Research on the Influence of Key Parameters of High-Speed Hairpin Permanent-Magnet Motors for Electric Vehicles on Electromagnetic Performance

Abstract

High-speed operation is a key pathway to higher power density in modern EV traction systems, and multi-parameter optimization is essential for enhancing its high-speed performance. This study investigates a 20,000 r/min interior double-V permanent-magnet flat-wire motor via finite-element simulations to systematically examine the effects of multiple interacting parameters—including flat-wire layer number, stator slot geometry, magnet grade, and rotor magnetic barrier angle—on the electromagnetic performance under high-speed operating conditions. The results indicate that increasing winding layers significantly reduces high-speed torque; an eight-layer design decreases torque by about 50% compared to a four-layer one, while a six-layer arrangement offers a favorable torque-loss trade-off. Wider slots lower the average torque but reduce torque ripple by approximately 27%, whereas deeper slots increase tooth flux density and reduce efficiency. Higher-grade magnets enhance air-gap flux and torque at elevated cost. Rotor magnet angle optimization reveals a trade-off between peak torque and ripple, with a symmetric 100°/100° design achieving balanced performance. These findings clarify structural–control interactions and support the multi-objective design of high-speed flat-wire permanent-magnet motors.

1. Introduction

Against the backdrop of the global “dual-carbon” strategy, new energy vehicles are rapidly developing toward higher efficiency, higher power density, and a higher level of system integration. As the core component of electric drive systems, high-speed permanent-magnet synchronous motors (PMSMs) have become a mainstream technical solution owing to their excellent torque response, wide high-efficiency operating range, and compact structure. In recent years, with the maximum speed of traction motors exceeding 20,000 r/min, flat-wire windings have been increasingly adopted in high-end new energy vehicles because of their advantages such as high slot fill factor, shortened end windings, and improved heat dissipation capability. However, the continuous increase in operating speed also leads to a sharp rise in electromagnetic losses under high-frequency conditions, a more severe temperature rise, and increasingly complex multi-physics coupling effects, which together impose significant constraints on further performance improvement of these motors [1,2,3].

At present, most studies on high-speed flat-wire motors primarily focus on the influence of a single parameter on torque, efficiency, or losses. However, the underlying mechanisms of several critical design parameters with strong impacts on motor performance—such as the number of flat-wire winding layers, stator slot dimensions, permanent magnet material, and magnet pole angle design—have not yet been systematically investigated. Although increasing the number of flat-wire layers can improve winding space utilization, it may significantly intensify proximity effects and aggravate AC losses. Moreover, the winding layer configuration must be coordinated with the stator slot dimensions to balance magnetic saturation and leakage flux. From the perspective of permanent magnet design, both the magnet grade and the pole angle configuration in a double-V rotor can regulate the air-gap flux distribution, thereby affecting torque capability, torque ripple, and iron loss.

With regard to winding structures, high-frequency losses in flat-wire windings have been predicted through an integration of analytical modeling and finite element simulations, which also examines the influences of slot–pole–phase combinations, the conductor layer number, and the fill factor on AC loss mechanisms [4]. Recent benchmark studies on high-speed heavy-duty traction motors further show that the choice between stranded and hairpin windings should be made jointly with thermal management and loss distribution, since continuous-operation performance can be limited by AC loss and temperature rise [5]. In addition to analytical/FE loss modeling for hairpin windings [6,7], practical mitigation measures such as coil transposition have been demonstrated to effectively suppress AC copper loss in high-speed machines [8,9].

In addition, removing conductors near the slot opening was shown to significantly reduce losses in the frequency range of 500 Hz to 1.3 kHz. The influence of flat-wire dimensions, the number of winding layers, and parallel paths on AC losses in permanent-magnet synchronous motors with maximum speeds of up to 12,000 r/min has been analyzed [10,11]. However, owing to the relatively low operating speeds considered, these studies did not fully reveal the evolution characteristics of high-frequency losses under ultra-high-speed conditions exceeding 20,000 r/min.

