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1 Space Distribution of Electromagnetic Forces of Induction Motor Fuminori Ishibashi Shibaura Institute of Shinichi Noda Toshiba Corporation, Fuchu-city, Recently, there has been increasing demand for silent motors, and induction motors are no exception. Electromagnetic noise is sometimes the predominant acoustic noise in these motors. In small motors, most of vibration and noise is caused by electromagnetic forces due to combination of harmonic fluxes in the air gap. In this study, the space distribution of fundamental and harmonic electromagnetic forces was studied using a search coil, FEM analysis and conventional equations. In 4P2.2kW motor, harmonic electromagnetic forces including the fundamental one were measured using 36 search coils on the inner surface of the stator teeth, and electromagnetic force space distribution at each frequency was obtained. It was also analysed by FEM, and the results were analytically checked by conventional equations. From these analyses, the space electromagnetic force distribution for various harmonics was confirmed. These results will be useful in developing and designing quiet motors. 1 Introduction Induction motors can be started directly from a power line and can run without an inverter if the inverter breaks down. As a result, they have been widely used for industrial purposes and in home appliances. However, due to global ecological considerations, vibration and sound need to be greatly reduced. Electromagnetic noise due to sine wave and inverter drive is sometimes jarring to the ear, and many researchers have studied ways to reduce acoustic noise[1,2,3,4]. Interaction of harmonic fluxes in the air gap of a motor produces electromagnetic force and magnestriction, and these factors cause the stator and the rotor to vibrate[5,6,7]. Therefore, it is important to analyse harmonic fluxes, electromagnetic forces and magnestriction. Structural characteristics, that is, natural frequency, also affect vibration and acoustic sound [8,9,10]. Harmonic fluxes have been studied by search coils and FEM, and the electromagnetic forces have been analyzed by mathematics and by FEM[11,12,13]. However, space distribution of electromagnetic forces have been mainly experimented from the viewpoint of slot harmonics and not of saturation effects[1419]. Few papers have dealt with the relation between mathematical and measurement results. In this paper, the electromagnetic forces space pattern of small squirrel cage induction motors, 4P-2.2kW, are measured using search coils and are calculated by FEM, and the resulting data are compared with values obtained from equations. All space patterns of the electromagnetic forces agree with each other, and the distribution of electromagnetic forces related to saturation is newly confirmed. 2 Experiment 2.1 Measuring method Table 1 shows the specifications of the experimental motor and the size of the search coil. The motor was specially built for this experiment, and has a larger air gap than a conventional motor. This larger air gap provides space for a search coil on a tooth inside the stator. The motor has a full pitch lap winding and a no-skew squirrel cage rotor, which does not suppress the generation of harmonic fluxes. Each search coil is pasted on the inside surface of a stator tooth. Electromagnetic force is measured as the square of the integrated output voltage of the search coil. Figure 1 shows the method for measuring the space pattern of the electromagnetic force. The phase of a specific frequency at a specific time from the reference search coil is measured for all search coils. This phase value is put into (1) and the wave form is obtained as a space distribution pattern. The motor drives at no-load. f=f sin(x) (1) where f: electromagnetic space force, F: amplitude of electromagnetic space force, x: phase at each position

2 2.2 Experimental results In Figure 5, the electromagnetic force mode of 200Hz and 300Hz originates from the saturation harmonic The electromagnetic force wave, that is, square of the integrated staff of the search coil voltage is shown in Figure 2. The spectrum of the electromagnetic force wave at 200V-50Hz on no-load is shown in Figure 3. In this figure, the fundamental component of 100Hz and the rotor slot component were large. Figure 4 shows the space pattern, that is, the mode at the 100Hz electromagnetic force wave obtained from (1). This pattern shows a distribution on straight line. Figure 5 shows a circular pattern for various frequencies. Table 1: Motor and search coil specification Items Type PhasePoleRotor Rating Voltage- Slots ( SR) Gap Search coil (mm) Number of Search coil Search coil interval Search coil Contents Totally Enclosed Squirrel cage V (semi-open) 1.5mm 1.0(W)80(L)0.18(T) 36 (stator teeth inner surface) degree (mechanical) Stator on straight line fluxes and can not to be calculated from an equation. These modes have not previously been clear. This measurement confirms the space distribution and the mode of the electromagnetic forces. Modes of fundamental flux, slot harmonics and saturation fluxes are shown in Table 2. The number of search coils is limited due to lack of pasting space and Figure 2: Electromagnetic time force wave(measured) Figure 3:Electromagnetictime force spectrum (measured) Amplitude Time force wave Space force wave Position Position Figure 4: Fundamental electromagnetic force space distribution ( measured ) Figure1: Electromagnetic force distribution

