4744 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 10, OCTOBER 2009

Effect of Magnetostriction Anisotropy in Nonoriented Electrical Steels onDeformation of Induction Motor Stator Cores

Sakda Somkun, Anthony J. Moses, and Philip I. Anderson

Wolfson Centre for Magnetics, School of Engineering, Cardiff University, Cardiff CF24 3AA, United Kingdom

Magnetostriction in nonoriented (NO) electrical steels is a harmful source of vibration and acoustic noise in electrical machines. It isfar more anisotropic than specific power loss, which results in more complexity in prediction of the vibration and acoustic noise. An inves-tigation of the anisotropy in magnetostriction and mechanical elastic properties of a NO steel is presented in this paper. Measurementsof deformation in the stator teeth of an induction motor model core were conducted in order to study the effect of the magnetostrictionanisotropy. Strain due to Maxwell forces in the air gap was calculated and compared with the measured deformation. Measurement re-sults indicate that anisotropic magnetostriction has a great impact on unsymmetrical deformation of the stator teeth of induction motorcores.

Index Terms—Acoustic noise, anisotropy, deformation, induction motors, magnetostriction, nonoriented (NO) electrical steels, vibra-tions.

I. INTRODUCTION

V IBRATION and acoustic noise of induction motors are in-creasingly of concern. The main sources of the vibration

and acoustic noise are Maxwell and magnetostrictive forces [1].The Maxwell force is principally present in the air gap, wherethere is a discontinuity in relative permeability of the materials[2]. The magnetostrictive force causes the dimensions of a mag-netic material to change when the material is magnetized. Themagnetostrictive force has been calculated to be responsible forup to 50% of the total electromagnetic force [3]. Hence, themagnetostriction is an important source of the core vibra-tion and acoustic noise.

Nonoriented (NO) electrical steel commonly used in elec-trical machines is often considered to be magnetically and me-chanically isotropic. However, there is still inherent anisotropyin its characteristics and resulting specific power lossesmeasured along different directions in the plane of laminations,causing a significant increase in flux density harmonics andoverall core losses [4], [5]. It has been reported that magnetome-chanically coupled properties such as magnetostriction in NOsteel can be far more anisotropic than its specific power losses[6]. The variation of peak magnetostriction at the same flux den-sity magnetized along different direction can be up to 400%.

Measured magnetostriction in electrical steels has been fedinto a finite element model (FEM) for calculating vibrationand deformation in electrical machines [7], [8] although theanisotropy in magnetostriction was not taken into account.

In this study, investigations of magnetostriction anisotropyin a NO electrical steel were conducted. The effect of magne-tostriction anisotropy on core deformation was examined usingmeasurements of localized strain in stator teeth of an inductionmotor model core, where the NO steel was subjected to alter-nating flux at different angles with respect to the rolling di-rection (RD) and the Maxwell force in the air gap. Strain due

Manuscript received March 07, 2009. Current version published September18, 2009. Corresponding author: S. Somkun (e-mail: somkuns@cardiff.ac.uk).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2009.2022320

to the Maxwell force and sketches of core deformation takingmechanical elasticity into account are also presented.

II. EXPERIMENTAL APPROACH

A. Study of Magnetostriction Anisotropy

Epstein strips of M400-50A NO steel, 305 mm long, 30 mmwide, were cut at 10 intervals from the RD to the transversedirection (TD). Three strips cut at each angle were tested. Theywere magnetized singly under sinusoidal induction at peak fluxdensity from 1.00 to 1.7 0.005 T, 50 Hz. Magnetostric-tion was obtained by double integral of the output signal of anaccelerometer fixed at the free end of the strip [9].

B. Mechanical Elasticity Measurement

The same grade and size of the material used in the magne-tostriction measurement were put in a tensile stress machine.One sample cut at each angle was tested. Tensile forces from1.50 to 4.00 0.02 kN were applied to each strip causing 100.0

1.3 to 266.7 3.3 MPa of tension. Longitudinal and trans-verse strains were measured by a Rosette resistant strain gaugeattached at the center of each sample. The modulus of elas-ticity along the longitudinal direction of the strip was calcu-lated by the slope between the tensile stress and the longitudinalstrain. Poisson’s ratio of the material was calculated as theratio between the transverse and longitudinal strain. Four mea-surements were carried out per sample.