In terms of stator slot design, a combined approach of analytical modeling and two-dimensional finite-element simulations has been employed to investigate the effects of geometric parameters—such as slot opening width, tooth width, and slot depth-to-width ratio—on skin and proximity effects [12]. Current harmonics and slotting effects can substantially increase copper, core, sleeve, and magnet eddy-current losses; hybrid modeling with experimental verification has been reported as an effective way to quantify these contributions [13,14,15].

The permanent magnet material is another key factor determining the air-gap flux density, demagnetization resistance, iron losses, and high-temperature stability. The air-gap flux density distribution and cogging torque characteristics were comparatively analyzed using four different permanent magnet materials [16]. The results demonstrated that appropriate optimization of magnet materials significantly contributes to reducing the cogging torque and enhancing the overall performance of PMSMs.

Regarding rotor topology, the performance of “U+1”, “double-V”, and “V+1” rotors was compared through simulation [17]. For a 150 kW flat copper wire motor exhibiting limitations in rated torque, torque ripple, and efficiency, the analysis indicated that a double-V rotor combined with an eight-layer winding offers superior overall performance. A V-type interior PMSM with a rated speed of 2865 r/min was examined, and a parametric model with the permanent magnet pole angle as a design variable was developed [18]. Finite-element simulations were conducted to reveal the influence of this angle on the cogging torque, output torque, and torque ripple. However, under high-speed operating conditions, systematic investigations into the effects of the permanent magnet pole angles in double-V rotors on various electromagnetic performance indices remain limited. Beyond conventional V and double-V rotors, recent works on commercial IPMSMs also indicate that the rotor barrier reconfiguration and local notching can simultaneously improve torque capability and reduce ripple, highlighting the value of systematic topology optimization for traction applications [19,20].

Although previous studies on individual parameters have established a solid foundation, for high-speed flat-wire motors with maximum speeds exceeding 20,000 r/min, the coupled influence mechanisms of several key design parameters—including the winding layer number, stator slot dimensions, permanent magnet grade, and magnet pole angle configuration in the double-V rotor—have not yet been systematically clarified. Therefore, this study focuses on an interior double-V-type high-speed permanent-magnet flat-wire motor with a maximum speed of 20,000 r/min. Based on finite element simulations and experimental validation, the effects of the winding layer number, stator slot dimensions, permanent magnet grade, and permanent magnet pole angles on electromagnetic performance are systematically investigated under multiple operating conditions, providing a theoretical basis for the engineering design of high-reliability permanent-magnet flat-wire motors.

2. High-Speed Flat-Wire Permanent-Magnet Drive Motor Model

2.1. Basic Parameters of the Motor

The key design parameters of the permanent-magnet flat-wire drive motor are listed in

Table 1. Key motor parameters.

Parameter	Value	Parameter	Value
Stator outer diameter	190 mm	Stator slot width	4.5 mm
Stator inner diameter	128 mm	Stator slot depth	15 mm
Rotor outer diameter	125 mm	Number of winding layers	7
Rotor inner diameter	53 mm	Flat wire size	3.55 mm × 1.6 mm
Slot–pole number	8 poles, 48 slots	Rated/peak power	40/94 kW
Rotor topology	Double-V type	Rated/peak torque	85/188 Nm

. Based on these parameters, a two-dimensional electromagnetic model of the motor was established, and the overall motor configuration is shown in Figure 1. To improve the slot fill factor and power density, the stator winding adopts a seven-layer distributed arrangement with a coil pitch of five; the corresponding stator slot structure is also illustrated in Figure 1. In addition, a three-dimensional topological model was constructed in SolidWorks 2021, as shown in Figure 2, to provide a more intuitive visualization of the motor structure.

On this basis, a two-dimensional transient finite-element model was developed for the 8-pole/48-slot motor to carry out the electromagnetic analysis. Considering both computational efficiency and solution accuracy, a one-eighth periodic model was adopted according to the structural symmetry. Mesh refinement was applied in the air-gap and tooth-tip regions, and a five-layer mapped mesh was arranged in the air gap to accurately capture the slotting-induced air-gap permeance distortion. The nonlinear magnetic properties of the silicon–steel laminations were considered, with local saturation taken into account up to 2.0 T. Simulations were performed under both the rated operating condition (4500 r/min) and the peak operating condition (6000 r/min). At each operating point, the current advance angle was adjusted to realize the maximum torque per ampere (MTPA) control strategy.

