The Multiphysics Analysis and Suppression Method for the Electromagnetic Noise of Permanent-Magnet Motors Used in Electric Vehicle

Abstract

A method for predicting the electromagnetic noise of a permanent-magnet motor based on the coupling of electromagnetic force and modal is proposed. Firstly, a theoretical analysis and finite element method are combined to establish an electromagnetic force analysis model for a 6-pole 36-slot permanent-magnet motor used in vehicles. The spatial order and frequency characteristics of the electromagnetic force are analyzed. Then, the modal array of the motor is calculated using the finite element method, and the main sources of the motor vibration noise are predicted by combining the electromagnetic force with the modal frequency array of each order. Finally, a vibration noise multiphysics simulation analysis model is established using the finite element method, and the electromagnetic noise is calculated. The simulation results are consistent with the predicted results, verifying the effectiveness of the analysis method.

1. Introduction

According to reference [1], the vibration and noise of motors and reducers are generally transmitted into the interior of the vehicle through two pathways: one is through the structural path and suspended into the interior of the vehicle; the second is through the air path, radiating to the cab and ultimately perceived by the driver. Reducing the vibration noise of permanent-magnet motors is of great significance for improving the comfort and reliability of electric vehicles. Scholars have conducted extensive research on the vibration and noise issues of 8-pole 48-slot permanent-magnet motors. Reference [2] theoretically analyzed the order and frequency characteristics of radial electromagnetic force, and optimized the vibration noise using the method of opening arc-shaped grooves on the rotor surface. Reference [3] established an analytical model for radial electromagnetic force considering current harmonics based on the Maxwell tensor method, and used the linear superposition method to obtain a prediction model for measuring point noise. The contribution of the radial electromagnetic force of each spatiotemporal order to measuring point noise was calculated. Reference [4] analyzed the radial air gap flux density, the harmonic components of electromagnetic force, and motor modes of the motor based on the finite element method. The magnetic pole eccentricity method was used to optimize the electromagnetic vibration noise of the motor. Reference [5] designed a U-shaped magnetic pole structure combining Halbach magnetization and rotor slotting, which weakened the amplitude of radial electromagnetic force harmonic waves, stator assembly vibration acceleration, and motor body sound pressure level. Reference [6] reduced the electromagnetic noise of 0 spatial order and 48 temporal order by optimizing the stator slot parameters. Reference [7] found that enhancing stator stiffness and reducing the amplitude of low-order electromagnetic forces can have a positive improvement effect on the vibration noise of the motor. Reference [8] used a genetic algorithm in the multi-objective optimization process of the prototype to identify a series of high-sensitivity parameters. It was found that torque fluctuations were the most sensitive to changes in stator slot width, the average torque was the most sensitive to changes in rotor magnet width, and the radial force wave amplitude was more sensitive to changes in the stator slot depth and rotor magnet clamping angle. Reference [9] analyzed the sources of abnormal noise excitation force in a surface-mounted external rotor permanent-magnet synchronous motor with 18 poles and 27 slots, and proposed a permanent-magnet magnetic-domain alignment structure to reduce vibration and noise. Reference [10] used a finite element method to establish a magnetic solid thermal multiphysics coupling model for a 6-pole 36-slot permanent-magnet motor. The research results showed that when considering temperature distribution and structural deformation, the vibration noise level of the motor can be more accurately predicted and evaluated. Reference [11] proposed a scheme of placing magnetic slot wedges at the slot position of a 4-pole 36-slot permanent-magnet synchronous motor as an example, which effectively weakened the harmonics of the magnetic field in the air gap and significantly reduced the vibration problem caused by the magnetic field. Reference [12] analyzed the sources of electromagnetic vibration noise in a 24-pole 36-slot fractional slot-concentrated winding built-in permanent-magnet synchronous motor, and reduced the vibration noise by introducing auxiliary slots. Reference [13] studied the vibration noise of a 10-pole 12-slot permanent-magnet synchronous motor and revealed that high-order spatial air gap forces can also induce a significant low-mode stator vibration, a phenomenon known as the modulation effect. In motors with this effect, the vibration amplitude caused by the tangential electromagnetic force is approximately half of the vibration amplitude caused by the radial electromagnetic force. Reference [14] studied the vibration noise of a 12-pole 54-slot V-shaped rotor permanent-magnet synchronous motor, and explored the effects of the air gap length and magnetic pole angle on vibration noise. It was found that by designing a segmented magnetic barrier for the rotor, noise can be significantly reduced. Reference [15] analyzed the electromagnetic noise of an 8-pole 24-slot permanent-magnet synchronous drive motor. By separately loading radial electromagnetic forces and comprehensively loading radial, tangential, and axial electromagnetic forces on the motor stator model, and comparing and analyzing electromagnetic noise, the study shows that tangential electromagnetic forces have a certain degree of influence on electromagnetic noise.

