Design and Optimization of an Interior Permanent-Magnet Synchronous Motor for Aircraft Drive Application

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The results of this work can be included in the design stage of interior permanent-magnet synchronous motors for aircraft drive applications.

Abstract

The torque performance of the interior permanent-magnet synchronous motor (IPMSM) must be further improved to satisfy the growing demand of aircraft drive application. To this end, this article focuses on the design optimization of the IPMSM structure in the aircraft drive systems to improve the torque density and reduce the torque ripple. A special fractional-slot winding and ∇-type magnetic-pole rotor topology are proposed as the optimized IPMSM structure compared with the structure of an existing motor. The simulations of the original and optimized structures at different current values reveal the variance of the torque in the average and ripple, mechanical and external characteristics, efficiency and steady-state temperature. The performance of an optimized prototype is analyzed by experimental testing, and the results show that an optimized motor has a higher torque density and lower torque ripple than the original one at the same speed and rated power, but it also has a higher temperature rise. However, the temperature rise value is acceptable in the experimental testing condition, so the validity of the design optimization method for the proposed structure is verified.

1. Introduction

With the evolution of aerospace, the aircraft drive systems are expected to offer continuous improvements in safety and high efficiency while reducing noise and costs [1]. Nowadays, with respect to the electrical motor, which is the key component of the current aircraft drive system, higher reliability and a higher power and torque density and a lower torque ripple are the future trend of development with advanced power electronics and control strategies [2]. Electrical motors are needed to satisfy the special requirements of the aircraft applications, like low maintenance costs, high torque density and high reliability. Hence, the options of the electrical motors are restricted to induction [3], reluctance [4] and permanent-magnet synchronous motors (PMSMs) [5], especially the PMSM, which is characterized with high power and torque density and efficiency, high torque/weight ratios and improved reliability [6,7] and has great potential in aircraft application.

PMSMs with different winding arrangements and rotor pole structures will bring impacts on the overall performance of the machine. Two possible winding arrangements can be used in the PMSM: the integer slot and fractional slot. An integer-slot winding has a number of slots/poles/phases equal to N (N = 1, 2…), while a fractional-slot winding does not. It has been demonstrated that a fractional-slot concentrated winding can offer significant advantages compared with an integer-slot winding, such as a lower torque ripple [8]. Furthermore, the use of a fractional-slot winding increases the leakage inductance, thus reducing the cogging torque, and can increase the fault tolerance capability [9,10]. The mutual inductance and fault tolerance of the PMSM can be influenced by a single- or double-layer winding topology [11].

As for the rotor pole structure, the PMSM can be classified as a surface-mounted PMSM (SPMSM) [12,13] and an interior PMSM (IPMSM); the latter one provides higher per-unit inductances and thus field-weakening capability [14]. The rotor magnetic-pole topology of the IPMSM can be taken as the optimal design method, and the currently known topology types are the “conventional type”, “U-type”, “V-type”, etc. The comparisons of four different rotor topologies for a distributed winding IPMSM are analyzed and reveal that the “V-type” has the lowest magnet mass, the “$\overline{W}$-type” has the largest d, q inductances and a higher rated torque than the others and the “segmented type” has a wider range of constant power speed operations than the “conventional type” [15]. In general, the IPMSM used in electrified vehicles with a “conventional type” permanent-magnet rotor has great low-speed performance while having a poor capacity under flux-weakening control [16]. Considering both factors mentioned above and high efficiency in the overall driving range, the “V-type” is the better option [17,18]. The cross-magnetization effect can be significantly reduced by the “∇-type” rotor structure; thus, the $d$-axis inductance is decreased, which can increase the output torque under the overload flux-weakening control in comparison with the “V-type”. In high-speed and high-torque-density applications, the “∇-type” is the best design among the “V-type”, “2V-type” and “∇-type” [19]. The torque ripple can also be reduced by the “∇-type” IPMSM with an asymmetric spoke [20]. The performance of the micro IPMSM with a “conventional type” and “spoke type” has been investigated, and the results show that the “spoke type” has a better output torque, while the “conventional type” has a lower torque ripple [21]. Figure 1 shows the four different rotor magnetic-pole topologies.