2.2. No-Load Electromagnetic Response Analysis

The no-load back electromotive force (BEMF) and its harmonic analysis obtained from the one-eighth model simulation are shown in Figure 3. The results indicate that the sinusoidal waveform of the no-load back BEMF is well-formed, with a low total harmonic distortion (THD). The cogging torque waveform under no-load conditions is presented in Figure 4a. The peak cogging torque reaches 0.089 N·m, with a relatively low ripple amplitude. Figure 4b shows the air-gap flux density distribution under no-load conditions. The waveform exhibits localized sawtooth-like distortion, which is mainly attributed to slotting effects and periodic variation in air-gap permeance. The peak air-gap flux density is 0.68 T, with no local saturation observed.

Further magnetic field analysis is shown in Figure 5. The magnetic flux lines are symmetrically and continuously distributed. The stator tooth magnetic flux density reaches 1.08 T, which remains below the saturation limit of silicon steel (2.0 T). However, the magnetic flux density in the rotor flux barrier region reaches 2.17 T, indicating deep saturation that increases the magnetic reluctance of the bridges, thereby suppressing leakage flux and guiding the main flux along the intended path.

2.3. Performance Analysis Under Load Conditions

2.3.1. Rated Operating Condition

To evaluate the motor’s performance under rated operation, simulations were conducted under a rated speed of 4500 rpm and a rated power of 40 kW, where the rated torque was achieved by adjusting the current advance angle. As shown in Figure 6, within one electrical period, the motor exhibits an average output torque of 85.6 N·m and a peak torque of 87.9 N·m, resulting in a torque ripple ratio of 2.7% (below the ISO 21782 [21] limit of 5%), indicating excellent torque smoothness and meeting the requirements for low-noise drive applications.

The magnetic field distribution under rated operating conditions is shown in Figure 7a. Compared with the no-load condition, armature reaction further enhances magnetic saturation in the rotor flux barrier, raising the local flux density to 2.4 T. Nevertheless, the overall distribution of magnetic flux lines remains uniform, and no significant flux leakage is observed at the ends.

2.3.2. Peak Operating Condition

At the peak operating condition of 95.8 kW and 6000 r/min, the motor delivers an average output torque of 152.4 N·m and a peak torque of 154.45 N·m while maintaining a relatively low torque ripple, as shown in Figure 6.

The magnetic field distribution under peak operating conditions is illustrated in Figure 7b. Compared with the rated operating condition, the armature reaction strengthens further. The flux density in the rotor flux barrier increases to 2.5 T, while the stator tooth flux density reaches 2.0 T, approaching the saturation limit.

The strong armature magnetic field generated by the q-axis current superimposes on the permanent magnet field, causing the main air-gap flux direction to deviate from the direct axis under peak-load conditions. This reflects the enhanced armature reaction and the redistribution of magnetic flux paths at high current loading. In addition, local saturation can be observed mainly in the stator teeth, which increases the local magnetic reluctance and contributes to the distortion of the magnetic field distribution.

3. Experimental Validation

An experimental platform for the PMSM analysis under multiphysics coupling conditions was established, as shown in Figure 8a. The platform consists of the test motor, a dynamometer, a controller, a power analyzer, and a data acquisition system, while the technical specifications of the core test equipment are listed in

Table 2. Technical specifications of core test equipment.

Instrument Name	Model	Key Performance Indicators
Power analyzer	WT1804E	Bandwidth: 5 MHz; accuracy: ±0.05%; harmonic analysis up to the 500th order
Oscilloscope	R&S RTM3004	Bandwidth: 400 MHz; sampling rate: 5 GSa/s
Industrial PC	Advantech 3202	CPU: Core i7-2600; main frequency: 3.4 GHz
Temperature sensor	PT1000	Accuracy: ±0.1 °C

.