The 8-pole 48-slot permanent-magnet motor is widely used in automotive drive motor schemes and has been extensively researched. There is limited research on 6-pole 36-slot permanent-magnet motors. However, in order to improve the power density of the electric drive system of electric vehicles, the speed of permanent-magnet motors continues to increase. In order to maintain the accuracy of motor control, the switching frequency of the motor controller needs to be continuously increased, resulting in significant losses. Compared to 8-pole 48-slot permanent-magnet motors, 6-pole 36-slot permanent-magnet motors are also integer slot motors, and the number of poles is close, which has a small impact on the span of the motor winding. At the same time, it has fewer poles, which can reduce the requirements for the switching frequency of the controller and reduce controller losses, and has great research value. This paper takes the 6-pole 36-slot permanent-magnet motor for vehicles as the research object and proposes an analysis and prediction method for the vibration noise of the permanent-magnet motor.

This article is organized as follows: In Section 1, the analysis and suppression methods of electromagnetic vibration noise in permanent-magnet motors are introduced. In Section 2, a theoretical analysis and finite element method are combined to establish an electromagnetic force analysis model for a 6-pole 36-slot vehicle permanent-magnet motor. Then, the spatial order and frequency characteristics of the electromagnetic force are analyzed. The finite element method is used to calculate its modal array. In Section 3, the main sources of the motor vibration noise are predicted by combining the electromagnetic force with the modal frequency array of each order. In Section 4, the effectiveness of the predicted vibration noise is discussed through a multiphysics field model. In Section 5, The research conclusions of this article are provided.

2. Materials and Methods

2.1. Electromagnetic Force Analysis

2.1.1. Analytical Method

In permanent-magnet synchronous motors, the air gap magnetic field includes the magnetic field generated by the permanent magnet and the magnetic field generated by the energized winding, which can be represented by a linear superposition of trigonometric functions. According to references [16,17,18,19], the influence of stator slotting on the air gap magnetic field can be corrected by relative magnetic permeability, and further solved by the Maxwell stress tensor method to obtain the radial electromagnetic force of the permanent-magnet motor. The derivation process of electromagnetic force is shown in Formulas (1)–(10).

The radial component of the magnetic flux density in the permanent magnetic field air gap can be expressed as follows:

$$B_{r\_pm}={\displaystyle \sum _n{B}_n}\cos (np\theta +np{\omega }_{r}t).$$

(1)

In the formula, $n$ is the spatial order of the permanent magnetic field air gap magnetic flux density, $B_n$ is the harmonic amplitude of the permanent magnetic field air gap magnetic flux density, $p$ is the number of pole pairs, $\theta$ is the spatial angle of the air gap magnetic flux density, ${\omega }_r$ is the mechanical angular velocity, and $t$ is the time.

The effect of stator slotting on the magnetic field can be understood as the modulation of the waveform of the air gap magnetic flux density by the relative magnetic permeability function, which can be expressed in the form of Formula (2):

$${\lambda }_{real}={\displaystyle \sum _i{\lambda }_i}\cos (i{Q}_s\theta ),$$

(2)

where $i$ is the order of relative magnetic permeability, ${\lambda }_i$ is the harmonic amplitude of the relative magnetic permeability, and $Q_s$ is the number of stator slots.

When considering the influence of stator slotting, the radial component of the no-load magnetic field air gap flux density can be approximately expressed as follows:

$$B_{r\_pm\_slot}=B_{r\_pm}{\lambda }_{real}={\displaystyle \sum _n}{\displaystyle \sum _i}{\displaystyle \frac{1}{2}}{B}_n{\lambda }_i\cos [(np\pm i{Q}_s)\theta +np{\omega }_{r}t].$$

(3)

According to Formula (3), it can be seen that the spatial order and frequency order of the harmonics of the air gap magnetic flux density in the no-load magnetic field are $[np\pm i{Q}_s,np]$, where $n=1,3,5\dots i=0,1,2\dots$.

