Zechen Li, Chong Di, and Xiaohua Bao*

(1. Hefei University of Technology, School of Electrical Engineering and Automation, Hefei 230009, China

2. Department of Electrical Engineering, LUT School of Energy Systems,Lappeenranta University of Technology, Lappeenranta 53851, Finland)

Abstract: Compared with changing the structure of a motor that has been manufactured, changing the type of stator winding is an economical and time-saving method to reduce the vibration and noise. Thus, a concentric single-double-layer star-delta (CSDLSD)winding for an induction motor is described in this paper with the aim of reducing the noise of the motor. By planning the turns relationship between the two parts of the winding, the harmonic component of the air-gap magnetic field can be decreased. Besides this, through adjusting the turns ratio in each slot of concentric winding per phase respectively, the waveform of the air-gap magnetic field becomes closer to a sinusoidal type. Three motors equipped with the CSDLSD winding and another two types of stator winding were analyzed. The theoretical analysis and the two-dimensional finite element method (2D-FEM) were combined to study the relationship between the harmonics of the air-gap magnetic field and the stator winding. Finally, a 2D fast Fourier transformation(2D-FFT) method was used to obtain the time-frequency spectrum of the air-gap flux density and electromagnetic excitation force,and compared with a natural vibration wave. The noise distribution was obtained using the harmonic response. The results of the theoretical analysis, 2D-FEM, 2D-FFT, and harmonic response corroborate each other such that the motor applying CSDLSD winding could reduce both the vibration and noise.

Keywords: Induction motor, concentric single-double-layer star-delta winding, 2D-FFT, vibration

1 Introduction1

Noise is a perennial issue of induction motors,research on motor vibration and noise has attracted increasing attention with the development of motor manufacturing technology[1]. Reducing aerodynamic noise and mechanical noise can be achieved by improving the working environment of the motor or by using manufacturing part with improved performance[2-3].However, the electromagnetic vibration cannot be reduced through application of the above methods.

Electromagnetic vibrations, leadings to electromagnetic noise, are caused by the electromagnetic excitation force, which is produced by the air-gap magnetic flux density. The harmonics of the air-gap magnetic field are decided by two parts, the permeance harmonic produced by the slot opening and the magnetomotive force (MMF) harmonic of the stator winding and the rotor winding[2]. The vibrational force waves are a function of the square of the air-gap magnetic flux harmonic, and the main source of noise results from the MMF produced by the interaction of both the stator winding and rotor winding[4-5]. The vibration and noise occur only when the frequency and vibration mode of the radial EMF harmonic are closed to the natural frequency of the motor and resource mode[6-7].The air-gap magnetic flux density wave of the induction motor generates radial and tangential electromagnetic excitation forces on the stator core teeth. The radial component, which makes the stator core vibrate and deform, is the main source of electromagnetic noise[8-10].

Methods have been explored to reduce vibration and noise. The use of permeance waves reveals all the air-gap magnetic field harmonics with proper orders,and provides comprehensive information about the radial electromagnetic excitation force[11-12]. Electromagnetic noise decreases as long as the harmonic component of the space air-gap flux wave is adjusted or reduced by a small amount[13].

Many previous literatures have studied methods thatwould change the structure of each part in order to influence the air-gap magnetic density so that the vibration and noise could be weakened. The authors in[14] examined the influence of slot-combinations on the flux and force pulsations. Novel methods were proposed in [8,15-17] to reduce the vibration and noise of induction motors by changing the skew slot structure of the rotor to weaken the harmonic amplitude of the rotor teeth. However, there are several side effects when equipped with skewed slot[15], such as axial drifting and transverse current. These side effects can be eliminated by using a double-skewed rotor[16], but the manufacturing technology of this structure is difficult to popularize. Thus, the rotor in [17] was proposed with four skewed slots. The structure of the induction motor must be changed in all the above methods, which is impractical for motors in service. The Maxwell tensor method is used in [18,19] to calculate the effects of the radial electromagnetic excitation force on stator deformation of the induction motor.

In view of the improving motor vibration and noise standards, the motor, especially complete motors,be optimized and reformed[20-21]. Comparing the economic and time input with changing the structure and tooth of the motor, adjusting and optimizing the stator windings is a more economical method with almost no side effect. The star-delta winding and concentric unequal turn winding both arise at the historic moment. The concept of the star-delta winding is similar to the use of multiphase windings,whichcould reduce phase-band harmonics by increasing the phase number[22]. However, the air-gap MMF of the two parts might be unbalanced[23-24].Another side effect is the additional harmonic content of the air-gap magnetic field, which might be generated due to the influence of the rotor magnetic flux on the stator magnetic field[25]. The research in[26] shows that the harmonic component of the air-gap magnetic flux density wave is much reduced because the distribution of coils in each tooth is closed to sinusoidal and the turn-number ratio is calculated reasonably. The concentric single-double-layer winding is an improved form of the concentric double-layer winding, which removes the insulation between coils in the same phase, so that material and time are both saved. Yet the fundamental wave winding factor of the air-gap magnetic field will also reduce while this type of winding is used.

