Structural Optimization Design and Analysis of Interior Permanent Magnet Synchronous Motor with Low Iron Loss Based on the Adhesive Lamination Process

Abstract

The interior permanent magnet synchronous motors (IPMSMs) are extensively applied in the field of new energy vehicles due to their high-power density and excellent performance control. However, the iron loss has a significant impact on their performance. This study conducts an optimization analysis on the processing technology of silicon steel sheets and motor structure, targeting the reduction of iron loss and the improvement of the motor’s integrated efficiency. Firstly, the influences of two iron core processing technologies on iron loss, namely gluing and welding, are compared. Through experimental tests, it is found that the iron loss density of the gluing process is lower than that of the welding process, and as the magnetic flux density increases, the difference between the two is expanding. Therefore, the iron loss test data from the adhesive process are employed to develop a variable-coefficient iron loss model, enabling precise calculation of the motor’s iron loss. On this basis, aiming at the problem of excessive iron loss of the motor, a novel topological structure of the stator and rotor is proposed. With the optimization goal of reducing the motor iron loss and taking the connection port of the air magnetic isolation slot and the gap of the stator module as the optimization variables, the optimized design of the IPMSM with low iron loss is achieved based on the Taguchi method. After optimization, the stator iron loss decreases by 13.60%, the rotor iron loss decreases by 20.14%, and the total iron loss is reduced by 15.34%. The optimization scheme takes into account both the electromagnetic performance and the process feasibility, it offers technical backing for the high-efficiency operation of new energy vehicle drive motors.

1. Introduction

Interior permanent magnet synchronous motor (IPMSM), with its characteristics of high-power density, wide speed regulation range, and excellent efficiency, has become the core power device in fields such as new energy vehicles and industry [1,2]. However, as motors develop towards high speed and high power density, the problem of iron loss has become increasingly prominent. It not only reduces the motor efficiency but also causes temperature rise, vibration, and noise, weakening the reliability of the system [3,4]. According to statistics, under high-speed operating conditions, the hysteresis loss and eddy current loss of the stator and rotor are particularly significant [5,6]. Therefore, how to reduce iron loss through material process optimization and structural innovation has become a key research direction for improving the comprehensive performance of IPMSM.

The processing technology and material properties of silicon steel sheets exert a decisive impact on the iron loss of IPMSM. References [7,8] studied the influence of iron loss of non-oriented electrical steels with different thicknesses during the shearing process and found that the iron loss of thinner specimens was significantly smaller. Reference [9] focused on investigating the correlation between heat treatment temperature control and the reduction ratio of iron loss. The research results show that maintaining the silicon steel material near the recommended annealing temperature can effectively reduce the hysteresis loss, and the total iron loss can be reduced by 58%. Reference [10] has found that burrs during the processing will lead to additional iron losses. Reference [11] primarily investigates the influence of materials on motor iron loss. The research results indicate that motors using soft magnetic composite (SMC) materials exhibit lower eddy current losses and higher motor efficiency. Reference [12] explored the effect of silicon content in silicon steel on iron loss. As the silicon content increased, the iron loss incurred by silicon steel showed a downward trend. Further, IPMSMs were manufactured using silicon steel sheets with silicon contents of 3.0%, 6.5%, and 6.7%. The test results showed that the motor with a silicon content of 6.7% had the minimum iron loss. References [13,14] conducted experimental investigations into the impact of the stamping process on the iron loss of non-oriented electrical steel sheets. The research indicated that the residual stress during the stamping process would hinder the magnetization process and increase the hysteresis loss. In addition, the processing technology of silicon steel also affects iron loss by changing the microstructure and magnetic domain characteristics of the silicon steel material.

