ENERGY LOSSES PREDICTION IN NON-ORIENTED SILICON IRON SHEETS

Transcription

1 ENERGY LOSSES PREDICTION IN NON-ORIENTED SILICON IRON SHEETS GHEORGHE PĂLTÂNEA, VERONICA PĂLTÂNEA *1, HORIA GAVRILĂ Key words: Non-oriented silicon iron, Energy losses, Mgnetic ojects, Energy losses prediction, Excess losses, Mgnetizing processes We report n investigtion nd theoreticl ssessment of power losses prediction in non-oriented silicon iron sheets (NO FeSi) M800-65A industril type, cut longitudinlly nd trnsverslly to the rolling direction. The loss ehviour of this mteril ws studied s function of frequency in the rnge of 5 Hz to 200 Hz t given mgnetic polriztion (J) of 0.5 T nd 1 T. Using the concept of loss seprtion for the dt nlysis, in the pproximtion of liner mgnetiztion lw nd low frequency limit, it cn e considered tht the excess losses cn e quntittively ssessed within the theoreticl frmework of the sttisticl loss model sed on mgnetic oject theory. 1. INTRODUCTION Non-oriented (NO) silicon iron lloys re soft mgnetic mterils with n pproximtely nisotropic grin texture. They re used in the friction of medium nd high power rotting mchines, nd for tht it is necessry to develop mgnetic circuit for electricl mchines with efficiency higher thn 95%, not only to sve energy, ut to void overheting nd shortening of the mchine lifetime. Improvement of the qulity of the sheets cn e relized y controlling numer of structurl prmeters: impurities, grin size nd crystllogrphic texture, residul nd pplied stresses etc. The NO FeSi sheets re produced ccordingly with the stndrds IEC nd nd re mnufctured in different qulities defined y the mount of silicon in the lloy. The percentge of silicon in the lloy cn vry from 1 to 3.7 %, nd to prevent the ging of the mteril is used luminium ( %). To increse the electricl resistnce of the sheets there re usully dded smll quntities of mngnese ( %) [1, 2]. Mgnetic cores of electricl mchines re prcticlly sujected to nonsinusoidl mgnetic flux density, generted y the pulsting wveforms of the mgnetic induction in the teeth of the sttor core or y the driving circuit, due to the pulsewidth modulted (PWM) voltges. Dt sheets from mnufcturers *1 Politehnic University from Buchrest, 313 Spl. Independenţei, Buchrest, Romni, E-mil: veronic.pltne@up.ro Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 58, 1, p , Bucrest, 2013

2 54 Gheorghe Păltâne, Veronic Păltâne, Hori Gvrilă 2 present the energy losses vlues of the mteril only t industril frequency (50 Hz/60 Hz) for selected pek mgnetic flux density (J p ) vlues [1]. These dt provide us poor informtion (e.g. P tot = 6.74 W/kg t J = 1.5 T, f = 50 Hz, nisotropy of loss 3%, µ r = [3]) for sic design of electromgnetic devices, used in predictive purposes. One cn improve it with the frequency chrcteristion nd the theoreticl losses model. The model for electromgnetic energy losses prediction sed on the sttisticl theory cn e used for NO FeSi sheet under sinusoidl nd non-sinusoidl induction wveform, in cse tht the working frequency is low enough to ensure uniform mgnetic flux penetrtion [4]. 2. ENERGY LOSSES SEPARATION METHOD The totl energy losses cn e decomposed into the sum of hysteresis, clssicl nd excess losses components. This seprtion llows to individully tret loss mechnisms occurring on different spce-time scles, s they were independent to ech other. The hysteresis losses re generted y fine-scle instilities nd cn e nlyzed y coercivity mechnisms. In the cse of eddy losses (clssicl) generted y eddy currents, the smple geometry is importnt. The mteril is treted like homogenous medium. The direct consequence of the mgnetic domins structure of the mteril is the excess losses which re very difficult to e determined, ecuse of the gret vriety of domin structures. One prefers to determine this type of losses only through mthemticl methods. The energy loss seprtion ws mde, using for the clcultion of clssicl energy losses (W cl ), in the pproximtion of liner mgnetiztion nd low frequency limit [2, 5], the following reltion: π σj pd Wcl = f, (1) 6 ρ where σ is the electricl conductivity, d is the thickness of the sheet, f is the frequency nd ρ is the density of the mteril. Further, the sum of excess losses W exc nd hysteresis losses W h is: W = W W = W + W (2) diff tot Mking grphicl extrpoltion of W diff to zero, the W h nd therefore the W exc, hve een determined [5]. Hysteresis energy losses nd excess losses re quntities directly relted to the eddy current pths closely surrounding the ctive domin wlls. cl h exc.

