Design and analysis of a high-performance surface inset permanent magnet motor with asymmetrical rotor

Abstract

This paper presents a novel design strategy for surface inset permanent magnet (SIPM) motors to suppress torque pulsations and maintain the high output torque by integrating the magnet skewing and asymmetrical rotor configurations. The magnet skewing is implemented within one magnet pole pitch to reduce cogging torque by avoiding excessive torque degradation, and the asymmetrical rotor is designed to improve the utilization of the torque components, thus to compensate the decreased torque due to the magnet skewing. To highlight the advantages of the proposed motor, a conventional SIPM motor is adopted for performance comparison with the aid of the finite element method. As a result, the proposed SIPM motor highly reduced the cogging torque (−79.7%) and torque ripple (−54.7%) while maintaining a high average torque when compared to the conventional SIPM motor.

Keywords

Asymmetrical rotor finite element method magnet skewing surface inset permanent magnet motors torque pulsations

1. Introduction

In recent years, the high-performance electric motors are popular owing to the increasing concern of energy efficiency and environmental protection. In particular, permanent magnet (PM) motors exhibit the advantages of high efficiency and torque density, which have been widely used in the fields of industry drives, vehicle traction, and domestic appliances [1,2]. The PMs are usually installed in the forms of surface mounted, surface inset, interior, and so on. Among the various PM motors, the surface inset permanent magnet (SIPM) motors are appreciated for electric propulsion applications due to their high mechanical robustness, good field weakening capability, and low manufacturing cost [3,4]. In the SIPM motors, the q-axis inductance is larger than the d-axis inductance due to the permeability of PM is close to air. Thus, the saliency effects can produce reluctance torque to improve the torque/power density and constant power speed range [5]. In addition, the saliency effects due to the unequal d − q axis inductances can also be used in the rotor position detection for sensorless control technique [6].

However, due to the salient structure and the coupling effects of magnetic fields, the SIPM motors suffer high torque pulsations. The undesired pulsating torques cause unacceptable vibration, acoustic noise, poor position and speed control, performance degradation, and even running failures, which must be minimized especially in high-performance applications. The approaches for suppressing torque pulsations in PM motors have been heavily investigated through the drive control method or design methods [7] The drive control methods can produce additional torque ripple to counteract the original torque pulsation, whereas this method generally increases copper losses due to the additional current injection [8]. The design methods can physically eliminate torque pulsations by modifying the motor structure itself. The skewing methods can reduce the cogging torque to be zero theoretically with one slot pitch skewing widely used in the industry [9]. The sinusoidal magnet poles can produce sinusoidal back EMF waveform, thereby to minimize both cogging torque and torque ripple [10]. The asymmetric rotor shape is applied for rendering the air gap flux density to reduce torque ripple additionally with iron loss reduction [11]. An alternative rotor design using axial pole shaping is proposed to achieve very small torque ripple with minimum average torque reduction [12]. The multi-grade permanent magnets are utilized to minimize torque pulsations and save the magnet cost [13]. In addition, the notching, pole arc optimization, selecting proper slot and pole number combinations can also effectively suppress torque pulsations as depicted in [14]. However, by adopting various traditional approaches, not only the cogging torque and torque ripple have been highly reduced, but also the torque density is degraded. For instance, the skewing method has the drawbacks of reducing the useful magnet flux linking the stator windings, thus to reduce the output torque. The literatures related to improving the torque density of PM motors are extensive but very limited to SIPM motors. In [15], the SIPM motor with high saliency ratio is obtained with unequal d − q axis air-gap length, which helps to obtain high reluctance torque and wide speed range. In [16], the SIPM motor adopts asymmetrical rotor structures aiming to improve the torque production by producing a rotor asymmetry, thereby making the reluctance torque and the magnetic torque reach a maximum at the same current phase angle. As the results show, the torque densities of the abovementioned SIPM motors are improved, whereas the torque pulsations are also enlarged Therefore, the techniques to reduce torque pulsations while keeping high torque are desired.

Fig. 1.

Motor configurations. (a) Basic model; (b) Proposed model.

