**Electromagnetic Field Analysis and Design of an E**ffi**cient Outer Rotor Inductor in the Low-Speed Section for Driving Electric Vehicles**

**Myeong-Hwan Hwang 1,2, Hae-Sol Lee 2,3, Se-Hyeon Yang 1,2, Hyun-Rok Cha <sup>1</sup> and Sung-Jun Park 2,\***


Received: 4 November 2019; Accepted: 3 December 2019; Published: 4 December 2019

**Abstract:** Currently, the eco-friendly vehicle market is growing continuously. In the automobile industry, various electric vehicle models are being developed, and several technological innovations are being made. Certain limited vehicle types, such as passenger cars, are being converted to electric vehicles; moreover, a variety of small electric vehicles, including smart mobility vehicles, are being developed. The driving motor of an electric vehicle, e.g., a brushless Direct Current motor (BLDC), is one of the key components that determine its driving performance. However, since the recent hike in prices of the rare earth magnets used in BLDCs, the development of induction motor with lower cost and a simple product structure has become essential. Therefore, this study proposes an optimized design for an outer rotor induction motor with high efficiency in the low-speed section for electric vehicles. The motor designed in this study is efficient for speeds less than 1000 rpm, and our experimental results prove that the prototypes can provide up to 84.8% efficiency. This optimized motor is expected to have widespread application in the eco-friendly vehicle market.

**Keywords:** outer rotor inductor; electric vehicle; high-efficiency; eco-friendly

#### **1. Introduction**

The eco-friendly vehicle market is expanding, and various electric vehicle models and associated technologies are being developed. Moreover, strict regulations are imposed on the average CO2 emissions and the particulate matter generation from internal combustion engine vehicles, such as gasoline- and diesel-fueled cars. As a result, electric vehicles are gaining acceptance in most countries, such as in Europe and the United States of America. Furthermore, limited vehicle types, such as passenger cars, are being converted into electric vehicles; moreover, various small electric vehicles, including smart mobility vehicles, are under development [1].

The driving motors in electric vehicles have a considerable influence on the driving performance, and are available in various configurations [2–5]. However, recently, the price of the rare earth magnets used in brushless DC motors (BLDCs) has rapidly increased, thus causing a rise in product prices, and therefore, decreasing their product price competitiveness. As a result, most of these vehicle manufacturers' profits are now being spent on material imports, causing a direct reduction in the profitability of their companies. Therefore, there is a growing technical need to replace BLDCs, and hence, developmental research on simply structured induction motors that are cheaper than BLDCs is indispensable [6–8].

Various approaches have been employed to improve the efficiency of induction motors; moreover, research and development is still ongoing. Typical methods include modeling using the finite element method [9,10], optimization using artificial neural networks (ANNs) coupled with the genetic algorithms (GAs) [11,12], development of the associated motor materials [13], and improvisation through magnetization of the barriers and slits [14].

Previously, Kumar et al. proposed a new approach to minimizing copper and iron losses and optimizing the efficiency of variable speed induction motor drives [15]. Their method was based on a simple induction motor field-oriented control model. However, they only used the conventional induction motor parameters, and as a result, some iron loss occurred. Additionally, Sakthivel and Subramanian proposed a new approach that utilizes particle swarm optimization (PSO) to evaluate the field efficiency of the induction motors by employing a model based on the modified induction motor equivalent circuits [16]. Similarly, Delgado et al. presented an optimization plan called "edge optimization," which is a simple recognition algorithm for induction motors, and has no derivative model. Their proposed approach relies on the hardware or software startup information of the motor for identification of all seven induction motor parameters, namely, the stator leakage inductance, rotor leakage inductance, stator resistance, rotor resistance, mutual inductance, mechanical inertia, and the friction coefficient [17].

Considering the parameters affecting the performance of induction motors, Faiz et al., using analytical statistics, demonstrated the negative impact of the power-supply unbalanced voltage on the efficiency of the induction motors, as well as the associated financial losses [18]. Similarly, Donolo et al. investigated the effects of voltage imbalance on the performance of induction motors. Using a sequence equivalent circuit, they determined the increase in losses of the induction motors and analyzed motors with open and closed rotor slots [19]. Jabr and Kar proposed experimental procedures for determining the mechanical parameters and the saturation characteristics [20], by employing an experimental procedure that facilitates easy measurement of the reactivity saturation characteristics of both the stator and the rotor. In addition, Rasouli et al. investigated possible induction motor parameter identification, with particular emphasis on the subset selection and reduction methods, such that the identification method could focus on the most important parameters [21]. Finally, Kostov et al. proposed an efficient approach to determine the equivalent circuit parameters of squirrel-cage induction motors based on genetic algorithms [22]. Moreover, when three data sets were used in their study, the maximum relative error of the estimated parameters with respect to the analysis values was found to be less than 1%.

In this study, shape optimization design for a low-cost, high-efficiency, outer rotor induction motor is performed based on electromagnetic field analysis and experimental observations. Therefore, an induction motor design with high efficiency, and hence, a high-power output in various speed ranges is proposed. This is achieved by targeting a low-speed and high-torque-section setup, to ensure that the motor provides high efficiency and high-power output at various driving speeds other than the rated speed. Note that an outer rotor induction motor is selected over an inner rotor induction motor, as the former has strong rotational inertia, a small rate of change of speed, and stronger structural characteristics compared to the latter. As the rated output and rated speed of the induction motor are determined in proportion to the frequency and number of poles, the basic design specifications are selected via a parameter-based formula.

The remainder of this paper is organized as follows. Section 2 presents the motor shape design and behavioral trends based on the induction motor design procedure. Through the understanding of the characteristics of outer rotor induction motors, the basic specifications are tuned by changing the number of poles. In Section 3, the feasibility of the basic design of the outer rotor induction motor is discussed using an electromagnetic field analysis assessment. Sections 4 and 5 report the production of prototypes of the optimally designed outer rotor induction motor and their overall characteristics. The design error is determined and minimized by comparing the electromagnetic field analysis values and the measured values. Finally, the conclusion is presented in Section 6.

#### **2. Outer Rotor Induction Motor**

An induction motor is a representative example of alternate current (AC) motors. Owing to the rotating magnetic field generated by the stator, an induction current is generated in the rotor of the electric conductors and a rotational torque corresponding to the slip is generated. Induction motors are divided into single-phase induction motors and three-phase induction motors, according to the type of AC power input; three-phase current is generally used, which can obtain a rotating magnetic field without any special techniques. As it does not step out like a synchronous motor, which is also an AC motor, it is considered suitable for loads with large torque fluctuations. However, it has difficultly in controlling the rotational speed, owing to the principle of obtaining torque through slip. Nevertheless, because the rotational speed can be freely controlled by the inverter circuit, thanks to the development of power electronics, this problem can be considered nearly solved.