3.1. Electromagnetic Performance Analysis Under Multiple Conditions

3.1.1. No-Load BEMF

The line-to-line BEMF was measured at intervals of 2000 r/min from 0 to 16,000 r/min and compared with the simulation results, as shown in Figure 9a. The measured BEMF increases linearly with speed (slope = 0.0173 V/r/min), closely matching the simulated trend. Above 4000 r/min, however, the measured values fall below the simulated ones, with a maximum deviation of 4.8% (815.25 V simulated vs. 736.74 V measured at 16,000 r/min). This discrepancy is primarily attributed to the reduction in permanent magnet remanence caused by the temperature rise, as well as the fact that eddy-current losses in the silicon–steel laminations were not fully accounted for in the finite-element model, leading to an 8.7% increase in the measured iron loss at 12,000 r/min. The harmonic spectrum of the no-load BEMF at 6000 r/min is presented in Figure 9b, demonstrating good sinusoidal fidelity and low harmonic distortion at this operating point.

3.1.2. Thermal Operating Characteristics

The thermal steady-state external characteristic test is essential for evaluating the motor’s performance under practical operating conditions. As shown in Figure 10, under the rated DC bus voltage of 630 V, the motor achieves a peak torque of 153 N·m, a base speed of 6000 rpm, and a peak power of 103 kW. The simulated and measured external characteristic curves exhibit a high level of consistency at this voltage level.

At 12,000 r/min, the measured torque is 4.46% higher than the simulated value (78.12 N:m vs. 74.78 N:m), primarily due to the actual magnet operating temperature being lower than the assumed value in the simulation, resulting in higher magnet remanence and thus higher torque. At 11,000 rpm, the measured power exceeds the simulation by 4.35% (100.5 kW vs. 96.14 kW), a discrepancy attributable to unmodeled inverter switching losses, resulting in a 12.8% increase in measured losses.

3.1.3. Motor Efficiency

Figure 11 compares the simulated and measured motor efficiency maps. The measured peak efficiency is 95.5% at 80 N·m and 4000 r/min, slightly lower than the simulated peak efficiency of 97%, resulting in a difference of approximately 1.5%. At the peak power point (153 N·m, 6000 r/min), the measured efficiency of 93.2% is slightly below the simulated 94.1%. This discrepancy can be mainly attributed to several factors: the winding temperature rise increasing copper losses (measured ΔT ≈ 15 °C), additional experimental losses not fully accounted for in the simulation (e.g., high-frequency iron losses and inverter switching losses), and measurement uncertainties, including voltage, current, torque, and speed deviations. Simplifications in material properties and loss coefficients in the simulation model may also contribute to small deviations. This high-efficiency region covers 88.12% of the speed–torque operating plane, exceeding the 85% requirement of GB/T 18488-2024 [22]. In contrast, the low-efficiency region (efficiency < 80%) is concentrated under high-speed, low-torque conditions (>14,000 r/min, <20 N·m), mainly due to increased iron losses under field-weakening control. The measured efficiency data at rated voltage are summarized in

Table 3. Motor efficiency test data at rated voltage.

Speed (rpm)	Torque (N·m)	DC Voltage (V)	DC Current (A)	Efficiency (%)
2000	153.01	631.06	63.46	80.02
4000	151.58	630.78	114.21	88.14
6000	150.62	630.58	164.69	91.13
8000	123.83	630.51	179.48	91.67
10,000	97.87	630.53	177.49	91.59
12,000	78.26	630.52	171.85	90.76
14,000	64.02	630.57	162.62	91.54
16,000	54.01	630.60	158.41	90.60
18,000	46.15	630.63	152.82	90.26

.

The simulated and measured efficiency maps demonstrate good agreement in the high-efficiency region, validating the model’s predictive capability. A local discrepancy is observed at the peak power operating point (153 N·m, 6000 r/min), where the measured efficiency of 93.2% is 0.9% lower than the simulated 94.1%. This difference is primarily due to experimental copper loss increases from the rise in winding temperature (ΔT ≈ 15 °C versus a simulated constant) and the demagnetization effect of the permanent magnets.

