases by 2.30% and 3.59%, respectively. For a span of 25 mm, there is a decrease of 0.359% in maximum torque ripple.

Both mechanical power and mechanical efficiency increased with an increase in span and increased with an increase in thickness, as depicted in Figure 18. With an increase in span from 23 mm to 27 mm, mechanical power increased by up to 1.02%, whereas an increase in thickness from 3.5 mm to 4.5 mm resulted in a maximum increase of 4.21%. With an increase in thickness from 3.5 mm to 4.5 mm, mechanical efficiency increased by up to 3.15%, while an increase in span from 23 mm to 27 mm led to a maximum increase of 0.769%.

Based on the characteristics of radial motors, it is believed that increasing the span direction will shorten the air gap distance between the permanent magnets, resulting in a section with a stronger permanent magnet magnetic density. However, increasing the thickness of the permanent magnets along the motor’s circumference has a relatively insignificant impact on power increase. This is because the effect on power is inversely proportional to the cube of the distance over which the slot interacts with the induced magnetic field.

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.