The radial component of the air gap magnetic flux density in the armature reaction magnetic field can be expressed as follows:

$$B_{r\_am}={\displaystyle \sum _{\upsilon }{B}_{\upsilon }}\cos (\upsilon N_0\theta \pm p{\omega }_{r}t).$$

(4)

In the formula, $\upsilon$ is the spatial order of the air-gap flux in the armature reaction magnetic field, $B_{\upsilon }$ is the harmonic amplitude of the air gap flux density in the armature reaction magnetic field, and $N_0$ is the number of unit motors. When the motor winding is a double-layer winding, it is the greatest common divisor between the number of slots and the number of pole pairs; when the motor winding is a single-layer winding, the motor composed of the poles and slots included in the smallest repetition period in the original motor can be regarded as a unit motor.

When considering the influence of stator slotting, the radial component of the armature reaction magnetic field air gap flux density can be approximately expressed as follows:

$$B_{r\_pm\_slot}=B_{r\_am}{\lambda }_{real}={\displaystyle \sum _{\upsilon }}{\displaystyle \sum _i}{\displaystyle \frac{1}{2}}{B}_{\upsilon }{\lambda }_i\cos [(\upsilon N_0\pm i{Q}_s)\theta +p{\omega }_{r}t].$$

(5)

The radial component of the synthesized magnetic field in the air gap can be approximately expressed as follows:

$$B_r=B_{r_{-}p{m}_{-}slot}+B_{r_{-}a{m}_{-}slot}.$$

(6)

If the influence of the tangential component of the magnetic flux density on the radial electromagnetic force is not considered, according to the Maxwell stress equation, the radial electromagnetic force can be approximately expressed as follows:

$$P_r\approx {\displaystyle \frac{B_r^2}{2{\mu }_0}}={\displaystyle \frac{1}{2{\mu }_0}}{(B_{r\_pm\_slot}+B_{r\_arm\_slot})}^2=P_{r1}+P_{r2}+P_{r3},$$

(7)

$$P_{r1}={\displaystyle \frac{1}{4{\mu }_0}}{\displaystyle \sum _{n=1,3,5}^{\infty }{\displaystyle \sum _i{B}_{n_1}{B}_{n_2}{\lambda }_{i1}{\lambda }_{i2}}}cos\{[(n_{1}p\pm i_1{Q}_s)\pm (n_{2}p\pm i_2{Q}_s)]\theta +(n_1\pm n_2)p{\omega }_{r}t\},$$

(8)

$$P_{r2}={\displaystyle \frac{1}{2{\mu }_0}}{\displaystyle \sum _{n=1,3,5}^{\infty }{\displaystyle \sum _i{\displaystyle \sum _v}}}{B}_n{B}_v{\lambda }_{i1}{\lambda }_{i2}\cos \left\{\left[(np\pm i_1{Q}_s)\pm (v{N}_0\pm i_2{Q}_s)\right]\theta +(n\pm 1)p{\omega }_{r}t\right\},$$

(9)

$$p_{r3}={\displaystyle \frac{1}{4{\mu }_0}}{\displaystyle \sum _v^{\infty }{\displaystyle \sum _i}}{B}_{v1}{B}_{v2}{\lambda }_{i1}{\lambda }_{i2}\cos \left\{\left[(v_1{N}_0\pm i_1{Q}_s)\pm (v_2{N}_0\pm i_2{Q}_s)\right]\theta +(1\pm 1)p{\omega }_{r}t\right\}.$$

(10)

The radial electromagnetic force distribution law of the motor considering stator slotting is shown in

Table 1. The radial electromagnetic force distribution law of the motor, considering stator slotting.

