4A8_1654

1654 PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011

The Study on Electromagnetic Force Induced Vibration and Noisefrom a Normal and an Eccentric Universal Motors

K. Shiohata1, R. Kusama2, S. Ohtsu3, and T. Iwatsubo4

1Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki, Japan2Toyota Ltd, Japan

3Yamagata, Hitachioomiya, Ibaraki 319-3111, Japan4Kansai University, Japan

Abstract— There are many harmonic components in the electromagnetic force caused byelectrical motors. The harmonic components induce the structural vibration and noise, frequently.The unbalanced electromagnetic pull force is generated between the rotor and the stator whenthe rotor is not corresponding to the center of the stator, that is, eccentric in the electrical motor.In the paper, first, the harmonic components of electromagnetic force caused from a normal andan eccentric universal motor are discussed numerically. Then, the effect of the difference of theharmonic components of electromagnetic force caused from a normal and an eccentric motor onthe structural vibration are discussed numerically. From the numerical simulation, the spectrumdistribution is different in the space region between a normal and an eccentric motor. And the12th time order components of electromagnetic force and an electromagnetic vibration and noiseof eccentric motor are larger than those of a normal motor.

1. INTRODUCTION

Universal motors shown in Fig. 1 have been the major source of power for power tools and vacuumcleaners since their early days. Recently, the motors have become to run in very high speed and togenerate much higher horsepower per unit weight and mechanical structure have become lighter andsmaller. As a result of these trends, mechanical vibration and noise are increasing. The lighteningof the motor core was also attempted, consequently the electromagnetic exciting force increased bymagnetically saturating, and the vibration and noise became easy to be generated. The reason ofnoise and vibration is the harmonic components of electromagnetic force caused from a motor. Thewaveform of an electromagnetic stress is shown as Fig. 2. By FFT in the time and space domainof the waveform, many harmonic components are obtained at one point along the inner bore of thestator

In the production of the electrical motor, it is difficult that the center of the rotor always coincidewith the center of the stator.

The unbalanced electromagnetic attractive force is generated between the rotor and the statorwhen the rotor does not coincide with the center of the stator, that is, eccentric in the electricalmotor.

In the eccentricity, there are two patterns. One is static eccentricity which rotor center does notcoincide with stator center, and the other is dynamic one which is generated by mass unbalances.

The unbalanced electromagnetic attractive force becomes a cause of the vibration and noisefrom the motor. Iwatsubo et al. [1] discussed the stability of induction motor. B. S. Rahman andD. K. Lieu discussed the relation between electromagnetic stress and radial offset [2].

Figure 1: Schematic of universal motor.

0

20

40

60

80

100

0 180 360

Electrical angle [deg]

Ele

ctr

om

agn

etic s

tress [kP

a]

Figure 2: Waveform of electromagnetic stress at aposition of rotational angle.

Progress In Electromagnetics Research Symposium Proceedings, Marrakesh,Morocco, Mar. 20–23, 2011 1655

In this study, the electrical, vibration, and noise characteristics are studied for static eccentricityrotor of universal motor. Ohts et al. reported the test equipment of universal motor and reportedthe electrical, the vibration, and the noise characteristics of the normal condition of the motor [3].

In the paper, the harmonic components of electromagnetic force and an electromagnetic vibra-tion and noise from universal motor with rotor eccentricity are numerically discussed comparingwith normal rotor. The magnitude of eccentricity is 0.2mm against air gap 0.4mm and, angle ofeccentricity is 0, 45, 90, and 135 degree.

2. ANALYTICAL METHOD

2.1. Harmonics Analysis of Electromagnetic StressThis analytical method has been presented by Kobayashi, et al. [4]. In this study, a two-dimensionalfinite element method is used. The electromagnetic force is calculated in two steps.

Magnetic flux density along the stator inner bore is calculated, taking into account the motionof the rotor and the eddy current in the rotor bars.