In order to minimize the motor’s iron loss and enhance its operational efficiency, it is difficult to achieve the desired effect only by improving the materials and processing technology. Therefore, it becomes essential to optimize the motor’s structure design to further reduce iron loss. Reference [15] reduced the harmonics of the rotor magnetomotive force by optimizing the ratio of the pole arc to the pole pitch of the magnet. By analyzing and comparing the iron loss and iron-loss density of three IPMSMs, the results showed that the efficiency of the optimized V-shaped IPMSM was improved under high-speed conditions. Reference [16] proposed a new rotor structure for the IPMSM to reduce the harmonic iron loss under high-speed field-weakening control. The prototype test results showed that the iron loss of the optimized motor decreased to 50% of its pre-optimization level, while the electromagnetic torque did not decrease significantly. Reference [17] used the Taguchi method to improve the magnet cavity of an IPMSM with a single-layer U-shaped magnet geometry, thereby reducing the motor’s iron loss and improving its operating efficiency. In Reference [18], a non-uniform air-gap was applied to the IPMSM rotor to achieve optimal eccentricity. Through the finite-element method simulation of the optimized motor model, the results indicated that not only was the motor’s iron loss notably decreased, and its efficiency enhanced, but the torque ripple was also reduced. Reference [19] adopts the Taguchi method for optimization design to minimize the losses of the motor and improve its operating efficiency. Variables are chosen as the stator yoke height, stator teeth width, permanent magnet thickness, and air gap length. Then, an analysis of variance is carried out to determine the optimal combination. The final results show that the efficiency of the motor is significantly improved, verifying the feasibility of this method. Reference [20] increased the number of winding layers aiming to decrease the harmonics in motor magnetomotive force and, thus, reduce the motor’s iron loss. In Reference [21], the position and diameter of the magnetic isolation holes were optimized through the establishment of a parametric model. The results demonstrated that the optimized I2V-type rotor topology led to a significant reduction in both iron loss. Reference [22] studied the influence of the scheme of the motor controller and the switching frequency on iron loss, then conducted experimental tests on two axial flux motor prototypes. The stator loss is estimated through experiments, and the stator temperature is monitored and used for thermal model simulation. The experimental results show that the smooth performance of the field-oriented control with a higher switching frequency can result in lower stator iron losses. Reference [23] proposed a loss optimization method, that determines the optimal current reference by minimizing stator losses under the ripple-free torque constraint. The performance of the loss optimization method is verified through the experiment of a 3.8 kW PMSM prototype. Reference [24] proposed an optimized PMSM with a segmented permanent magnet structure. The genetic algorithm is employed to determine the final optimized design scheme, and a prototype is manufactured. Through a comparison between the finite element results and the experimental test results, it is shown that the efficiency of the optimized PMSM is greatly improved. Reference [25] in order to minimize the rotor losses of the PMSM and improve the power density, the comprehensive constraints of electromagnetic and mechanical performances are taken into account. The finite element method is employed to analyze the performance of the motor, and multi-physical field analysis is carried out, including electromagnetic field analysis, rotor loss analysis and so on. According to the optimized design results, a prototype is manufactured and experimental tests are conducted. The experimental results confirm the accuracy and validity of the optimal design.

Based on the above research, this paper systematically quantifies the loss difference between the adhesive bonding and welding processes through the iron-loss experiment of ring specimens. The experimental results show that under the same operating conditions, the iron loss exhibited by silicon-steel sheets prepared by the adhesive-bonding process is lower than by the welding process, and as the magnetic-flux density increases, the difference between the two expands. Based on the iron loss test data of the adhesive process, a variable coefficient iron loss model is established to accurately compute the motor’s iron loss. Further, aiming at the problem of excessive iron loss in an IPMSM, an improved topological structure is proposed to reduce the motor’s iron loss. To determine the optimal design structure, a multi-objective optimization design of its key parameters is carried out based on the Taguchi experimental method.

2. Variable Coefficient Iron Loss Model Based on the Process Analysis of Silicon Steel Sheets

Iron loss is not only closely related to material properties but also directly associated with processing technology. The influence of adhesive bonding and welding processes on iron loss is crucial in motor manufacturing. In this section, the impact of these two processes on the motor iron loss will be analyzed, and iron loss experiments will be conducted on silicon steel sheet ring specimens. This provides theoretical basis and experimental support for the optimization of motor design.

2.1. Principle Analysis of Welding and Adhesive Bonding Processes

The stator and rotor cores of the motor are formed by stacking and connecting non-oriented silicon steel sheets. With the improvement of technology, the adhesive bonding process has gradually become a popular research topic. Figure 1 shows the schematic diagrams of the adhesive bonding and welding processes for silicon steel sheets, intuitively present the differences in their physical structures.

The welding process forms spot welds to connect metal materials by means of local heating and melting. During this process, it may cause local performance changes in the silicon steel sheets due to high temperature, resulting in the distortion of the hysteresis loop and, thus, increasing the hysteresis loss. The presence of welding points will also disrupt the uniformity of the magnetic circuit, leading to additional stray losses. In contrast, the adhesive process, through a non-thermal connection method, can well preserve the original magnetic properties of the silicon steel sheets and effectively reduce the hysteresis loss. The uniform distribution of the adhesive layer helps to reduce the edge effect of the eddy current and lower the eddy current loss. Meanwhile, the stable magnetic circuit structure can reduce additional losses.

