A novel method to predict the influence of rotor structures on the core loss of permanent magnet synchronous machines

Abstract

Permanent magnet synchronous machines (PMSMs) are widely used owing to high power density, high efficiency, etc. Core losses account for a significant component of the total loss in PMSMs beside winding losses. Therefore, it is necessary to consider core losses when designing PMSMs according to actual research applications. In this paper, taking four typical rotor structures (surface-mounted, embedded, “—” shape, “V” shape) as examples, an analysis method is proposed to predict the influence of different rotor structures on core loss of PMSMs. In the case of the same stator and winding structures, due to the influence of the rotor structure on the magnetic circuit, the corresponding variation law of the magnetic field in the stator core is studied. This method analyzes the radial and tangential components of magnetic flux density vector of the 4 representative points (stator tooth tip, middle tooth and yoke part), and then evaluates the entire core loss through finite element analysis results. In order to verify the method, a prototype was manufactured. The experimental results show good performance of the proposed method of this paper. It provides reference for selecting the appropriate rotor structure and designing the corresponding PMSM according to different specification.

Keywords

Permanent magnet synchronous machines rotor structure core loss magnetic field distribution magnetic flux density

1. Introduction

In recent years, with the continuous improvement of the magnetic properties and high temperature resistance of permanent magnet materials, PMSMs with different rotor topologies have emerged in endlessly. For surface-mounted PMSMs, the core loss is reduced mainly by optimizing the design of the permanent magnet, the size of the slot, and changing the number of pole pairs.

For the “V” shape interior PMSMs, [1] introduced a simplified concentrated parameter magnetic circuit model method to calculate the core loss by areas. A method is proposed to that takes into account the pole arc angle and significantly reduce harmonics, magnetomotive force and core loss in [2]. Ref. [3] introduced an improved core loss calculation method of interior PMSMs. According to the armature reaction theory, the magnetic flux density distribution of air gap, stator teeth and yoke was analyzed. The eddy current loss of the stator teeth caused by the no-load air gap magnetic flux density and the armature reaction air gap magnetic flux density also considers the influence of the pole arc coefficient and the number of slots per pole per phase on the loss. Ref. [6] introduced the influence of harmonics on the core loss of stator teeth and yoke under the field weakening control of an interior high-speed PMSM. Ref. [7] introduced the analytical calculation method of the core loss of the stator teeth and yoke under the open circuit and short circuit conditions of the multilayer interior distributed winding permanent magnet motor. Ref. [8] introduced the influence of magnetomotive force harmonics on the performance of the motor during high-speed field weakening control in the multi-layer interior PMSM design with a wide constant power speed range. The number of stator slots and the equivalent number of rotor slots can reduce the core significant influence of losses and torque ripple.

In this paper, according to the prototype design specification in actual scientific research projects, four different rotor structures (surface-mounted, embedded, “—” shape, “V” shape) PMSM stator core variation law have been studied. And through finite element calculation to compare the core loss of each machine running under rated load conditions. Finally, the accuracy of the finite element calculation is verified through the experiment of the prototype.

2. Motor design specification

The motor design specification is shown in Table 1.

Table 1
The main parameters of 370 kW PMSM

Parameter Value Parameter Value

Rated power/kW 370 Rated speed/rpm 3185

Maximum power/kW 550 Maximum speed/rpm 6000

Rated torque/Nm 1110 Rated AC voltage/V 440

Outer diameter of stator/mm 482 Silicon steel sheet B20AT1500

Insulation class H Cooling system Water

Parameter	Value	Parameter	Value
Rated power/kW	370	Rated speed/rpm	3185
Maximum power/kW	550	Maximum speed/rpm	6000
Rated torque/Nm	1110	Rated AC voltage/V	440
Outer diameter of stator/mm	482	Silicon steel sheet	B20AT1500
Insulation class	H	Cooling system	Water

Fig. 1.

Magnetic field distribution of four types of PMSMs with different rotor structures under rated load.

Four different stator structures are proposed, all of which use 72-slot 12-pole double-stacked windings. Due to the harsh operating conditions of the motor, the rotor uses samarium-cobalt permanent magnets. The thickness and amounts of permanent magnets used in the four schemes are also the same. When the motor is working at rated load (speed 3185 rpm, torque 1110 Nm, AC voltage 440 V), the stator magnetic field and core loss results of the four rotor structures are compared and analyzed.