4. Investigation of Key Factors Affecting Motor Electromagnetic Performance

4.1. Effect of the Number of Flat-Wire Winding Layers

4.1.1. Mechanism

To investigate the influence of the number of flat-wire winding layers on the electromagnetic performance of the high-speed flat-wire motor, the stator slot dimensions and slot fill factor were fixed. The number of winding layers varied from four to eight, as shown in Figure 12. The conductor thickness and interlayer spacing were adjusted for each case while maintaining a current density of 17.5 A/mm², ensuring consistent electrical loading across all designs. Corresponding winding parameters are provided in

Table 4. Winding parameters for different layers.

Parameter	4 Layers	5 Layers	6 Layers	7 Layers	8 Layers
Flat-wire width (mm)	3.52	3.52	3.52	3.52	3.52
Flat-wire height (mm)	2.55	2.04	1.70	1.46	1.275
Flat-wire spacing (mm)	0.1	0.1	0.1	0.1	0.1
d-axis current (A)	−69	−55	−46	−39	−34
q-axis current (A)	142	113	94	81	71
Phase current (A)	157	126	105	90	79
Current density (A/mm2)	17.5	17.5	17.5	17.5	17.5
Phase resistance (Ω)	0.02	0.04	0.05	0.07	0.09

.

Changing the layer count alters the electromagnetic behavior of the motor. As shown in Figure 13, the torque output in the high-speed constant-power region decreases significantly with increasing winding layers. Figure 14 further shows that the electromagnetic loss is minimally affected by the layer number below 4000 r/min but becomes much more sensitive above 5000 r/min, where high-frequency effects are more pronounced. These results indicate that layer count variation modifies the air-gap field distribution and conductor magnetic coupling, which in turn affects the torque ripple, AC resistance, and loss distribution.

4.1.2. Speed–Torque Characteristic Analysis

Figure 13 presents the speed–torque characteristics of the motor with different numbers of flat-wire winding layers.

Below base speed, the torque output remains largely unaffected by layer variation, as the torque in this region is regulated by closed-loop control, which dynamically compensates for electromagnetic parameter changes such as inductance and flux linkage. Moreover, AC losses are minimal in the low-speed constant-torque region (below about 4000 r/min), further reducing the influence of the layer number on the steady-state torque. Therefore, in the design of the constant-torque operating region, the selection of the number of winding layers should primarily focus on optimizing loss, thermal management, and cost, rather than altering the torque output capability.

In the high-speed constant-power region, the output torque decreases significantly as the number of winding layers increases. At 20,000 r/min, the torque of the eight-layer winding is approximately 50.87% lower than that of the four-layer winding. This behavior is attributed to increased magnetic saturation within the slots due to multi-layer windings, which reduces the effective air-gap flux density. Under field-weakening control, higher current is required to compensate for the reduced flux linkage. However, the elevated inductance limits the current response, while sharply increased high-frequency AC losses further constrain the torque capability in the high-speed region.

4.1.3. Speed–Electromagnetic Loss Characteristic Analysis

Figure 14 shows the variation in total electromagnetic loss with motor speed for different winding layer configurations. Below 4000 r/min, the influence of the layer number is limited. Above 5000 r/min, the loss increases significantly, and the differences among the configurations become more pronounced. This is due to the combined increase in AC copper loss and core loss at higher speeds. Enhanced skin and proximity effects mainly increase the winding AC loss, while the core loss rises with speed for all configurations. Therefore, the differences among the layer configurations are mainly determined by the copper loss component.

Electromagnetic losses initially rise then fall with increasing layers, peaking at five layers. Compared to the five-layer design, losses decrease by 14.73% for the six-layer configuration. Considering both the torque characteristics in Figure 13 and the electromagnetic loss characteristics in Figure 14, the six-layer winding provides a relatively balanced compromise among the investigated configurations.

4.2. Coupled Effects of Stator Slot Dimensions

The stator slot geometry—width, depth, and shape—is critical to the motor’s electromagnetic, thermal, and power density performance. The slot area governs the conductor cross-section, current density, and copper losses. Enlarging the slot reduces copper loss but extends the magnetic path, raising iron loss and distorting the air-gap field. A narrow slot opening suppresses the cogging torque yet increases leakage flux, while a deeper slot improves space utilization but risks local saturation. Thus, the slot width-to-depth ratio requires multi-objective optimization to balance electromagnetic and thermal performance.