From the above calculation results, electromagnetic force is calculated by using the Maxwellstress equation:

σr =1

2µ0

(B2

r −B2t

)(1)

where Br and Bt are radial and tangential magnetic flux density, respectively. In Fig. 2, thecalculated distribution of radial electromagnetic force at one point along the inner bore of thestator is shown. These distributions are calculated at several points along the inner bore of thestator. The number of points depends on the meshes divided by using the finite element method.Radial electromagnetic force stress therefore consists of many frequency components along the innerbore of the stator. However, because the frequency is low, the fundamental component has only asmall influence on the vibration and acoustic noise.

The electromagnetic density is expressed by the Fourier series as follows:

σr =∑

k

∑

l

ak,l sin(kx− lω t + αk,l) (2)

where ω (= 2πf) is frequency of the stator current (rad/s), k and l are the space and time harmonicorder, respectively. And akl and αkl are amplitudes and phases of the harmonic components andare calculated as follows:

ck,l =∫∫

σr sin(kx− lω t)dtdx (3)

dk,l =∫∫

σr cos(kx− lωt)dtdx (4)

ak,l =√

c2k,l + d2

k,l (5)

αk,l = tan−1

(ck,l

dk,l

)(6)

Figure 3 shows the example of the spectrum of electromagnetic stress Calculated harmonics areplotted in the k-l plane. A negative time-harmonic order indicates backward rotation of the elec-tromagnetic waves. On the other hand, the space order k participates in the deformation in theradial direction along the stator circumference. The relation between circular mode order n andspace order k is

n = k × (p/2) (7)

2.2. Transformation of Electromagnetic Stress into Exciting Force for the Structural VibrationCalculationTo calculate three-dimensional structural vibration, it is necessary to transform the electromagneticforce stress calculated by two-dimensional analysis into three-dimensional electromagnetic force.Figs. 4(a), (b) show this transformation. The electromagnetic stress is calculated along the innerbore in two dimensions as shown in Fig. 4(a) and the unit is Pascal. On the contrary, the excitingforce on the structure is actually in three dimensions as shown in Fig. 4(b) and the unit is Newton.


60

0

100

200

0

-60

Spa

ce h

amon

ic o

rder

k

0

60

Time harmonic order l

Magnitude (

kP

a)

Figure 3: Spectrum of electromag-netic stress.

(a) (b)

Figure 4: Transformation of electromagnetic force into structuralexciting force. (a) Electromagnetic force stress (two dimensions).(b) Excting force of structure analysis (three dimensions).

Figure 5: Configuration of the test apparatus. Figure 6: Cross section of the universal motor.

When the motor is not a skew structure, the electromagnetic stress in the axial direction isalmost constant. The exciting force on the structure is therefore also assumed to be constant inthe axial direction. When the structure is divided as shown in Fig. 4(b), it is necessary to calculatethe exciting force on element m (m = 1,. . . , M). First, the center of gravity of the element m (rm,θm) is calculated in terms of polar coordinates. Then the electromagnetic stress σm is calculatedby Eq. (2) at point (rm, θm). And the electromagnetic force fm is calculated by multiplying byarea Sm of element m. Next, the electromagnetic force fm is distributed at the nodes of elementm. In this analysis, the electromagnetic force is distributed at the nodes of element m equally. Thesame calculation is carried out for all elements. Finally, the exciting force on the entire structureis determined.

3. ANALYSIS OF ELECTROMAGNETIC FORCE STRESS

3.1. Analytical Model

The rotational speed of rotor (armature) at no load condition is 24000 rpm, and the rated consumedelectrical power is 1100 W. The air gap is 0.4 mm in the radial direction. The number of rotor(armature) slot is 12. It is possible to use the universal motor even in both of alternating currentand direct current. The number of carbon brush is 2 and the number of segment is 24. Then, alliron cores laminate silicon sheet of the 0.5 mm thickness in order to decrease eddy current loss andexothermic reaction. Fig. 5 shows the configuration of test apparatus used in this study, includingthe universal motor. Fig. 6 shows the cross section of the universal motor.