Radial Electromagnetic Force	Amplitude	Spatial Order	Frequency Order
$p_{r1}$	${\displaystyle \frac{1}{4{\mu }_0}}$$B_{n_i}{B}_{n_i}{\lambda }_{i1}{\lambda }_{i2}$	$(n_{1}p\pm i_1{Q}_s)\pm (n_{2}p\pm i_2{Q}_s)$	$(n_1\pm n_2)p$
$p_{r2}$	${\displaystyle \frac{1}{2{\mu }_0}}$$B_n{B}_v{\lambda }_{i1}{\lambda }_{i2}$	$(np\pm i_1{Q}_s)\pm (v{N}_0\pm i_2{Q}_s)$	$(n_1\pm 1)p$
$p_{r3}$	${\displaystyle \frac{1}{4{\mu }_0}}$$B_{v_1}{B}_{v_2}{\lambda }_{i1}{\lambda }_{i2}$	$(v_1{N}_0\pm i_1{Q}_s)\pm (v_2{N}_0\pm i_2{Q}_s)$	$(1\pm 1)p$

. According to Table 1, the spatial order and frequency of the electromagnetic force of the 6-pole 36-slot permanent-magnet motor are analyzed and shown in

Table 2. The radial electromagnetic force $p_{r1}$ distribution law of the 6-pole 36-slot permanent-magnet motor, considering slotting.

n2	n1
	1	3	5	7	9	11	13	15	17	19	21	23
1	0,0 6,6	6,6	/	/	(6,30)	(6,30) (0,36)	(0,36) (6,42)	(6,42)	/	/	(6,66)	(6,66) (0,72)
3	6,6	0,0	6,6	(6,30)	(0,36)	(6,42)	(6,30)	(0,36)	(6,42)	(6,66)	(0,72)	(6,78)
5	/	6,6	0,0 (6,30)	6,6 (0,36)	(6,42)	/	/	(6,30)	(0,36) (6,66)	(6,42) (0,72)	(6,78)	/
7	/	(6,30)	6,6 (0,36)	0,0 (6,42)	6,6	/	/	(6/66)	(6,30) (0.72)	(0,36) (6,78)	(6,42)	/
9	(6,30)	(0,36)	(6,42)	6,6	0,0	6,6	(6,66)	(0,72)	(6,78)	(6,30)	(0,36)	(6,42)
11	(6,30) (0,36)	(6,42)	/	/	6,6	0,0 (6,66)	6,6 (0,72)	(6,78)	/	/	(6,30)	(0,36)
13	(0,36) (6,42)	(6,30)	/	/	(6,66)	6,6 (0,72)	0,0 (6,78)	6,6	/	/	/	(6,30)
15	(6,42)	(0,36)	(6,30)	(6,66)	(0,72)	(6,78)	6,6	0,0	6,6	/	/	/
17	/	(6,42)	(0,36) (6,66)	(6,30) (0,72)	(6,78)	/	/	6,6	0,0	6,6	/	/
19	/	(6,66)	(6,42) (0,72)	(0,36) (6,78)	(6,30)	/	/	/	6,6	0,0	6,6	/
21	(6,66)	(0,72)	(6,78)	(6,42)	(0,36)	(6,30)	/	/	/	6,6	0,0	6,6
23	(6,66) (0,72)	(6,78)	/	/	(6,42)	(0,36)	(6,30)	/	/	/	6,6	0,0

. The spatial order and frequency order of the electromagnetic force in the table are expressed in the form of “m, n”, where “m, n” in parentheses represents the spatial order and frequency order of a low-order electromagnetic force considering the first-order tooth harmonic situation. The amplitude of motor vibration is inversely proportional to the fourth power of the electromagnetic force order. The smaller the electromagnetic force order, the greater the impact on vibration. However, the lowest two orders of the electromagnetic force for a 6-pole 36-slot permanent-magnet motor are order 0 and order 6. Therefore, only these two orders of electromagnetic force are analyzed in the table. Higher orders of electromagnetic force have little effect on vibration noise and will not be analyzed here. The high-order electromagnetic forces omitted in Table 2 and

Table 3. The radial electromagnetic force $p_{r2}$ distribution law of the 6-pole 36-slot permanent-magnet motor, considering slotting.