One advantage of the outer rotor induction motor is that the generated torque increases with an increase in the cross-sectional area of the permanent magnet, and its structure is advantageous for prevention of scattering of the magnet. However, it is difficult to rotate at high speeds due to problems with mechanical stability and the possibility of demagnetization. Nevertheless, the outer rotor induction motor has numerous advantages in mechanical performance. First, to accommodate the stator, the outer rotor is larger than the rotor of the inner rotor induction motor. Owing to an increased rotor size, the inertia increases, thereby reducing the torque ripple and the cogging torque and providing smooth and stable operation, even at lower speeds. Second, it normally generates a higher torque compared to similar sized inner rotor induction motors. The torque is a magnetic force multiplied by the air gap radius (magnitude of magnetic flux), which is related to the output of the induction motor. For the same induction motor diameter, the outer rotor induction motor has a larger air gap area than that of the inner rotor induction motor, and larger air gaps can produce higher power. Third, a larger radius of the air gap also results in an increased "lever arm" for torque generation. In an outer rotor induction motor, the larger the diameter of the rotor, the higher the number of poles the rotor can accommodate, which further increases the magnetic flux.

The outer rotor induction motors have shorter accumulation compared to the inner rotor induction motors with similar performance characteristics. Their smaller size and a higher torque production facilitate their application as in-wheel induction motors in electric vehicles and propellers in remote-controlled model drones. In the case of high-precision applications, such as optical drives, their smooth and consistent speeds have an advantage over other induction motor types. Moreover, in various load applications, such as industrial power tools, pumps, fans, and blowers, the high inertia of outer rotor induction motors can reduce the load changes and provide a stable output torque. Due to the specific design advantages of outer rotor induction motors, they are commonly applied in fans and blowers. The outer rotor can serve as a hub for the fan or blower impeller. It provides a compact case and acts as a heat sink for the impeller to rotate, which facilitates induction motor cooling.

#### **3. Outer Rotor Induction Motor Design Outer Rotor Induction Motor**

To design the outer rotor induction motor for application in electric vehicles, the basic design specifications were determined considering the driving characteristics of electric vehicles. Then, the equivalent circuit method and the finite element method were primarily applied to the design process. The typical characteristics of the outer rotor induction motor were identified. After identifying the performance problems through prototype production, the design was optimized to make it more similar to the prototype by adjusting the number of poles.

#### *3.1. Basic Design Specification Selection*

An electric vehicle motor has a limited battery capacity; therefore, the input voltage was limited to 48 V. For low-speed operation, the rated speed was limited to 1000 rpm or less. The design targets were a 1.2-kW rated output, 80% efficiency, 12 Nm torque, and an output density of 0.5 kW/kg or more.

#### *3.2. Electrical Steel Selection*

There are two types of electrical steel sheets: Oriented and non-grain oriented sheets. The former is an electrical steel sheet in which the crystal magnetization is aligned in the rolling direction and is mainly used in transformers or reactors. A non-grain oriented electrical steel sheet exhibits uniform magnetic properties in the rolling and other directions, and is mainly used as a material for electric motor cores. Non-grain oriented electrical steel sheets are further divided into two types, depending on their thickness: 0.5 and 0.35 mm. There are 10 types of 0.5 mm sheets, which range from 50PN370 to 50PN1650 depending on the silicon content. There are five types of 0.35 mm sheets, ranging from 35PN320 to 35PN560, depending on the silicon content. As the first two digits of the label represent the iron plate thickness and the last three digits represent the iron loss value, it is advantageous to use a thinner steel plate to reduce the Eddy current losses, and to select a material with a lower iron loss.

The electrical steel used in this study was S08 0.35T, 35PN230 according to the POSCO standards. This was a non-grain oriented electrical steel sheet with a density of 7.6 kg/dm3, a maximum iron loss of 2.3 W/kg, a minimum magnetic flux density of 1.62 T, and a space factor exceeding 95%.

#### *3.3. Number of Poles and Slot Combination*

The number of slots in the squirrel-cage rotor must be carefully determined considering the number of stator slots. In addition to the noise generated during operation or starting, the starting torque causes a significant change in the rotor position, and the primary cause of abnormal torque is the mismatch between the stator and rotor slot combinations.

For three poles, the number of grooves in the stator is preferably a multiple of three. A multiple of 6, 12 or 18 may be selected for 2, 4 or 6 poles, respectively, as detailed in Table 1. It is common for the number of rotor slots to exceed the number of stator slots. Furthermore, designing a difference of more than 20% between the number of stator and rotor slots can reduce the motor noise and the leakage reactance. Moreover, the higher the number of grooves, the better the output, maximum torque, efficiency, and the power factor. However, this setup also reduces the coil space factor; therefore, appropriate values must be selected.


**Table 1.** Stator and rotor combination according to pole number.

For this study, the number of poles for the design was selected as 6, which could yield the same torque at lower frequency compared to 8 poles, as detailed in Table 2. For high output and high efficiency, the number of stator and rotor slots was 72 and 88, respectively.

**Table 2.** Rated speed and torque depending on pole number.


#### *3.4. Motor Dimensions*

In order to design an outer rotor motor in this study, it was necessary to determine the outer diameter of the rotor. First, we considered mounting of the motor on an electric bike, with its volume being equivalent to D2*L*, which is proportional to the motor output and torque and which determines the motor thermal stability. The detailed dimensions of the stator and the rotor of motor were determined through application of the design procedure. The relevant formulae and associated values in millimeters (mm) are presented in Table 3.


**Table 3.** Rotor and stator dimensions in mm.

#### **4. Analysis of Induction Motor Characteristics via Electromagnetic Field Analysis**

#### *4.1. Slot Combination*

The stator and rotor slot combination to yield the optimal conditions with regards to the output, efficiency, torque, and the weight was derived according to the pole number fluctuations with 16 poles, as demonstrated in Figure 1. With a higher number of slots, the output and the torque were found to improve, as shown in Table 4. Moreover, higher efficiencies were obtained in a certain range. Considering the overall characteristics of the motor, the optimal characteristics could be obtained with a combination of 90 stator slots and 124 rotor slots, as indicated by the blue box in Figure 1. Table 4 lists the motor characteristic data values along with the torque values.

**Figure 1.** Graphs of motor characteristics according to slot combination.


**Table 4.** Motor characteristics according to slot combination.

#### *4.2. Stator Slot Shape*

Figure 2a depicts a stator slot opening. With an increase in the stator slot opening, the output increases, and the efficiency decreases, as shown in Figure 2b. In Figure 2a, SOAng is the stator slot opening angle, and SO-S is the slot opening. TW\_S is the width of the stator rotor, and SD\_S is the slot depth of the stator. Note that the coil thickness for winding should be considered, i.e., only the slot opening with dimensions larger than the winding thickness should be selected.