3. Core loss analytical calculation method

Generally, the core loss under load conditions can be decomposed into the hysteresis loss component Ph and the eddy current loss component Pe, where the eddy current loss can be expressed in the time domain form [3], namely $\begin{eqnarray}\displaystyle P_{t}=P_{h}+P_{e}=k_{h}fB_{\max }^{2}+{\displaystyle \frac{1}{2{\pi}^{2}}}k_{e}{\displaystyle \frac{1}{T}}\int _{0}^{T}\left(\displaystyle \mathop{\sum }_{n=1,3,5,\ldots }^{\infty }{\displaystyle \frac{\partial B({\omega}t)}{\partial t}}\right)^{2}dt & & \displaystyle\end{eqnarray}$ (1) where, k _h and k _e are respectively the hysteresis loss coefficient and eddy current loss coefficient determined by the characteristics of soft magnetic materials.

Fig. 2.

Four magnetic flux density calculation points of the stator core of the PMSM.

Fig. 3.

Magnetic flux density of four points of four PMSMs with different rotor structures varies with rotor position and the cloud diagram.

Fig. 4.

Elliptic magnetic flux density diagrams of point A of four PMSMs with different rotor structures.

Fig. 5.

Elliptic magnetic flux density diagrams of point B of four PMSMs with different rotor structures.

Fig. 6.

Elliptic magnetic flux density diagrams of point C of four PMSMs with different rotor structures.

Fig. 7.

Elliptic magnetic flux density diagrams of point D of four PMSMs with different rotor structures.

Fig. 8.

The amplitude of each harmonic component at point B of four PMSMs with different rotor structures.

Fig. 9.

Core loss distribution cloud diagram of four PMSMs with different rotor structures.

On the basis of obtaining the magnetic flux density of each part of the motor, the core loss of the stator teeth and yoke can be expressed as $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}\displaystyle P_{t\_e}={\displaystyle \frac{1}{2{\pi}^{2}}}k_{e}{\displaystyle \frac{1}{T}}\int _{0}^{T}\left(\mathop{\sum }_{n=1,3,5,\ldots }^{\infty }{\displaystyle \frac{\partial B_{n,t}({\omega}t)}{\partial t}}\right)^{2}dt\\ \displaystyle P_{t\_h}=k_{h}fB_{t\_\max }^{2}\\ \displaystyle P_{y\_e}={\displaystyle \frac{1}{2{\pi}^{2}}}k_{e}\frac{1}{T}\displaystyle \int _{0}^{T}\left(\mathop{\sum }_{n=1,3,5,\ldots }^{\infty }{\displaystyle \frac{\partial B_{n,y}({\omega}t)}{\partial t}}\right)^{2}dt\\ \displaystyle P_{y\_h}=k_{h}fB_{y\_\max }^{2}.\end{array}\right. & & \displaystyle\end{eqnarray}$ (2)

Therefore, the stator core loss can be obtained by adding the tooth core loss and the yoke core loss [4,5].

4. Magnetic field analysis of stator core

This paper adopts the method of calculating the magnetic field of different rotor positions under the whole electric cycle to analyze the magnetic field of four rotor structures. When the rotor rotates, the waveforms of radial and tangential components of magnetic flux density vector of the typical position inside the iron core are analyzed. Fourier analysis is performed on the magnetic flux density to obtain the amplitude of each harmonic component of the magnetic flux density. So, in the core loss calculation, the actual magnetic field changes of different parts can be considered. Considering the periodic conditions of a 12-pole 72-slot motor, the time-stepping finite element method is used to analyze the magnetic field under one pole [9–13].

The magnetic circuit of a PMSM is composed of permanent magnets, air gaps and cores. In a PMSM, the permanent magnet provides magnetic flux to the outer magnetic circuit, and the majority of the magnetic flux is the basis of the electromechanical energy conversion. There is also a part that does not form a leakage field with the turns of the armature winding. Figure 1 shows the magnetic field distribution of the four rotor topologies at rated load.

Table 2
Losses of four types of PMSMs

Losses (kW) Surface-mounted Embedded “—” shape “V” shape

Core loss 1.6202 1.7745 1.7780 1.5833

Losses (kW)	Surface-mounted	Embedded	“—” shape	“V” shape
Core loss	1.6202	1.7745	1.7780	1.5833

Fig. 10.

Test bench and controller.

Fig. 11.

Comparison of finite element method, analytical calculation method and experimental results.