3 the maximum number of measuring modes is also limited. Furthermore, higher order harmonic flux produces a small search coil voltage and makes it difficult to measure correctly. 2 nd (100Hz) 4 th ( 200 Hz) 6 th ( 300 Hz) 20 th (1000 Hz) 3 Finite element method FEM is used to calculate the flux distribution of the motor and the mode of the electromagnetic force is derived by the same method as in the experiment. With non-linear 2-dimensional static electromagnetic FEM in Table 3, flux simulation is done through rotation of the rotor. In order to obtain the time variation of the electromagnetic force in the air gap, the rotor is synchronously rotated with stator current phase. The time wave of electromagnetic force at the gap centre and at the centre of the stator tooth is shown in Figure 6. Figure 7 shows the spectrum of the time force wave. Other than slot harmonics components, saturation components, such as 200Hz, 300Hz and 400Hz, appear. The 2-pole span of electromagnetic force is shown in Figure 8 and its spectrum in Figure 9. In this graph, the second component (2-cycle in 2-pole span) is the largest, and is the fundamental component. This is second for the fundamental 4-pole flux. The stator slot component, 18 th, and the rotor slot component, 22 nd, also are produced. As in the experimental procedure, the time wave of Figure 6 is analysed by Fourier Series, and the amplitude and phase of the harmonics are calculated. The phase of each time harmonics at each point is substituted into (1), and the space distribution pattern mode is obtained for the FEM simulation. The space electromagnetic force distribution of the fundamental wave and harmonics by FEM is shown in Figure 10. Table 3: Magnetic FEM 22 nd (1100Hz) 42 nd (2100Hz) Program Magnetostatic non-linear Figure 5: Electromagnetic force pattern ( measured ) Rotation of rotor 2-dimentional FEM 396 points Table 2: Mode of space electromagnetic force (measured) Mode Mode Rotation position degree pitch Number of elements Number of nodes 8705 Circumferential points 1024 on circle at air gap center Layer of gap

2 nd ( 100Hz ) 4 th (200Hz) Figure 6: Electromagnetic time force ( FEM ) 30 6 th ( 300Hz ) 22 nd ( 1000Hz ) Figure 7: Electromagnetic time force spectrum (FEM) 24 th (1200Hz) 44 th ( 2200Hz ) Figure

4 2 nd ( 100Hz ) 4 th (200Hz) Figure 6: Electromagnetic time force ( FEM ) 30 6 th ( 300Hz ) 22 nd ( 1000Hz ) Figure 7: Electromagnetic time force spectrum (FEM) 24 th (1200Hz) 44 th ( 2200Hz ) Figure 8: Electromagnetic space force ( FEM ) Figure 10: Electromagnetic space force distribution ( FEM) Table 4: Mode of electromagnetic space force (FEM) Mode Mode 100 (2) (22) (4) (24) 12 Figure 9: Electromagnetic space force spectrum ( FEM ) 300 (6) (42) (20) (44) 16

5 In one circle at the air gap of the motor, that is, in 4-pole flux distribution, the fundamental electromagnetic force, 100Hz, produces an 8-pole pattern, mode 4. The fourth electromagnetic time force produces a 16-pole pattern, mode 8. Figure 10 shows that space harmonic force has no relation to time harmonic force. The space pattern of the force mode does not yield to frequency of force. The mode is shown in Table 4.From Figure 10 and this table, FEM also reveals a space electromagnetic force distribution related to saturation, such as 200Hz and 300Hz. These have not previously been clear. Mode and frequency of electromagnetic force are calculated in Table 5 for the experimental motor for various combinations of integers h and k. For specific electromagnetic time force frequency, Table 5 yields various modes with combination of order of harmonics. Generally, a smaller mode affects the vibration of a structure and produces acoustic noise. 5 Discussion and conclusions 4 Mode calculation The largest is the electromagnetic vibration and noise due to the rotor slots. This has been studied and its frequency and mode is calculated as follows. where m1,m2: mode, h, k: integral, Zs, Zr: number of slots (stator, rotor), fs: electromagnetic force frequency, fsource frequency, s: slip Experimental, simulated and analytical results are summarised in Table 6, and show good agreement. The mode by slot harmonics agrees with the minimum mode calculated by (2) and (4). Modes of electromagnetic force at 200Hz and 300Hz relate to the saturation of electrical steel sheets and these can not be calculated by an equation. These modes are confirmed in Table 6. The results are summarised as follows. m1=±hzs±kzr (2) Space distribution of electromagnetic force related to saturation is confirmed. fs=zr/(p/2) (3) In mode of electromagnetic force, experimental m2=hzskzr+p (4) results, FEM simulation and mathematical values fs=(zr/(p/2)2) f (5) agree. These results will be useful in design and development of low-vibration and low-noise induction machines. Table 6 : Comparison of modes Table 5 : and mode Modes (Stator harmonic order, Rotor harmonic order) (1,-1),32(2,-1),68(3,-1),76(-1,-1),104(4,-1), 112(-2,-1),140(5,-1),148(-3,-1),184(-4,-1) (1,1),28(2,1),64(3,1),80(1,-1),100(4,1), 116(2,-1),136(5,-1),152(3,-1),188(4,-1),224(5,-1) (-1,-1),24(-2,1),60(-3,1),84(1,1),96(-4,1), 120(2,1),132(-5,1),156(3,1),192(4,1),228(5,1) (2,-2),24(3,-2),48(1,-2),60(4,-2)96(5,-2),120(-1,-2), 156(-2,-2),192(-3,-2),228(-4,-2),264(-5,-2) (2,2),20(3,2),52(1,2),56(4,2),92(5,2), 124(1,-2),160(-2,-2),196(3,-2),232(4,-2),268(5,-2) (-3,2),20(-2,2),52(-4,2),56(-1,2),88(-5,2), 128(1,2),164(2,2),200(3,2),236(4,2),272(5,2) Order Modes Measured FEM Calculated unable ( to calculate)