Furthermore, as the stator tooth thickness increases, as shown in Figure 2c, the output and efficiency increase, as well because it is in proportion to the thickness. However, such an increase in tooth thickness renders the motor predominantly iron-based, which increases its weight.

Finally, as the stator slot height increases, the overall output and efficiency decrease (Figure 2d). However, for this study, it was necessary to increase the winding area to accommodate as many windings as possible. Therefore, it was essential to secure a certain slot area, even if it decreased the output and efficiency slightly.

#### *4.3. Rotor Bar Shape*

Considering the rotor shape design (Figure 3a), with increases in the bar thickness and the depth, as shown in Figure 3b,c, respectively, the motor output and efficiency increases as well. In Figure 3a, SetBack is the depth of the rotor slot opening, and SD-R is the slot depth of the rotor. Furthermore, SO-R is the width of the rotor slot opening. Accordingly, the slot area becomes wider, which yields increased power output due to the increased amount of aluminum.

An increase in the rotor slot opening corresponds to an increased power output (Figure 3d); however, the efficiency is inversely related. Therefore, the slot opening of the bar should be set to the optimal point in terms of output and efficiency.

#### *4.4. Lamination*

As shown in Figure 4, increasing the lamination increases the efficiency, and above a certain level of lamination, it reduces the power output of the induction motor. After the efficiency exceeds a certain level, the graph exhibits a saturation-like behavior, showing a very slight change. In this study, considering the output density, an optimum level of 30 mm was selected, which yields the highest efficiency compared to weight.

**Figure 2.** Graphs of motor characteristics according to stator slot shape: (**a**) Stator slot shape; graphs of output and efficiency according to (**b**) slot opening, (**c**) tooth thickness and (**d**) slot height.

**Figure 3.** Graphs of motor characteristics according to rotor bar shape: (**a**) Rotor bar shape; graphs of power output and efficiency according to (**b**) rotor bar thickness, (**c**) rotor bar height and (**d**) rotor slot opening.

**Figure 4.** Graphs of motor characteristics according to lamination.

#### *4.5. Wire Diameter and Turn Count*

For winding optimization, it is necessary to determine the wire diameter and turn count by considering the stator's space factor. In this study, the optimal point was derived by fixing this space factor to be less than 45%, and through adjustment of the wire diameter and the turn count. Examination of the turn count trend revealed that the output, efficiency, torque, and the current density tend to decrease as the turn count increases, as shown in Figure 5. The point at which the desired output relative to the efficiency was obtained was considered the optimal point. The characteristics according to the turn count are listed in Table 5.

**Figure 5.** Graphs of motor characteristics according to turn count.



#### *4.6. End Ring Design*

Due to the use of distributed windings, the coil end rings had a greater height than that obtained for concentrated windings. Therefore, when the rotor was die-cast, it was necessary to produce a rotor end ring of similar height to increase the output and efficiency. Figure 6 depicts the structure of such a rotor end ring. Generally speaking, however, if the end ring height increases continuously, this may result in an increase in the overall motor weight, thus yielding a reduced output density. In this study, the windings were set as fixed components and the motor characteristics were observed with the variation in height of the rotor end ring. When this height exceeded a certain level, the efficiency curve became saturated (Figure 7). The point with the best motor characteristics relative to the weight was identified as the optimal point.

Table 6 shows the motor characteristics according to the motor end ring structure. The output efficiency weight was analyzed when the end ring of the motor was increased from 10 mm to 15 mm. The motor end ring is 80.8% efficient at 10 mm thick and 81.3% at max. 15 mm.

**Figure 6.** Rotor end ring structure of outer rotor induction motor.

**Figure 7.** Graphs of motor characteristics according to rotor end ring structure.


**Table 6.** Motor characteristics according to rotor end ring structure.

#### *4.7. Summary of Trend Analysis*

As the design optimization progressed, the influence of each item on the motor characteristics was determined and the motor was reconstructed. Table 7 summarizes these trends and elucidates the characteristics of the outer rotor induction motor. The rated output, efficiency, and weight, are directly related to the output density, which are indicated by arrows. The factors with considerable changes are indicated by red arrows.


**Table 7.** Trend analysis of motor characteristics.

#### **5. Fabrication of Outer Rotor Induction Motor Prototype and Performance Evaluation Device**

Based on the design data, an induction motor prototype was fabricated to allow comparison of the electromagnetic field analysis results with actual experimental data. The device used for evaluating the performance of the fabricated inductor (speed, torque, efficiency, etc.) is also discussed in this section.

#### *5.1. Fabrication of Outer Rotor Inductor*

Figure 8 shows three-dimensional (3D) modeling images and photographs of the actual outer rotor inductor and the assembled outer rotor inductor. In detail, Figure 8a,b shows a 3D drawing of the inductor stator and rotor, respectively, while Figure 8c shows the winding method for the inductor stator. Figure 8d shows the actual stator fabricated based on the drawing, which was manufactured using a 35PN230 non-grain oriented electrical steel sheet with 90 slots. Figure 8e shows the inductor rotor core, which was manufactured using the same material as the stator. Figure 8f shows the coil winding of the stator. The turn count was 15 and the wire diameter was 0.45 mm. The winding was produced with four reels and 6 poles in parallel. Finally, Figure 8g shows the assembled fabricated outer rotor inductor.

(**g**)

**Figure 8.** Three-dimensional (3D) modeling images and photographs of actual fabricated components of the outer rotor (induction motor and assembled device: 3D drawing of (**a**) stator and (**b**) rotor; (**c**) two-dimensional (2D) drawing of winding; produced (**d**) stator, (**e**) rotor, (**f**) winding and (**g**) assembled outer rotor inductor.

#### *5.2. Outer Rotor Inductor Performance Evaluation Device*

Figure 9a shows the inductor test equipment. The test equipment employed in this part of the study was a dynamo system produced by Dr. Staiger Mohilo & Co. GmbH (Lorch, Germany). The dynamo system was equipped with a servo motor to simulate load conditions, a torque sensor to measure the motor torque, and a power analyzer that could assess a variety of electrical conditions. Therefore, this device could measure the overall performance of the motor. Figure 9b shows the motor configuration installed into the test equipment. Measurements were performed under test conditions of 25 ◦C and 50% humidity. A certain frequency was applied according to the number

of poles. To perform measurements in the 1000 rpm section, which was the rated speed section, the efficiency, power, torque, and power factor were measured by adjusting the load from 0 to 800 rpm.

**Figure 9.** Inductor test equipment and test device configuration: (**a**) Induction motor test equipment, (**b**) test device configuration.

#### **6. Inductor Performance Evaluation**

In accordance with the design procedure for the outer rotor induction motor, the overall shape design and operating trends were first identified using the electromagnetic field analysis design tool described above. An actual motor having the shape-optimized model was then fabricated and tested.