The aim of this work is to improve the performance of the IPMSM including the power and torque density and reduce the torque ripple and noise based on an original “V-type” IPMSM. Therefore, an optimized structure is proposed from the aspects of the stator winding and rotor pole topology to satisfy those requirements. This paper compares the optimized structure with the original structure by means of the finite element method (FEM). According to the simulation results, the analysis of the no-load magnetic density distribution, electromagnetic force (EMF), cogging torques, high-speed stress, temperature rise, torque ripples and efficiency performance proves the feasibility of the optimized structure. In addition, the experimental test is carried out, and the results coincide exactly with the simulation analysis. This article is organized as follows. Section 2 presents the original machine details of the IPMSM and the structure optimization of the fractional-slot single-and-double-layer hybrid winding and “∇-type” rotor magnetic-pole topology. In Section 3, the performance comparison of the original and optimized structures is studied by the simulation. And then, the steady-state performance of a prototype IPMSM analyzed in the experimental test is shown in Section 4, which can verify the validity of proposed structure, and the conclusions are drawn in Section 5 finally.

2. Materials and Methods

The details of an original machine in the aircraft drive system are the materials for the optimization scheme. Based on these, the optimizations mainly focus on the winding arrangement and rotor magnetic-pole topology, and the performances of different optimization schemes are compared in this section.

2.1. Basic Structure of Original V-Type IPMSM and Motor Performance

A V-type IPMSM with the structure of the 48-slot stator with the 8-pole used in the aircraft drive system is shown in Figure 2.

The design parameters like the rated power, current, speed range and main dimensions of the motor are listed in

Table 1. Main design parameters and motor dimensions of V-type machine.

Design Parameters	Values
DC bus voltage	320 V
Rated power	30 kW
Maximum power	60 kW
Rated current	115 A
Maximum current	250 A
Rated speed	3000 rpm
Rated power factor	0.95
Maximum efficiency	≥96.7%
Maximum torque	200 N·m
Maximum speed	≥10,000 rpm
Stator outside diameter	180 mm
Stator inside diameter	118 mm
Rotor outside diameter	116.6 mm
Range of stacked iron core length	135–150 mm
Stator slots	48/36
Pole pairs	4

. The rated output power of the motor is 30 kW at 3000 rpm. The maximum efficiency of the motor needs to exceed 96.7%.

2.2. Optimization of the Stator Windings

In order to reduce the torque ripple and cogging torque of the motor, the optimized structure adopts a fractional slot, and the slot number equals to 36. The stator windings of 36 slots could not be designed to a single-layer winding; meanwhile, considering the purpose of the winding materials and cost savings, a single-and-double-layer hybrid winding is proposed for the optimization, instead of a double-layer stacked winding [22,23]. The single-and-double-layer hybrid winding is essentially a deformation of the double-layer winding. The hybrid winding is connected according to the shorter span, which has a good material-saving and energy-saving effect [24]. The double-layer stacked and hybrid winding arrangements are drawn in Figure 3.

The comparison of the structural parameters for the double-layer stacked winding and single-and-double-layer hybrid winding is listed in

Table 2. Comparison of double-layer and single-and-double-layer hybrid winding.

Winding Parameter	Double-Layer Winding	Hybrid Winding
Pole/slot	8/36	8/36
Number of slots per pole and phase	1.5	1.5
Number of slots for single layer	0	24
Number of slots for double layer	36	12
Average pitch (slot number)	4.0	3.667
Number of coils	36	24

. It can be seen that compared with the double-layered winding, the hybrid winding can effectively shorten the average pitch of the winding and furthermore save material usage of the end winding and reduce the number of coils per unit.

In particular, the single-and-double-layer hybrid winding has two different slot types, the single layer and double layer, to be determined. Assuming that the number of conductors per slot in the single layer slot is $N_1$, the number of conductors per slot in the double layer slot is $N_2$. Three optimization schemes for the number of turns have been obtained. The motor-related parameters of each scheme are calculated and compared as shown in

Table 3. Different winding turn schemes and calculation results.