v	n
	1	3	5	7	9	11	13	15	17	19	21	23
1	0,0 6,6	6,6	/	/	(6,30)	(6,30) (0,36)	(0,36) (6,42)	(6,42)	/	/	(6,66)	(6,66) (0,72)
−5	/	6,12	(6,12) 0,18	(0,18) 6,24	(6,24)	/	/	(6,48)	(6,48) (0,54)	(0,54) (6,60)	(6,60)	/
7	/	(6,12)	6,12 (0,18)	0,18 (6,24)	6,24	/	/	(6,48)	(6,48) (0,54)	(0,54) (6,60)	(6,60)	/
−11	(0,0) (6,6)	(6,6)	/	/	6,30	(6,30) 0,36	(0,36) 6,42	(6,42)	/	/	(6,66)	(0,72)
13	(0,0)	(6,6)	/	/	(6,30)	6,30 (0,36)	0,36 (6,42)	6,42	/	/	/	(6,66)
−17	/	(6,12)	(6,12) (0,18)	(0,18) (6,24)	(6,24)	/	/	6,48	0,54	6,60	/	/
19	/	(6,12)	(6,12) (0,18)	(0,18) (6,24)	(6,24)	/	/	/	6,48	0,54	6,60	/
−23	(0,0) (6,6)	(6,6)	/	/	(6,30)	(0,36)	(6,42)	/	/	/	6,66	0,72

are represented by the symbol “/”.

From Table 2, it can be seen that the low-order radial electromagnetic force $p_{r1}$ of a 6-pole 36-slot permanent-magnet motor under no-load mainly includes the spatial 0th order and spatial 6th order. The frequency orders of the 0-order electromagnetic force in space mainly include 0, 36, and 72, among which the electromagnetic force with a frequency order of 0 is not considered. The electromagnetic force with a frequency order of 36 and 72 generated by the interaction between the fundamental wave of the permanent magnet, the harmonic of the permanent magnet, and the first-order stator tooth harmonic needs to be given special attention.

According to Table 1, the spatial and frequency orders of the electromagnetic force $p_{r2}$ of the 6-pole 36-slot permanent-magnet motor are analyzed and shown in Table 3. From Table 3, it can be seen that the low-order radial electromagnetic force formed by the interaction between the permanent magnetic field and the armature reaction magnetic field of a 6-pole 36-slot permanent-magnet motor mainly includes the spatial 0th order and spatial 6th order. The frequency order of the 0-order electromagnetic force in space is mainly 0, 18, 36, 54, and 72. Its sources can be divided into two categories: one is generated by the interaction between the harmonic of the armature reaction magnetic field and the harmonic of the permanent magnetic field, and the other is generated by the interaction between the fundamental or harmonic of the armature reaction magnetic field, the harmonic of the permanent magnetic field, and the first-order tooth harmonic. The electromagnetic force with a frequency order of 36 is mainly generated by the interaction between the fundamental or harmonic of the armature reaction magnetic field, the harmonic of the permanent magnetic field, and the first-order tooth harmonic, with a relatively large amplitude. The frequency orders of the 6th order electromagnetic force in space are mainly 6, 12, 24, 30, 42, and 66. The electromagnetic force with frequency order 6 is mainly formed by the interaction between the fundamental waves of the permanent magnetic field and the armature reaction magnetic field, with the highest amplitude. The electromagnetic force with a frequency order of 12 is mainly formed by the interaction between the low-order harmonics of the permanent magnetic field and the low-order fundamental wave of the armature reaction magnetic field, with a relatively large amplitude. Other frequencies of electromagnetic force are formed by the interaction of permanent magnetic field harmonics, armature reaction magnetic field harmonics, and first-order tooth harmonics, which mainly have a significant impact near the natural frequency of the 6th mode in space.

2.1.2. Finite Element Method

The research object of this article is an embedded V-shaped permanent-magnet synchronous motor with 6 poles and 36 slots. The design specifications of the motor are shown in

Table 4. Design indicators.

Parameter	Value	Unit
Rated power	30	kW
Rated voltage	220	V
Rated speed	3000	rpm
Maximum speed	9000	rpm

.