In PMSM, the distribution of the leakage field is very complicated [14–17]. For surface-mounted PMSMs, most of the leakage magnetic circuit is composed of air. The magnetic permeability of air is small and the magnetic resistance is large. The influence of the ferromagnetic part is negligible. For embedded PMSMs, there is a small amount of magnetic flux leakage on the rotor core, and the magnetic field distribution is basically the same as that of the surface mount type. For the “—” shape interior PMSMs, a magnetic isolation bridge is used to isolate the magnetic field. A small part of the core of the rotor permanent magnet slot has a small amount of magnetic leakage, and the magnetic field distribution is slightly different from that of the surface mount type and the embedded type. As for the “V” type interior PMSMs, the permanent magnets are placed in sections within the core. Even if a magnetic isolation bridge is used for magnetic isolation, the magnetic flux leakage is still relatively large, and the magnetic leakage coefficient σ is relatively large. Therefore, for permanent magnet motors with different rotor structures, the magnetic field changes in the stator core are different [18–21].

Points at the same position of the four motor schemes are taken, and the radial and tangential components of the magnetic flux density vector of the corresponding split unit of the stator core are calculated. Take the points A and B at the top of the tooth, take the point C at the middle of the tooth, and take the point D at the yoke. The specific positions of the points are shown in Fig. 2.

Figure 3 shows the magnetic flux density calculation results of motors with different rotor structures at points A, B, C, and D. Figure 4 shows the elliptical magnetic field at point A on the tooth tip. Figure 5 shows the elliptical magnetic field at point B of the tooth tip. Figure 6 shows the elliptical magnetic field at point C of the tooth. Figure 7 shows the elliptical magnetic field at point D of the yoke.

It can be seen from Figs 3–7 that the change of magnetic flux density is non-sinusoidal regardless of the stator tooth tip, middle tooth, or yoke. Therefore, the influence of the rotating magnetic field on the motor stator loss must be considered when calculating the loss. Especially in the tooth tip area where points A and B are located, the rotating magnetic field occupies a large proportion, and the harmonic magnetic field is closed at the tooth tip. At point D of the stator yoke, the magnetic close component is significantly larger than the radial component, and a nearly elliptical rotating magnetic field is formed. Only at point C in the middle of the stator teeth, the radial component of the magnetic flux density is much larger than the tangential component, forming a nearly sine wave magnetic field, which can be considered as a pure alternating magnetic field.

For PMSMs with four rotor structures with the same stator and winding structure, the magnetic flux density changes at the same position still have certain similarities, and the difference is mainly due to the influence of magnetic flux leakage. It can be seen from the magnetic flux density distribution cloud chart that the magnetic flux leakage at the rotor core of the —-shaped interior and V-shaped interior motors is quite obvious.

Fourier analysis is performed on the magnetic flux density radial component Br and tangential component Bt of the stator A, B, C, and D of the four rotor structure motors by the harmonic analysis method. Only the analysis results of top B points are listed here, as shown in Fig. 8. The core loss at point B in the motor is caused by the odd harmonics in the magnetic flux density. Among them, the surface mount type is more affected by the 3rd harmonic, the “—” shape interior type is more affected by the 3rd and 5th harmonics, and the “V” shape interior type is more affected by the 3rd and 5th harmonics. The 5th and 7th harmonics have a greater impact, while the embedded ones are more affected by the 3rd, 5th, 7th, and 9th harmonics.

5. Comparative analysis of core loss calculation results

On the basis of magnetic field analysis, the loss parameters are obtained by fitting the loss data of silicon steel sheets at different frequencies, and the loss of the entire core is estimated. The core loss distribution cloud chart is shown in Fig. 9.

The magnetic flux density of the yoke of the four motors is significantly smaller than that of the teeth, and the core loss of the stator is also smaller than that of the teeth. It can be clearly seen from Fig. 9 that the stator core loss is unevenly distributed, and the location of the maximum point of motor loss for different rotor structures is different. For surface mount motors, the loss distribution of the entire stator teeth is relatively uniform. For “—” shape interior PMSM, the loss at the top of the tooth is large, and the loss at the root of the tooth is small. For “V” shape interior PMSM, the core loss is larger only at the notch of the tooth top edge, and the loss in the other parts is more uniform than other motors. For the embedded motor, the loss of the entire tooth is obviously larger than the other three motors. In the small figure on the left of 10(b) obtained by changing the loss range, it can be clearly seen that the maximum core loss appears at the root of the tooth. The stator core losses of the four motors are shown in Table 2.

