Analysis of electromagnetic torque of induction motors with two different doubly skewed rotors

Abstract

Induction machines with conventional skewed rotor have lower starting torque compared with non-skewed rotor induction motors. In order to improve the electromagnetic torque, an induction motor with two different doubly skewed rotors was proposed in this paper. The fundamental electromagnetic torque and harmonic electromagnetic torque are analyzed by the virtual displacement method. Theoretical analysis shows that both doubly skewed rotor induction motor without middle ring (DSRIMWOMR) and doubly skewed rotor induction motor with middle ring (DSRIMWMR) can efficiently reduce the harmonic torque. The reduction of harmonic torque can improve the starting torque and reduce the torque ripple. The validity of the analytical method was verified by a large number of three dimensional (3-D) finite element simulations. Results of 3-D finite element analysis (FEA) indicated that both DSRIMWOMR and DSRIMWMR can improve starting torque compared with the conventional skewed rotor induction motor. Furthermore, the optimal skew width for improving the starting torque and reducing torque ripple was ascertained according to different 3-D finite element simulations.

Keywords

Starting torque torque ripple doubly skewed rotor induction motor skew width 3-D finite element method

1. Introduction

Induction motor will still be widely used in the future, owing to its long service life, and a series of advantages. In the application of small and medium induction motors, low noise, high efficiency and high torque performance are required. Vibration and electromagnetic noise resulted from slot harmonics are more or less suppressed by a skewed rotor. Moreover, efficiency and torque performance will be improved by proper skew angle in skewed rotor induction motors [1, 2]. However, some researchers also presented that skewed rotor induction has some disadvantages, for instance, inter-bar current, axial drifting and reduction of starting torque [3]. Considering these problems, our laboratory proposed two different doubly skewed rotor induction motors [4, 5]. Moreover, air-gap magnetic field density, radial electromagnetic force and electromagnetic noise were analyzed and verified by finite element simulations in [4, 5], but no more specific details about torque performance have been shown. The similar herringbone skewing techniques had been used [6, 7], which overcame the disadvantages of conventional skewing techniques. The research in [6, 7] indicated that the torque ripple and unbalanced magnetic force are efficiently suppressed by using the herringbone teeth. But the techniques were applied in permanent-magnet motor to study torque performance. Therefore, in order to make better use of these doubly skewed rotor induction motors, their torque performance needs to be studied in detail.

To improve the electromagnetic torque performance, skewing technology has been extensively studied in the most of the following literature. Using step-skewing magnet to reduce torque ripple in Permanent-Magnet Motors is an effective method [8, 9]. Zhu et al. proposed that the torque ripple will be reduced at rated load condition by optimizing the current phase advance angle and skewed angle [10]. All of those proved that the decrease of torque ripple is not linearly related to the increase of the skewed angle. For the sake of studying the starting processes of skewed rotor induction machines, Fu et al. proposed an approach in using a multi-slice, time stepping 2-D eddy current finite element method [11]. The 2-D finite element method mentioned in [11] is more effective than traditional magnetic circuit method in calculating the starting torque. Due to the rapid development of computer capacity, the 3-D finite element analysis (FEA) was presented [1, 12, 13], and the computational cost was small but the result was more accurate.

This paper gives detailed comparisons of the analysis model, starting torque and torque ripple between doubly skewed rotor induction motor without middle ring (DSRIMWOMR) and doubly skewed rotor induction motor with middle ring (DSRIMWMR). The results in this study reveal that both DSRIMWOMR and DSRIMWMR can improve torque performance in starting process and steady state, due to reduction of harmonic torque. Starting torque of DSRIMWOMR and DSRIMWMR can reach at least twice its rated torque, but conventional skewed rotor induction machines can’t provide such a large starting torque. Results of 3-D finite element analysis indicated that DSRIMWMR has a higher starting torque and a lower torque ripple than DSRIMWOMR. Another objective of this paper is to find the best skew width which makes maximizes the starting torque and minimizes torque ripple according to different simulations.

Figure 1.

3-D FEA models of two different skewed rotors. (a) 3-D model of a half doubly skewed rotor without middle ring. (b) 3-D model of a half doubly skewed rotor with middle ring.