A six-pole model was selected as the initial model for production and performance evaluation. Comparison of the electromagnetic field analysis and actual measurement results revealed that the efficiency of the latter was at least 30% lower. To improve the efficiency, the frequency was increased in order to accelerate the induction motor. Thus, the design was optimized by varying the frequency by increasing the number of poles; as a result, the difference between the electromagnetic field analysis and measurement results was found to be reduced.

#### *6.1. 6-Pole Model Performance Evaluation*

The motor constructed using the shape-optimized model was utilized and the motor efficiency, torque, and output were tested by varying the voltage with respect to the frequency. To obtain the rated speed of 1000 rpm with 6 poles, a frequency of 55 Hz was required, and the efficiency was measured to be 53% under those conditions. Experiments performed with varying frequencies and voltage values revealed that a higher frequency corresponds to higher efficiency, but lower output and torque. In addition, the driving voltage was adjusted based on 48 V, and was found to be proportional to the output and torque, but inversely proportional to the efficiency, which is contrary to the results obtained for frequency. These results are presented in Figure 10 and Table 8.

**Figure 10.** *Cont.*

**Figure 10.** *Cont.*

**Figure 10.** Graphs of motor characteristics according to voltage and frequency for the outer rotor inductor with 6 poles: Voltage\_frequency of (**a**–**o**): 41.7 V\_55 Hz, 51.9 V\_65 Hz, 25.3 V\_80 Hz, 47.2 V\_80 Hz, 51.9 V\_80 Hz, 31.3 V\_100 Hz, 34.4 V\_100 Hz, 43.2 V\_100 Hz, 46.7 V\_100 Hz, 51.9 V\_100 Hz, 54.1 V\_100 Hz, 62.3 V\_100 Hz, 69.2 V\_100 Hz and 36.6 V\_120 Hz, respectively.



#### *6.2. 10-pole Model Performance Evaluation*

For the 6-pole design and measurement, improved efficiency with increased frequency was confirmed. While maintaining the rated speed, consistent at 1000 rpm, the pole number of the fabricated motor was changed to 10. The subsequent experiment was conducted in the same manner as the experiment with 6 poles. Based on the rated speed, 90 Hz frequency was applied for 10 poles. The efficiency was found to be increased compared to the 6-pole model, with a confirmed maximum of 77%. This result validates the approach of changing the number of poles to improve the efficiency. The detailed results are shown in Figure 11 and Table 9.


**Table 9.** Motor characteristics according to voltage and frequency for outer rotor inductor with 10 poles.

**Figure 11.** *Cont.*

**Figure 11.** Graphs of motor characteristics according to voltage and frequency for outer rotor inductor with 10 poles: Voltage\_frequency of (**a**–**h**): 36.7 V\_90 Hz, 46.7 V\_90 Hz, 52.7 V\_90 Hz, 34.6 V\_100 Hz, 46.7 V\_100 Hz, 46.3 V\_110 Hz, 49.6 V\_110 Hz and 52.7 V\_110 Hz, respectively.

#### *6.3. 16-pole Model Performance Evaluation*

To improve the efficiency of the induction motor, the number of poles of the motor was increased to 16 poles during fabrication. In terms of the experimental method, this study evaluated the performance of the outer rotor inductor in the same manner as the 10-pole model. Figure 12 shows graphs of the motor characteristics of the inductor according to the number of poles and voltage frequencies; the experimental results for each frequency are shown. The experiment was conducted within a frequency range of 126–140 Hz, and a maximum efficiency of 84.8% was experimentally confirmed. With 16 poles, the frequency for the rated speed was 140 Hz, and in terms of the measured values, at 33.2 V, the efficiency was 82.7%, the output was 1.2 kW, and torque was 11.4 Nm. As such, the design through the electromagnetic field analysis and the results of the actual manufactured outer rotor inductor were found to be consistent. In the case of a lesser number of poles of the induction motor, the coil end extended, causing extensive copper loss, and therefore, degrading the efficiency. Through this experiment, this study verified the method of improving the efficiency of a large induction motor by increasing the number of poles. The detailed results are presented in Table 10.

**Table 10.** Motor characteristics according to voltage and frequency for outer rotor inductor with 16 poles.


**Figure 12.** Graphs of motor characteristics according to voltage and frequency of outer rotor inductor with 10 poles: Voltage\_frequency of (**a**−**f**): 32.3 V\_126 Hz, 35 V\_126 Hz, 33.2 V\_137 Hz, 33 V\_138 Hz, 23.9 V\_140 Hz and 33.2V\_140 Hz, respectively.

#### **7. Conclusions**

In this paper, the basic theory and design procedure of an outer rotor induction motor were described; moreover, a drive motor shape was designed using the equivalent circuit method and the finite element method. Based on the basic shape design, an optimized design was developed by adjusting the number of poles.

For effective application of an induction motor to an electric vehicle, a design yielding improved efficiency and power density, which are the most critical factors, is required. In this study, the design variables that affect the efficiency and power density of an outer rotor induction motor were classified. Furthermore, by analyzing the trends appearing through variable adjustments, the effects of each variable on the efficiency and output were determined.

An outer rotor induction motor has a large outer diameter and short axial length. Further, additional poles are known to be required, compared to those of a typical inner rotor induction motor. This is because the coil pitch is increased according to the employed distributed winding method. Moreover, the amount of available windings was reduced, owing to the larger outer diameter; as a result, there was a longer coil pitch and a reduced number of available windings. This aspect may have yielded the measurement results obtained in this study for the outer rotor induction motor with 6 poles. Superior results were obtained when the motor was fabricated with a higher number of poles. This is because the narrower pole spacing reduced the coil pitch, significantly increasing the usable range of the coil compared to the six-pole model; hence, the efficiency measured in the actual performance evaluation matched the analytical efficiency value. Use of a pancake-shaped winding in the motor, with a large outer diameter and a short axial length, appeared to be effective. This approach was also found to be more advantageous in terms of output density, because the maximum output can be increased with application of the driving voltage when the motor characteristics were obtained at a voltage lower than the driving voltage.

Thus, to achieve the maximum performance of an electric vehicle with an outer rotor induction motor, characteristics such as high torque of the motor parts in the low-speed range, high efficiency in the operating range, and a relatively small battery to allow low-voltage operation and to reduce the overall weight are required. To realize these characteristics, a pancake-shaped outer rotor induction motor, which is different than that of an inner rotor induction motor, was designed in this study. Furthermore, the important design variables were derived through shape optimization design and production of many prototypes. The motor was then optimized to meet the performance indicated by the electromagnetic field analysis. The performance evaluation device confirmed that the test results were similar to the designed results, and the validity of the design was verified. In the future, this outer rotor induction motor design is expected to be widely applied to electric vehicles and bicycles.