ANSYS MAXWELL2023R1 manufactured by ANSYS Corporation in Pittsburgh USA was used in establishing the finite element analysis model for electromagnetic force. Apply zero magnetic vector boundary on the outer circle of the stator and achieve periodic symmetry of the magnetic circuit through the master–slave constraint combined with the reverse magnetic potential method. Use the rotating coordinate system and sliding grid technology to handle the rotor motion. By using a multi-scale grid strategy to refine the mesh model, a 3 mm structured grid is used in the iron core area, and the air gap is implemented with three layers of radial refinement to 0.3 mm and optimized for circumferential refinement. At the same time, a local refinement layer with a transition coefficient of 0.7 is set in the tooth slot area. The electromagnetic calculation process uses a transient solver to extract the concentrated electromagnetic force on the stator teeth, and obtains the spatial distribution order and temporal harmonic distribution of the electromagnetic force through time–frequency conversion. The structural parameters of the finite element model are shown in

Table 5. The main parameters of the motor structure.

Parameter	Value	Unit
Number of slots	36	/
Outer diameter of the stator	190	mm
Inner diameter of the stator	125	mm
Air-gap length	0.6	mm
Core length	100	mm
The number of conductors per slot	128	/
Width of the stator teeth	6.6	mm
Width of the stator slot opening	3.0	mm

, and the cross-sectional view of the permanent-magnet synchronous motor model is shown in Figure 1.

The magnitude of the radial electromagnetic force of the motor is mainly determined by the radial air gap flux density. The established finite element model is used to analyze the air gap flux density under no-load and load conditions. In the analysis of the no-load air gap magnetic field, the amplitude of the armature current is set to zero, assuming that no current passes through the winding. The air gap radius is set to 62.2 mm, and the motor speed is 3000 r/min. In the analysis process of the load air gap magnetic field, based on the permanent magnetic field analysis model, a sinusoidal current with an amplitude of 100 A and an air-gap radius of 62.2 mm is applied to the three-phase winding. Analyze and obtain the radial air gap magnetic density waveform and FFT spectrum, as shown in Figure 2.

Comparing the no-load and load conditions of the motor, it can be found that the radial air gap flux density and the load radial air gap flux density are both odd orders. In the load condition, due to the introduction of current harmonics, the harmonic content is high and the amplitude of each order harmonic increases, resulting in a decrease in the sinusoidal waveform of the air gap flux density.

Based on the obtained no-load air gap magnetic flux density and load air gap magnetic flux density, the radial electromagnetic force at the air gap radius is calculated using the Maxwell stress equation, as shown in Figure 3. The distribution of the radial electromagnetic force over time and space obtained using 2D Fourier transform is shown in Figure 4.

From Figure 4, it can be seen that the low-order electromagnetic force of the 6-pole 36-slot motor is mainly the spatial 0th order and spatial 6th order. The frequency of the 0th order electromagnetic force includes the 18th harmonic and 36th harmonic, and the amplitude of the 0th order electromagnetic force of the 36th harmonic is greater than that of the 18th harmonic. The frequency orders of the 6th order electromagnetic force in space are mainly the 6th, 12th, 24th, 30th, and 66th harmonics, with the larger amplitudes being the 6th and 12th harmonics, consistent with the theoretical analysis results.

2.2. Modal Analysis

Modal analysis can accurately identify the various natural frequencies and modal shapes of a motor. The natural frequency is a specific frequency of the motor structure during free vibration. When the external excitation frequency is close to or equal to these natural frequencies, the motor may resonate, leading to an increased vibration. By analyzing the modal shapes of the motor, the vibration patterns at different frequencies can be understood, which helps to determine the main contributing modes of the motor vibration and provides a basis for the subsequent vibration control and noise suppression. This article uses the finite element method to solve the free mode of the motor stator and its components. When establishing the modal finite element analysis model, ANSYS Workbench 2023R1 manufactured by ANSYS Corporation in Pittsburgh USA was used to analyze the stator mode of the motor using a free modal approach. Due to the absence of rotor skewed poles and a similar axial electromagnetic force distribution in the motor, the axial mode of the model is ignored. The modal shapes and natural frequencies of the stator and its components obtained from the solution are shown in

Table 6. Modal of a 6-pole 36-slot motor.

Modal Order	Stator	Stator with Casing	Modal Order	Stator	Stator with Casing
0			4
	6323.3 Hz	6539.3 Hz		2505.7 Hz	5028.5 Hz
2			5
	522.3 Hz	1181.8 Hz		3715.5 Hz	6725.2 Hz
3			6
	1400.3 Hz	3027.9 Hz		7306.8 Hz	8415 Hz

.

