A Novel Interior Permanent Magnet Machine with Magnet Axis Shifted Effect for Electric Vehicle Applications

Abstract

This paper proposes a novel interior permanent magnet (IPM) machine with asymmetrical PM configuration. Different from the traditional IPM counterparts, the proposed machine can perform a magnet axis shifted (MAS) effect. The magnet axis is shifted towards the reluctance axis so that a higher resultant torque capability can be obtained. Firstly, the configuration and the basic principle of the proposed machine are described. The design parameters are optimized to improve the torque capability, and the effect of the PM asymmetry ratio on the torque performance is then evaluated in detail. In addition, the major electromagnetic characteristics of the optimized machine are investigated and compared with those of the Prius 2010 IPM machine by finite element method (FEM). The results demonstrate that the proposed asymmetrical PM configuration can achieve the torque improvement due to the MAS effect.

1. Introduction

Due to high torque density and high efficiency, permanent magnet (PM) machines have gained extensive attention recently. Amongst the conventional PM machines, interior PM (IPM) machines are regarded as popular choices for electric vehicles [1,2]. In order to improve the reluctance torque (RT) component, PM-assisted synchronous reluctance machines (PM-SynRMs) are extensively investigated in [3,4,5]. However, the conventional IPM machines suffer from a compromised utilization ratio of magnet torque (MT) and RT components, whose optimal current angles differ by 45 electrical degrees theoretically. In order to deal with this issue, dual rotor [6], hybrid rotor [7,8], and asymmetrical PM-SynRMs [4,9] were developed in recent years. However, the former two machines have relatively complicated structure and the latter one suffers from significant flux leakage as well as sophisticated magnetic flux paths.

The purpose of this paper is to propose a magnet axis shifted (MAS) IPM (MAS-IPM) machine with an asymmetrical PM arrangement, which aims to improve the torque component utilization ratio, and hence the torque density. In this paper, the configuration and the operating principle of the proposed machine are described. The effects of the PM asymmetry ratio on the torque performance are evaluated, and the design parameters are optimized to improve the torque capability. In order to validate the MAS effect of the proposed asymmetrical PM arrangement, the major electromagnetic characteristics of the optimal MAS-IPM machine are analyzed and compared with those of the Prius 2010 IPM machine (Toyota Motor Corporation, Tokyo, Japan) by finite element method (FEM).

2. Machine Configuration and Basic Principle

The configurations of the Prius 2010 IPM machine and the proposed MAS-IPM machine are shown in Figure 1a,b, respectively. For a fair comparison, the two machines share the same stator structure, active stack length, air gap length, current density and PM usages, as shown in

Table 1. Key common design parameters of Prius 2010 IPM and Mas-IPM machines.

Items	Parameters
Stator outer diameter (mm)	264
Air gap length (mm)	0.75
Rotor outer diameter (mm)	160.4
Rotor inner diameter (mm)	100
Active stack length (mm)	50.8
Peak current (A)	246
Rated speed (rpm)	3000
PM volume per pole (mm3)	12,802

. The main feature of the MAS-IPM machine refers to an asymmetrical “▽”-shaped PM rotor structure, in which the lengths of the second-layer two PMs are unequal to achieve the MAS effect.

For the conventional IPM machine, the optimal current angles β_PM and β_R when the MT and RT components reach their peak values are different, the difference of which is expressed as

$${\gamma }_s={\beta }_{PM}-{\beta }_R$$

(1)

In the traditional IPM machine with a symmetrical rotor configuration, as we know, the current angle difference γ_s is theoretically an electrical angle of 45. On the other hand, in the proposed machine, since the magnet axis is shifted towards the reluctance axis due to the asymmetrical PM arrangement, the difference of the current angles γ_s can be significantly reduced, which can further improve the torque capability.