3.2. Modeling of Electromagnetic Field Analysis

In the electromagnetic field analysis, 2-D FEM analysis is applied and ANSYS software is used.The elements are defined in the radial and circumferential directions and the 4-nodal point solid isused. Air-gap is divided especially in detail in consideration of the rotor eccentricity. Fig. 7 showsthe FEM model for the electromagnetic field analysis. The degree of freedom is 14752.

It is defined for the amount of eccentricity ε and the angle of eccentricity φ based on a rotorcenter position in the state without the eccentricity as shown in Fig. 8.


Figure 7: FEM model. Figure 8: Definition of eccentricity.

0

2000

4000

6000

0 200 400 6000

Ca

l[H

z]

Exp [Hz]

2779Hz

Housing

Stator

Assemblye

Figure 9: Comparison of natural frequency.

Figure 10: 2nd Circular mode of housing (2779 Hz).

3.3. Modeling of Structural Vibration Analysis

In the structural vibration analysis, 3-D FEM analysis is applied and ANSYS software is used.The degree of freedom is 54186. To make the model with high accuracy, the impact tests aredone for stator, housing and motor assembly. From the tests, vibration modes, natural frequenciesand modal damping are analyzed. The measured and calculated natural frequencies are shown inFig. 9. Fig. 10 shows the 2nd circular mode of housing in the motor assembly at 2779 Hz. Thedifference between the measured and calculated natural frequency of the parts is about 7%. Fromthe comparison, the accuracy of the structural vibration model is well.

4. MUMERICAL SIMYULATION

4.1. Electric Magnetic Force

By using FEM software ANSYS, magnetic flux is calculated. The contour of the magnetic fluxdensity distribution for a normal and an eccentric motor is shown in Fig. 11. The magnitude andangle of the eccentricity is 0.2 mm and 45 degrees, respectively. The maximum of the magnetic fluxdensity is about 2 T.

In the air-gap, the magnetic flux density is the maximum in the 45 degrees and 225 degrees. Inthe normal rotor, the magnetic flux density is symmetry in the original point. On the contrary, inthe eccentric motor, the magnetic flux density is not symmetry in the original point.

By FFT analysis following Eq. (2), the harmonic components of the magnitude of the electro-magnetic stress is obtained. Fig. 12 shows the spectrum of the electromagnetic stress for a normalrotor. From the Fig. 12, The electromagnetic stress of 0th, 12th, 24th time order component areparticularly dominant. The 12th, 24th components influence the vibration and noise. The electro-magnetic stress at 12th time order is fundamental component caused by the number of rotor slot.Fig. 13 shows the electromagnetic stress of the 0th to 10th space order component of 12th timeorder.

The electromagnetic stress at 12th time order when it is 0.1 mm, 0.2 mm, and 0.3 mm in theamount of eccentricity is shown in figure. From the Fig. 13, the following are discussed.

(1) The electromagnetic force component at the odd number of the space mode doesn’t exist whenthe rotor is not eccentric.


(a) Normal motor (ε=0) (b) Eccentric motor (ε=0.2, ϕ=45deg)

Figure 11: Contour of the magnetic flux density.

-40 -30 -20 -10 0 10 20 30 40010

20300

1

2

3

4

5

6

Ele

ctr

om

agn

etic

str

ess

kP

a]

Time order, l

Space order

k

12th

24th

Figure 12: Spectrum of electromagnetic stress in thetime and space region.

Figure 13: The harmonic components of the electro-magnetic force stress at 12th time order in 45 degreedirection.

(2) The magnitude of electromagnetic force at the space order depends on the amount of eccen-tricity, but the magnitude correlation is not constant.

(3) The magnitude of electromagnetic force depends on the space order, but the magnitude cor-relation is not constant.

