Comparison of traditional,quasi-Halbach array and interior permanent magnet configurations for outer rotor brushless AC machines

Abstract

The study in this paper compares three permanent magnet (PM) brushless AC machine topologies with external rotor configuration, which are attractive for in-wheel electric drive applications. All machines use the same stator but have different rotor geometries: a conventional surface PM structure, a surface quasi-Halbach PM array structure, and an interior V-shaped PM structure. For these topologies, the volume of the PM material is the same. A numerical simulation based on finite element analysis was carried out for the three cases to evaluate and compare their behaviour in terms of torque density, magnetic flux density, and torque ripple.

Keywords

Brushless motor external rotor interior magnets permanent magnets quasi-Halbach array

1. Introduction

The advantages of in-wheel motor utilization for direct-drive traction has been extensively discussed in the literature [1, 2, 3]. Additionally, for in-wheel applications, motors with an outer rotor are more suitable. There are studies addressing outer rotor radial flux machines [1], especially radial flux permanent magnet (PM) machines, since they present high torque density and high efficiency [4].

In this context, this paper develops a comparative study of three radial flux PM motor topologies with outer rotors. All machines consist of a stationary armature with a fractional number of slots per pole per phase assembled around a shaft. The outer rotors have different configurations with respect to the position and magnetization of the PMs. However, in order to perform a fair comparison between the three addressed topologies, in all cases the volume of permanent magnet material is set to be the same and the stator is also identical. The first topology employs conventional surface mounted PMs (SPMSM), the second case uses a surface mounted PM quasi-Halbach array (QHSPMSM), and the third one considers V-shaped inset PMs (IPMSM).

The study uses Finite Element Analysis (FEA) carried out with the aid of a commercial package. The materials considered for the machines are: rotor core – AISI steel 1010; PMs – sintered NdFeB grade N35; copper windings; and stator core – laminated magnetic steel Aperam E230 ${}^{\text{TM}}$ . Additionally, some important characteristics of the machines are given in Table 1.

Table 1
Specifications of the proposed models

Description	Value
Air-gap radial lenght	0.6 mm
Estimated efficiency and PF	90.4%, 0.9
PM volume and weight	57.14 cm ${}^{3}$ /0.44 kg
Number of coils per phase	18
Number of phases/turns per coil	3/4
Number of stator slots/pole number	54/60
Rated power	3.17 kW
Rated torque/speed	40 Nm/758 rpm
Stack length/stator outer diameter	50 mm/200 mm
Winding fill factor	0.55

Figure 1.

Surface mounted PM rotor with $\alpha_{p}=$ 0.9. The parts indicated are: 1 – rotor core, 2 – PMs, 3 – stator core, and 4 – windings.

The machine volume was obtained from the electrical and magnetic loading characterized by $A_{rms}$ (effective linear current density), $B_{\delta}$ (peak fundamental air-gap induction) and $k_{w1}$ (winding factor). The calculated rotor machine volume $V_{r}$ is 0.00156 m ${}^{3}$ . If $B_{\delta}=$ 0.8 T, $A_{rms}=$ 16 kA/m and $k_{w1}=$ 0.9, then, according to [10]:

$\displaystyle V_{r}=\frac{T}{2\sigma}=\frac{T\sqrt{2}}{\pi k_{w1}A_{rms}B_{% \delta}}=\pi R^{2}L,$ (1)

where $T$ is the rated torque and $\sigma$ is the airgap shear stress.

The ratio between the machine radius $R$ and the axial length $L$ was chosen to be eight for an in-wheel motor since this enhances the torque, although it is also limited by the wheel rim. The design procedure for the conventional topology did not go through an optimization process; an applied parametrical analysis was performed instead.

A section of the first topology is shown in Fig. 1. Based on a previous parametric analysis, the pole arc coefficient, i.e. the ratio between the pole pitch and the arc length of the PM, was defined as 0.9 ( $\alpha_{p}=$ 0.9). The radial thickness of the PMs for this case is 2 mm.

The second topology, i.e. a surface mounted quasi-Halbach PM array machine, with its section shown in Fig. 2, applies the same pole arc coefficient as the first topology, i.e. $\alpha_{p}=$ 0.9. The PMs have radial and circumferential magnetization, as identified in Fig. 2. In order to keep the same magnetic volume as the conventional SPMSM, the radial length of the PMs is 1.803 mm.