Parameter	Scheme I	Scheme II *	Scheme III
$N_1$	17	18	19
$N_2$	18	16	14
Total number of turns per phase	312	312	312
Maximum slot fill rate	0.77	0.73	0.77
Average pitch	44.8 mm	45.3 mm	45.7 mm
Fundamental winding factor	0.944	0.948	0.953
Rated output torque	97.7 N·m	98.2 N·m	98.6 N·m
Efficiency	97.02%	97.03%	97.03%

* The optimization results of the stator winding adopted in this article is scheme II.

. It can be seen that as the proportion of single-layer turns $N_1$ increases, the fundamental winding coefficient of the motor increases, which is beneficial to obtaining a higher large output torque. However, at the same time, it follows that a larger average pitch of the winding can increase the amount of winding material and motor copper consumption. In addition, different single-and-double-layer turn assignments also have a significant impact on the coil space factor.

2.3. Optimization of the Rotor Magnetic-Pole Topology and Different Dimension Schemes

With the aim of improving the torque density and increasing the torque under the overload flux-weakening control, the optimized structure adopts the “∇-type” magnetic-pole rotor topology. Figure 4 draws the brief structure of the permanent magnets at each pole and gives the introduction to the dimension parameters. To reduce the production and manufacturing costs of the motor, the dimensions of the three permanent magnets at each pole are identical.

The rotor permanent magnet’s dimension and arrangement will have a significant impact on the cogging torque and torque ripple. The basic methods proposed for reducing the cogging torque are the adjustment of the magnet arc width relative to the pole pairs. The embedded depth, length and width of the three parts of the permanent magnets can be adjusted to reduce the torque ripple [25,26]. To save analysis and calculation time, the optimization of the rotor pole topology uses the Taguchi method [27,28] to calculate the structural parameters tagged in Figure 4. And for a better torque characteristic, the sensitivity-based optimization method is applied [29]. The optimization results of the ∇-type topology of three different dimension schemes are displayed in

Table 4. Comparison of different rotor structural parameters.

Parameter	Scheme I	Scheme II *	Scheme III
$O$	17 mm	18 mm	19 mm
$D_1$	3.5 mm	4.5 mm	5.5 mm
$D_2$	1.6 mm	2 mm	2.4 mm
$L_1$	16 mm	18 mm	20 mm
$L_2$	16 mm	18 mm	20 mm
$H$	2.5 mm	3 mm	3.5 mm
$W_1$	1.1 mm	1.3 mm	1.5 mm
$W_2$	0.8 mm	1 mm	1.2 mm
Cogging torque (peak-to-peak value)	4.3 N·m	2.9 N·m	1.4 N·m
Rated output torque (average value)	97.5 N·m	98.2 N·m	95.1 N·m
Torque ripple	9.07%	7.1%	8.6%

* The structural parameters adopted in this article are scheme II.

. Considering the cogging torque (because the cogging torque is generated by the interaction between the permanent magnet and the stator core and without a winding current, the average value is 0, so the comparison value is the peak-to-peak value), rated output torque and torque ripple, scheme II has a better comprehensive performance.

The comparisons between those schemes are based on the analysis of the motor’s overall performance, which includes the average torque, torque ripple, anti-demagnetization ability, mechanical stress and motor temperature rise. After that, considering the material quantity and production cost assessment, scheme II is determined as the optimal scheme.

3. Simulation Results and Analysis

The design method and theoretical development in the previous sections should be validated by the simulation and test analysis. A time-stepping finite element (FE) simulation analysis is used to model the IPMSM with the original and optimized structures. The motor performance under different speeds and operating conditions is simulated.

3.1. Results and Discussion: No-Load Magnetic Density Distribution and Electromagnetic Force (EMF)

It is necessary to analyze the no-load magnetic density distribution firstly, because the no-load air-gap magnetic density fundamental component amplitude can be seen as an elementary assessment index of the output torque capability. The no-load magnetic density distribution of the original and optimized structures and EMF are simulated at the rated speed of 3000 rpm. The simulation result of the magnetic field is symmetrical, and part of the motor nephogram of the no-load magnetic density distribution is shown in Figure 5.

In Figure 5, the saturation of the rotor bridges in both structures can be seen. But compared with the original structure, the magnetic density of the stator teeth and yokes of the optimized structure is higher.

Further, the harmonic analysis of the air-gap flux density distribution is carried out and reveals that the air-gap magnetic fields mainly comprise the components of four pole pairs. The fundamental components of the air-gap magnetic densities are 0.78 T and 0.94 T, respectively, as shown in Figure 6.