4.2. Vibration Caused by Electromagnetic ForceThe electromagnetic stress is transformed to structural exciting force by procedure in the Sec-tion 2.2. The exciting force is added to the housing in the motor model and the vibration of thesurface is calculated. The displacement of the housing center of the normal and the eccentric motor(ε = 0.2mm, φ = 45 deg) at the natural frequency 2779Hz is shown in Figs. 14(a), (b) by contours.Both contours are different a little. Then, the difference is compared quantitatively.

Then, the 8 positions are chosen to discuss the difference of the displacement between the normalmotor and the eccentric motor. Fig. 15 shows the displacement of a normal rotor and eccentricmotor (ε = 0.2mm, φ = 45 deg) in the 8 locations shown in Fig. 16. From the figure, the followingare discussed.

(1) The displacement of the eccentric motor is larger than that of the normal motor.(2) The ratio of the maximum displacement is about 1.23.(3) Both displacement of the normal motor and the eccentric motor is larger at 3© and 7©.

4.3. Noise Caused by Electromagnetic ForceThe noise radiated from the surface of the motor housing is calculated by BEM (Boundary ElementMethod) which is named as the Acoustics contained in the software “LMS Virtual Lab.”. In Fig. 17,the contours of noise of the normal and the eccentric motor (ε = 0.2mm, φ = 45deg) are shown.The locations in the axial direction are the center of housing same as the Fig. 14. In Fig. 17, themagnitude of noise is shown. The locations in the circumferential are the same as Figs. 14 and 15,and the locations in the radial direction are 1m outside from the housing. The mean value of noise


X

Y

Z

(a) normal motor (b) eccentric motor

Min

Max

Figure 14: Contour of displacement of the housing (ε = 0.2mm, ϕ = 45 deg).

Figure 15: Displacement of housingcaused by elec-tromagnetic force at 2779Hz.

X

Y

Figure 16: Location of calculation of vibration of thecross section of housing.

(a) Normal motor (b) Eccentric motor

Figure 17: Contour of noise of the motor.

of 8 positions of the normal motor and the eccentric motor is 69 dB and 72 dB respectively. Fromthe figure, the following are discussed.

(1) The magnitude of noise in the 45 deg, 135 deg, 225 deg and 315 deg directions is dominant.(2) The distribution of noise is almost the same between the normal motor and the eccentric

motor.(3) The distribution of noise in the eccentric direction is a little bit difference.(4) The magnitude of noise from the eccentric motor is overall larger than that from the normal

motor.(5) The maximum of the mean value of noise of the normal motor is 3 dB larger than that of the

eccentric motor.

5. CONCLUSION

The harmonic components of electromagnetic force and an electromagnetic vibration and noisefrom universal motor with eccentricity were numerically discussed comparing with those of normaluniversal motor and the following are concluded. From the results, the 12th time order componentsof electromagnetic force and an electromagnetic vibration and noise of eccentric motor are largerthan those of a normal motor. In addition, although the electromagnetic force harmonic components


at the even number of the space mode exist when the rotor is non-eccentric or eccentric, that ofthe odd number of the space mode doesn’t exist when the rotor is not eccentric.

REFERENCES

1. Iwatsubo, T., et al., “Vibration analysis of an induction motor under electromagnetic force,”Transactions of the Japan Society of Mechanical Engineers, Vol. 60, No. 680, 103–108, 2003(in Japanese).

2. Raman, B. S., “The origin of permanent magnet induced vibration in electrical machines,”ASME, Vol. 113, 476–481, 1991.

3. Ohts, S., K. Shiohata, and T. Ogata, “A method for analyzing electromagnetic-force–inducednoise from a universal motor,” APVC2005 Proceedings of the Asia Pacific Vibration Confer-ence, Malaysia, 2005.

4. Kobayashi, T., F. Tajima, M. Ito, and S. Shibukawa, “Effect of slot combination on acousticnoise from induction motors,” IEEE Transactions on Magnetics, Vol. 33, No. 2, 2101–2104,1997.

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