2.2. Experimental Verification of Iron Loss for Ring Specimens

To validate the impact of the adhesive bonding process and the welding process on iron loss, in this study, ring specimens made of silicon steel sheets were selected for the iron loss test experiment. The thickness of the silicon steel sheets used is 0.2 mm, and the model is 20WTG1500, the excitation alternating frequency is in the range of 50 Hz to 1000 Hz, the excitation range is from 0 to 1.8 T, and the test temperature is maintained at room temperature of 25 °C. The ring specimens are surrounded by the primary coil and the secondary coil. The primary coil is responsible for applying an alternating magnetic field to the ring specimens, and the secondary coil is used to sense the magnetic flux changes in the specimens. The number of turns of the coils should be appropriate to ensure that the power amplifier will not be overloaded and that the required field strength during magnetization can be achieved. The calculation formulas for the primary coil and the secondary coil are as follows [26]:

$$\begin{array}{l}{N}_1={\displaystyle \frac{HL}{I}}\\ N_2={\displaystyle \frac{U}{2\pi fBS}}\end{array}$$

(1)

In Equation (1): H is the magnetic field strength, L is the effective length of the magnetic circuit, I is the maximum output current, U is the maximum output induced voltage, N₁ is the winding turns number of the primary side, and N₂ is the winding turns number of the second side. Place the annular specimen into the thermostatic chamber and maintain a constant temperature to prevent the effect of temperature on iron loss. Connect the annular specimen to the soft magnetic alternating current measuring instrument through the fixture. Input the basic parameters of the annular specimen (such as inner and outer diameters, thickness, density, etc.) on the parameter setting interface of the computer for the specimen and input the frequency and the magnitude of the excitation to be tested on the control interface. Data calibration is required before starting the test. After the test data converge through multiple tests, the iron loss test results can be read on the computer. The specific iron loss experimental test platform is shown in Figure 2, and the test result is shown in Figure 3:

Through the iron loss test experiment of the ring specimens, the iron loss density curves of the adhesive bonding process and the welding process under different frequencies and magnetic flux densities are obtained as shown in Figure 4. As the frequency and the magnetic flux density increase, the iron loss density gradually increases, and with the increase in the frequency, the increasing trend of the iron loss density becomes more obvious. Under any magnetic flux density and frequency, the iron loss density of the adhesive bonding process is smaller than that of the welding process, and as the magnetic flux density increases, the difference in iron loss density between the two also expands. When the magnetic flux density is less than 1 T, the gap between the iron loss density curves of the two is not obvious, and the iron loss density of the adhesive bonding process is only about 2% smaller than that of the welding process. When the magnetic flux density is between 1 T and 1.5 T, the difference between the two is about 4%. When the magnetic flux density is greater than 1.6 T, the difference between the two exceeds 6%.

2.3. Modeling of the Variable Coefficient Iron Loss Model Based on the Iron Loss Data of the Adhesive Process

Iron loss is composed of three parts: hysteresis loss, eddy current loss, and additional loss. Hysteresis loss occurs during the magnetization and demagnetization processes of magnetic materials, resulting from the irreversible rotation of magnetic domains and the irreversible displacement of domain walls. Eddy current loss arises from the induction of electric currents in conductors under alternating magnetic fields; these currents form closed loops within the conductor, generating Joule heat and thus energy loss. Additional loss arises from a combination of complex factors, including manufacturing defects in magnetic materials, non-ideal magnetic circuit structures, and special effects at high frequencies, leading to extra energy dissipation. Figure 5 shows the iron loss density data of the adhesive process under different magnetic flux densities and frequencies. Based on this, a variable coefficient iron loss model is established to further analyze the iron loss of an IPMSM [27]. A high-precision variable coefficient iron loss model is established as shown in Equation (2).

$$P_{\mathrm{Fe}}=k_{\mathrm{h}}(f,B)f{B}^{\alpha }+k_{\mathrm{c}}(f,B)f^2{B}^2+k_{\mathrm{e}}(f,B)f^{1.5}{B}^{1.5}$$

(2)

In Equation (2), P_Fe is the iron loss per unit mass, k_h is the hysteresis loss coefficient, α is the Steinmetz coefficient, k_c is the eddy current loss coefficient, k_e is the additional loss coefficient, f is the frequency, and B is the amplitude of the magnetic flux density. The loss coefficients change with the variation in the magnetic flux density and frequency, which are obtained through fitting in MATLAB 2019b. The Steinmetz coefficient α is 1.45, and the expressions of k_h and k_c are as follows:

$$\begin{array}{cc}{k}_{\mathrm{h}}(f,B)& =2.42\times {10}^{-3}\times f^2-3.4\times {10}^{-4}\times f\times B+7.3\times {10}^{-7}\times B^2\\ & +1.15\times {10}^{-2}\times f+7.52\times {10}^{-5}\times B+1.68\times {10}^{-2}\\ k_{\mathrm{c}}(f,B)& =9.64\times {10}^{-6}\times f^2-2.93\times {10}^{-8}\times f\times B+6.34\times {10}^{-11}\times B^2\\ & -5.32\times {10}^{-5}\times f-1.97\times {10}^{-7}\times B+5.65\times {10}^{-4}\\ k_{\mathrm{e}}(f,B)& =1.35\times {10}^{-3}\times f^2-8.91\times {10}^{-9}\times f\times B+7.83\times {10}^{-6}\times B^2\\ & -2.66\times {10}^{-3}\times f-2.27\times {10}^{-5}\times B+1.21\times {10}^{-4}\end{array}$$