Taking the loss of “—” shape interior motor as a benchmark, the difference in total loss is: surface mount −12.82%, embedded −16.69%, and “V” shape interior 7.98%. Four motors have the same amount of stator core, rotor permanent magnets, and copper. When the rated speed and output torque and power are the same, the total loss is somewhat different, and due to the difference in rotor structure and magnetic circuit, the loss distribution of the four motors Significantly different.

Compared with surface mount motors, embedded motors have larger magnetic flux density waveform distortion, and larger harmonic losses lead to increased stator core losses; “—” shape interior PMSM is affected by the 3rd and 5th harmonics, which leads to increased stator core losses ; “V” shape interior PMSM has more magnetic leakage, so the total magnetic flux is significantly smaller than the other three motors, and the stator core loss is relatively small.

6. Verification

Considering the design specifications, manufacturing difficulty, economic cost and other factors, the “—” shape interior PMSM was finally manufactured in this project [22,23]. The experimental bench and controller are shown in Fig. 10.

The experimental verification method is as follows:

Increase the motor speed to 6000 r/min through the inverter;

The inverter stops working, so that the motor will naturally slow down to a standstill; record the relationship between time and speed. The motor speed is 6000 r/min when it is zero;

Obtain the power loss at different moments through the deceleration curve of the motor.

In order to verify the accuracy of the analysis of the influence of different rotor structures in this paper, the finite element calculation results, the calculation results of formula (1), and the experimental results of the core loss of the prototype at different speeds are shown in Fig. 11.

It can be seen from Fig. 11 that the finite element calculation results, analytical calculation results and experimental results are consistent within the acceptable error range. The analytical calculation result is smallest, because analytical calculation is based on some mathematical assumptions when dealing with boundary conditions, which cannot be achieved in practice. The experimental result is the largest. It’s because the power loss of the motor measured by the experimental method includes the mechanical loss of the motor (bearing loss, frictional and windage Loss). And the higher the speed, the greater the mechanical loss. Therefore, the method proposed in this paper is effective and can be used to predict the core loss of the motor under each rotor structure.

7. Conclusion

For motors with different rotor structures (surface-mounted, embedded, “—” shape, “V” shape), in the case of the same stator and winding, due to the influence of the rotor structure on the magnetic circuit, the magnetic field variation law in the stator core is not the same. Through the analysis of the radial and tangential components of magnetic flux density vector of the stator tooth tip, tooth part and yoke part, it can be seen that compared with the surface mount motor, the magnetic flux density waveform distortion of the embedded motor is larger; “—” shape interior PMSM suffers 3 times, The 5th harmonic has a greater impact; the “V” shape interior PMSM has more magnetic leakage, so the total magnetic flux is significantly smaller than the other three motors. The embedded and “—” shape interior PMSM have higher stator core loss, and the loss distribution of motors with different rotor structures is very different. The rotor structure should be reasonably selected according to the application and the heat dissipation of the stator and rotor of the motor.

Footnotes

Acknowledgements

This research was financially supported by the National Natural Science Foundation of China (Grant No. 51677005), the National Key Research and Development Program (No. 2017YFB0102402) and China Scholarship Council (No. 201906030192).

References

Jagadeesh

Jahns

T.M.

and Ayman

E.L.-R.

, Core Loss Prediction Using Magnetic Circuit Model for Fractional-Slot Concentrated-Winding Interior Permanent Magnet Machines, IEEE, 2010, pp. 1004–1011.

Chai

Liang

and Pei

, Analytical method for iron losses reduction in interior permanent magnet synchronous motor, IEEE Transactions on Magnetics 51(11) (2015), 1–4.

Tao

and Xuhui

, Stator Teeth Eddy-Current Loss Analysis of Interior Permanent Magnet Machine During Flux Weakening, IEEE, 2013, pp. 1226–1230.

Fan

and Wen

, Armature-reaction magnetic field analysis for interior permanent magnet motor based on winding function theory, IEEE Transactions on Magnetics 49(3) (2013), 1193–1201.

Fan

and Wen

, An Improved Model of Estimating Iron Loss for Interior Permanent Magnet Synchronous Machine, IEEE, 2013, pp. 1–5.

Kuttler

Benkara

and Friedrich

, Impact of the Field Weakening on the Iron Losses in the Stator of an Internal Permanent Magnet Synchronous Machine, IEEE, 2014, pp. 4188–4195.