The EMF waveforms and harmonic components’ distribution for the two different structures are shown in Figure 7. The fundamental component values of the EMFs for the two structures are 108 V and 116 V, respectively, and the effective values are 76 V and 82 V; the optimized structure is the higher one. The total harmonic distortion (THD) contents of the EMF waveforms are calculated, and the original one is 12.3%, while the optimized one is 3.4%, and the corresponding waveforms are closer to the ideal sinusoidal waveform.

It can be seen from above that the optimized structure has a larger amplitude of the air-gap magnetic density and the EMFs fundamental component compared to the original structure, which can improve the output torque capability and torque density.

3.2. Results and Discussion: Torque Performance

After the no-load performance analysis, the average output performance of the two structures with different driving currents is simulated by adopting the control strategy of the maximum torque per ampere (MTPA) method. At the same time, the original motor is tested under the same current condition, and the results and the test data are compared in Figure 8.

And the test data curve trend is similar to the simulation curve trend, but slightly lower, which validates the rationality of the simulation model.

There are some mismatches between the simulation results and experiments in Figure 8. The average output torque of the simulation data and the test at the rated condition is around 89 N·m and 99 N·m, respectively. And the average output torque of the simulation data and the test with the limited condition is 196 N·m and 209 N·m, respectively. The difference is caused by the actual value and simulation results of the iron loss at high frequency. In the simulation, the power supply is the ideal sinusoidal wave. However, in the real test, the power supply comes from the converter, which brings higher harmonics and more iron loss. Further, due to the increase in the iron loss, the average output torque of the test is lower than the simulation data.

The torque–current phase angle characteristic curves of the two structures with the rated current (115 A) fed are shown in Figure 9. The motor of the optimized structure achieved maximum torque at 34°, while the motor of the original structure achieved maximum torque at 35°. It should be noted that the simulation results are slightly higher than the actual value because the mechanical loss is not completely considered.

Focusing on the no-load condition, the cogging torques of the two structures are compared. The waveforms of the cogging torque in the no-load condition at a speed of 3000 rpm show that the peak–peak torque of the optimized structure is 2.9 N·m, and the original is 3.1 N·m. Figure 10 and

Table 5. Cogging torques with or without skewed slot of both structures.

Parameter	Skewed Angle	The Original	The Optimized
Cogging torque (peak-to-peak value)	0°	3.1 N·m	2.9 N·m
	7.5°	0.9 N·m	0.8 N·m

indicate that the cogging torques are greatly reduced in both structures if the stator skewed-slot angle is changed from 0° to 7.5°. The peak–peak cogging torque value of the optimized structure is nearly similar to the original one.

The torque waveforms of the two structures under the rated operating condition are shown in Figure 11 and

Table 6. The output average torque and torque ripple of both structures.

Condition	Parameter	The Original	The Optimized
Without skewed slot	Average torque	98.3 N·m	98.2 N·m
	Torque ripple	14.9%	7.1%
With skewed slot	Average torque	96.4 N·m	96.6 N·m
	Torque ripple	7.9%	3.6%

. The torque ripple percentage of the optimized structure is reduced from the original 14.9% to 7.1%.

The output torque comprises many harmonic torques of different frequencies, such as the 6th and 12th, which are shown in Figure 11b,d. The largest harmonic percent of the torque for the original structure is 4.6% and 7.2% corresponding to the 6th and 12th, respectively, and the largest harmonic percent of the torque for the optimized structure is 3.3% and 5.5% corresponding to the 6th and 12th, respectively, under the no skewed-slot condition, and the largest harmonic percent of the torque for the original structure is 2.5% and 3.2% corresponding to the 6th and 12th, respectively, and the largest harmonic percent of the torque for optimized structure is 1.0% and 2.1% corresponding to the 6th and 12th, respectively, under the skewed-slot condition, from which it can be clearly seen that the harmonic order of the output torque is 6k (k = 1, 2, 3 …). It is shown that the lowest harmonic order of the output torque is 6 and the other harmonic orders of the output torque are the multiples of the lowest harmonic order. The torque ripple is caused by the 5th and 7th air-gap harmonic magnetic fields and MMFs produced by the currents of the stator windings. It is indicated that the harmonic torque produced by air-gap harmonic magnetic fields and slot effects influences the machine performance most seriously and should be reduced by slot or rotor skewing.