3 3 Energy losses prediction in non-oriented silicon iron sheets EXPERIMENTAL RESULTS In this pper two NO FeSi (M800-65A) sheets of mm 2 re investigted. One smple ws cut longitudinlly, nd the other trnsverslly to the rolling direction. The physicl properties of this mteril re: thickness d = 0.65 mm, density ρ = kg/m 3, electricl conductivity σ = S/m, sturtion polriztion J s = 1.8 T. The smples were chrcterized etween 0 Hz nd 200 Hz using n industril Single Sheet Tester (Brockhus Messtechnik), which is device for fst mesurements. The Brockhus Single Sheet Tester offers n AC frequency chrcteristion nd provides the hysteresis cycle, the reltive mgnetic permeility nd the totl power losses dt. Fig. 1 Specific energy loss nd its components in the cse of NO FeSi sheet (longitudinlly cut) versus mgnetizing frequency t pek polriztion: ) J p = 0.5 T; ) J p = 1 T. In Fig. 1 nd Fig. 2 the vritions of W tot versus frequency f were determined through experimentl procedure. The vritions of W cl were clculted with (1), W h nd W exc were otined s presented in chpter 2.

4 56 Gheorghe Păltâne, Veronic Păltâne, Hori Gvrilă 4 The dependences J(H), mesured on rolling (RD) nd trnsversl (TD) directions nd presented in the dt sheets [3], hve so smll differences, tht the mnufcturers consider this type of lloy s isotropic one. In this pper, s one cn see in Fig. 1 nd Fig. 2, in the cse of the energy losses cn e oserved some differences etween the vlues, mesured on RD nd TD directions, so tht n nlysis of losses, on the esy nd hrd xes, ws considered necesry. Fig. 2 Specific energy loss nd its components in the cse of NO FeSi sheet (trnsverslly cut) versus mgnetizing frequency t pek polriztion ) J p = 0.5 T; ) J p = 1 T. One cn notice tht with the increse of pek polriztion the energy loss shpes tend to hve liner vrition nd the most importnt loss is the hysteresis one (W h ) t lest up to 150 Hz [6]. Also, ecuse the non-oriented FeSi lloys do