2. Analysis model

Through the theoretical analysis, both DSRIMWOMR and DSRIMWMR can reduce the radical electromagnetic force, owing to reduction of slot harmonics [5]. The axial force resulting in axial drifting will be offset to a certain extent, due to its special doubly skewed rotor structure. In addition, the torque performance of DSRIMWOMR and DSRIMWMR will also be improved by reduction of the slot harmonic. In this paper, the torque characteristic of DSRIMWOMR and DSRIMWMR are analyzed by theoretical explanations and simulations. Figure 1 shows two different models of doubly skewed rotor without middle ring and doubly skewed rotor with middle ring.

As shown in the 3-D models, the structure of doubly skewed rotor without middle ring and doubly skewed rotor with middle ring are modified from the conventional skewed rotor. The conventional skewed rotor was divided into two halves of skewed rotors in the middle. Then the two halves of skewed rotors are combined in the opposite direction into an integral doubly skewed rotor without middle ring. The biggest difference between DSRIMWOMR and DSRIMWMR is that the DSRIMWMR has the middle ring at an intermediate position. Therefore the first step in establishing the FEA model of DSRIMWMR is to establish a middle ring, the second step is to rotate one skewed rotor by half rotor slot pitch angle, and the following steps are as the same as doubly skewed rotor without middle ring. All the design parameters of the two different doubly skewed rotors induction motors are the same, and the main design parameters are shown in Table 1. The bar material of the doubly skewed rotors is cast_ aluminum_75C, and steel material of rotor and stator is DW465_50.

Table 1
Main parameters of prototype motor

Parameters	Value
Rated power (kW)	1.5
Number of poles	4
Core length (mm)	120
Air gap length (mm)	0.25
Stator slot number	24
Rotor slot number	22
Stator outer diameter (mm)	130
Rotor outer diameter (mm)	79.5

3. Analysis method

In order to explain the difference of torque performance between DSRIMWOMR and DSRIMWMR, it is necessary to analyze the distribution of the flux density in the air gap of the machines [14, 15].

3.1 Air-gap magnetic field

The air-gap flux density composition includes the fundamental magnetic flux density, stator harmonic flux density, and rotor harmonic magnetic flux density. The fundamental magnetic flux density which is calculated under the condition of sinusoidal distribution includes the stator fundamental magnetic flux density and rotor fundamental magnetic flux density. The air-gap magnetic field density can be expressed as follows [4]

$\displaystyle b_{\textit{all}}=B_{s}\cos\left({p\theta-\omega_{1}t_{1}}\right)% +B_{r}\cos\left({p\theta-\omega_{1}t-\varphi_{sr}}\right)+\sum\limits_{\nu_{% \nu}}{B_{\nu}}\cos\left({\nu\theta-\omega_{1}t-\varphi_{v}}\right)+\sum\limits% _{\mu_{\mu}}{B_{\mu}}\cos\left({\mu\theta-\omega_{\mu}t-\varphi_{\mu}-\alpha}\right)$ (1)

where $B_{s}$ and $B_{r}$ are the amplitude of stator fundamental magnetic flux density and the amplitude of rotor fundamental magnetic flux density respectively, $B_{\nu}$ and $B_{\mu}$ are the amplitude of the stator harmonic magnetic flux density and amplitude of rotor harmonic magnetic flux density respectively, $p$ is the number of pole pairs, $\nu$ and $\mu$ are the order of stator harmonics and the order of rotor harmonics respectively, $\varphi_{sr}$ is the initial phase angle between stator fundamental flux density and rotor fundamental flux density, $\varphi_{\nu}$ and $\varphi_{\mu}$ are the initial phase angle of stator harmonic magnetic and the initial angle of rotor harmonic magnetic respectively, $\alpha$ is the skew angle of rotor harmonic field along the axial direction, $\omega_{1}$ and $\omega_{\mu}$ are the angular frequency of fundamental magnetic field and the angular frequency of rotor harmonic field respectively, which can be expressed as Eq. (2), especially in the beginning of starting process, $\omega_{\mu}$ is equal to $\omega_{1}$ .

$\displaystyle\omega_{\mu}=k_{2}\frac{Z_{2}}{p}\left({1-s}\right)\omega_{1}+% \omega_{1},k_{2}=\pm 1,\pm 2,\pm 3,\cdots$ (2)

where $Z_{2}$ is the number of rotor slots, $s$ is the slip.

Figure 2.