Due to the use of the fractional-slot winding in the optimized structure, the torque ripple can be effectively reduced compared to the original structure according to the simulation results. Similarly, the torque ripples of the two structures significantly decreased after the slot is skewed while with a slight decrease in the average output torque. It shows that the optimized structure is beneficial to reduce the torque ripple and noise in the aircraft application.

3.3. Results and Discussion: Torque–Speed Characteristic and Efficiency Performance

To examine the speed range of the constant torque output operation and output torque capability in a high-speed situation, the output torque and power performance of the two structures with different speeds are simulated with the field-weakening control method. Under the maximum driving current (250 A) and DC bus voltage equal to 320 V, the torque–speed and power–speed characteristic curves are drawn as in Figure 12. The original constant output speed turning point is around 3400 rpm, while the optimized one is around 3700 rpm. The maximum output torque and power value of the optimized scheme can satisfy the original requirements, and the constant torque speed range of the optimized scheme is marginally wider. However, in the high-speed range, there is a significant improvement in the output torque/power than the original structure, which means the optimized structure has more advantages in high-speed and high-torque-density applications.

Moreover, in the operating speed range, the efficiency distribution of the motor within the operating range acquired through the simulation is shown in Figure 13. The difference in the highest efficiency area between the two structures is not noticeable, and the two structures can both reach around 97% in a wide speed range. The efficiency of the two structures meets the requirement of the highest efficiency of 96.7%, while the optimized structure has higher efficiency during high-speed operation conditions compared with the original one. Because wind friction losses are neglected, the efficiency simulation results are slightly higher than the actual value.

In summary, focusing on the requirements of the output power and torque, the optimized structure can perfectly replace the original structure in practical application. And the superior high-speed output torque capability makes it more advantageous in high-speed situations.

3.4. Results and Discussion: Safety Factors (Maximum Stress and Temperature Rise)

When low-coercivity magnets are used in the IPMSM, there is a risk that the permanent magnets will irreversibly demagnetize due to the application of the flux-weakening control. The demagnetization can easily occur due to the thinner permanent magnets used in the optimized structure under the same current conditions. Therefore, it is necessary to determine that there is no irreversible demagnetization that occurs within the normal operating range of the motor, especially in the extreme condition.

The permanent magnets used in the optimized structure are the same as in the original one; the material is called N38UH. Using the B-H curve as a reference, the simulation with three different temperatures is carried out under a 250 A current and at a speed of 10,000 rpm. The results shown in Figure 14 reveal that in the normal operating range, the “∇-type” permanent magnets’ demagnetization is severer in the inner V-shape part. The demagnetization parameters are listed in

Table 7. The comparison of permanent magnets’ demagnetization parameters.

Structure	Magnet Temperature	Inflection Point	Average Magnetic Flux Density	Min. Magnetic Flux Density
The original	100 °C	0.00 T	0.75 T	0.55 T
	160 °C	0.15 T	0.65 T	0.45 T
	180 °C	0.30 T	0.62 T	0.43 T
The optimized	100 °C	0.00 T	0.59 T	0.43 T
	160 °C	0.15 T	0.52 T	0.35 T
	180 °C	0.30 T	0.47 T	0.32 T

and show that the demagnetization is not irreversible.

The mechanical structure strength of the rotor is a key factor when analyzing the safety of the motor when the motor is running at high speed. So, the stress distribution of the rotor is simulated by the 3-D model at the speed of 10,000 rpm, and the established 3-D models of the two different structures are shown in Figure 15. The setup of the rotor materials is listed in

Table 8. The setup of material parameters.

Parameter	Rotor Core	Permanent Magnet
Density	7650 kg/m3	7500 kg/m3
Young’s modulus	2 × 1011 Pa	1.8 × 1011 Pa
Poisson’s ratio	0.3	0.3

.