Figure 2.

Machine with quasi-Halbach array rotor with $\alpha_{p}=$ 0.9. The numbers shown are: 1 – radially-magnetized PMS , 2 – circunferentially-magnetized PMs.

Figure 3 shows the rotor configuration with V-shaped inset PMs, where each pair of magnets produces a pole. In this case, the magnets are rectangular, and again, to keep the same PM volume, the thickness is 1.2 mm and the width is 8 mm.

Figure 3.

Machine with inset V-shaped PMs rotor.

Based on a previous parametric analysis, the angle of the magnets with respect to the tangential surface of the rotor core was defined as 35 degrees.

2. Results and discussion

The FEA was performed to evaluate the magnetic induction in the air-gap and saturation in the rotor back-iron. Additionally, performance parameters such as torque, back-EMF, and cogging torque were also evaluated in order to compare the different topologies.

Figure 4.

Machine torque comparison.

Figure 4 shows the torque values for the three topologies. The IPMSM reached 37.95 Nm of average torque, whereas the SPMSM achieves 39.01 Nm, and the QHSPMSM, 40.50 Nm. These curves were generated with an AC current producing quadrature flux with an rms effective current density of 6.92 A/mm ${}^{2}$ applied to the three-phase windings.

The torque ripple was calculated according to [5],

$T_{ripple}=100\left({\frac{T_{\max}-T_{\min}}{T_{avg}}}\right)\quad,$ (2)

Where $T_{max}$ and $T_{min}$ are the maximum and minimum torques measured and $T_{avg}$ is the faverage torque.

Figure 5.

Air-gap radial flux densities for the three topologies.

Figure 6.

Radial component of magnetic flux density spectrum on a line arc with radial length equals to the outer radius of the stator core.

It can be observed in Fig. 4 that the QHSPMSM machine achieved the highest torque value and the IPMSM presents highest torque ripple. For applications that require better control or low torque ripple, the SPMSM and QHSPMSM topologies would be more interesting.

Figure 5 shows the results for the magnetic induction produced by the PMs only, using the machine arrangements discussed in the previous section.

The rms values of the air-gap induction, calculated from the waveforms shown in Fig. 5, are 0.80 T for the conventional arrangement, 0.84 T for the quasi-Halbach array and 0.78 T for the arrangement with PMs embedded in the rotor.

Figure 6 shows the spectrum of the space distribution of the radial component of magnetic induction $B_{r}$ in the air-gap for the three topologies. The fundamental component of $B_{r}$ for the IPMSM is 1.05 T, for the SPMSM is 1.08 T, and for the QHSPMSM is 1.1 T.

The fundamental component of Br is responsible for the electro-dynamic torque generation, which is consistent with the results of Fig. 4, i.e. the QHSPMSM presents higher levels of mean torque.

Figure 7 shows the induced open-circuit phase voltage at 780 rpm. The rms values of the voltage are 68.95 V, 70.65 V and 73.35 V for the IPMSM, SPMSM and QHSPMSM, respectively.

Figure 7.

Open-circuit phase induced voltages in the three topologies.

Higher voltage was obtained with the surface mounted quasi-Halbach PM array machine because to the greater fundamental component of $B_{r}$ . The QHSPMSM machine presents higher induced voltage than the SPMSM and IPMSM due to the higher induction value caused by the presence of tangential magnetization magnets.

Even though the magnetic induction in the air-gap presents high levels of distortion, the machines show low harmonic distortion in the open-circuit phase voltage, which is due to the number of slots per pole per phase being equal to 0.3, which is fractional winding with pitch shortening. Figure 8 shows the FFT of the induced voltage of the three machines.

The IPMSM machine presents the lowest harmonic distortion with a value of 1.61% followed by 2.54% for the QHSPMSM and 1.98% for the SPMSM. The fractional number of slots per pole per phase with coil short pitching was fundamental to the limiting of the harmonic distortion in the induced voltage, which is good for performing control techniques and increasing the performance of the device.

Figure 8.

Induced voltages FFT for the three models.

Figure 9 shows the cogging torque value for the three machines. The IPMSM resulted in 485.05 mNm peak-to-peak against the SPMSM with 137.93 mNm and the QHSPMSM with 131.83 mNm, which is relatively small compared to the mean rated value of torque. This is mainly because of the number of slots per pole per phase being equal to 0.3.