Schematics of two different doubly skewed rotors. (a) Schematics of rotor without middle ring. (b) Schematics of rotor with middle ring.

The schematic diagrams are shown in Fig. 2, where $L$ is the half rotor length, $b_{sk}$ is the skew width, $R$ is half of the rotor outer diameter, $\beta$ is two half rotors staggered angle of DSRIMWMR. The skew angle $\alpha_{1}$ of DSRIMWOMR is expressed as

$\displaystyle\alpha_{1}=\pm\mu\frac{b_{sk}Z}{R\Delta l}$ (3)

However, though the skew width of DSRIMWMR is the same in the axial direction, the value of $\alpha$ is different. Assumed that the skew angle of right part rotor is $\alpha_{2}$ , the relative skew angle of left part rotor is $\alpha_{3}$ .

$\displaystyle\alpha_{2}=\mu\frac{b_{sk}Z}{R\Delta l}$ (4) $\displaystyle\alpha_{3}=-\mu\frac{b_{sk}Z}{R\Delta l}-\mu\beta$ (5)

3.2 Air-gap magnetic co-energy

The air-gap magnetic co-energy will be changed in the starting process, which will generate starting torque. The air-gap magnetic co-energy can be expressed as [6, 14]

$\displaystyle W_{m}=\int_{V}{\frac{b_{\textit{all}}^{2}}{2\mu_{0}}}dv=\frac{2% Lg}{2\mu_{0}}\frac{r}{p}\int_{0}^{2\pi}{b_{\textit{all}}^{2}}d\theta$ (6)

where $\mu_{0}$ is the permeability of vacuum, $V$ is the volume of air gap, $g$ is the radial length of air gap, $r$ is the average radius of air gap, $\theta$ is the displacement angle.

It is obvious that the magnetic co-energy is very complex when the harmonic magnetic fields are considered. In order to deal with this problem, it is necessary to consider the following hypotheses:

Combining with the Eqs (1) and (6), the air-gap magnetic co-energy between the fundamental magnetic flux density and high-order harmonic magnetic flux density is equal to zero, due to their different orders. Therefore, the fundamental air-gap magnetic co-energy between stator fundamental magnetic flux density and rotor fundamental magnetic flux density can be calculated as follows

$\displaystyle W_{m}^{\prime}=\frac{\pi\textit{Lgr}}{\mu_{0}}\left({B_{s}^{2}+B% _{r}^{2}+2B_{s}B_{r}\cos\varphi_{sr}}\right)$ (7)

Once the order of stator harmonics ( $\nu$ ) and the order of rotor harmonics ( $\mu$ ) are equal, the harmonic air-gap magnetic co-energy in the starting process is not equal to zero, which can be expressed as follows

$\displaystyle W_{m}^{\prime\prime}=\frac{\pi\textit{Lgr}}{\mu_{0}}\{(B_{\nu}^{% 2}+B_{\mu}^{2})+\sum\limits_{\nu_{\nu}}{\sum\limits_{\mu_{\mu}}{B_{\nu}B_{\mu}% }}\cos[(\omega_{\mu}-\omega_{1})t-(\varphi_{\mu}-\varphi_{v}+\alpha)]\}$ (8)

In this paper, the order of 2 ${}^{\text{nd}}$ rotor slot harmonic and order of 2 ${}^{\text{nd}}$ stator slot harmonic will be equal, which will produce the harmonic air-gap magnetic co-energy. However, in the starting process of induction motor, many orders of stator harmonic magnetic field and rotor harmonic magnetic field are likely to be equal. In summary, harmonic air-gap magnetic co-energy varies greatly in the starting process.

3.3 Electromagnetic torque

Assuming that the virtual displacement angle of rotor is $\Delta\delta$ , the variation of fundamental air-gap magnetic co-energy is $\Delta W_{m}^{\prime}$ and the variation of harmonic air-gap magnetic co-energy is $\Delta W_{m}^{\prime\prime}$ , then according to the virtual displacement method, the electromagnetic torque which is caused by fundamental air-gap magnetic co-energy can be expressed as [6, 14]

$\displaystyle T_{e}^{\prime}=p\frac{\Delta W_{m}^{\prime}}{\Delta\delta}=\frac% {\pi\textit{lrpg}}{\mu_{0}}(2B_{s}B_{r}\sin\varphi_{sr})$ (9)