5 5 Energy losses prediction in non-oriented silicon iron sheets 57 not hve such pronounced vlue of mgnetic nisotropy, there re no significnt differences (more evident in the cse of high mgnetic polriztion nd high frequencies) etween the losses vlues, mesured in the cse of longitudinlly nd trnsverslly cut sheets. 4. STATISTICAL INTERPRETATION OF EXCESS LOSSES The model for electromgnetic energy loss prediction sed on the sttisticl theory of losses [5, 7] cn e used for soft mgnetic lloys if the working frequency is sufficiently low to ensure n uniform mgnetic flux penetrtion. The model relies on the physiclly sed ide of loss seprtion. The sttisticl model considers tht the lrge-scle pttern of mgnetic domins cn e descried in terms of the dynmics of n sttisticlly independent mgnetic ojects (MO). A mgnetic oject represents group of neighoring intercting domin wlls nd reduces the losses prolem to the investigtion of the min physicl properties of n s function of frequency, pek polriztion nd mteril microstructure. This theory reduces the dependence of excess energy losses on oth pek polriztion nd mesurement frequency to common mechnism [5, 8]. The physicl mechnism tht genertes excess losses in soft mgnetic mterils is sed on the competition etween the pplied externl mgnetic field nd the locl counterfields, highly inhomogeneous, determined y the eddy currents nd microstructurl interctions [5]. For ech vlue of the verge polriztion rte the mgnetiztion process in given cross section of the smple cn e descried in terms of n simultneously ctive mgnetic ojects. The dynmic ehviour of single MO is ruled, in this cse, y liner dependence of the excess dynmic field H Φ exc cting on the pexc MO, where H exc =, Φ J is the mgnetic flux rte of chnge correspondingly provided y the MO, p exc is the density of excess power loss, J is the mgnetic polriztion nd the proportionlity constnt is determined y the dmping effect of eddy currents [9 12]. When there re n simultneously ctive MO's, Φ must e, on the verge, frction 1/n of the totl flux rte SJ imposed to the smple (S is the cross-sectionl re of the proe), so tht reltionship of the form H exc 1 n is expected, which ctully turns out to e [10] pexc pexc H w H exc = = =, J (3) 4J f n where p

6 58 Gheorghe Păltâne, Veronic Păltâne, Hori Gvrilă 6 H w ( w) with vlue of the dimensionless coefficient G = 4σG SJ f, (4) p ( w) 4 = 3 π k 1 ( 2k + 1) 3 = The min property of the quntity n ppering in (3) is tht it is expected to e function n(h exc, {P}) of the excess field H exc nd set of {P} prmeters chrcterizing the microstructure nd the domin structure of the mteril. Some mthemticl interpoltions proved tht the NO FeSi lloy, long oth longitudinl nd trnsversl directions, oeys simple liner lw: n ( H,{ P} ) exc n0 + H exc =, (5) H where the microstructurl informtion is now crried y n 0, which represents the limiting numer of simultneously ctive MO's when f 0 nd y the mgnetic field H 0. The phenomenologicl prmeters (n 0, H 0 ) cn e determined y liner interpoltion of the grphicl dependence n(h exc ) (Fig. 3). 0 Fig. 3 Numer of ctive mgnetic ojects n versus the dynmic field H exc t pek polriztion J p = 0.5 T: ) longitudinlly (n 0 = , H 0 = A/m); ) trnsverslly (n 0 = , H 0 = A/m) cut smples). In the cse of J p = 1 T the vlues re: n 0 = , H 0 = A/m (longitudinlly cut smple) nd n 0 = , H 0 = A/m (trnsverslly cut smple). The knowledge of n 0 nd H 0 permits one to predict through (6) the ehvior of excess losses (W exc ): W 2 ( n H ) n = 2J p 4H0H w H exc clc 0 (6)

7 7 Energy losses prediction in non-oriented silicon iron sheets 59 nd, y using the prmeters identified efore, the shpes of the determined W exc re presented in Fig. 4. Fig. 4 Comprison etween the experimentl vlues (W exc ) nd the predicted (W exc-clc ) ehviour of excess losses in NO FeSi lmintions: ) longitudinlly cut smples; ) trnsverslly cut smples. The theoreticlly predicted totl loss (W tot-clc ) is therefore otined through:

8 60 Gheorghe Păltâne, Veronic Păltâne, Hori Gvrilă 8 W = W W W (7) tot clc h exp + cl + exc clc, where W h-exp hs the vlue of W h, determined in chpter 2 (Fig. 5). Fig. 5 Comprison etween the experimentl vlues (W tot ) nd the predicted (W tot-clc ) ehviour of totl losses in NO FeSi lmintions: ) longitudinlly cut smples; ) trnsverslly cut smples. Also, sed on the theoreticl vlues of the totl loss (W tot-clc ) nd the exctly clculted clssicl loss (W cl ), one cn perform n nlyticl determintion of hysteresis loss (W h-clc ), which cn e compred to the vlues otined from the experimentl mesurements (Fig. 6).