3. Results

Due to the wide operating speed range of electric vehicles, in order to better analyze the noise response of the motor in the full speed range, the possible resonance points of the main low-order radial electromagnetic force of the motor during a multi speed range operation were first predicted. The electromagnetic force (0,36) has a low order and large amplitude, resulting in a significant vibration noise. The electromagnetic forces (0,54) and (6,66) intersect with the natural frequencies of the 0th and 6th modes, respectively, which may cause a significant vibration noise. The main distribution of the predicted noise is shown in Figure 5.

4. Discussion

In order to verify the effectiveness of the electromagnetic force and modal coupling analysis method, a multphysics coupling simulation model was established. According to reference [20,21], a simulation model was established as shown in Figure 6. In the multiphysics field analysis model, the electromagnetic force finite element model, modal finite model, and harmonic response coupling analysis method are simultaneously used to solve the vibration noise response. The electromagnetic force acting on the stator teeth was calculated using a two-dimensional electromagnetic model, and the electromagnetic force was reflected in the form of the concentrated force. The obtained electromagnetic force on the teeth was imported into the three-dimensional structural model. Combined with the modal analysis results of the three-dimensional structural model, the modal superposition method was used to solve the surface vibration acceleration of the casing. An air domain was established at a distance of 1m from the far field, and the surface acceleration of the casing was added to the inner surface of the air domain. Then, the noise at a distance of 1m from the far field of the motor was solved.

By using the multiphysics coupling simulation model mentioned above, the vibration acceleration of the motor under the rated operating condition of 3000 rpm in this paper was simulated, and the vibration acceleration on the surface of the casing was obtained as shown in Figure 7. Through an analysis of Figure 7, it can be seen that the frequency of the vibration acceleration is the same as the frequency of the excitation force wave, both of which are even multiples of the fundamental frequency of the motor current. It can also be seen that the maximum vibration acceleration of the motor in this paper is at the 18th and 36th harmonics. Combined with the analysis of the radial electromagnetic force of the motor mentioned above, it is mainly caused by the harmonics (0,18) and (0,36) of the radial electromagnetic force.

Based on the multiphysics coupling model established above, a finite element simulation was carried out on the noise spectrum characteristics of the motor in the full speed range of 1000–9000 rpm in this paper. To obtain accurate results, the noise-equivalent radiation power-level waterfall diagram was obtained by increasing the step size at 100 rpm, which is shown in Figure 8. It can be seen that when the operating frequency is close to 36th, 54th and 66th harmonics, the amplitude of the electromagnetic noise is large. In addition, there are sound power peaks at 6600 Hz and 8360 Hz, which are similar to the natural mode 0th and 6th order, and resonance phenomena occur. The resonance point predicted by the method based on the electromagnetic force and modal coupling is basically the same as the results of the multiphysics simulation.

5. Conclusions

This article takes the 6-pole 36-slot permanent-magnet motor for vehicles as the research object and proposes an analysis and prediction method for the vibration noise of the permanent-magnet motor. The main conclusions are as follows:

(1) The low-order electromagnetic force of a 6-pole 36-slot motor mainly consists of the spatial 0th order and spatial 6th order. The frequency of the 0th order electromagnetic force includes 18th and 36th harmonics, and the amplitude of the 0th order electromagnetic force of the 36th harmonic is greater than that of the 18th harmonic. The frequency of the 6th order electromagnetic force in space is mainly the 6th, 12th, 30th, and 42nd harmonics, with the larger amplitudes being the 6th and 12th harmonics.

(2) Through modal analysis, it can be concluded that in the modal distribution of a 6-pole 36-slot motor, the modes corresponding to the low-order radial electromagnetic forces of order 0 and order 6 are order 0 and order 6.

(3) There are intersections between the radial electromagnetic forces (0,54) and (6,66) and the natural frequencies of the 0th and 6th modes, where a significant vibration noise is generated. The electromagnetic force (0,36) has a lower order and a larger amplitude, resulting in a larger amplitude of the electromagnetic noise. The method of predicting the distribution of the electromagnetic vibration noise based on the electromagnetic force and modal coupling is basically the same as the results of the multiphysics simulation, which proves the effectiveness of this method.