**Author Contributions:** Conceptualization, M.-H.H. and H.-S.L.; data curation, H.-S.L.; formal analysis, S.-H.Y.; methodology, M.-H.H.; supervision, S.-J.P.; validation, H.-R.C. and M.-H.H.; visualization, H.-S.L.; writing—original draft, M.-H.H.; writing—review and editing, S.-J.P.

**Funding:** This study has been conducted with the support of the Korea Institute of Energy Technology Evaluation and Planning as "Developing image big data based real time detection system for detecting defective module applied to solar power plant (KETEP 20183010014230).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Optimal Design of PMSM Based on Automated Finite Element Analysis and Metamodeling**

#### **Yong-Min You**

Department of Automotive Engineering, Honam University, Gwangju 62399, Korea; ym.you@honam.ac.kr; Tel.: +82-62-940-5499

Received: 30 October 2019; Accepted: 4 December 2019; Published: 9 December 2019

**Abstract:** To obtain accurate optimal design results in electric machines, the finite element analysis (FEA) technique should be used; however, it is time-consuming. In addition, when the design of experiments (DOE) is conducted in the optimal design process, mechanical design, analysis, and post process must be performed for each design point, which requires a significant amount of design cost and time. This study proposes an automated DOE procedure through linkage between an FEA program and optimal design program to perform DOE easily and accurately. Parametric modeling was developed for the FEA model for automation, the files required for automation were generated using the macro function, and the interface between the FEA and optimal design program was established. Shape optimization was performed on permanent magnet synchronous motors (PMSMs) for small electric vehicles to maximize torque while maintaining efficiency, torque ripple, and total harmonic distortion of the back EMF using the built-in automation program. Fifty FEAs were performed for the experimental points selected by optimal Latin hypercube design and their results were analyzed by screening. Eleven metamodels were created for each output variable using the DOE results and root mean squared error tests were conducted to evaluate the predictive performance of the metamodels. The optimization design based on metamodels was conducted using the hybrid metaheuristic algorithm to determine the global optimum. The optimum design results showed that the average torque was improved by 2.5% in comparison to the initial model, while satisfying all constraints. Finally, the optimal design results were verified by FEA. Consequently, it was found that the proposed optimal design method can be useful for improving the performance of PMSM as well as reducing design cost and time.

**Keywords:** automation; finite element analysis; PMSM; DOE; optimization; metamodeling

#### **1. Introduction**

The necessity of eco-friendly vehicles has been highlighted owing to environmental pollution and depletion of fossil fuels. Global electric car stocks are growing rapidly, crossing the 3 million vehicle threshold in 2017. The estimated demand for electric vehicles by 2030 is 100 to 140 million. The core of an electric vehicle is the electric powertrain, which consists of a traction motor, a reduction drive, an inverter, and a power delivery module. Permanent magnet synchronous motors (PMSMs) have been mainly used as a traction motor for electric vehicles because they have high efficiency and high output power density characteristics.

Several studies have been conducted on the PMSMs used in electric vehicles that require various characteristics such as torque, efficiency, and harmonic distortion (THD). Optimal design is essential to satisfy the various design requirements of PMSM at once. Optimal design is a method of finding the values of design variables to obtain an optimal solution within a range of constraints. The optimal design for PMSMs is created by combining design methods such as the analytical model, magnetic equivalent circuits (MEC) model, and finite element analysis (FEA) with optimal design algorithms [1–8]. First of all, there are studies on optimal design using the analytical model [1,2]. In [1], the optimal design of a PMSM based on the magnetic field analytical model was determined. The objective function used in that study consisted of efficiency, electrical time constant, and mechanical time constant. The experimental results showed that the efficiency increased by 1%. To minimize torque ripple, a novel analytical solution of a PMSM was proposed [2]. The stator current was optimized considering magnetic saturation using an analytical expression. The following are studies on optimization using the MEC model [3,4]. In [3] it was reported that the MEC optimization method combined with an optimization algorithm can optimize the volume and energy loss of a PMSM. A novel MEC model of a PMSM to obtain the maximum efficiency, minimum weight, and price was developed [4]. K-means clustering algorithm was utilized to obtain the best solution out of the eight clusters. Finally, some research on optimization combined with FEA have been published [5–7]. The work in [5] performed multi-objective shape optimization of a PMSM based on FEA and particle swarm optimization algorithm. Five rotor topologies were compared, aimed at efficiency, flux-wakening rate, and price. The work in [6] proposed an optimization process of a PMSM to optimize the weight, output power, and suitability. It performed shape optimization of permanent magnets and rotor core using FEA with the fuzzy inference system strategy. Using a novel memetic algorithm, an optimal design based on FEA to minimize torque ripple in a PMSM was created [7]. In [8], multi-physics and multi-objective optimization of a PMSM based on FEA and analytical magnetic model were studied. Although the FEA optimization method combined with optimization algorithm has the highest accuracy, it has high computational cost [5].

There are two main ways to optimize design variables: To combine the optimal algorithm with design methods directly and combine the optimal algorithm with the metamodel from the results of design of experiments (DOE). Metamodel is a mathematical model that approximates the relationships between design variables and responses. DOE is an application of statistics aimed at designing experimental methods and analyzing the results to identify relationships between design variables and responses. First, directly connecting the optimal algorithm with the design methods can determine the best solution more clearly [9]. However, this method takes a long time to optimize and it is difficult to predict the design time. Additionally, if the formulation of the optimal design is wrong, it is difficult to find the best solution. In the case of optimization by creating metamodels using DOE results, it is possible to predict the optimal results by analyzing the sensitivity between design variables and target goals. In addition, the time taken for the optimization design is clear. However, the number of DOE and test points must be selected properly, and the metamodel must be made correctly. Meanwhile, non-automated DOE requires a lot of effort and time because mechanical modeling and analysis must be performed as many times as DOE. Although a large number of DOEs are required to achieve good optimal design results, it takes a significant amount of effort and time. The work in [10] reported optimization results using response surface methodology combined with metamodels from the DOE results. To produce DOE results, a total of 15 models were made and 15 FEAs were conducted. The study in [11] optimized a PMSM by combining an optimal algorithm and metamodel, i.e., the genetic algorithm and the Kriging model, based on DOE. In that study, to obtain the DOE results, several models had to be designed and FEAs were required.

The novelty of this distinguishes it from previous studies for the following reasons: First, optimal design can be easily processed based on a novel automated DOE procedure based on FEA, so it can be done faster and more accurately. In general, DOE by FEA consists of modeling process using CAD tools, analysis condition setting process for FEA, FEA process, and post process for extracting and organizing results. To obtain a reliable optimal design result, a large number of DOE have to be carried out. However, the conventional method of manually performing the process was complicated and time consuming, and thus the number of DOE was limited [10–18]. However, using the automated DOE process proposed in this study, not only can the DOE be easier but also the number of DOE can be dramatically increased, resulting in high reliability of the optimal design result. The proposed automated design method is expected to reduce the design cost and time. Moreover, it can be used to find the optimal solution for various design problems as well as PMSMs. In addition, since the proposed procedure is based on commercial tools, it has a ripple effect that can easily apply optimal design in academia and industry.