9 9 Energy losses prediction in non-oriented silicon iron sheets 61 c d Fig. 6 Exmples of experimentl nd predicted dependences of the quntity W diff = W tot W cl = = W h + W exc on the squre root of frequency in NO FeSi lmintions. The zero-frequency vlue W diff (0) = W h is otined y grphicl extrpoltion. (, longitudinlly cut smples t J p = 0.5, 1 T nd c, d trnsverslly cut smples t J p = 0.5 nd 1 T). 5. CONCLUSIONS The theoreticl interprettion of the experimentl results on energy excess losses in soft mgnetic mterils provides promising convenient tool to look into the connection etween dynmic losses nd microstructure of smples. The vlues otined through nlyticl expressions re in good ccord with the experimentl ones. The sttisticl model is very ccurte method for the prediction of the excess energy losses in soft mgnetic lloys. The theoreticl interprettion of the experimentl results on power losses in soft mterils hs shown tht the function n(h exc, {P}) provides promising tool to look into the connection etween

10 62 Gheorghe Păltâne, Veronic Păltâne, Hori Gvrilă 10 dynmic losses nd microstructure of soft mterils. In severl cses, single function n(h exc, {P}) cn e ssocited with given mteril nd the liner lw is the esiest one. This lw is very dequte for NO FeSi lloys. The hrd mgnetiztion xis hs pronounced contriution on the vlues of W h in the cse of trnsverslly cut smple, which re higher tht in the cse of the sheets cut prllel to the rolling direction, ecuse the spin mgnetic moments must lign to the direction of the externl field, which is pplied horizontlly. ACKNOWLEDGEMENTS This work ws supported y grnt of the Romnin Ntionl Authority for Scientific Reserch, CNDI UEFISCDI, project numer PN-II-PT-PCCA Received on 21 Septemer 2012 REFERENCES 1. H. Gvrilă, H. Chiric et l., Mgnetism tehnic şi plict, Editur Acdemiei Române, F. Fiorillo, Mesurement nd Chrcteriztion of Mgnetic Mterils, Elsevier Acdemic Press, Electricl Steel Ctlogue. 4. A. Nicolide, S. Öner, Considertions on the mgnetiztion chrcteristics of soft mgnetic mterils, Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 56, 4, pp , G. Bertotti, Hysteresis in mgnetism, Elsevier Acdemic Press, Veronic Păltâne, G. Păltâne, Elen Helere, I.V. Nemoinu, E. Czcu, Mgnetic mesurements from low to high frequency on morphous rion of Co 67 Fe 4 B 14.5 Si 14.5 nd prediction of excess losses with the sttisticl loss model sed on mgnetic (OM) theory, OPTIM 2010, Brşov, Români, 2010, pp G. Păltâne, V. Păltâne, I.V. Nemoinu, Mgnetic properties of non-oriented silicon iron sheets in cse of externl pplied therml tretments, Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 55, 4, pp , G. Bertotti, Physicl interprettion of eddy current losses in ferromgnetic mterils. I. Theoreticl considertions, J. Appl. Phys., 57, pp , G. Bertotti, Generl properties of power losses in soft ferromgnetic mterils, J. Appl. Phys., 57, pp , G. Bertotti, Physicl interprettion of eddy current losses in ferromgnetic mterils, IEEE Trns. Mgn., 24, 1, pp , H. J. Willims, C. Kittel, Studies of the propgtion velocity of ferromgnetic domin oundry, Phys. Rev., 80, pp , F. I. Hănţilă, Mthemticl models of the reltion etween B nd H for nonliner medi, Rev. Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 19, 3, pp , 1974.