(3)

3. Modeling and Optimization Analysis of IPMSM

In this section, the traditional structure of the IPMSM is first described, based on the variable coefficient iron loss model described in Section 2.3, the iron losses of the motor under rated operating conditions are calculated in detail. Furthermore, aiming at the problem of excessive iron losses in the motor, a novel stator–rotor topology is proposed. This paper theoretically analyzes the feasibility of the proposed structure in reducing motor iron loss and verifies the effectiveness of the improved structure via finite element simulation and calculation.

3.1. The Structure and Parameters of the Traditional IPMSM

In this paper, an IPMSM is selected as the research object, and the main structural parameters are shown in

Table 1. Basic parameters of the motor.

Parameter	Unit	Value
Number of pole pairs	\	4
Number of stator slots	\	48
The length of the air gap	mm	0.5
Stator inner diameter	mm	98
Stator outer diameter	mm	154
Rotor inner diameter	mm	97
Rotor outer diameter	mm	40
Axial length	mm	160
Rated speed	rpm	5300
Rated torque	N·m	68
Rated power	kW	38
Rated efficiency	\	94%
Winding resistance	mΩ	9.8
Inductor	mH	0.13

.

The permanent magnets of the motor adopt a single-layer V-shaped structure. Similar triangular air magnetic isolation slots are added on both sides of the magnetic poles near the surface of the rotor core in the direction of the magnetic pole centerline. This structure can make the distribution of the magnetomotive force of the permanent magnets in the air-gap closer to a sine wave, effectively reducing the torque ripple of the motor. Figure 6 is a comparison diagram of the torque of the motor with and without the air magnetic insulation groove structure. After adding the air-assisted magnetic insulation groove, the torque ripple decreases from 19.14% to 4.84%.

There are significant differences in the magnetic flux density distributions in different regions of the motor stator and rotor. In this paper, the stator and rotor cores are divided into seven regions according to the characteristics of the magnetic flux density distribution, namely the outer part of the stator yoke, the inner part of the stator yoke, the stator tooth tip, the stator tooth body, the stator tooth bottom, the part of the rotor magnetic pole, and the part of the rotor near the rotating shaft. And select multiple characteristic points within each region. The specific regional distribution is shown in Figure 7.

Based on the finite element theory of the two-dimensional electromagnetic field, the radial and tangential magnetic flux densities at the characteristic points of each region are extracted. According to the principle of Fourier harmonic decomposition in this paper, the waveforms of the radial and tangential magnetic flux densities are decomposed into the fundamental wave and a series of higher harmonics, which are, respectively, substituted into the iron loss model with variable coefficients for calculation, and the iron loss of the core of the entire motor is obtained by summation. To simplify the calculation process, taking the central points of the stator region A and the rotor region F as examples in this section, the radial component of magnetic flux density and the tangential component of magnetic flux density, and the harmonic decomposition process are shown in detail. The specific magnetic flux density decomposition is shown in Figure 8 and Figure 9 below.

The motor used in this paper is an integral slot motor, which does not contain even harmonics and only considers odd harmonics. The iron loss of the motor stator is mainly generated by the fundamental wave and a series of higher odd harmonics. The rotor rotates synchronously with the fundamental wave component of the synthetic magnetic field generated by the three-phase armature current. Therefore, the fundamental wave of the rotor magnetic flux density does not generate iron loss, and the iron loss is mainly generated by higher harmonics. By separately inserting the magnetic flux density amplitudes of the fundamental wave and harmonics into the variable–coefficient iron loss model, the losses of each region of the stator and rotor can be obtained, and the specific calculated values are shown in

Table 2. Losses in various regions of the motor core.

Area	Radial (W/Kg)	Tangential (W/Kg)	Quality (Kg)	Loss (W)
A	12.13	38.21	4.88 × 10−2	2.46
B	24.56	22.61	4.45 × 10−2	2.10
C	49.19	21.68	2.13 × 10−2	1.51
D	56.09	0.11	8.08 × 10−2	4.54
E	49.45	48.56	2.49 × 10−3	0.24
F	21.41	17.16	5.39 × 10−1	20.79
G	21.71	25.57	6.16 × 10−2	2.91

.