C. Measurement of Localized Strain in a Stackof Induction Motor Stator Laminations

Twenty stator and rotor laminations of M400-50A NO steelwere also used to construct an induction motor model core [10].A four-pole double-layer stator winding with 120 fractionalpitch was selected. No rotor windings were used. The 36 statorteeth are each 10 apart. Foil-type resistance strain gauges wereattached to measure localized strain in the stator teeth cov-ering from 0 to 90 as shown in Fig. 1. Core dimensions arelisted in Table I.

0018-9464/$26.00 © 2009 IEEE

SOMKUN et al.: EFFECT OF MAGNETOSTRICTION ANISOTROPY IN NONORIENTED ELECTRICAL STEELS 4745

Fig. 1. Winding configuration of the induction motor model core, and locationsof strain gauges and search coils.

TABLE IDIMENSIONS OF THE INDUCTION MOTOR MODEL CORE

Single turn search coils were wound around the teeth wherethe strain gauges were located so that the tooth flux densitycould be calculated from the induced voltage. A stress dueto the Maxwell force in the air gap acting on the radial directionof each stator tooth is given by

(1)

where is the permeability of free space [11]. The stator teethare under uniaxial loading via the Maxwell force along the ra-dial direction. Therefore, the strain due to the Maxwell force

in the radial direction of the tooth was then calculated fromHooke’s law as

(2)

The motor model core was magnetized by a three-phasevoltage source at sinusoidal line–line voltage 173 1 V,50 Hz. At this voltage level, the average at the back iron ofthe core was 1.31 0.01 T, which for this geometry meantthat in the teeth was around 1.60 to 1.70 0.01 T, typicalin three-phase induction machines. The strain gauges wereconnected with a built-in strain bridge data acquisition card(DAQ). The localized strain and induced voltage were sampledat the rate of 50 kS/s and processed by a LabVIEW program.

Fig. 2. Variation of � at (a) �� � 1.70 T, 50 Hz, (b)� , and (c) �with �.

Fig. 3. (a) Modulus of elasticity � and (b) Poisson’s ratio � at different �.

III. EXPERIMENTAL RESULTS AND DISCUSSIONS

A. Magnetostriction and Elasticity of the Material

Peak-to-peak magnetostriction under sinusoidal mag-netization at 1.70 T, 50 Hz at 0 to 90 is shownin Fig. 2(a). The curve represents the averaged value of thethree samples. The maximum variation from sample to sampleis 1.2 m/m. tends to increase with . at 90is about 3.5 times greater than that along the RD, and was upto 5.5 times greater at 1.00 T. Texture plays a significantrole in this phenomenon [6]. There is more 90 domain wallmotion when magnetized along the TD resulting in high mag-netostriction. Although magnetostriction of NO steel is stronglyanisotropic, the anisotropy in specific power loss still complieswith the standard (EN10106:2007). Fig. 3 shows modulus ofelasticity and Poisson’s ratio . These are less texture depen-dent than magnetostriction. approximately increases with ,which means the deformation due to the Maxwell force is more

4746 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 10, OCTOBER 2009

Fig. 4. Waveforms of (a) ����� and (b) ����� and � ���� in the 50 tooth.

affected near the RD. is around 0.300 0.005, which is typ-ical in steel, and the maximum value is 0.37 0.005 at 40 .

B. Localized Strain and Deformation of the Stator Core

Fig. 4(a) depicts an instantaneous flux density wave-form in the 50 tooth. The measured localized strain inthis tooth compared with strain due to Maxwell forcecalculated from (2) using the measured is shown in Fig. 4(b).Fig. 4(b) also shows that does not return to its value at thedemagnetized state, which is typical in magnetostriction wave-forms of soft magnetic materials under alternating current (ac)magnetization [11]. At this tooth, 1.70 T causes the max-imum of to be 5.22 0.07 m/m, but it still less thanand there is a phase shift between and . This is due tothe well-known stress effect (via Maxwell force) on magne-tostriction. Moreover, this phase shift can also be explained bythe hysteresis between magnetostriction and applied magneticinduction.