Table 1

Specifications of the investigated motors

Item	Unit	Value
Stator outer radius	mm	44
Airgap length	mm	0.5
Rotor inner radius	mm	15
Motor axial length	mm	52
Magnet grade	-	Ferrite/0.40 T
Steel sheet	-	NSSMC 50H470/1.81 T

In this paper, a novel design strategy for SIPM motors is proposed to suppress torque pulsations and maintain the high output torque by integrating the magnet skewing and asymmetrical rotor configurations. The magnet skewing is implemented within one magnet pole pitch to reduce cogging torque by avoiding excessive torque degradation, and the asymmetrical rotor is designed to improve the utilization of the torque components, thus to compensate the decreased torque due to the skewing. The design principle is illustrated in detail, and the motor characteristics ware analyzed by the finite element method (FEM). To highlight the advantages of the proposed motor, a conventional SIPM motor is adopted for performance comparison with the same motor size, materials, and operating conditions.

2. Modeling of the SIPM motors

2.1. Motor configurations

The conventional surface inset PM motor with six slots and four PM poles, referred as the basic model, is shown in Fig. 1(a). The proposed surface inset PM motor with skewed magnets and asymmetrical rotor, nominated as the proposed model as shown in Fig. 1(b). It is worthy to note that the asymmetrical rotor poles are positioned at the right side of the magnet poles when the counterclockwise rotation is assumed, to shift the maximum position of reluctance torque, thus to improve the utilization of the torque components for a higher total torque. Both models keep the same motor size, magnet amounts, rotor iron cores, and stator with windings. The main motor specifications are summarized in Table 1.

Fig. 2.

Design schematic diagram of the proposed model.

Fig. 3.

Torque segregation process using the FPM.

2.2. Design principle of the proposed motor

The cogging torque arises from the interaction between the rotor PMs and stator slotted iron structure, which can be minimized by the step skewing. The skewing angle between two adjacent steps is equal to $\begin{eqnarray}\displaystyle {\theta}_{skewing}={\displaystyle \frac{{\pi}\cdot HCF(2p,Q)}{npQ}} & & \displaystyle\end{eqnarray}$ (1) where n is the number of skewing steps, p is the number of magnet pole pairs, Q is the number of stator slots, and HCF is a function of the highest common factor.

To prevent the torque performance from severe degrading, the skewing is established within one magnet pole pitch by the constraint as $\begin{eqnarray}\displaystyle n{\theta}_{skewing}+{\theta}_{m}\leq {\theta}_{pm} & & \displaystyle\end{eqnarray}$ (2) where θ_pm is the angular spacing of the magnet pole pitch and θ_m is the angular spacing of two adjacent magnets, which are illustrated in Fig. 2(a).

In the d − q coordinates, the d_e-axis and q_e-axis of the proposed model can be determined based on the equivalent magnet pole and salient pole as shown in Fig. 2(b) and 2(c), and the electromagnetic torque can be obtained from the d − q rotating reference frame briefly expressed as $\begin{eqnarray}\displaystyle T=T_{mag}+T_{rel}={\displaystyle \frac{3p}{2}}\left[{\lambda}_{pm}I_{a}\cos {\beta}+{\displaystyle \frac{1}{2}}(L_{de}-L_{qe})I_{a}^{2}\sin 2({\beta}+{\beta}_{s})\right] & & \displaystyle\end{eqnarray}$ (3) where T_mag and T_relare the magnetic and reluctance torques, 𝜆_pm is the magnet flux linkage, I_a is the phase current, L_de and L_qe are the inductances of two axes, 𝛽 is the current angle, and 𝛽_s is the shift angle due to the asymmetrical effects.

3. Characteristics analysis by the FEM

3.1. Analysis approach

Due to the non-symmetrical structure of the proposed model, the 3-D FEM is utilized to analyze the motor characteristics for the better accuracy results. Furthermore, to reveal the contribution of the proposed model, the frozen permeability method (FPM) is utilized to provide visible insights into the separation of both the magnetic and reluctance torques in (5) [17,18]. The torque segregation process using the FPM with the aid of the FEM is shown in Fig. 3. Firstly, a no-load analysis is carried out and the rotor position and current phase angle are initialized based on the analysis results for the back EMF. Secondly, the total electromagnetic torque is obtained with all excitations. Then the PMs are removed and the reluctance torque is determined. The magnetic torque is finally obtained by subtracting the reluctance torque from the total torque.

Fig. 4.

Comparison of back EMFs.

Fig. 5.

Harmonics analysis of the back EMFs.

Fig. 6.

Comparison of cogging torques.