To study the coupling effects of the stator slot geometry, the flat-wire dimensions and slot fill factor were fixed, while the slot depth h_s and slot width b_s were varied. The values for h_s were 14.5, 15.0, 15.5, 16.0, and 16.5 mm, and those for b_s were 4.3–5.0 mm in 0.1 mm increments, resulting in 40 simulation cases.

4.2.1. Torque and Torque Ripple Correlation Analysis

Figure 15a illustrates the variation in average torque with the stator slot depth and width under rated conditions. The simulation results show that while the torque fluctuates only slightly with slot depth (14.5–16.5 mm), it decreases notably from 86.35 N·m to 82.96 N·m as the slot width increases from 4.3 mm to 5.0 mm. This reduction stems from the lower magnetic reluctance at wider slot openings, which enhances leakage flux, diverts effective flux from the main magnetic path, weakens the air-gap field, and ultimately reduces the electromagnetic torque output.

Figure 15b further illustrates how the torque ripple varies with the stator slot depth and width. Under rated conditions, the torque ripple remains relatively low, in the range of 3–4 N·m. Increasing the slot depth leads to only a slight reduction in torque ripple, whereas increasing the slot width suppresses it more effectively, from 4.165 N·m to 3.02 N·m. This trend is mainly attributed to the fact that a wider slot opening modifies the local air-gap permeance distribution and weakens slotting-related harmonic components. Although the associated increase in leakage flux reduces the average torque, it also contributes to smoother air-gap field distribution and lower local magnetic saturation, thereby reducing both cogging torque and torque ripple. In addition, the multi-layer arrangement of the hairpin winding helps improve the magnetomotive force (MMF) distribution, and this combined effect further mitigates harmonic components and reduces torque pulsation. Wider slots also provide greater flexibility for the flat-wire winding layout, which is beneficial for suppressing slotting effects.

4.2.2. Correlation Analysis of Flux Density Distribution

The flux density in stator teeth is a key indicator of magnetic circuit design rationality and saturation risk. As shown in Figure 15c, under rated conditions, the peak stator tooth flux density shows no clear monotonic trend with slot width. In contrast, it exhibits a positive correlation with slot depth, increasing steadily from 1.80 T to 1.89 T as depth grows from 14.5 mm to 16.5 mm. This rise is attributed to the reduced cross-sectional area of the tooth flux path caused by deeper slots. Excessive flux density may induce local saturation, significantly increasing iron loss, reducing efficiency, and aggravating the rise in winding temperature due to prolonged heat dissipation paths, thereby raising thermal risks.

4.2.3. Correlation Analysis of Efficiency and Slot Dimensions

Figure 15d shows the efficiency versus stator slot dimensions. Increasing both the slot width and depth reduces overall efficiency, with depth having a stronger effect: efficiency falls from 94.2% to 92.1% (a reduction of 2.1%) as depth increases from 14.5 mm to 16.5 mm, while widening the slot from 4.3 mm to 5.0 mm decreases efficiency from 94.5% to 93.0% (a reduction of 1.5%). This difference occurs because a greater slot depth raises the stator tooth flux density more directly, pushing local operation toward saturation and increasing iron losses nonlinearly, thereby affecting efficiency more significantly.

Thus, stator slot design constitutes a multi-objective optimization involving the average torque, torque ripple, flux density, and efficiency. The results indicate that wider slots suppress torque ripple but reduce the average torque and efficiency, while deeper slots offer little torque improvement yet intensify saturation and efficiency loss. Following trade-off analysis, the optimal design (point A in Figure 14) adopts a slot width of 4.5 mm and depth of 15.0 mm, balancing high torque output, low torque ripple, and controlled saturation under rated conditions.

4.3. Effect of Permanent Magnet Materials

PM properties, notably the maximum energy product and thermal stability, directly govern the achievable air-gap flux density and motor demagnetization resistance. Higher remanence enhances torque density yet requires a joint optimization of temperature performance and cost relative to operating conditions and economic constraints. To quantify the influence of magnet materials, five grades of NdFeB were selected for comparison. Generally, higher grades feature greater remanence and coercivity.