In this paper, a concentric single-double-layer star-delta (CSDLSD) winding based on the present two types of sinusoidal winding, star-delta winding and concentric low harmonic winding, is proposed to eliminate the two side effects discussed in section 1. Through analysis of the influence of the winding ampere-turn distribution on stator MMF, the possibility of weakening the high-order harmonics of the stator air-gap MMF by adjusting the winding type is explored. The relationship between the radial electromagnetic excitation force and air-gap magnetic flux density distribution under no-load and load conditions is studied in section 2. Based on the above research, a 2-pole induction motor with a rated power of 11 kW is simulated by 2D-FEM in section 3, while the air-gap magnetic flux density date are processed by 2D-FFT and harmonic analysis, thus, the time-frequency distribution of the vibration and the noise spectrum are obtained in section 4.

2 Analysis of concentric single-double-layer star-delta winding

2.1 Basic theory

The CSDLSD winding is proposed on the basis of applying the ratio calculation theory of concentric low harmonic winding into each phase of star-delta winding. Thus, the harmonic components of the air-gap magnetic field are weakened by especially specific orders, and the waveform of the current distribution along the circumference is very close to sinusoidal.

Fig. 1 Vector diagram of CSDLSD winding

Fig. 1 shows not only the series relationship between the two parts of the star and delta winding,but also the phase relationship between the three-phase,including currents, impedance and electromotive force(EMF). The phase current in the star part is not only 30° ahead of that in the delta part, but alsotimes as large as that in the delta part. In order to balance the MMF and avoid the side effect caused by the unbalanced magnetic pull force, the winding turns ratio should meet the equation,theoretically. Therefore, the turns number of the pole-phase group of the delta part winding should beimes as much as that of the star part.

In order to ameliorate the situation that subharmonics would occur in the star-delta winding when the ratio of turns number between the star part and delta part cannot reach the ideal numerical value.Hence, considering the advantages of the selection method of concentric low harmonic winding, a CSDLSD winding schematic is shown in Fig. 2.

Fig. 2 Schematic of CSDLSD winding

The slot w, nearest to the current axis of phase A in the delta part (AΔ), is shown in Fig. 2. Because of the characteristics of the concentric low harmonic windings, the space electric angle difference is such that the slot lag axis is α/2, where α=2πp/Z1is the slot angle. The current in AΔphase behinds AYphase by 30°, and leads the current in the -CYphase by qα degree, where q is the number of slots per phase and pole q = Z1/2mp. Then, the space electric angle w of the kth coil edge lagging the AΔaxis can be expressed as

When k＜w, the symbol fetch +, when k＞w, the symbol fetch -.

In Fig. 2, j is the number of coil layers. The single layer coil and upper coil of the double-layer coil select j = 1, and the lower coil of the double-layer coil selects j = 2.kjφdenotes the time electric angle of the difference between the coil edge of the kth slot and the phase A current axis in the delta part of the j layer.

2.2 Analysis of magneto motive force

From the MMF and phase relationship in Fig. 1,the harmonic MMF of the delta part can be expressed as

The axis of the AYphase winding is taken as the space coordinate dot, and the coincidence of the maximum current and AYphase winding axis is taken as the initial time phase. Fph±vis the magnitude of harmonic MMF when the harmonic MMF decomposes into positive and negative parts. The formula for solving the harmonic MMF is given in (3). When the MMF is positive, choose +; reverse, -. ωt and θsare the time electric angle difference with the maximum AC current of a layer element in a certain slot, and the space electric angle difference between the AYphase axis, respectively.

The total MMF amplitude can be calculated from the magnitude of the positive and negative MMF as

The total delta winding harmonic MMF can be obtained by superimposing the space vector of each phase and the time-phase of the current flowing through each phase. The harmonic MMF of the total winding is the sum of the MMF of the star part and the delta part.

According to the turn number distribution characteristics of the CSDLSD windings, the winding coefficient kwvis obtained as

In the formula, t is the number of slots of a single layer coil in a polar phase group, yiis the pitch of coils in a polar phase group between ith slots and a certain phase axis, and Niis the turn number of ith coils.