The stress distributions of the two schemes are simulated at the speed of 10,000 rpm, and Figure 16 shows parts of the rotor nephogram of the stress. As the figure shows, the maximum value of stress is near 150 MPa in both structures, and the max points are both mainly distributed at the radial and circumferential magnetic bridge connections. However, the limited stress of the traditional steel type B35AV1900 is around 300–400 MPa; hence, the mechanical structure strength of the optimized structure satisfies the safety request.

If the motor shell and cooling methods of the optimized structure are different from the original structure, the production costs and manufacturing difficulty should be reassessed, and the comparison complexity will increase. So, the simulation of the temperature rise of the optimized structure is carried out with the same motor shell and cooling methods. Firstly, the equivalent cooling model is built using the Motor-CAD (ver. 11.1.5.1) software as shown in Figure 17. And then, the validation of this model is verified through comparing the temperature rise of the original to the real motor test temperature rise data. A thermal network method is adopted during the temperature rise calculation for fast computation speed and accuracy because the heat transfer phenomena are complex. The discrete data and simulation results with varied output power are illustrated in Figure 18, and all the data of different power values are obtained with a rated speed of 3000 rpm. (It should be noted that in the real limited condition, the motor should only operate at a rated speed and output power of 60 kW for 3 min under a 180 °C temperature limit, so the 60 kW temperature simulation only needs to use the temperature value at 3 min, but not the one at stable status, as a reference.)

The winding temperature of the equivalent model is close to the test data when the power is equal to 30 kW and 50 kW. Hence, the cooling model design method can be used to assess the optimized cooling model and evaluate the temperature rise in the rated condition (30 kW and 115 A). But in the limited condition (60 kW and 250 A), the simulation and evaluation results can only be used as a trend reference, but they are not very precise.

The temperature mismatch between the original and test data is recorded in

Table 9. The maximum winding temperature mismatch at different output powers.

The Output Power	Original Data	Test Data	Maximum Mismatch/Time
30 kW	102.0 °C	100.0 °C	+2.0 °C/+2.0%/20 min
50 kW	133.8 °C	140.3 °C	−6.5 °C/−4.6%/4 min

. The percentage of the mismatch at the 30 kW and 50 kW output power are in the acceptable range, especially at 30 kW, and the simulation original data are even higher than the test, which can further improve the safety of the motor at the rated power before manufacturing.

The test data are higher than the simulation original data at 50 kW, which is mainly caused by two reasons. First, the actual iron loss in the experiment is bigger than the simulation one. Further, the effect of the distribution of the iron loss to the stator temperature field is more obvious, which causes the temperature of the windings to be higher. Secondly, in the simulation, the cooling system adopts the typical and ideal axial water jackets. However, the test cooling structure is not completely the same as the axial water jackets, which is more complex. Then, the real water jackets worsen the heat dissipation of the cooling system. With these differences, the test data are higher than the simulation result.

Based on the analysis above, using the same cooling model design method to build the optimized cooling model is acceptable. The steady-state highest temperature rise data are compared with the original data to evaluate the temperature at the rated output power. In the rated power condition, the temperature of the major motor component is listed in

Table 10. The steady-state highest temperature of major motor component.

Part of Motor	The Original	The Optimized
Stator core temperature	77.3 °C	78.0 °C
Rotor core temperature	85.2 °C	87.8 °C
Magnet temperature	85.4 °C	87.9 °C
Winding temperature	96.5 °C	101.5 °C

and the temperature rise process is illustrated in Figure 19 as an example of the simulation. Under the same external cooling conditions, the windings’ temperature is 5% higher than the original one.

4. Experimental Result

After those simulations and the analysis in Section 3, optimized scheme II is a viable option according to the simulation results. With the aim of reducing the cost of manufacturing, except for the optimized components, all the other parts are consistent with the original motor structures, and then we assemble them into a prototype motor. Before the assembly, the weight of the important parts like the cores, magnets and windings are measured. It should be noted that in the same part of the motor, two different structures use the same material. The comparison of the materials’ quantity between the two different structures is represented in

Table 11. The materials’ quantity of motor.

Parameter of Motor	The Original	The Optimized	Change amp.
Axial length of the core	146 mm	136 mm	10 mm/−6.8%
Mass of stator core	10.25 kg	9.42 kg	−8.1%
Mass of rotor core	5.98 kg	5.48 kg	−8.4%
Mass of magnets	1.62 kg	1.48 kg	−8.7%
Mass of windings	4.86 kg	4.53 kg	−6.8%
Total mass	22.70 kg	20.91 kg	−8.0%

.