As can be seen from Table 2, before the improvement, under the rated operating conditions, the stator iron loss of the motor is 520.80 W, the rotor iron loss is 189.60 W.

3.2. Novel Topological Structure of IPMSM

In order to reduce the iron loss of the motor, this section conducts an optimization design from the perspectives of both the stator and the rotor of the motor. On the one hand, the magnetic circuit is optimized through the modular design of the stator to reduce local magnetic flux density saturation, thereby reducing hysteresis loss. The harmonic magnetic field is suppressed to reduce high-frequency eddy current loss. On the other hand, by optimizing the structure of the magnetic isolation slots of the motor rotor, the interference of the harmonic magnetomotive force-generated by the permanent magnets on the air-gap magnetic field can be effectively suppressed, thus, reducing the iron loss of the motor. The novel topological structure of the IPMSM divides the stator into 24 modules. The air magnetic isolation slots near the surface of the rotor core of adjacent magnetic poles are connected, and at the same time, the air magnetic isolation slots at the bottom of the same magnetic pole are also connected. The improved novel topological structure of the motor is shown in Figure 10.

Through finite element analysis, the magnetic flux density contour map shown in Figure 11 and the magnetic flux density amplitudes of the characteristic points before and after the improvement, as listed in

Table 3. Comparison table of magnetic flux density amplitudes of feature points before and after improvement.

Key Point	Magnetic Flux Density Before Improvement (T)	Magnetic Flux Density After Improvement (T)
a	1.49	1.42
b	1.27	1.19
c	1.28	1.25
d	1.59	1.55
e	1.57	1.56
f	1.15	1.06
g	0.79	0.26

, are obtained. In the motor with traditional structure, the stator tooth body and tooth tip are colored darker, indicating that the magnetic flux density is relatively saturated. The magnetic flux density at the magnetic isolation slots of the rotor is also saturated. After adopting the novel topological structure, the saturation degree of the motor’s magnetic flux density decreases significantly.

Figure 12 displays the motor’s air-gap magnetic flux density and its harmonic decomposition diagram. After adopting the novel topological structure, the amplitudes of the 3rd, 5th, 11th, and 17th harmonics of the air-gap magnetic flux density are all effectively weakened. Thus, the innovative topological structure can efficiently decrease the harmonic content within the air-gap magnetic flux density waveform, thereby further effectively reducing the motor’s iron loss.

4. Optimized Design of the Novel Topological Structure Based on the Taguchi Method

In this section, the Taguchi method is mainly adopted to conduct the optimized design of the proposed novel topological structure. By analyzing the influence of each optimization variable on the iron loss and the relative importance degree of these influences, the matching design of key structural parameters in the novel topological structure is achieved.

4.1. Orthogonal Experimental Design

In this paper, the stator rotor iron losses under the rated operating condition of the motor are selected as the optimization objectives. The constraint condition is that the decrease in the motor’s rated electromagnetic torque does not exceed 10% of the rated electromagnetic torque prior to the structural improvement. The geometric parameters of the connection port structure of the air magnetic isolation slot and the gap of the stator module are selected as the optimization variables, multi-objective optimization design is carried out based on the Taguchi method, and the influence of each optimization variable on each objective function is analyzed to obtain the optimal design scheme of the IPMSM.

According to the improved novel topological structure, the selected optimization variables are shown in Figure 13, which are, respectively, represented as A, B, and C. Variables A, B, and C are the lengths of straight lines L₁, L₂, and L₃ respectively. Among them, L₁ and L₂ are, respectively, the sizes of the openings connecting the air magnetic isolation slots. If the values of L₁ and L₂ are too large, it will lead to a significant decrease in the motor torque. In addition, to ensure that the permanent magnet has a certain mechanical support, the length of the iron core separating the two air magnetic isolation slots below the rotor is 6.2 mm. Therefore, the value range of L₁ in this paper is 1 mm–3 mm, and the value range of L₂ is 0.1 mm–0.3 mm. L₃ is the gap of the stator module. In case the value is excessively large, it will increase the magnetic leakage, which will also cause a significant decrease in the motor torque. Therefore, the value range of L₃ is 0.1 mm–0.3 mm. According to the upper and lower limit ranges of each design variable, three level values of each factor are uniformly selected to form a factor level table, as shown in

Table 4. Control factor level table.

Factor Level	A/mm	B/mm	C/mm
I	1	0.1	0.1
II	2	0.2	0.2
III	3	0.3	0.3

.

Based on the quantity of optimization variables (i.e., the number of factors) and the number of levels corresponding to each factor, the corresponding orthogonal table L₉ (3³) is constructed, as presented in

Table 5. L₉ (3³) orthogonal table.