Most of the previous studies have been applied to optimal design using metamodel generated in one way. There have been a lot of optimizations recently using a single metamodeling technique such as Kriging and response surface method [10–18]. However, since a suitable metamodel is different according to each design problem and condition, it is necessary to select the best metamodel through accuracy evaluation after generating several metamodels. This is because the accuracy of the metamodel must be high to obtain good optimal design results. In this study, metamodels of objective functions and constraints are generated in 11 ways, and the most accurate metamodels are selected through the root mean squared error (RMSE) test, respectively.

In this study, shape optimization is performed for a PMSM to maximize the torque while maintaining efficiency, torque ripple and THD in the back electromotive force (EMF). First, the design target specification of a PMSM for small electric vehicles is established, and the characteristics of the initial model are analyzed using FEA. To improve the accuracy of the design results, DOE is performed using FEA. After the creation of metamodels using the DOE results, the optimal values are obtained by the optimal algorithm. The optimal Latin hypercube design (OLHD) technique [19] is applied for the DOE, and the appropriate DOE number and test point number are selected to produce accurate metamodels. To perform DOE easily and accurately, this study proposes an automated DOE procedure through linkage between an FEA program and an optimal design program. Using the DOE results, the relationship between the design and output variables are analyzed by screening. To generate an accurate metamodel, the RMSE tests are performed on eleven metamodels for each output variable, and the best metamodels are selected for each output variable. Optimization based on metamodels is performed, and the global optimization algorithm hybrid metaheuristic algorithm (HMA) [20] is utilized as the optimal algorithm. The overall process of this study is represented in a flowchart, as shown in Figure 1.

**Figure 1.** Flowchart of the overall research procedure.

#### **2. Finite Element Analysis**

The target specifications are determined by referring to the Renault's Twizy with a torque of 57 N·m and an output power of 13 kW at 2100 rpm. In this study, a PMSM is selected as the design model, and the target output power is 15 kW which should satisfy 60 N·m at 2387 rpm.

#### *2.1. Initial Model*

Figure 2 and Table 1 show the structure and specifications of a 15 kW PMSM for a small electric vehicle, respectively. The PMSM has 8 poles, 36 slots, and distributed winding.

**Figure 2.** Structure of initial permanent magnet synchronous motor (PMSM) model (1/4 model).


**Table 1.** Specifications of analysis model.

The electromagnetic, mechanical and thermal properties of the 35PN210 core material are shown in Table 2. Core loss is the sum of hysteresis loss, eddy-current loss, and excess loss, and is calculated by Equation (1). The core loss varies with frequency, but the analysis is based on 60 Hz.

$$P\_{\mathfrak{c}} = K\_{\mathfrak{h}} f(B\_m)^2 + K\_{\mathfrak{c}} (fB\_m)^2 + K\_{\mathfrak{e}} (fB\_m)^{1.5} \tag{1}$$

where *Pc* is the core loss, *Kh* is the hysteresis loss coefficient, *Kc* is the eddy current loss coefficient, *Ke* is the excess loss coefficient, *f* is the frequency, and *Bm* is the amplitude of the alternating flux component.

The electromagnetic, mechanical and thermal properties of permanent magnets are shown in Table 3. V-shaped N38UH grade NdFeB are applied to concentrate the magnetic flux. The magnetic flux density and coercivity decreased with increasing temperature, but the analysis is conducted at 20 ◦C.


**Table 2.** Properties of electrical steel.



#### *2.2. No Load Analysis*

Characteristic analysis of the initial model is performed by FEA under the no load condition without current excitation. When the rotor of the initial model rotates at the rated speed, back EMF is induced in the stator winding. Since the back EMF simulation is performed while rotating the rotor under the no load condition, the equivalent circuit when the PMSM operates as a generator should be considered, as shown in Figure 3. The voltage equation of the equivalent circuit is shown in Equation (2). However, since no current flows in the armature winding under the no load condition, the terminal voltage and the no load EMF are the same. The back EMF of phase A can be obtained by Equation (3), and the analysis result by FEA is illustrated in Figure 4a.

$$
\dot{V} = \dot{E}\_0 - (\dot{j}(X\_a + X\_l) + R\_a)\dot{I}\_a \text{ [V]} \tag{2}
$$

where . *<sup>V</sup>* is the terminal voltage, . *E*<sup>0</sup> is the no load EMF, *Xa* is the armature reation reactance, *Xl* is the leakage reactance, *Ra* is the armature resistance and *Ia*. is the load current.

$$E\_a = \text{N}\mathcal{Q}\omega\alpha\text{cosat [V]}\tag{3}$$

where *Ea*. is the back EMF of phase A, *N* is the number of the amarture turns, ∅ is the magnetic flux and ω is the electrical angular velocity.

THD is an important factor in the electrical equipment and power systems. THD can be obtained by adding the harmonic components to the fundamental wave components of voltage or current as shown in Equation (4) [21]. A higher THD increases the core loss in electric machines, which can reduce the efficiency and generate excessive heat. The harmonic analysis result of the back EMF waveform is shown in Figure 4b, and the THD of the back EMF calculated by Equation (4) is 3.52%.

$$V\_{\rm THD} = \frac{\sqrt{V\_2^2 + V\_3^2 + V\_4^2 + \dots + V\_n^2}}{V\_1} \times 100\tag{4}$$

where *V*THD is the THD of the back EMF, *V*<sup>1</sup> is the RMS voltage of the fundamental frequency and *Vn* is the RMS voltage of nth harmonic.

**Figure 3.** The equivalent circuit of PMSM (generator mode).

**Figure 4.** The back EMF of initial model under the no load condition: (**a**) Waveform; (**b**) Harmonic.

#### *2.3. Load Analysis*

Target specifications are 15 kW and 60 N·m at 2387 rpm as shown in Table 1. To perform load analysis, a current condition satisfying the target torque of 60 N·m at 2387 rpm should be found. Through static torque analysis, the current condition is determined as the RMS value of 146 A and phase angle of 25◦. As shown in Figure 5a, the average torque is 59.95 N·m and the torque ripple is 5.09% of torque. The core loss is interpreted as shown in Figure 5b, and total losses are the sum of the core loss and copper loss. The output power of the motor is calculated as the product of torque and angular velocity, and the efficiency can be calculated from the output power and total losses of the motor. The efficiency of the initial model is calculated to be 91.42%.