Figure 9.

Cogging torque simulation of the three machines.

Figure 10.

Reluctance torque on the IPMSM machine.

The IPMSM machine is the only one of the three that presents reluctance torque, which is caused by the difference in the direct and quadrature axes inductances.

Figure 10 shows the reluctance torque obtained for the IPMSM machine. A transient simulation was performed without the presence of PMs and with current in the windings. The SPMSM and QHSPMSM topologies presented zero reluctance torque due to the presence of uniform air-gap where the direct and quadrature axis inductances are the same.

The reluctance torque, together with the relative higher level of cogging torque in the IPMSM, produce higher ripple of torque in this machine, as observed in Fig. 4.

Table 2 presents a summary of the data obtained for the three models for comparing the results.

Table 2

Main machine results

Description	SPMSM	IPMSM	QHSPMSM
Average torque	39.01 Nm	37.95 Nm	40.50 Nm
Torque ripple	2.36%	8.12%	4.1%
RMS flux density	0.80 T	0.78 T	0.84 T
Fundamental flux density	1.08 T	1.05 T	1.1 T
RMS induced phase voltage	70.65 V	68.95 V	73.35 V
Induced phase voltage THD	1.98%	1.61%	2.54%
Max cogging torque	137.93 mNm	485.05 mNm	131.83 mNm
Mean reluctance torque	0.00 mNm	103.26 mNm	0.00 mNm

From the point of view of torque density, the QHSPMSM presented the best results where there are more possibilities of design in the dimensions and pole arc coefficient between of the magnets. Also, due to the shielding effect of the topology with quasi-Halbach arrays, the volume of back-iron can be reduced in comparison with the other two topologies, which is an advantage because it leads to a rotor with a comparatively lower inertia. Low inertia is an important issue in automotive drive motors.

According to [8], machines with embedded magnets have reluctance torque that contributes to the machine torque generated by the direct and quadrature axes inductance difference. In the proposed model, the reluctance torque value was of little influence. The design of machines with interior magnets becomes interesting due to the mechanical protection of the magnets, better effective use of the air-gap magnetic flux and the option of working with different magnet angles to set the flux density distribution. However, the IPMSM presented higher levels of torque ripple. Those characteristics may still be improved with a correct optimization method applied while designing the machine. It is important to observe that the topology with interior PMs requires a rotor with increased radial length, which results in a heavier rotor with a comparatively higher inertia. However, rectangular magnets are easier to assemble and magnetize, and it is possible to use commercial magnets or even ferrite magnets with a magnetic flux concentrator and, hence, reduce the cost.

Due to the shielding effect in the topology with quasi-Halbach arrays, the volume of back-iron can be reduced in comparison with the other two topologies, which is an advantage because it leads to a rotor with a comparative lower inertia. Low inertia is an important issue in automotive drive motors.

The topology with interior PMs requires a rotor with increased radial length, which leads to a heavier rotor with a comparatively higher inertia. However, rectangular magnets are easier to assemble and magnetize and it is possible to use commercial magnets or even ferrite magnets with a flux concentrator, and hence reduce the cost.

3. Conclusion

This paper shows a comparison of three machine topologies with external rotor and different arrangements of magnets with the same stator. Performance parameters such as torque, torque ripple, cogging torque, open-circuit induced voltage were analyzed and characteristics of each machine for in-wheel electric drive applications were briefly discussed.

In short, mean torque levels of the QHSPMSM were found to be 3.7% higher than the SPMSM and 6.3% higher than the IPMSM. Torque ripple is also higher in the IPMSM because this is the only topology that has reluctance force due to the difference between the d- and q-axis inductances. For applications that require low inertia, a QHSPMSM is a better choice, because it has the smallest back-iron, due to the shielding effect. In this aspect the IPMSM requires the largest back-iron because of the V-shaped PMs that are be embedded into the core. In terms of manufacturing, the simplest topology is the SPMSM.

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Comparison of traditional,quasi-Halbach array and interior permanent magnet configurations for outer rotor brushless AC machines

Abstract

Keywords

1. Introduction

Table 1 Specifications of the proposed models

References

Table 1
Specifications of the proposed models