From Table 11, it can be seen that, compared with the original one, the optimized scheme brings a reduction of nearly 8% in the total mass of the motor and especially reduces 8.7% of the use of the permanent magnets, thereby significantly reducing the cost of the motor. With the basically equivalent output torque capability, the axial length of the core is reduced by 10 mm; therefore, the power density of the motor can be effectively improved.

The optimized prototype motor was manufactured by adopting the new arrangement of the stator windings and “∇-type” magnetic-pole rotor topology and is displayed in Figure 20. The experiments shown in Figure 21 have been carried out on a prototype motor under the closed-loop current control in the laboratory. In the operation, the prototype motor with a commercial variable-frequency drive is mechanically connected to the generator for providing the input torque. The generator is used as the power supply of 380 V/50 Hz and connected to the water resistance load.

The measurement system of the prototype motor has three parts: a measuring instrument of the torque and the power, which is used to monitor the torque and the power of the rotor shaft by a torque transducer, and its accuracy degree is ±0.1%; a multifunctional digital power meter, which is used to measure the voltages, currents and powers of each-phase stator winding for the prototype motor, and the measurement accuracies of the voltage, current and power are ±0.1 V, ±0.1 A and ±0.1 kW, respectively; and an incremental encoder, with a resolution of 1024 cycles/r, which is used to obtain the speed signal.

The calibration experiments were carried out on the prototype motor in the laboratory under the no-load and with-load conditions within the speed range of 1000–9000 rpm, and the EMFs, mechanical and external characteristics, efficiency, temperature rise were measured in the experimental platform shown in Figure 22.

The no-load experiments were carried out on both the original and optimized motors, and the experiment data of the EMFs are recorded. The waveform of the line-to-line EMFs under the no-load condition and with the speed of 3000 rpm is shown in Figure 23.

The three-phase per-phase resistance is 0.01565 Ω and 0.017 Ω, respectively, in the experiment and simulation. The effective value of the line-to-line EMFs in Figure 23 is 134.4 V, and then the value of the phase EMFs is 77.6 V. In the same operating condition, the value of the original motor is 123.5 V and 71.3 V, respectively. Comparing the experiment data and simulation results, the consistency between the simulations and experimental data can be easily seen in

Table 12. The comparison of the experiment data and simulation results of EMFs.

Parameter	Value	The Original	The Optimized
Simulation result	Line EMFs	132.2 V	142.0 V
	Phase EMFs	76.4 V	82.0 V
Experiment data	Line EMFs	123.5 V	134.4 V
	Phase EMFs	71.3 V	77.6 V

.

The average output torque and output active power of the motor at different rotor speeds were recorded and the characteristic curves are illustrated in Figure 24 when the driving current of the stator is kept at 250 A.

From Figure 24, it can be seen that the constant output torque of 205 N·m can be achieved under the rotor speed of 3000 rpm and the constant output power of 65 kW can be fulfilled between the rotor speed of 3000 rpm and 9000 rpm, which means the optimized motor can satisfy the output requirements of the original motor in Table 1. And the maximum values of the constant output torque and power are both higher than the original one; the output performance has been improved by the new structures.

The efficiencies of the prototype motor at different speed and load conditions were computed by measuring the output power from the rotor shaft and the active power in the grids. The test speed range is between 1000 rpm and 9000 rpm, and the output power range is between 10 kW and 60 kW. The efficiencies data are calculated at a stable operating temperature when the output power is under 40 kW. For 60 kW, the efficiencies data are calculated when the operation time is 180 s. Selecting the efficiencies data corresponding to real operating conditions from 20 to 60 kW, at intervals of 1000 rpm, the results are listed in

Table 13. The efficiencies at different speeds and load conditions.

Output Power	The Efficiencies at Different Rotor Speeds
	1000 rpm	2000 rpm	3000 rpm	4000 rpm	5000 rpm	6000 rpm	7000 rpm	8000 rpm
20 kW	0.959	0.948	0.952	0.958	0.940	0.860	0.778	0.908
40 kW	0.970	0.952	0.968	0.971	0.959	0.902	0.907	0.926
60 kW	0.969	0.949	0.963	0.978	0.965	0.960	0.927	0.871

.