The electromagnetic torque which is caused by harmonic air-gap magnetic co-energy can be expressed as

$\displaystyle T_{e}^{\prime\prime}=p\frac{\Delta W_{m}^{\prime\prime}}{\Delta% \delta}=\frac{\pi\textit{lrpg}}{\mu_{0}}(2\sum\limits_{\nu_{\nu}}{\sum\limits_% {\mu_{\mu}}{B_{\nu}B_{\mu}\sin\delta_{\nu\mu}}})$ (10)

where the $\delta_{\nu\mu}$ is the harmonic torque angle, which can be written as

$\displaystyle\delta_{\nu\mu}=(\omega_{\mu}-\omega_{1})t-(\varphi_{\mu}-\varphi% _{\nu}\pm\alpha)$ (11)

The fundamental electromagnetic torque remains the same in the steady state, and the harmonic electromagnetic torque is small. But in the starting process, the harmonic torque contains a large synchronous torque and asynchronous torque, which can’t be ignored.

From the theoretical analysis mentioned above, it is not difficult to find that harmonic torque angle in the beginning of starting can be rewritten as

$\displaystyle\delta_{\nu\mu}=(\varphi_{\mu}-\varphi_{\nu}\pm\alpha)$ (12)

Properly skew angle can make the sine of harmonic torque angle (sin $\delta_{\nu\mu}$ ) equal to zero, which can efficiently reduce the harmonics of electromagnetic torque. Hence, the difference of electromagnetic torque in starting process with two different doubly skewed rotors induction motors is generally caused by different amplitude of harmonic magnetic flux density and harmonic torque angle.

Figure 3.

Sketch of compound harmonic torque. (a) The compound harmonic torque of DSRIMWOMR. (b) The compound harmonic torque of DSRIMWMR.

Besides, there exists different harmonic torque angle between the two halves of skewed rotors, so the compound harmonic electromagnetic torque will be further reduced. As is shown in Fig. 3, it is obvious that the compound harmonic electromagnetic torque ( $T_{e}^{\prime\prime}$ ) is lower than that of a standard rotor induction motor. The harmonic torque of the right part rotor of DSRIMWOMR ( $T_{e1}^{\prime\prime}$ ), and the harmonic torque of the left part rotor of DSRIMWOMR ( $T_{e2}^{\prime\prime}$ ) can be expressed as follows

$\displaystyle T_{e1}^{\prime\prime}=\frac{2\pi\textit{lrpg}}{\mu_{0}}\left[{% \sum\limits_{\nu_{\nu}}{\sum\limits_{\mu_{\mu}}{B_{\nu}B_{\mu}\sin(\varphi_{% \mu}-\varphi_{v}+\alpha_{1})}}}\right]$ (13) $\displaystyle T_{e2}^{\prime\prime}=\frac{2\pi\textit{lrpg}}{\mu_{0}}\left[{% \sum\limits_{\nu_{\nu}}{\sum\limits_{\mu_{\mu}}{B_{\nu}B_{\mu}\sin(\varphi_{% \mu}-\varphi_{v}-\alpha_{1})}}}\right]$ (14)

The harmonic torque of the right part rotor of DSRIMWMR ( $T_{e3}^{\prime\prime}$ ), and the harmonic torque of the left part rotor of DSRIMWMR ( $T_{e4}^{\prime\prime}$ ) can be expressed as follows

$\displaystyle T_{e3}^{\prime\prime}=\frac{2\pi\textit{lrpg}}{\mu_{0}}\left[{% \sum\limits_{\nu_{\nu}}{\sum\limits_{\mu_{\mu}}{B_{\nu}B_{\mu}\sin(\varphi_{% \mu}-\varphi_{v}+\alpha_{2})}}}\right]$ (15) $\displaystyle T_{e4}^{\prime\prime}=\frac{2\pi\textit{lrpg}}{\mu_{0}}\left[{% \sum\limits_{\nu_{\nu}}{\sum\limits_{\mu_{\mu}}{B_{\nu}B_{\mu}\sin(\varphi_{% \mu}-\varphi_{v}+\alpha_{3})}}}\right]$ (16)

The following conclusions can be obtained by the analytic method mentioned above:

The fundamental electromagnetic torque of the two different doubly skewed rotor induction motors is almost constant in the steady state. However, owing to the rapid variation of air-gap magnetic co-energy, the fundamental electromagnetic torque will reach the maximum in the starting process.