2.3 Analysis of radial electromagnetic excitation force

The air-gap synthetic MMF comprises three parts:main wave MMF, harmonic MMF of stator winding,and harmonic MMF of rotor winding.

When the core magnetoresistance is neglected,the instantaneous value of the air-gap flux can be expressed as the product of the instantaneous value of the air-gap synthetic magnetizing potential and the instantaneous value of the air-gap synthetic permeance.In order to weaken the harmonic component of the air-gap flux density, it is necessary to reduce the higher harmonic component of the synthetic MMF and the AC component of the synthetic permeance.Because the AC component of the air-gap permeance is the side effect of slotting on stator and rotor, the change of winding type will not have a serious impact on air-gap permeance. Selection of theturn number,connection mode, and parallel branch number of windings could weaken the higher-order harmonic component and reduce the higher-order harmonic winding coefficient by changing the air-gap synthetic MMF, which would affect the harmonic magnetic field established by the stator winding MMF in the air-gap.Thus, the method could weaken the harmonic content of the air-gap magnetic density .

The amplitude of the air-gap flux density Bvis constrained by the harmonic orders, current, and the maximum air-gap flux density, as shown as

The radial electromagnetic excitation force generated by the harmonic magnetic field of the stator and rotor windings is squared function of the stator and rotor windings harmonic magnetic field. The magnetic field produced by the interaction of the two magnetic fields is the main factor, as given as

In the formula r = μ ± ν is the order of force waves, and the vibration noise induced by the radial electromagnetic excitation force waves is closely related to the magnitude of the force waves. The separate influences of the stator flux density and rotor flux density on the radial electromagnetic excitation force are small and negligible for electromagnetic noise. Thus, the molecule of the second approximate equation (10) leaves only the part of the stator-rotor flux density interacting with each other. Tab. 1 shows the main force wave orders that cause large deformation of the induction motor core when 36/28 slot is applied.

Tab. 1 Order of electromagnetic force with slot combination 36 and 28

It can be seen from Tab. 1 that when the number of stator harmonics is -29, 31, -53, 55, the stator yoke will produce serious type 2 deformation, while the -23,25, -59, 61 stator harmonics cause type 4 deformation.The two vibration modes of the stator is shown in Fig. 3.Usually, the deformation amplitude is proportional to r4, and the force waves, of which not less than six times, have little effect on the stator deformation,which is generally not considered.

Fig. 3 Vibration mode of the stator

3 Finite element modeling

The above analytical method was used to analyze the magnetic density and the electromagnetic excitation force when the CSDLSD windings were equipped. Because of the saturation effect and the nonlinearity of the magnetic circuit of the motor, it is difficult to accurately calculate the magnitude of the magnetic density and radial electromagnetic excitation force by the analytical method, so the exact calculation is carried out by 3D-FEM. In this simulation, a squirrel cage induction motor with general two poles,11 kW, Y160M is used, and the motor parameters are listed in Tab. 2. At present, the actual 11 kW 2-pole motor manufactured by the motor factory is usually equipped with 12 or, 24, or 48 slots of stator. Themore slots per pole phase, the more favorable the ratio of turns of CSDLSD windings, the greater the reduction of vibration and noise. In order to improve the simulation accuracy and shorten the simulation time simultaneously, the motor with 36 slots of stator was chosen for this study.

Tab. 2 Induction motor parameters

In order to analyze the air-gap magnetic density more accurately using 2D-FEM, the density of the air-gap mesh partition should be increased manually.In order to be both timely and accurate, the air-gap is divided into four layers with the mesh element length of 0.22 mm as the model in Fig. 4 . The total mesh number was 653,154, including: stator core 71,101,rotor core 1997, air-gap 283,047, stator winding 218,505, rotor guide bar and end ring 52,638, and axis 21,634. Because this paper mainly studies the vibration and noise caused by the influence of the stator winding on the air-gap magnetic field, the partition of the air-gap and stator winding is refined to ensure the accuracy of simulation.

Fig. 4 FEM model of the induction motor with 36/28 slots

The winding mode of the 36 slot stator CSDLSD winding in simulation is shown in Tab. 3, and Fig. 5 gives out the expansion diagram of the CSDLSD winging. Before simulation, excitation and impedance should be added to the star winding and delta winding respectively. The impedance relationship between the two-part windings is given in reference [16], and expressed as

Tab. 3 The winding mode of the CSDLSD winding

Fig. 5 Expansion diagram of CSDLSD winding with 36 slots

4 Results of finite element analysis

4.1 Simulation results of current and voltage

Fig. 6 displays a comparison of the current in the no-load case using traditional short-distance double-layer winding, star-delta winding, and CSDLSD winding. The cross-axis titles of the three current-time simulation diagrams are the same, all of which are time. Thus, when the three diagrams are compared, the cross-axis titles and units are labeled only under the third diagram. The current amplitude of the traditional winding is the lowest and it is not stable at zero-crossing point. The CSDLSD windings can not only further increase the current amplitude, but also stabilize the current throughout the period.