Number of Experiments	A	B	C
1	I	I	I
2	I	II	II
3	I	III	III
4	II	I	II
5	II	II	III
6	II	III	I
7	III	I	III
8	III	II	I
9	III	III	II

.

4.2. Calculation and Analysis of Experimental Results

Under the rated operating condition, finite element software (Maxwell 2021) is employed to analyze the magnetic flux density at each point of the motor’s iron core. Then, the variable coefficient iron loss model is employed to calculate the iron losses of the stator and rotor cores. The specific calculation results are shown in

Table 6. Iron loss calculations.

Number of Experiments	PFes (W)	PFer (W)
1	534.79	86.12
2	455.78	152.73
3	430.16	133.73
4	471.85	68.94
5	573.36	70.87
6	523.11	63.51
7	457.46	73.77
8	535.36	89.11
9	481.72	68.77

.

To analyze the relative importance degree of the influence of the three optimization variables on the stator and rotor iron losses, it is necessary to conduct an average value analysis and a variance analysis on the results of the nine groups of orthogonal experiments.

4.2.1. Average Value Analysis

By calculating the average values, the variation in the stator and rotor iron losses of the IPMSM with each level value of each factor can be analyzed. Furthermore, the combination of the level values of each factor that minimizes the stator and rotor iron losses can be obtained.

First, the overall average value m of each column in

Table 7. Overall average.

	PFes (W)	PFer (W)
Calculation results	495.95	89.73

is calculated, and its calculation formula is as follows [28]:

$$m={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{m}_i}}{n}}$$

(4)

where m_i is the test result of the ith test in a column in Table 6, and n is the number of tests. According to Equation (4), the overall average value analysis is carried out on the test results of each column in Table 6, and the calculation results are shown in Table 7.

Moreover, the average value of a specific performance index at each level of every factor is calculated. Taking the average value of the stator iron loss P_Fes at the level of factor A as an example for calculation, it is shown in Equations (5)–(7). The average value of the stator iron loss P_Fes at level 1 of factor A is:

$$\begin{array}{cc}{m}_{P_{Fe\mathrm{s}}A(1)}& ={\displaystyle \frac{P_{Fes1}+P_{Fes2}+P_{Fes3}}{3}}\\ & ={\displaystyle \frac{534.79+455.78+430.16}{3}}\\ & =473.58\mathrm{W}\end{array}$$

(5)

Similarly, the average values of the stator iron loss P_Fes at levels 2 and 3 of factor A can be figured out, with the process of calculation shown below.

$$\begin{array}{ll}{m}_{P_{Fes}A(2)}& ={\displaystyle \frac{P_{Fes4}+P_{Fes5}+P_{Fes6}}{3}}\\ & =522.77\mathrm{W}\end{array}$$

(6)

$$\begin{array}{ll}{m}_{P_{Fe}A(3)}& ={\displaystyle \frac{P_{Fe7}+P_{Fe8}+P_{Fe9}}{3}}\\ & =491.51\mathrm{W}\end{array}$$

(7)

Similarly, the average values of the rotor iron loss under each level of each factor can be obtained. The specific calculation results are shown in

Table 8. Average values for each factor and at each level.

Factor	Level	PFes (W)	PFer (W)
A	I	473.58	124.19
	II	522.77	67.77
	III	491.51	77.22
B	I	488.03	76.28
	II	521.50	104.24
	III	486.99	92.79
C	I	531.09	79.58
	II	469.78	96.81
	III	486.99	92.79

.

Table 8 shows that the magnitudes of the values of the three factors have an impact on the iron loss. As the values of factor A and factor B increase, the stator iron loss first increases and then decreases. As the value of factor C increases, the stator iron loss first decreases and then increases. The combination of the level values of each factor that minimizes the stator iron loss are A (1), B (3), and C (2). As the value of factor A increases, the rotor iron loss first decreases and then increases. As the values of factor B and factor C increase, the rotor iron loss first increases and then decreases. The combination of the level values of each factor that minimizes the rotor iron loss are A (2), B (1), and C (1), and the level values of each factor that minimize the rotor iron loss are also different from each other. Thus, it is essential to comprehensively evaluate the relative significance of each optimization variable’s impact on iron loss and torque. Additionally, variance analysis should be performed on the orthogonal test results to derive the optimal combination of each factor’s levels that balance both iron loss and torque.