**Figure 5.** Torque and core loss of the initial model under the load condition: (**a**) Torque; (**b**) Core loss.

#### **3. Design Optimization**

#### *3.1. Design Process*

The design optimization process for maximizing the average torque, while maintaining THD of the back EMF, efficiency, and torque ripple, is shown in Figure 6. The objective function, constraints, thermal condition, and design variables are established, as described in Equations (5)–(9) and Figure 7. To improve the average torque, the average torque is set as both an objective function and a constraint, with a goal of 2% improvement over the initial model. THD of the back EMF and the efficiency are set as constraints to maintain the same level as the initial model. The torque ripple is set below 10%, which is an acceptable level as a traction motor for electric vehicles [22]. To improve the accuracy of the design results, DOE is performed using FEA. Because DOE using FEA requires a significant amount of time and effort, interworking is conducted between the FEA and optimal design programs, which are ANSYS Maxwell and PIAnO, respectively, to automatically perform DOE. When the analysis and extraction of results for one experiment is finished, the values of the design variables are automatically changed to perform the FEA at the next DOE point. From the DOE results, sensitivity analysis between design variables and output variables is conducted using screening, and each metamodel for output variables is generated. RMSE test was conducted to evaluate the predictive performance of the metamodels, and the best metamodel is selected for each output variable. Based on the selected metamodels, the optimal values are obtained using the HMA.

#### Objective function


Design variables (based on the value of the initial model)

$$\begin{array}{l} -4 \text{ mm} \le \text{DV1 (Barrier length)} \le 10 \text{ mm} \\ -1.0 \text{ mm} \le \text{DV2 (Rib thickness)} \le 0.5 \text{ mm} \\ -1.0 \text{ mm} \le \text{DV3 (Teeth width)} \le 0 \text{ mm} \\ 0 \text{ mm} \le \text{DV4 (Teeth thickness)} \le 1.0 \text{ mm} \\ 0 \text{ mm} \le \text{DV5 (Barrier gap)} \le 2.0 \text{ mm} \end{array}$$

(9)

**Figure 6.** Optimization design process.

**Figure 7.** Shape design variables.

The mechanical constraints of the barrier length are set from a range that facilitates the flow of magnetic flux to a range that inhibits the flow of magnetic flux very much, as shown in Figure 8a. Rib thickness is set to be at least 1 mm in consideration of workability at manufacture and mechanical rigidity at high speed, as shown in Figure 8b. Figure 8c shows the mechanical constraints of the teeth width, and the range is set so that the slot is smaller than the initial model and maintains the proper

fill factor. The range of teeth thickness is set up to reduce the saturation of the magnetic flux at the tip of the teeth and maintain the proper fill factor, as shown in Figure 8d. Barrier gap size affects the formation of magnetic flux and the motor performance since the permanent magnet position also changes. Therefore, its mechanical constraints are set as shown in Figure 8e.

**Figure 8.** Mechanical constraints of design variables: (**a**) DV1 (barrier length); (**b**) DV2 (rib thickness); (**c**) DV3 (teeth width); (**d**) DV4 (teeth thickness); (**e**) DV5 (barrier gap). Notes: The values of the design variables are relative to the values of the initial model.

#### *3.2. Automated DOE Procedure*

To perform DOE, the shape of design variable should be changed. However, when DOE is processed manually, the shape of each model is drawn using the CAD tool. Next, the designed shape should be imported into the FEA program and the FEA should be performed for each model. After FEA, the post process is required to calculate the desired result. As manual DOE requires a lot of effort and time, this study suggests the automation of the DOE process. First, the Maxwell's parametric sweep setup function is used to change the shape of design variables without using the CAD tool. The use of this function can change the shape of the FEA model by inputting numerical values in the Maxwell program. Next, Maxwell's Macro function is used to perform DOE using PIAnO, an optimal design program. As the design variables change, the vbscript and batch files are created to automatically change the shape of the FEA model. In addition, vbscript and batch files are generated for FEA under the no load and load conditions for each experiment. Vbscript and batch files also are generated to output and quantify the torque, core loss and FFT analysis results of the back EMF obtained through FEA. The files created through the Macro function are shown in Figure 9. Next, the interface configuration between Maxwell and PIAnO for automation is shown in Figure 10. To process DOE in PIAnO, the files created in Maxwell are imported as shown in Figure 10a, and the script for calculating the output variables is shown in Figure 10b.

**Figure 9.** Vbscript, batch, and output files using the Macro function of Maxwell.


**Figure 10.** *Cont.*


**Figure 10.** Interface configuration with Maxwell using PIAnO: (**a**) Interface setting; (**b**) Script for calculating output variables.

#### *3.3. Design of Experiment*

The number of experiments and the number of test points are determined in three steps [23]. First, the number of experiments should be selected according to the number of design variables. When the number of design variables is ten or less, the number of experimental points is determined by Equation (10),

$$\text{nEXP} > 1.5 \times \text{nSAT} = 1.5 \times \frac{(\text{nDV} + 1) \times (\text{nDV} + 2)}{2} \tag{10}$$

where nEXP is the number of DOE, nSAT is the number of saturation, and nDV is the number of design variables.

Next, the number of DOEs that can be used as test points for evaluating the accuracy of the metamodel should be secured by Equation (11):

$$\text{nEXP} > \min\left[\frac{(\text{nDV} + 1) \times (\text{nDV} + 2)}{2}, 10 \times \text{nDV}\right] + (5 \times \text{nDV})\tag{11}$$

Because five design variables are used in this study, the number of DOE should be more than 46 by Equations (10) and (11). Therefore, the number of DOE is determined to be 50, which is a multiple of the design variables. If fifty experiments are manually operated, a significant amount of effort and time would be required. However, in this study, automation is implemented so that DOE can be easily developed and design cost can be reduced. Finally, the number of test points for evaluating the accuracy of the metamodel is determined to be five by Equation (12),

$$\text{nEXP\\_ts} > \min[\text{nEXP} \times 10\%, \ 10 \times \text{nDV}] \tag{12}$$

where nEXP\_ts is the number of test points.

The OLHD technique is applied to determine the sampling point of the DOE. OLHD is a type of DACE sampling technique developed for computational experiments. In the computer experiment, because there are no random errors, only the bias error should be considered and the test point should be spread evenly inside the design area. OLHD improves the space-filling property by using the optimum conditions and spreads the test points evenly; thus, even if there are several test points, they can be selected efficiently. DOE for fifty test points selected by OLHD is easily performed using the automated program. Sensitivity analysis is conducted to analyze the correlation between the design variables and design results. Figure 11 shows that the barrier length has the highest impact on the output variables among the five design variables. However, as shown in Table 4, even the most optimal experimental point among the 50 experiments does not satisfy the constraints. Therefore, metamodeling based on DOE results is conducted.