Fig. 6 Comparison of current between motors with three different types of windings under no load

The current waveform of the traditional short pitch double-layer winding is not ideal because the main harmonic content is 5th order and 7th order. The current waveform of the star-delta series windings is not satisfactory as the winding turns ratio of the star and delta part is much different to. The error results in incomplete elimination of the 5th and 7th harmonics, and other harmonics may be produced. The distorted current leads to the unsatisfactory MMF of the stator, which might increase the vibration and noise, reduces the efficiency, and generate additional torque.

A comparison of the induction potential of motors with three types of windings is given in Fig. 7. Under the circumstance that the induction potential curves of the three windings are reasonable, the waveforms of the CSDLSD windings are closer to the sinusoidal type, the amplitude of which is slightly higher than those of the other two windings.

Fig. 7 Comparison of electromotive force between motors with three different types of windings under no load

4.2 Analysis of radial electromagnetic excitation force

The winding coefficients of the induction motors with three types of windings can be accurately calculated by a 2D-FEM simulation, as shown in Tab. 4.

Tab. 4 kw of the induction motor with different winding types

From the data in Tab. 4, it can be seen that compared with traditional windings, star-delta windings could increase the fundamental wave while weakening the higher-order harmonics, especially for the 5th and 7th harmonics, the weakening rate of which reaches approximately 70%. However, the effect of weakening some harmonics is very small, e.g.,the rate for the 17th harmonics is only 11%. CSDLSD windings not only further improve the fundamental wave winding coefficient, but also weaken other sub harmonics based on the star-delta winding. Because the effect of changing the windings on MMF harmonics is generally limited to phase-band harmonics, the effect of tooth harmonics is not considered for the increase is equal to the fundamental wave.

The radial air-gap flux density of the induction motors equipped with three different windings is compared in Fig. 8. Compared with the irregularities of the waveforms of the other two windings, the CSDLSD windings not only slightly increase the amplitude of the air-gap flux density, but also tend to sinusoidal law because of the considerable reduction of the harmonic of the air-gap synthetic MMF. In order to basically ensure that the other parameters of the three different stator winding motors are maintained, an optimal solution cannot be obtained for the turn number of each winding. Therefore, the harmonic component of the magnetic flux density waveform of the traditional short pitch double-layer winding and star-delta winding motor is larger. In an actual motor, the optimal winding turns will be adopted according to the specific motor, so serious torque ripple will not occur.

Fig. 8 Comparison of radial flux density in the air-gap between motors with three different types of windings

The amplitude and harmonic content of the radial air-gap magnetic density directly affect the radial electromagnetic excitation force and thus determine the magnitude of vibration and noise of the motor. As shown in Fig. 9, the difference of the radial electromagnetic excitation force amplitude among the three windings is rather obvious, and the radial electromagnetic excitation force amplitude of the star-delta windings is relatively stable in some specific locations. However, due to the restriction of the turns number choice, the electromagnetic excitation force may still be considerably improved overall. The electromagnetic excitation force distribution of CSDLSD windings is more balanced along the circumference, and its amplitude is the smallest of the three. This is consistent with the analytical results that the CSDLSD windings can reduce vibration and noise.

Fig. 9 Comparison of electromagnetic force between motors with three different types of windings

Figs. 10 and 11 apply the FFT method to compare and analyze the circumstances of no load, 25% load,50% load, 75% load, and full load, respectively, the radial air-gap flux density and the radial electromagnetic excitation force of CSDLSD windings.From the figure, the harmonics of the stator and rotor teeth are not weakened because the number of stator and rotor teeth and slots correlate with the relationship Kz1,2±p. With the increase of the load torque, the stator current increases with the rotor current, and the amplitude of the higher-order harmonic component in the current increases. However, the attenuation of certain harmonics by CSDLSD windings is enhanced,and the fundamental wave amplitude is inversely related to the load variation.

Fig. 10 FFT of radial air-gap flux density under different load torques

Fig. 11 FFT of radial electromagnetic force under different load torques

Generally, when calculating the radial air-gap magnetic density by FEM, the result obtained by simulation is distributed according to time, then, the harmonic frequency distribution of the air-gap magnetic density is obtained by FFT. However, the magnetic density is a multi-factor variable related to both time and space. The order and frequency have the possibility of overlap. The results obtained from a single analysis for themagnetic flux density are only one-sided, not objectively and completely. Therefore,the air-gap magnetic density collected can be decomposed into 2D, including space and time, with the help of Matlab software programming to achieve a more comprehensive analysis of the effect of magnetic density distribution.