4.2.2. Analysis of Variance

Based on the analysis results of the overall mean, although the optimal parameter combination that minimizes the iron loss can be determined, there are significant differences in the optimal parameter configurations for reducing the iron loss. In order to quantitatively evaluate the influence weights of each design parameter on the iron loss, it is necessary to further conduct a variance analysis, and then select the combination of the levels of each factor while taking the iron loss into account [29]. The following are the variance calculation procedures for the stator and rotor iron losses under each factor:

$$S_A={\displaystyle \frac{{\displaystyle \sum _{\mathrm{i}=1}^N{(m_{A(j)}-m)}^2}}{N}}$$

(8)

To illustrate, the calculation process of the variance of the stator iron loss under factor A is shown below.

$$\begin{array}{cc}{S}_{P_{Fes}A}& ={\displaystyle \frac{1}{3}}\left[{\left(m_{P_{Fes}A(1)}-m\right)}^2+{\left(m_{P_{Fes}A(2)}-m\right)}^2\right.\left.+{\left(m_{P_{Fes}A(3)}-m\right)}^2\right]\\ & ={\displaystyle \frac{1}{3}}\left[{\left(473.58-495.95\right)}^2+{\left(522.77-495.95\right)}^2\right.\left.+{\left(491.51-495.95\right)}^2\right]\\ & =413.25\end{array}$$

(9)

Similarly, Equation (8) is used to calculate the variances of the rotor iron loss under each factor. The specific calculation results are shown in

Table 9. Variance under each factor.

Factor	PFes (W)	PFer (W)
A	413.25	608.8
B	341.98	130.85
C	666.50	54.19

.

Taking the effect degree of factor A on the iron loss as an example, the contribution rates of each factor to the iron loss and the rated output torque are calculated [30]. The results are shown in

Table 10. Analysis table of stator and rotor iron loss contribution rate.

Factor	PFes (W)	PFer (W)
A	29.07%	76.69%
B	24.05%	16.48%
C	46.88%	6.83%

.

$$\begin{array}{ll}{K}_{S_{P_{Fe\mathrm{s}}}A}& ={\displaystyle \frac{K_{S_{P_{Fes}}A}}{K_{S_{P_{Fes}}A}+K_{S_{P_{Fes}}B}+K_{S_{P_{Fes}}C}}}\times 100\%\\ & ={\displaystyle \frac{413.25}{413.25+341.98+666.50}}\times 100\%\\ & =29.07\%\end{array}$$

(10)

Table 10 indicates that factor C exerts the most significant influence on the average value of the stator iron loss, while factor B has the least impact. The level value that minimizes the average value of the iron loss, that is, C (2), is selected. Factor A has a greater impact on the average value of the rotor iron loss, and factor C has the least impact. The level value that minimizes the average value of the rotor iron loss, that is A (2), is selected. The degree of importance of factor B’s influence on the stator iron loss is greater than its influence on the rotor. Therefore, for factor A, the level values that minimize the average value of the iron loss are selected, that is, B (1) and B (3). Finally, two optimization schemes for the level values of each optimization variable are determined: Scheme One is A (2), B (1), and C (2) and Scheme Two is A (2), B (3), and C (2).

4.3. Optimization Scheme Results Finding

After implementing the final optimization scheme featuring the new topological structure, the stator and rotor iron loss values of the motor under the rated operating condition are obtained, and they are compared with the results of the traditional structure, as shown in Figure 14. The comparison of electromagnetic torque between the two optimization schemes and the traditional motor is shown in Figure 15.

Figure 14 and Figure 15 illustrate that after adopting the optimization scheme with the new topological structure, at the rated operating condition, the electromagnetic torque of the conventional motor structure is 68.23 N·m, while those of Optimization Schemes One and Two are 64.66 N·m and 63.90 N·m, respectively. Compared with the conventional structure, Optimization Scheme One exhibits a 5.23% reduction in electromagnetic torque, and Optimization Scheme Two shows a 6.35% reduction. The discrepancy between the two optimized schemes is relatively minor, for Optimization Scheme One, the stator iron loss decreases by 10.22%, the rotor iron loss increases by 26.07%, and the total iron loss decrease by 0.53%; for Optimization Scheme Two, the stator iron loss decreases by 13.60%, the rotor iron loss decreases by 20.14%, and the total iron loss decreases by 15.34%. The degree of iron loss reduction in Optimization Scheme Two is greater, and the stator and rotor iron losses are synergistically optimized. Therefore, in this paper, Optimization Scheme Two is determined as the final optimization scheme.

Further analysis is conducted on the back electromotive force, efficiency and magnetic flux linkage of the traditional structure and the optimized scheme. The simulation waveform is shown in Figure 16, Figure 17 and Figure 18 below, and the specific results are listed in the following

Table 11. Comparison analysis table of motor losses and efficiency.

