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Introduction

Amidst pressing environmental challenges and ecological uncertainties, the imperative to curb carbon emissions and foster a sustainable and resilient energy landscape has gained momentum over the past decades. Electric machines play a crucial role to achieve net zero carbon footprint as being used in a variety of applications from electric vehicles to renewable energy generation [1]. Permanent Magnet Synchronous Machines (PMSMs) have been widely used in such applications thanks to their high efficiency and high-power density [2]. Numerous studies investigated the performance analysis of external rotor PMSMs, with a particular focus on evaluating their characteristics in accordance with design specifications [3] [4] [5]. The purpose is to enhance efficiency, develop new materials, and optimize the design parameters while respecting the effectiveness and feasibility of the machine. These machines are widely used in electric vehicle applications. They present good efficiency with low maintenance as well as low noise and vibration [1] [7]. In this context, stages of the design work by means of FEM 2D software, EMWorks2D, are presented for an external rotor PMSM and analyzed in terms of power, torque, rotational speed, cogging torque, and torque ripple. The results of numerical calculations related to variations in geometric sizes of magnet pole arc coefficient are highlighted.

Problematic Definition

Enhancing the cogging torque in PMSMs remains a common design issue for machine designers. The low value of cogging torque improves the efficiency of PMSMs and reduces noise and vibration. This can lead to smoother and quieter operations, improved energy efficiency, better accuracy, and longer lifespan.

An external rotor surface PMSM, having 12 slots - 8 poles, is designed using SOLIDWORKS and simulated by EMWorks2D as a powerful electromagnetic software. The study consists of varying the magnet pole arc from full pitch to 31°. The limit on the magnet pole arc variation is done until the magnet pole arc is the same as the slot pitch. Figure 1 shows the studied structure for full pitch magnet pole arc.
 

Fig. 1. 12 Slots-8 Poles External Rotor Surface PMSM for Full Pitch Magnet Pole Arc

Design Specification of the Studied Topology

The first step of the design is to generate the required parameters which are divided into 2 categories: PMSM specification mentioned in Table 1 and geometric design variables shown in Table 2 [6]. 
 

According to mentioned variables, the 2D design of the studied machine is presented as follows using Solidworks. The arrows’ direction in each magnet pole indicates its polarity. For this topology, the slot pitch is equal to 30° and the pole pitch is 45°. Consequently, the variation of the magnet pole arc is done from 45° to 31° by step of 2°. 
 

Fig. 2. Design Specification of the Studied PMSM for Full Pitch Magnet Pole Arc
 

Figures 3 and 4 show an explanation of the surface magnet pole arc variation. It is done from full pitch to 31° by step of 2°. For no full pitch magnet pole arc, the studied structure may resemble inset PMSM. Whereas, it is a surface PMSM where the height of the inter-pole is lower and does not align with magnet’s height.
 

Fig. 3. Topology Specification: 12 Slots- 8 Poles External Rotor Surface PMSM for 2 Cases of Magnet Pole Arc Measure



Fig. 4. Magnet Pole Arc Variation and Inter-Pole Presentation
 

For the material used, Neodymium is used for the permanent magnets having 1.12 T remanence and presenting a relative permeability equal to 1.05. For the iron core loss, AISI 1010 steel is used. It is a preferred material for stator and rotor yoke thanks to its saturation magnetic flux density which can reach 2.4T.

EMWorks Simulation Settings

After finishing the design of the machine based on the geometric parameters, a study in the EMWorks2D interface is presented (Figure 5). Users must pay attention to five parts to move to the electromagnetic simulation. First, adequate materials for each defined component must be applied with respect to their materials specifications. Second, boundary conditions on the edge of the outer air are needed so its magnetic vector potential must be equal to 0 weber/m. The third step focuses on the virtual work applied to the rotor and the magnets. Then, the mesh control, which plays an important role in the accuracy of the electromagnetic results, must be fixed. Lastly, the windings of the three-phase PMSM are determined based on the distribution of the winding and the operational mode of the machine.
 

Fig. 5. EMWorks2D Study Details

Results and Discussion

The external rotor PMSM operational aspects for different magnet pole arc values are simulated and analyzed and the results are displayed below.

Magnetic Flux Density

Figure 6 presents the magnetic flux density in the studied PMSM for full pitch and 31° magnet pole arc. It is clear that the magnetic fields are widely spread across the opening poles due to the inter-pole. The inter-pole, acting as an electromagnetic conductive material, facilitates the dispersion of the electromagnetic field within its region and effectively mitigates the saturation concentrated between the two magnet poles.
 

(a)	(b)

Cogging Torque 

The cogging torque was simulated for each magnet pole arc from 45° to 31° under open circuit conditions as shown in Figure 7. It can be observed that the cogging torque is high for different magnet pole arc values until it reaches 33°. It was balanced between 0.39 N.m and 0.49 N.m.  For 33°, cogging torque is equal to 0.26 N.m. The optimal value of the cogging torque, 0.067 N.m, is obtained when the magnet pole arc is equal to 31° (Figure 8).
 

Fig. 7. Cogging Torque Produced by the External Rotor PMSM by Varying Magnet Pole Arc Across Different Rotor Positions
 

Fig. 8. Cogging Torque Produced by the ERPMSM by Varying Magnet Pole Arc
 

Back EMF and Output torque

Back EMF for one phase for both full pitch and 31° magnet pole arc is presented in Figure 9. The back EMF for full pitch is more trapezoidal compared to 31° magnet pole arc. This is explained by the presence of higher harmonics numbers compared to 31° magnet pole arc design. Harmonics values are estimated by using Fast Fourier Transform (FFT) as illustrated in Figure 10.  Higher harmonics affect the sinusoidal formation after summation contributing to a trapezoidal waveform. A more sinusoidal phase EMF contributes to less noise, vibration and fewer ripples. Figure 11 presents the output torque results of each studied machine which are regrouped in Table 3. The output torque for both machines is practically the same having a value of 0.88 N.m. Whereas, it presents a high percentage of torque ripples of 94.38% for full pitch magnet pole arc and a low value of 17.04% for 31° magnet pole arc.
 

Fig. 9. Back EMF According to Rotor Position for Full Pitch & 31° Magnet Pole Arc



Fig. 10. FFT of Back-EMF for the Studied Cases



Fig. 11. Output Torque as Function as Rotor Position for PMSM with Full Pitch and 31° Magnet Pole Arc
 

Magnet Arc	Average Torque (N.m)	Torque Ripple (%)
Full Pitch	0.89	94.38
31°	0.88	17.04

Table 3. Output Torque and Torque Ripples Calculation for the Studied Machines
 

Conclusion

References