The no-load magnetic fields of the two machines for comparison are plotted in Figure 2. It can be seen that the magnet d-axis is shifted by an angle in the proposed MAS-IPM machine, while the reluctance d-axis remains unchanged. It means that the magnet and reluctance axes become closer compared with the Prius 2010 machine. As a result, the difference of the current angles γ_s of the proposed machine can be reduced and the corresponding total torque is improved, confirming the feasibility of the MAS effect.

3. Optimization of The Proposed MAS-IPM Machine

In order to maximize the torque capability by effectively employing the proposed MAS effect, some design variables are selected to be optimized, as shown in Figure 3. The peak current 246 A was used for obtaining the maximum torque, which is accordance with that of Prius 2010 machine. A coefficient α is defined as l_pm1/l_pm2 to describe the asymmetry level of PM1 and PM2, which is associated with the MAS effect. The design global optimization is performed by a multi-objective genetic algorithm with the constraints of the overall sizing, e.g., stator outer diameter and stack length, as shown in Table 1. The optimization target is to maximize the average torque and minimize the torque ripple, the corresponding weight factors of which are 1 and 0.5, respectively. In addition, the major design parameters of the optimized IPM machines and their variation ranges are presented in

Table 2. Definitions and variation range of the design parameters of proposed MAS-IPM machine.

Items	Descriptions	The MAS-IPM Machine
h1 (mm)	thickness of PM1	3.5~4.5
h2 (mm)	thickness of PM3	2.5~3.5
lpm1 (mm)	length of PM1	7~21
lpm2 (mm)	length of PM2	20~25
lpm3 (mm)	length of PM3	25~35
α	lpm1/lpm2 (the asymmetry ratio)	0.3~0.9

.

For illustrating the definition of the torque component utilization ratio, the diagram for the torque separation of a conventional IPM machine is shown in Figure 4. The torque component utilization ratios of the MT and RT u_pm and u_r are defined as follows

$$u_{pm}=\frac{{MT}_{comp}}{{MT}_{max}}$$

(2)

$$u_r=\frac{R{T}_{comp}}{R{T}_{max}}$$

(3)

where MT_comp and RT_comp are MT and RT when the total torque reaches the peak value, and MT_max and RT_max denote their maximum values of MT and RT.

A preliminary model is obtained based on the global optimization. To better illustrate the influence of α on torque performance, the single parameter optimization is performed. The torque component utilization ratios of MT and RT as functions of different asymmetry coefficients α are presented in Figure 5. With the increment of α, the RT utilization ratio u_r is increasing proportionally until α reaches 0.8, where u_r reaches the peak value of 93.77%. At the same time, the MT utilization ratio u_pm decreases with the increase in α, which is attributed to the weakening of the MAS effect in that case. Nevertheless, Figure 6 shows the toque component variation with the asymmetry coefficient. It shows that the total torque and the MT component can be improved with the increment of α until it reaches 0.8. The improvement in the MT component can be explained by the increase in PM usage, despite u_pm decreasing. The RT component is almost invariant because the rotor steel lamination remains unchanged.

After the optimization, the optimal asymmetrical structure is confirmed. The optimized design parameters of the proposed MAS-IPM machine are obtained, i.e., h₁ = 3.9 mm, h₂ = 2.7 mm, l_pm1 = 18.4 mm, l_pm2 = 23 mm, l_pm3 = 33 mm, and α = 0.8.

4. Performance Comparison

4.1. No-Load Performance

The back-EMFs at rated speed of the two investigated machines are shown in Figure 7. It can be found that the root-mean-square (RMS) EMF of the proposed machine is 20.2% higher than that of the Prius machine. Meanwhile, it shows that the MAS-IPM machine exhibits better sinusoidal back-EMF than the conventional machine. The cogging torque waveforms are illustrated in Figure 8. It can be seen that the Prius 2010 machine exhibits higher cogging torque than the MAS-IPM machine. This is mainly attributed to lower THD of the back-EMF of the proposed MAS-IPM machine.