Figure 16a illustrates the variation in air-gap flux density over one electrical period for different magnet materials under the rated operating condition. A higher magnet grade results in a greater flux density amplitude, primarily due to its increased remanence. In PMSMs, this directly enhances the average electromagnetic torque, as shown in Figure 16b. Among the evaluated materials, N52UH achieves the highest flux density amplitude (1.16 T) and average torque (85.605 N·m), delivering the best overall performance.

4.4. Effect of Permanent Magnet Pole Angle

In PMSM rotor design, the magnet pole angle is a key parameter for optimizing the magnetic field distribution. Adjusting the pole angles of different layers enhances BEMF sinusoidality and reduces torque ripple, as specific combinations can suppress targeted air-gap field harmonics. However, excessive segmentation may increase leakage flux and introduce new harmonic issues. To investigate this waveform optimization mechanism in a dual-layer V-type configuration, the pole angles of layers L₁ and L₂ are defined as θ₁ and θ₂, respectively, as shown in Figure 17.

Under the constraint of fixed PM dimensions, θ₁ and θ₂ were varied to examine their coupled effects on electromagnetic performance. Specific pole angle combinations are listed in

Table 5. Permanent magnet pole angle parameters.

Parameter	Index 1	Index 2	Index 3	Index 4	Index 5
L1 magnet pole angle, θ1 (°)	80°	90°	100°	110°	—
L2 magnet pole angle, θ2 (°)	80°	90°	100°	110°	120°

, resulting in a total of 20 simulation cases (the case with θ₁ = 120° was excluded due to geometric interference).

Figure 18a illustrates the average torque variation with the magnet pole angles under rated conditions. Increasing θ₁ from 80° to 110° expands the pole coverage of the L₁ layer and reduces the main flux-path reluctance, raising the air-gap flux density and thus the torque. For relatively small θ₁ (80–90°), increasing θ₂ enhances the auxiliary excitation from the L₂ layer, further boosting torque. For larger θ₁ (100–110°), further increases in θ₂ can induce inter-layer magnetic field interaction, causing local saturation and a transient torque dip; torque later recovers somewhat as the field redistributes and saturation eases.

Figure 18b shows the influence of pole angles on torque ripple. Increasing θ₂ improves the symmetry of the L₂-layer poles, suppressing low-order air-gap harmonics and reducing torque ripple. In contrast, increasing θ₁ raises pole-edge leakage flux and excites higher-order harmonics, thereby increasing torque ripple.

The simulation data further indicate that a maximum torque of 91.62 N·m is achieved at θ₁ = 110° and θ₂ = 80°, though the efficiency decreases by 3.2% due to severe magnetic leakage. Conversely, the minimum torque ripple of 2.38 N·m occurs at θ₁ = 80° and θ₂ = 120°, despite a 14.5% torque reduction. While equal angles are conventionally used for simplicity, a differentiated design offers higher performance. Considering trade-offs between torque, ripple, efficiency, and manufacturability, the balanced design θ₁ = θ₂ = 100° provides 85.61 N·m of torque (6.5% lower than maximum) and 3.85 N·m of torque ripple, with favorable efficiency and manufacturability.

5. Conclusions

This study investigates the electromagnetic performance of a 20,000 r/min IPM motor with a dual V-shaped rotor through finite-element analysis, supported by experimental validation of the baseline prototype. Excessive winding layers degrade inductance and limit high-speed torque, while an intermediate layer configuration offers the optimal balance between torque and loss. Increasing the stator slot width reduces torque ripple by improving field uniformity, whereas deeper slots lower efficiency due to saturation. Optimized slot dimensions achieve the best efficiency–smoothness trade-off. High-grade magnets enhance torque at increased cost, necessitating a cost–performance evaluation. Symmetric pole angles provide balanced torque and smoothness, while asymmetric angles favor either maximum torque or minimum ripple.

Future research will prioritize stator slot dimensions and winding layers based on parameter weighting, conducting electromagnetic–thermal–mechanical co-design. The coupled effects of rotor topology and magnet materials under high-efficiency and extreme conditions will also be explored.