Whether in the starting process, or in the steady state, the harmonic electromagnetic torque of two different doubly skewed rotor induction motors can be reduced by optimum harmonic torque angle, lower amplitude of harmonic magnetic flux density, and the compound harmonic torque.

Table 2

3-D FEA mesh statistics of DSRIMWOMR

3D model	Mesh elements
Band	276032
Stator	38364
Rotor	102030
Bar	158433
Outer region	261997
Inner region	51588
Shaft	2104

4. Simulations and results

In order to illustrate the torque performance of two different doubly skewed rotor induction motors, 3-D finite-elements simulations for four different rotor designs are established in the 3-D transient field to calculate electromagnetic torque at rated load operation. The initial skew width is chosen as a rotor pitch for three different skewed rotor induction motors. In simulating the starting process, moment of inertia and damping of machine are also required to be coupled to the FEM models. Besides, the initial angular velocity of FEA models was set to $-$ 500 rpm [16]. FEA models were meshed by the auto-mesh generator. For example, the mesh elements of DSRIMWOMR are shown in Table 2, the total number of mesh elements is 901634. The simulations were carried out with time step of 0.0004 second and stop time of 0.2 second. The total CPU time was 291 hours.

Based on the theoretical analysis of the Section 3, the electromagnetic torque is closely related to air-gap magnetic flux density. Hence, it is necessary to analyze the components of air-gap magnetic flux density. The radial distribution of air-gap flux density for conventional skewed rotor induction motor, DSRIMWOMR and DSRIMWMR are shown in Fig. 4. The axial stepping length of the motor is 5 mm, and the circumferential stepping angle is 3.6 mechanical degrees. In order to make a clearer comparison of the air gap flux density for different skewed slot rotors, their axial air-gap flux density are analyzed by the Fourier analysis.

Figure 4.

Radial distribution of air-gap flux density for different rotor designs. (a) Conventional skewed rotor induction motor. (b) DSRIMWOMR. (c) DSRIMWMR.

Figure 5.

Harmonic distribution of air-gap flux density for different rotor designs.

The FFT spectra of air-gap flux density for different rotor designs are shown in Fig. 5, which directly illustrates that DSRIMWOMR and DSRIMWMR can reduce harmonics of magnetic flux density. It is apparent that doubly skewed rotor induction motors can reduce the 10 ${}^{\text{th}}$ , 12 ${}^{\text{nd}}$ , 21 ${}^{\text{st}}$ and 23 ${}^{\text{rd}}$ harmonic magnetic flux density. But the 5 ${}^{\text{th}}$ , 7 ${}^{\text{th}}$ space harmonics of DSRIMWOMR and DSRIMWMR are higher than those of standard rotor induction motor, it caused possibly by the reduction of fundamental magnetic flux density.

The 3-D FEA simulated torque curves in starting process for four different rotor designs are shown in Fig. 6. The purpose of using the low pass filter to filter the high-speed harmonic torque is to compare the harmonic torque clearly. After comparing Fig. 6a–d, it can be observed that the torque dip caused by 1 ${}^{\text{st}}$ rotor slot harmonic magnetic flux density is obviously reduced in skewed rotor induction motor, especially in the DSRIMWMR, which is related to the reduction of the 1 ${}^{\text{st}}$ rotor slot harmonic magnetic flux density. Besides, comparing with Fig. 6a and d, the torque dip caused by 1 ${}^{\text{st}}$ stator slot harmonic is also reduced owing to the compound harmonic torque which was mentioned in Fig. 3. The same case also occurs in the torque dip caused by 5 ${}^{\text{th}}$ space harmonic magnetic flux density.

The simulated values of starting torque, maximum torque and starting current are summarized in Table 3. It is obvious that the skewed rotor induction motors reduce the starting torque and maximum torque. However, compared with the conventional skewed rotor induction motor, DSRIMWOMR and DSRIMWMR can improve the starting torque. DSRIMWMR has a higher starting torque that may be caused by proper harmonic torque angle, and may also be related to inter-bar currents [16, 17], which needs further research. It is usual to require that induction motor provide instantaneously at least twice its rated torque [17]. Based on simulated results in Table 3, the doubly skewed rotor induction motors can meet this requirement.