	Traditional Structure	Optimization Plan
Copper loss	776.34 W	776.34 W
Stator loss	520.80 W	449.97 W
Rotor loss	189.60 W	151.42 W
Permanent magnet eddy current loss	1.19 W	2.58 W
Mechanical friction loss	800 W	800 W
Rated output power	37.87 kW	35.46 kW
Rated input power	40.15 kW	37.64 kW
Efficiency	94.32%	94.21%

.

The electromagnetic torque of the traditional structure is 68.23 N·m, and that of the optimization scheme, is 63.90 N·m. Compared with the traditional motor, the electromagnetic torque of the optimization scheme decreases by 6.35%, and the constraint condition is that the decrease does not exceed 10%, which meets the constraint condition. In addition, the back electromotive force of the optimization scheme decreases slightly, so the rated output power of the optimization scheme will be slightly reduced. When the motors of the traditional structure and the optimization scheme are under rated operating conditions, their efficiencies remain almost unchanged, but the maximum efficiency of the optimization scheme reaches 95.4%, which is 1.38% higher than that of the traditional structure motor. The simulation results align with the theoretical analysis, demonstrating the viability of the optimization scheme.

The optimization scheme effectively reduces the iron loss of the motor. However, it also leads to a slight decrease in torque. Therefore, the motor excitation was increased to ensure that the electromagnetic torque of the optimized scheme matches that of the traditional structure. By doing so, we could observe the changes in motor losses.

Table 12. Loss comparison analysis table.

	Traditional Structure	Optimized Design Scheme to Increase Incentives
Rated speed	5300 rpm	5300 rpm
Rated current	162.5 A	168.4 A
Winding resistance	9.8 mΩ	9.8 mΩ
Stator iron loss	520.80 W	449.97 W
Rotor iron loss	189.60 W	151.42 W
Copper loss	776.34 W	833.74 W
Permanent magnet eddy current loss	1.19 W	2.55 W
Mechanical friction loss	800 W	800 W
Rated output power	37.87 kW	37.87 kW
Rated input power	40.15 kW	40.14 kW
Efficiency	94.32%	94.34%

presents the variations in each loss component and efficiency after increasing the excitation:

After increasing the excitation, the electromagnetic torque and rated output power of the optimized scheme remain consistent with those of the traditional motor. The copper loss of the optimized scheme motor increases. The total loss of the traditional motor is 2287.93 W, with iron loss plus copper loss being 1486.74 W. The total loss of the optimized scheme motor after increasing the excitation is 2237.68 W, with iron loss plus copper loss being 1435.13 W. Compared with the traditional motor, the iron loss of the optimized scheme motor decreases significantly, and the total loss also decreases, while the rated efficiency of the motor remains almost unchanged. This further demonstrates the feasibility of the optimized scheme.

5. Conclusions

This paper focuses on the iron loss optimization problem of the IPMSM. Through a systematic analysis of the iron cores manufactured by the adhesive bonding process and the welding process, a deep study is conducted on the differences in iron loss density between the two. The research reveals that the iron core produced by the adhesive bonding process, with its unique non-thermal connection characteristics, can effectively avoid the degradation of the silicon steel sheets’ magnetic properties caused by the high temperature during welding, thus, exhibiting a lower iron loss density. As the magnetic flux density increases, the difference in iron loss between the adhesive bonding process and the welding process shows a more significant trend, and this conclusion has been effectively verified in multiple sets of comparative experiments under different frequency conditions.

Based on the advantages of the iron loss data of the adhesive bonding process, this paper constructs an iron loss model with variable coefficients and calculates the losses of an 8-pole 48-slot IPMSM. It is found that in the rated operating scenario, the stator iron loss of the motor is 520.80 W, and the rotor iron loss is 189.60 W. Aiming at the problem of excessive iron loss of the motor, a novel topological structure of the stator and rotor is designed, and the Taguchi method is introduced to carry out the matching design of key parameters such as the air-assisted slot connection port and the stator module gap of the IPMSM. During the optimization process, multiple groups of variable level combinations are set, and analysis of variance is used to quantify the relative importance of the influence of each variable’s influence. The optimal level values of each optimization variable are then determined, resulting in an optimized structure with both theoretical reliability and engineering practicality obtained. Through simulation verification, compared with the traditional structure, the stator iron loss of the optimized motor is significantly reduced by 13.60%, the rotor iron loss is reduced by 20.14%, and the total iron loss is reduced by 15.34%. This achievement not only confirms the effectiveness of the proposed structure in reducing iron loss but also further improves the operating efficiency of the motor.

The research results of this paper provide an important reference for the process selection and optimization of the motor iron core, reveal the key role of the collaborative optimization of the manufacturing process and structural design in reducing iron loss, and have positive significance for promoting the development of high-efficiency motor technology and helping new energy equipment to save energy and increase efficiency.