The maximum efficiency of the prototype motor is 97.8% at the rotor speed of 4000 rpm and output power of 60 kW, while the maximum efficiency of the original motor is 96.7%. Furthermore, from the calculation and analysis, the efficiency area above 90% is around 79.5% of the whole test area, and the area proportion, for which the efficiency is over 80%, is about 96.58%. Compared with the original motor, the high-efficiency area is expanded, and the maximum efficiency is also improved by the optimization.

As for the temperature rise of the prototype motor, considering that the limited temperature value is around 180 °C, the load experiments are carried out with two different kinds of loads at the same speed of 3000 rpm. The constant power load is 30 kW while the constant torque load is 191 N·m, and those conditions represent the rated operation and limited condition, respectively. The temperature curves of the motor are illustrated in Figure 25.

It can be seen from Figure 25a that the steady-state temperature of the prototype motor at the rated load is around 110 °C and the original temperature is 100 °C; both of them are under the limited temperature of 180 °C. When the motor at the rated load and different speeds is in normal situations, the temperature of the motor can stabilize before 30 min, and our testing usually lasts for around 12 h to confirm the temperature can remain stable. It proves that the prototype motor can safely run in the rated operation condition for a long time. The simulation analysis in Section 3.4 shows that the maximum temperatures of the same condition are 105 °C and 100 °C, respectively, which is consistent with the experimental result. And Figure 25b shows that in the limited condition, the prototype motor temperature is 20 °C higher than the original one because of the worse heat dissipation capacity brought by the new winding arrangements and the reduction in motor volume. With the 191 N·m load, the motor temperature will reach 180 °C when the operating time is 250 s, which is quicker than the original motor, and the rise trend is close to the simulation results shown in Figure 20. Although the temperature rise is bad for the safety of the motor, to improve the power density and reduce the torque ripple, it is still acceptable in the safe range.

Under the rated condition, the average output torque was measured, and the torque ripple was calculated from the waveform of the output torque. The records of the measured torque and harmonic distribution are shown in Figure 26, which verify the simulation content in Figure 11. And the calculated torque ripples are listed in

Table 14. The torque of the experiment data.

Parameter	The Original Motor	The Optimized Prototype
Average torque	95.3 N·m	94.8 N·m
Torque ripple	18.5%	5.4%

. From Table 6 in Section 3.2, by applying the optimized structures, the torque ripple is reduced from 14.9% to 7.1% without the skewed slot. Based on the experimental test, the actual corresponding value changes from 18.5% to 5.4%. The simulation and experimental results both validate the improvement in the torque ripple by the optimized structure.

5. Conclusions

In this paper, an IPMSM with the optimized structure using fractional-slot single-double-layer hybrid stator windings and ∇-type magnetic-pole rotor topology based on a basic structure was presented. Both the rated condition and limited condition were simulated and tested in the experiment, and the EMFs, cogging torque, average torque, efficiency, temperature and torque ripple were analyzed. The following was found:

After adopting the new single-and-double-layer hybrid winding and ∇-type magnetic-pole rotor topology, the optimized structure is basically equivalent in terms of the output torque, operating range, efficiency, etc., but the torque ripple has been significantly reduced either in the simulation or experiment.

In addition, with the amount of material usage cut down, the manufacturing cost has also been reduced. The reduction in the motor volume and the new type of winding arrangements worsen the capability of the heat to dissipate. The temperature of the optimized structure is higher than the original one in the rated and limited conditions. The experiment shows that the steady-state temperature of the prototype motor is below the maximum limited temperature, and the optimized machine is able to operate 250 s before its temperature reaches the limit of 180 °C. Therefore, the optimized prototype can completely satisfy the request of aircraft drive systems.

The findings of this comparison analysis can be used in the design stage of an IPMSM aiming to reduce the torque ripple in a high-speed situation, such as aircraft application. Furthermore, there is potential for the improvement in the rotor magnetic-pole topology, including the shape and dimensions of the magnets. In addition, the safety of the motor can also be improved in terms of new cooling methods and the motor shell structure.