Table 2

FEM analysis results

Item	Unit	Basic model	Proposed model
Back EMF	V	58.9	52.3
THD of back EMF	%	22.8	4.1
Cogging torque	Nm	0.069	0.014
Torque (Average)	Nm	0.55	0.55
Magnetic torque^∗	Nm	0.44/0.48	0.42/0.44
Reluctance torque^∗	Nm	0.11/0.16	0.13/0.14
Torque ripple	%	67.3	30.5

^∗a/b is defined as the utilization factor (UF), and a is the utilized average torque value that contributes to the total average torque, while b is the maximum average torque value of torque components.

3.2. Back EMF and cogging torque

The comparison of back EMFs in phase are shown in Fig. 4. Figure 5 shows the corresponding harmonics analysis by the fast Fourier transform (FFT). It is found that the proposed model by the improved magnet skewing still degrades the back EMF by 11.2% when compares to the basic model. However, it is effective to minimize the harmonics of back EMF, which shows that it contains 82.0% less harmonics than the basic model as listed in Table 2, wherein the total harmonic distortions (THDs) of the back EMF is calculated by $\begin{eqnarray}\displaystyle THD=\sqrt{\displaystyle \mathop{\sum }_{i=2}^{\infty }E_{i}^{2}}/E_{1} & & \displaystyle\end{eqnarray}$ (4) where E₁ is the fundamental amplitude of back EMF, and E_i is the harmonic component.

Figure 6 shows the comparison of cogging torques. The peak-to-peak value of cogging torque in the proposed model is 0.014 Nm, which is reduced by 79.7% when compared with that of the basic model, as listed in Table 2.

Fig. 7.

Torque characteristics. (a) Basic model; (b) Proposed model.

Fig. 8.

Comparison of magnetic torques.

Fig. 9.

Comparison of electromagnetic torques.

Fig. 10.

Harmonics analysis of electromagnetic torques.

3.3. Torque characteristics

The torque characteristics of both models with respect to current phase angles are displayed in Fig. 7, wherein the average torque values are obtained by feeding the stator windings with sinusoidal current excitations by 3 Arms/mm². To evaluate the contribution of the proposed model, a utilization factor (UF) is defined as the ratio of the utilized average torque component and its corresponding peak average torque component, which is expressed as $\begin{eqnarray}\displaystyle UF_{mag}={\displaystyle \frac{T_{u,mag}}{T_{pk,mag}}};\quad UF_{rel}={\displaystyle \frac{T_{u,rel}}{T_{pk,rel}}}; & & \displaystyle\end{eqnarray}$ (5) where T_{u, mag} and T_{u, rel} are average values of the utilized magnetic torque and reluctance torque which contribute to the maximum total average torque, T_{pk, mag} and T_{pk, rel} are the peak average values of each torque component.

The results show that the magnetic toques of both models obtain the maximum values at 0° with the UFs of 91.7% and 95.5%, respectively. The reluctance torque of the basic model gets the maximum value at 45° with the UF of 68.8%, whereas in the proposed model, the reluctance torque obtains the maximum value at 30° with a UF of 92.9%. Figure 8 and Fig. 9 compare the transient analysis results of the magnetic torque and total electromagnetic torque, which show that the torque ripple of the proposed model is significantly minimized. The torque ripple of the proposed model is reduced by 54.7%, while maintaining the same average torque as the basic model as listed in Table 2. Figure 10 shows the harmonics analysis of electromagnetic torques, which indicates that the dominant 6th, 12th, and 18th harmonics are highly reduced in the proposed model which is in accord with the harmonics reduction of back EMFs.

4. Conclusion

This paper has presented a novel design strategy for SIPM motors to suppress torque pulsations and maintain high output torque by integrating the magnet skewing and asymmetrical rotor configurations.

The design principle was illustrated in detail, and the motor characteristics ware analyzed by comparing to a conventional SIPM motor with the aid of the finite element method. As a result, the proposed motor highly reduced the cogging torque by 79.7% and torque ripple by 54.7% without torque degradation when compared to the conventional motor.

Footnotes

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China, under Grant 51707107 and 51737008, in part by the Young Scholars Program of Shandong University, China, under Grant 2018WLJH29, in part by the projects funded by the China Postdoctoral Science Foundation, under Grant 2017M612269 and 2018T110688, and in part by the Youth Talent Support Program of Chinese Society for Electrical Engineering, under Grant JLB-2019-113.

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