Tang

and Wen S

, Analysis of Stator Iron Loss in Interior PM Machines Under Ppen and Short-Circuit Conditions, IEEE, 2013, pp. 1227–1234.

Gianmario

Paolo

and Alfredo

, Core losses and torque ripple in IPM machines: Dedicated modeling and design tradeoff, IEEE Transactions on Industry Applications 46(6) (2010), 2381–2391.

Tariq

Nino-Baron

and Strangas

, Iron and magnet losses and torque calculation of interior permanent magnet synchronous machines using magnetic equivalent circuit, IEEE Transactions on Magnetics 46(12) (2010), 4073–4080.

10.

Han

S.H.

Jahns

and Soong

, A magnetic circuit model for an IPM synchronous machine incorporating moving air gap and cross-coupled saturation effects, in: Proc of IEEE International Electric Machines & Drives Conference, 2007, pp. 21–26.

11.

Carter

F.W.

, The magnetic field of the dynamo-electric machine, Electrical Engineers Journal of the Institution of 64(359) (1926), 1115–1138.

12.

Zhu

Z.Q.

and Howe

, Instantaneous magnetic field distribution in brushless permanent magnet dc motors. III. Effect of stator slotting, IEEE Transactions on Magnetics 29(1) (1993), 143–151.

13.

Zhu

Z.Q.

and Howe

, Instantaneous magnetic field distribution in permanent magnet brushless dc motors. IV. Magnetic field on load, IEEE Transactions on Magnetics 29(1) (1993), 152–158.

14.

Boughrara

Ibtiouen

Zarko

and Touhami

, Magnetic field analysis of external rotor permanent magnet synchronous motors using conformal mapping, IEEE Transactions on Magnetics 46(9) (2010), 3684–3693.

15.

Boughrara

Zarko

Ibtiouen

and Touhami

, Magnetic field analysis of inset and surface-mounted permanent magnet synchronous motors using Schwarz-Christoffel transformation, IEEE Transactions on Magnetics 45(8) (2009), 3166–3178.

16.

Alam

F.R.

and Abbaszadeh

, Magnetic field analysis in eccentric surface-mounted permanent magnet motors using an improved conformal mapping method, IEEE Transactions on Energy Conversion 31(1) (2016), 333–344.

17.

Hanic

Zarko

and Hanic

, A novel method for no-load magnetic field analysis of saturated surface permanent magnet machines using conformal mapping and magnetic equivalent circuits, IEEE Transactions on Energy Conversion 31(2) (2016), 740–749.

18.

Hafner

Franck

and Hameyer

, Accounting for saturation in conformal mapping modeling of a permanent magnet synchronous machine, COMPEL: The International Journal of Computation & Mathematics in Electrical and Electronic Engineering 30(3) (2011), 916–928.

19.

Moreira

and Lipo

T.A.

, Modeling of saturated AC machines including air gap flux harmonic components, IEEE Transactions on Industry Applications 28(2) (1992), 343–349.

20.

Ojaghi

and Nasiri

, Modeling eccentric squirrel-cage induction motors with slotting effect and saturable teeth reluctances, IEEE Transactions on Energy Conversion 29(3) (2014), 619–627.

21.

Feng

and Zhang

, A novel method for the core loss calculation in the surface-mounted permanent magnet synchronous machine, International Journal of Applied Electromagnetics and Mechanics 56 (2018), 427–444.

22.

Pluta

, Directional properties of loss components in electrical steel sheets, International Journal of Applied Electromagnetics & Mechanics 44(3) (2014), 379–385.

23.

Cvetkovski

and Petkovska

, Multi-objective approach of design optimisation of axial flux permanent magnet motor, International Journal of Applied Electromagnetics & Mechanics 51(1) (2016), 115–123.

A novel method to predict the influence of rotor structures on the core loss of permanent magnet synchronous machines

Abstract

Keywords

1. Introduction

2. Motor design specification

Table 2 Losses of four types of PMSMs Losses (kW) Surface-mounted Embedded “—” shape “V” shape Core loss 1.6202 1.7745 1.7780 1.5833

6. Verification

7. Conclusion

Footnotes

Acknowledgements

References

Table 2
Losses of four types of PMSMs

Losses (kW) Surface-mounted Embedded “—” shape “V” shape

Core loss 1.6202 1.7745 1.7780 1.5833