6 References [1] Sperling,P-G, Experience in the Prediction of Electromagnetically Generated Machine Noise, Siemense Review, Vol., No.3,pp (1970) [2] Kobayashi,T., Tajima,F., Itou,M. and Koharagi,H. [12] Ishizaki,A. Liang,G-h and Saito,K., Quantitative Effect of slot combination on acoustic noise from study on harmonics in air gap flux density of induction motors, IEEE Trans. Magnetics, induction motor, Trans. IEE Japan,Vol.109-D am Vol.33,No.2,pp (1998) No.10,pp ( ) [3] Ishibashi,F., Noda,S. and Mori,S., Electromagnetic vibration of small squirrel cage three-phase induction motor, Trans.IEE Japan,Vol.112-D,No.3,pp (1993-3) [4] Ishibashi,F.,Kamimoto,K., Noda,S. and Itomi,K., [14] Kako,F., Tsuruta,T., Nagaishi,K. and Kohmo,H, Small Induction Motor Noise Calculation, IEEE Experimental study on magnetic noise of large Trans. Energy Conversion,Vol.18,No.3,pp.357- induction motors, IEEE Trans. Power Appr. Syst., 361(2003-9) Vol.PAS-102,No.8 (1983) [5] Verdyck,D., Belmans,R., Geysen,W. and Leuven, K. U., An Approach to Modelling of Magnetically Excited Forces in Electrical Machines, IEEE Trans. Magnetics, Vol.29,No.2, pp (1993-3) [6] Sasaki,T., Takada,S., Saeki,S., Ishibashi,F. and Noda,S., Mmagnetostriction of Electromagnetic Steel Sheets under AC Magnetization Superimposed with Higher Harmonics Trans.IEE Japan, Vol.112-A,No.6,pp (1992) [7] Ishibashi,F., Noda,S., Yanase,S. and Sasaki,T., Magnetostriction and Motor Vibration, Trans.IEE Japan, Vol.123-A, No.6, pp (2003-6) [8] Girgis,R.S. and Verma,S.P., Method for accurate determination of resonant frequencies and vibration behaviour of stators of electrical machines, IEE PROC.,Vol.128, No.1, pp.1-11 (1981) [9] Noda,S., Mori,S., Ishibashi,F. and Itomi.K., Effect of Coils on Natural Frequencies of Stator Cores in Small Induction Motors, IEEE Trans. Energy Conversion, Vol.EC-2, No.1, pp (1987-3) [10] Ishibashi,F., Kamimoto, K.,Noda,S. and Itomi,K., Natural frequency of stator core of small induction motor, IEE Proc.-Electr. Power Appl.,Vol.150, No.2, pp (2003-3) [11] Binns,K.J. and Schmid,E., Some concepts involved in the analysis of the magnetic field in cage induction machines, Proc.IEE.,Vol.122, pp (1975) [13] Ishibashi,F. and Kobayashi,K., Experimental Study on Harmonic Magnetic Fluxes of Small Squirrel Cage Induction Motor, Trans. IEE Japan, Vol.110, No.8, pp (1990-8) [15] Yacamini,R., Chang,S.C. and Smith,K.S., Noise generation in marine motors,trans.imar.e.(uk), Vol.107,Part4.pp (1995) [16] Verma,S.P. and Balan,A, Measurement techniques for vibration and acoustic of electrical machines, Sixth international Conference on Electrical Machines and Drives, pp (1993) [17] Chang,S.C., Electrical noise in small electrical Motors, International Conference on Electrical Machines and Drives, pp (1997) [18] Shiohata,K., Nemoto,K., Nagawa,Y., Sakamoto,S., Kobayashi,K.,Itou,M.and Koharagi,H., A method for analyzing electromagnetic-force-induced vibration and noise analysis, Trans. IEE Japan, Vol.118-D,No.11,pp ( ) [19] Vijayaghavan,P. and Krishnan,R., Noise in Electric Machines : A Review, IEEE Trans.Industry Applications,Vol.35,No.5, pp (1999) [20] Ishibashi,F., Kamimoto,K., Ogino,I. and Noda,S., Space Flux Pattern of Air Gap in Induction Motors, Trance. on Industry Appl. IEE Japan, Vol.124,No.11,pp ( )

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