Peak-to-peak values of (b), (c) are com-pared with at 1.70 T in Fig. 2. For this stator windingconfiguration, the flux concentrates in stator teeth at the centerof the phase windings (20 , 50 , and 80 tooth in Fig. 1); as aresult, the peak flux density in the stator teeth varies from 1.60to 1.70 T. Therefore, at 20 , 50 , and 80 are thehighest and slightly decreases with due to the increasein modulus of elasticity. The localized strain is affected by themagnetostrictive anisotropy since its peak-to-peak value ata range from 0 to 20 is lower than that at the other an-gles. In this angular range, drops drastically even thoughthe magnetostriction increases with . However, the variationof from sample to sample at 0 and 10 is high. Thus,there is a possibility of having a negative slope to the curve inthis region.

Stresses due to Maxwell force calculated by (1) in the0 –90 teeth captured at 0 , 45 , and 90 are shown inFig. 5. At a given time, the fundamental component of com-pletes one cycle in a quarter of the stator. This indicates thatthere are four waves of within the stator, which is equal to

Fig. 5. Stress due to Maxwell force, � in the 0 to 90 teeth.

Fig. 6. Representation of deformation in the stator teeth at �� � 0 , 45 , and90 .

the pole number. As a result, a deformation mode shape withthe same number of stator poles dominates the core deformationand vibration [2], [12]. It is also observed that the fundamentalcomponent of 0 is opposite 90 becausethe fundamental frequency of is double that of the flux den-sity. Therefore, it can be generalized that there is a Maxwellforce wave causing stress on the radial axis of the stator teeth.The cycle number of this wave is equal to the pole number ofthe stator winding and it travels around the stator teeth at a rateof twice the supply frequency. This wave is distorted due to thesaturation of tooth flux density and also the flux concentration

SOMKUN et al.: EFFECT OF MAGNETOSTRICTION ANISOTROPY IN NONORIENTED ELECTRICAL STEELS 4747

in the teeth at the center of the phase windings (the 20 , 50 ,and 80 tooth in this case).

If magnetostriction of the core material is ideally isotropic,the couple between the Maxwell force and magnetostriction willcause symmetrical deformation in the stator teeth with the modeshape corresponding to the pole number. However, since themagnetostriction is highly anisotropic, unsymmetrical deforma-tion in the induction motor core occurs as shown in Fig. 6. Thedeformation along the radial axis of the stator teeth was obtainedfrom the measurement of localized strain. The deformation inthe tangential axis was calculated using the measured Poisson’sratio. As expected at 0 , the lowest deformation occursat the 50 tooth according to 0 in Fig. 5, and thephase shift between and causes deformation atthe 60 tooth to be lower than that at the 40 tooth. High defor-mation occurs at 0 , 20 , 30 , 80 , and 90 teeth. However, thelow deformation in the 10 tooth makes the deformation wavemore complex. Although there is only one deformation wave at

45 and 90 , the deformation in the teeth near the TD isgreater than in those near the RD due to the anisotropy in mag-netostriction resulting in the unsymmetrical deformation.

IV. CONCLUSION

Magnetostriction in NO electrical steels can be far moreanisotropic than their mechanical elastic properties and specificpower loss. Maxwell force in a motor core air gap creates adeformation in stator teeth with the mode shape equal to thepole number of the stator winding. This deformed shape travelsaround the stator teeth at double the frequency of the powersource. Winding configuration, saturation in flux density, androtor slot harmonics can distort the mode shape, but the greatestimpact comes from the high anisotropy in magnetostriction. Itcauses unsymmetrical deformation of the stator teeth. The ac-curacy of deformation, vibration, and acoustic noise predictionin induction motors could be improved if the magnetostrictionanisotropy was taken into account. The impact of anisotropicmagnetostriction on the local and global deformation and vi-bration of motor cores under loaded conditions is also anothersubject that should be studied.

ACKNOWLEDGMENT

The authors would like to thank ThyssenKrupp ElectricalSteel GmbH for providing the samples and P. Klimczyk forcarrying out magnetostriction measurements. S. Somkun wouldalso like to thank The Royal Thai Government for sponsoringhis doctoral study.

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