Figs. 12 and 13 show the results of the time-frequency 2D FFT of the radial air-gap flux density and radial electromagnetic excitation force.The distribution of each harmonic in time and space is also shown. The amplitude of each harmonic gradually increases with the growth of frequency from 50 Hz to 800 Hz. When the frequency isbetween 800 Hz and 1 200 Hz, the amplitude gradually decreases. In the process of increasing the frequency from 1 200 Hz to 1 600 Hz, the amplitude of each harmonic gradually increases, showing a law-approximating periodicity.

Fig. 12 2D-FFT of radial air-gap flux density under no load

Fig. 13 2D-FFT of radial electromagnetic force under no load

After the result of the radial electromagnetic excitation force was obtained, the harmonic response could be analyzed.

To analyze the harmonic response of the motor stator, the meshes of the stator teeth were encrypted when introducing the 2D-FEM simulation model, and the mesh length was set to 0.1 mm. The motor shell and stator core were both included in the modal analysis model, as shown in Fig. 14. At last, the number of elements was 86 273. Besides this, the frequency and vibration mode of the natural frequency are given in Tab. 5, compared with the frequency and order of the partial electromagnetic force shown in Tab. 6. Vibration and noise would occur under these consistent frequencies.

Fig. 14 3D model of harmonic analysis

Tab. 5 Amplitude of electromagnetic force with differentwinding types

Tab. 6 Natural frequency of stator

The frequency and order of the main electromagnetic force can be seen in Tabs. 5 and 6,which are matched to the natural frequency and mode of the stator at 1 385 Hz. Thus, the vibration and noise at the frequency are caused. The amplitude of the vibration velocity of the stator with different types of windings is given in Fig. 15.

The maximum vibration point of the motor occurred in the vicinity of 1 385 Hz. The amplitude of the vibration velocity with traditional short pitch doublelayer winding, star-delta winding, and CSDLSD winding is 4.85 mm/s, 2.12 mm/s, and 1.24 mm/s,respectively. The value reduced by 0.88 mm/s when the star-delta winding was switched to CSDLSD winding.

Fig. 15 Amplitude of vibration velocity of stator with different types of windings

Because the main contributor of noise is electromagnetic vibration, the excitation of the noise analysis applies the results of the harmonic response analysis, and the noise is transformed from the vibration of the stator surface. Fig. 16 shows the acoustic pressure and the sound pressure level at 1 385 Hz with a traditional short pitch double-layer winding; at different positions the noise pressure is not the same,varying with the magnetic field distribution.

Fig. 16 Acoustic pressure and sound pressure level at 1 385 Hz with traditional winding

Fig. 17 compares the simulation results of the harmonic analysis with three different windings. The noise amplitude of the star-delta winding is similar to that of the traditional winding, but the CSDLSD winding can reduce slightly at different frequencies,especially in the mid-frequency band. The results of the harmonic analysis prove that CSDLSD windings can reduce motor noise.

Fig. 17 Noise with different types of windings

5 Conclusions

The target harmonic MMF of the stator winding cannot be eliminated when the turns number of the star-delta winding does not reach the ideal ratio. In this paper, the error is reduced by the proposal of a CSDLSD winding and the design theory is presented.

First, the air-gap magnetic flux density and radial electromagnetic excitation force distribution of the induction motor equipped with CSDLSD winding was analyzed by ananalytical method. It can be concluded that the CSDLSD winding reduces almost all orders,especially the lower orders such as 5th, 7th, 11th, and 13th order harmonics of the air-gap magnetic field, by optimizing the ampere-turn distribution of the stator winding. The effect of less harmonic component of the air-gap flux density resulted in the decrease of the radial electromagnetic excitation force. Second,comparing the air-gap magnetic field and the electromagnetic excitation force of the three motors model in 2D-FEM, the harmonic component of the motor with CSDLSD is the lowest, and the waveform of the air-gap flux density is the nearest to sinusoidal type. The harmonic responses are concluded by the spectrum of time-frequency of the air-gap flux density and force. Thus, the amplitude of velocity of the stator surface with different types of winding was attained, and the value was weakened by 3.61 mm/s and 0.88 mm/s.Finally, the simulation shows that, compared with the other two types of motor, the noise of the motor with CSDLSD winding decreased by 10 dB/A.

The above results prove that the proposed winding is a promising option for decreasing electromagnetic vibration and noise.