**Figure 11.** Sensitivity analysis using screening.


#### *3.4. Metamodeling*

Five test points are selected to evaluate the metamodel, and eleven metamodels are generated for each output variable. The metamodel can be classified into a regression model and an interpolation model. The regression model, i.e., polynomial regression (PR), radial basis function regression (RBFr), ensemble of decision trees (EDT), and multi-layer perceptron (MLP), smoothens the noise data because they do not pass through the test points exactly. Therefore, this model is useful for real experiments with random errors. PR allows free choice of regression terms [24]. RBF is easy to design and generalize, and has strong tolerance to input noise [25]. EDT is advantageous for expressing nonlinearity in large amounts of data. MLP is type of deep learning algorithm and has the advantage of being able to represent the nonlinear relationships between input and output variables [26]. In contrast, the interpolation model, i.e., Kriging and radial basis function interpolation (RBFi), is well suited for function approximation using analytical results without random errors because it passes through the test points exactly. The estimated equation of the Kriging model was defined to eliminate bias and thereby minimize error variance [27]. Thus, a numerically robust model is provided. RBFi was first popularized in the machine learning community and has been used in computer graphics [28].

The accuracy of the metamodel is a very important factor in the optimal design using metamodel [12]. This is because the predictive performance of the metamodel affects the reliability of the optimal design. Most of the existing studies have been metamodeled by a single method such as Kriging and RSM, and the accuracy evaluation has not been performed [10–18]. In this study, however, metamodels for the objective function and constraints are generated in 11 ways provided by PIAnO, and the best metamodels are selected, respectively, by comparing the RMSE test results to evaluate the metamodel accuracy. The predictive performance of the metamodel is evaluated by the RMSE test and is calculated by Equation (13) [23],

$$\text{RMSE} = \sqrt{\frac{1}{\text{nEXP\\_ts}} \sum\_{i=1}^{n \text{EXP\\_ts}} \left[ y(X\_i) - \hat{y}(X\_i) \right]^2} \tag{13}$$

where *y*(*Xi*) is the value of the real function and *y*ˆ(*Xi*) is the value of the metamodel.

Through the RMSE test, the predictive performances of the metamodels are evaluated for the output variables. The RMSE test showed the best predictive performance of RBFr as a metamodel of the average torque as shown in Table 5. Similarly, the RMSE tests are conducted on the metamodel for efficiency, torque ripple, and THD of the back EMF. Based on the test results, the metamodels with the best predictive performance for each output variable are selected for use in the optimal design, as shown in Table 6.


**Table 5.** RMSE test results of metamodels for the objective function.


**Table 6.** Selected metamodels of the output variable by RMSE test.

#### *3.5. Design Optimization Based on Metamodel*

The HMA, a global optimization algorithm, is used for the optimal design based on the metamodel. The HMA was proposed in 2016 by Park [20]. HMA can determine the global optimum faster than other global optimizers owing to the combined advantages of improved constrained differential evolution and modified cuckoo search.

The optimum design results predicted from the metamodel based HMA are shown in Table 7 and verified through FEA. The predicted results showed that the average torque, THD of the back EMF, efficiency and torque ripple results are similar to the FEA results. Therefore, the automated DOE procedure and the generation and evaluation of the metamodel were verified. The average torque of the optimal model was 2.5% better than the initial model, and the torque ripple increased slightly, as shown in Figure 12. THD of the back EMF and efficiency set by the constraints were slightly improved. Although the torque ripple of the optimal model is 7.822%, it is very acceptable as a traction motor for electric vehicles [22].


**Table 7.** Optimization results.

**Figure 12.** Torque waveforms.

#### *3.6. Consideration of Optimal Design Results*

Figures 13 and 14 show the flux distributfion and flux density of the initial and optimal models, respectively. In comparison to the initial model, the rib thickness and barrier length of the optimal model were reduced, and the barrier gap was increased. As the rib thickness decreased, the unnecessary flux flow between the north pole and south pole through the rotor rib was reduced. In addition, the flux flow was smoothly improved owing to the reduction in barrier length, and consequently, more flux passed through the stator core. The improvements in the magnetic flux flow and the change in reluctance can be considered to be the cause of the increase in the back EMF and torque [29]. Owing to the improvements of in the flux flow, the back EMF of the optimum model was 35.0 V, which showed an improvement of 7.4% in comparison to 32.6 V of the initial model, as shown in Figure 15. In addition, owing to the sinusoidal improvement in the waveform of the back EMF of the optimal model, the THD was slightly improved from 3.414% to 3.065%.

**Figure 13.** Flux distribution under no load condition: (**a**) Initial model; (**b**) Optimal model.

**Figure 14.** Flux density under no load condition: (**a**) Initial model; (**b**) Optimal model.

**Figure 15.** Back EMF waveforms.

#### **4. Conclusions**

This paper presented shape optimization of a PMSM for small electric vehicles to maximize torque while maintaining efficiency, torque ripple and THD of the back EMF. To improve the accuracy of the optimal design results, DOE was performed using FEA. This study proposed an automated DOE procedure through linkage between an FEA and optimal design programs to perform DOE easily and accurately. Parametric modeling was performed for the FEA model to change the shape variables automatically, and automation-related files were created using Maxwell's Macro function. In addition, an interface was established to link the FEA program with PIAnO, an optimal design program. Using the built-in automation program, 50 FEAs for the experimental points selected by OLHD were easily performed. From the DOE results, the relationship between the design and output variables was analyzed by screening. Among the five design variables, the barrier length was found to have the greatest effect on the output variables. Eleven metamodels were created for each output variable and RMSE test was conducted to evaluate the predictive performance of the metamodels. Consequently, the metamodels with the best predictive performance for each output variable were selected. Finally, the optimization design based on the metamodel was determined using the HMA to find the global optimum. The objective average torque improved by 2.5% over the initial model while satisfying all the constraints. The optimal design results were finally verified by FEA.

The proposed automated design method is expected to reduce design cost and time. Moreover, it can be used to find the optimal solution for various design problems as well as PMSMs. By following the procedure given below, the proposed optimal design method can be applied to any type of motor without any special constraints. First, in order to change the shape of the optimum design variable automatically, the dimension of the optimal design variable should be set using Maxwell's parametric sweep setup function. Next, determine the values that you want to extract from Maxwell and create vbscript and batch files to extract them. Finally, an interface setting must be performed to accommodate Maxwell's output values in an optimization program called PIAnO.

Optimization of multi-physics systems by simulation takes significant computing time for each simulation run, and its process depends on numerous runs, making it difficult and expensive [30]. However, using the automated DOE procedure suggested in this study can reduce design cost and time, so I think multi-physics analysis is possible in the near future. In the next project, I will consider multi-physics analysis that takes into account the mechanical and thermal properties.

**Funding:** This study was supported by research fund from Honam University, 2017 and the National Research Foundation of Korea (NRF). Grant funded by the Korea government (MSIT). (No. NRF-2018R1C1B5046117).

**Acknowledgments:** The author express gratitude to PIDOTECH and FRONTIS for their technical support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**


#### **References**


© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