Table 3

Simulated starting properties for the four rotor designs

Rotor design	Starting torque (Nm)	Maximum torque (Nm)	Starting current (A)
Conventional skewed rotor	20.88	25.76	21.83
Doubly skewed rotor without a middle ring	21.02	27.91	23.35
Doubly skewed rotor with a middle ring	23.89	27.52	22.42

Figure 6.

Torque performance in the starting process with different rotor designs. (a) Non-skewed rotor. (b) Conventional skewed rotor. (c) Doubly skewed rotor without a middle ring. (d) Doubly skewed rotor with a middle ring.

Figure 7.

Torque performances in the starting process for DSRIMWOMR and DSRIMWMR at rated load operation. (a) The skew width of 40% rotor slot pitch. (b) The skew width of 91.7% rotor slot pitch. (c) The skew width of 100% rotor slot pitch. (d) Relationship between starting torque and skew width.

Figure 8.

Speed-times curve and torque ripple characteristics for two types of doubly skew induction motor at rated load operation. (a) The skew width of 40% rotor pitch. (b) The skew width of 91.7% rotor slot pitch. (c) The skew width of 100% rotor slot pitch.

Figure 9.

Peak to peak torque ripple varies with different skew width of DSRIMWOMR and DSRIMWMR.

In order to illustrate more clearly the relation between the harmonic torque angle and starting torque, more FEA simulations on torque performances in starting process for DSRIMWOMR and DSRIMWMR are shown in Fig. 7. Through theoretical analysis mentioned above, the harmonic torque angle varies with the skew angle, and the skew angle varies with the skew width of the DSRIMWOMR and the DSRIMWMR. According to a large number of FEA simulations, the relationship between starting torque and skew width is investigated in Fig. 7d. It is not difficult to find that starting torque does not always increase as the skew width increases, which will reach maximum when the skew width is 91.7% of the rotor slot pitch. This phenomenon can be explained by Eq. (10), as it is possible that the skew width of the 91.7% rotor slot pitch will make the torque angle reach $\pi$ /2.

Figure 8 gives the details about their speed performance at rated load operation. The vibration of speed in steady state is mainly caused by the torque ripple. It is apparent that the skew width has a great influence on the torque ripple, just as the theoretical analysis does. The main reasons for the decrease of torque ripple are two factors. One is the lower amplitude of harmonic magnetic flux density, and the other is compound harmonic torque. It can be observed that torque ripple of DSRIMWOMR is lower than that of DSRIMWMR from Fig. 8a, but torque ripple of DSRIMWOMR is higher from Fig. 8b. Therefore, it is necessary to reveal the relationship between the torque ripple and the angle of the skewed slot more concretely, which is shown in Fig. 9. There is no doubt that the torque ripple will decrease as the skew width increases, the similar situation also occurred in [1, 6]. Furthermore, the torque ripple of DSRIMWOMR is further reduced when the skew width is chosen to be as 91.7% rotor slot pitch (a stator slot pitch), owing to lower amplitude of harmonic magnetic flux density. The same case also occurred in DSRIMWMR when the skew width is chosen to as a rotor slot pitch.

5. Conclusion

This paper focus as the comparisons of electromagnetic torque, especially the starting torque and the torque ripple between the doubly skew rotor induction motors. The torque performance at rated load operation conditions are calculated by 3-D FEA. The results know that both DSRIMWOMR and DSRIMWMR can improve the starting torque compared with the conventional skewed rotor motor. Moreover, doubly skewed rotor induction motor with middle ring has a higher starting torque compared with the one without middle ring when the skew width is between 60% rotor slot pitch and 130% rotor slot pitch. The starting torque of DSRIMWOMR and DSRIMWMR will reach the maximum when the skew width is chosen to be as stator slot pitch. The torque ripple of DSRIMWOMR and DSRIMWMR will be reduced as skew width increases. Furthermore, the torque ripple of DSRIMWOMR will be further reduced when the skew width is chosen to be as stator slot pitch, and the torque ripple of DSRIMWMR will be further reduced when the skew width is chosen to be as rotor slot pitch. In effect, when the skew width is chosen as a stator slot pitch, the DSRIMWMR can meet the higher torque performance requirements.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Funds of China (No. 51677051 and No. 51377039), Anhui Province Key Laboratory of Large-scale Submersible Electric Pump and Accoutrements.

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