4.2. Torque Characteristics

The on-load torque characteristics of the Prius 2010 and the MAS-IPM machines are shown in Figure 9 and Figure 10. The torque separation results obtained by the frozen permeability method [10,11] are shown in Figure 9a,b, respectively. Due to the asymmetrical PM configuration, γ_s of the proposed MAS-IPM machine is reduced by 15 electrical degrees compared to the Prius IPM machine.

4.3. Torque/Power vs. Speed Curves

The field-weakening capability is a key characteristic for the traction machines for electric vehicles. The torque/power-speed curves are shown in Figure 11a,b, respectively. It demonstrates that the proposed machine can achieve higher torque and power capability over a whole speed range.

4.4. Iron Loss and Efficiency Maps

The loss in the machine mainly contains the iron and copper losses. The iron, hysteresis, eddy current, and copper losses can be calculated by

$$P_i=P_h+P_e$$

(4)

$$P_h=K_{h}f{B}_m^{\alpha }$$

(5)

$$P_e=K_e{f}^{\gamma }{B}_m^{\delta }$$

(6)

$$P_c=3R_a{I}_a^2$$

(7)

where P_i, P_h, P_e, and P_c are iron, hysteresis, eddy current, and copper losses, respectively; K_h and K_e are the coefficients of hysteresis and eddy current losses, respectively; f is the operating frequency of the machine; B_m is the flux density; α, γ, and δ are the coefficients of the empiric formula; R_a is the armature winding resistance; and I_a is the phase current RMS value.

The iron losses of the two machines are given in Figure 12. It can be observed that the two machines show similar iron losses when the speed is lower than 6000 rpm. Besides, due to lower THD of the back-EMF, the MAS-IPM machine shows lower iron loss under high speed range. The efficiency maps of the two machines are illustrated in Figure 13. The maximum efficiency of the MAS-IPM machine is 0.7% higher than that of the Prius 2010. It can be seen that the high efficiency over a wider operating region can be achieved in the MAS-IPM machine due to its lower iron loss. The related electromagnetic performances of the two machines are given in

Table 3. The electromagnetic performance of the two investigated machines.

Items	Prius 2010 Machine	MAS-IPM Machine
RMS back-EMF (V)	104.42	125.31
Rated torque (Nm)	255.44	262.27
Reluctance torque (Nm)	166.36	157.21
Magnet torque (Nm)	89.08	105.09
Peak cogging torque (Nm)	1.21	0.83
γs (elec. deg.)	45	30
Torque pulsation (%)	12.3	18.2
upm (%)	80.21	83.77
ur (%)	91.24	93.31
Maximum efficiency (%)	97.4	98.1

. As a whole, the MAS effect of the proposed asymmetrical PM configuration for the torque improvement is confirmed. Meanwhile, compared to the Prius IPM machine, the proposed machine exhibits higher RMS flux linkage, RMS back-EMF and lower cogging torque, as well as higher MT, RT utilization ratio, and operating efficiency.

5. Conclusions

A novel IPM machine with a MAS effect is proposed in this paper. Due to the asymmetrical PM configuration, the proposed machine benefits from the reduced γ_s, improving the MT and RT utilization ratios. Hence, the total torque can be further improved. Based on FEM, the design variables of the proposed MAS-IPM machine are optimized to maximize the torque capability by defining an asymmetry ratio. Afterwards, the electromagnetic characteristics of the proposed MAS-IPM machine are investigated and compared with those of the Prius 2010 machine. It can be found that the proposed machine shows higher RMS back-EMF, lower total harmonic distortions, and lower cogging torque. In addition, the MAS-IPM machine exhibits a higher peak torque, a higher high-speed power maintaining capability, as well as wider high efficiency operating regions. In summary, the results confirm the MAS effect of the proposed asymmetrical PM configuration due to its performance improvement. A prototype of the MAS-IPM machine will be manufactured and the test results will be reported in due course.