Field computation with finite element method applied for diagnosis eccentricity fault in induction machine
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1 Proceedngs of the Internatonal Conference on Recent Advances n Electrcal Systems, Tunsa, 216 Feld computaton wth fnte element method appled for dagnoss eccentrcty fault n nducton machne Moufd Mohammed, Tahar Bah 1 Electrcal Department, Faculty of Scence Engneerng, Annaba Unversty, Annaba, Algera Laboratory of Automatc and Sgnal Annaba (LASA) mohammedmoufd@yahoo.fr; tbah@hotmal.fr Abstract Ths paper deals wth analyss of the magnetc feld by usng FEM and numercal computaton of the electromagnetc characterstcs of Inducton machne. The knowledge of electromagnetc characterstcs s very mportant n performance analyss of electrcal machnes. The purpose of ths nvestgaton s to use the feld computaton by fnte element model to evaluate, detect and dagnoss fault of the statc eccentrcty effect on the vector potental and feld magnetc. The result of smulaton of our model allows us to clearly see the effect of the eccentrcty on the electromagnetc quanttes of the nducton squrrel machne. Keywords Inducton machne, modelsaton, fnte element methode, eccentrcty, dagnoss, smulaton. I. INTRODUCTION The sudden damage of the nducton motors, whch are generally used as part of the product lne n the ndustry, can lead to stop the whole process. Therefore, the dagnoss of the lack of tme s mportant to prevent the spread of the fault on the product range. Energy converson n an nducton motor (convertng electrcal energy nto mechancal energy) s through the magnetc energy n the ar gap. However, the dsplacement effect of the rotor (eccentrcty) drectly affects the course of the magnetc flux (magnetc reluctance) [1,2]. Accordng to the model developed n ths work, we could ntroduce and study the consequences of the eccentrcty phenomenon on the magnetc quanttes of the machne through the magnetc vector potental. The complexty related to the spatal dstrbuton of local forces [3,4] to calculate a resultant force has been surmounted due to the flexblty of our program allows us to consder the effect of changng the rotor poston by adjustng ts coordnates n the program. In the followng sectons, we propose the problematc wll be resolved by our proposed model n ths paper. In the thrd secton, we consder the development of the model usng the formulaton of magnetc vector potental. Next, we present the smulaton results and ther nterpretatons. II. STATEMENT OF THE PROBLEM Our study s to see the evoluton of magnetc varable (magnetc feld and vector potental) along the axs of movement (x) of the rotor for 25% of the value of the argap. Comparng the smulaton results n the default case (wth eccentrcty) wth those of the healthy case, we can see the mpact of eccentrcty on the magnetc quantty of the asynchronous machne. Stator Rotor y x x Fgure.1 Balanced of the rotor along x axs. ISBN: (196) Edtors: Tarek Bouktr & Rafk Nej
2 Proceedngs of the Internatonal Conference on Recent Advances n Electrcal Systems, Tunsa, 216 III. MODEL OF INDUCTION MACHINE To determne the feld dstrbuton at each tme-step, a two dmensonal transverse secton of the nducton motor s represented, n reducng the problem to two dmensons [5,6]. The transent magnetc feld n terms of magnetc vector potental (A); The permeablty of ar s defned by µ = H/m; Conductvty (σ) and current densty (J s ), can be expressed as: B rh A d t curl curl A d J s A. A K M A 1 curl curl t A t j K F M AF j j j j x x y y d J A (1) The consttutve lnear relatonshp of ferromagnetc materal s: Where, B: flux densty; H: magnetc feld; µ r : permeablty relatve. To solve the general dffuson equaton (1) a classcal weghted resdual method wth frst order shape functons we obtan the followng ntegral form [7,8]: ω : ponduraton functon. Wth the followng lnear approxmaton for the vector potental: Then, we obtan the followng algebrac form: s d J s (2) (3) (4) IV. SIMULATIONS AND DISCUTION The fnte element model descrbed above to evaluate the effects of rotor eccentrcty n the ar gap on the vector potental magnetc and the magnetc feld [9,1]. The fgure 2 shows the geometry of the nducton machne wth four poles, 36 slots n the stator and 32 rotor bars The dscretzaton of the geometry wth fnte element s shown n fgure Fgure 2 Inducton machne geometry Fgure 3 Grd of the doman The equpotental of potental vector magnetc s shown by the fgure Fgure 4 Equpotentel of potental vector magnetc ISBN: (197) Edtors: Tarek Bouktr & Rafk Nej
3 Proceedngs of the Internatonal Conference on Recent Advances n Electrcal Systems, Tunsa, 216 V. EFFECT OF THE ECCENTRICITY A) Potental vector magnetc The fgure.5 shows the spatal dstrbuton of the potental vector magnetc for each element of the geometry. spatal dstrbuton of potentel magnetc North poles A(A.m) y(m) x(m).1.2 South poles Fgure.5 Spatal dstrbuton of potental vector The projecton of the spatal dstrbuton of magnetc vector potental presented n Fgure.5 on the plane zx allows us to obtan the potental vector magnetc n the healthy case (fgure6.a) and wth fault, that s to say that the rotor s balanced along the x axs (fgure 6.b) s llustrated by fgure 6. North poles b. Wth fault Fgure.6 Effect of the eccentrcty on the potental vector magnetc In the healthy cases (Fgure 6.a) we fnd that the shape of the spatal dstrbuton of the magnetc vector potental s symmetrcal. Furthermore, the same fgure shows that we have the same absolute ampltude on the four poles of the nducton machne. Aganst by, n the case wth defect (Fgure 6.b), the thckness of the ar gap s not unform, then the shape of the magnetc potental s not symmetrcal and the absolute value of magnetc potental s not unform n the four poles. The change n the poston of the rotor (eccentrcty) occurs wth the change of magnetc reluctance. Indeed, when the ar gap reduces, so, the magnetc reluctance also reduces, therefore the ampltude of the magnetc vector potental ncreases. By aganst, when the ar gap ncreases we see the opposte effect. South poles a. healthy case ISBN: (198) Edtors: Tarek Bouktr & Rafk Nej
4 Proceedngs of the Internatonal Conference on Recent Advances n Electrcal Systems, Tunsa, 216 B) Magnetc feld The fgure.7 shows the spatal dstrbuton of the magnetc feld (absolute values) for each element of the geometry. Fgure.7 Spatal dstrbuton of magnetc feld The projecton of the spatal dstrbuton of magnetc feld presented n Fgure.7 on the plane zx allows us to obtan the magnetc feld n the healthy case (fgure 8.a) and wth fault, where the rotor s balanced along the x axs (fgure 8.b), s llustrated by fgure 8. b. Wth fault Fgure.8 Effect of the eccentrcty on the magnetc feld In healthy cases, the ar gap s healthy, therefore unform along the contour of the ar gap. Ths s expressed by the symmetry of the shape of the magnetc feld dstrbuton observed n Fgure 8.a. By aganst, the fgure 8.b (wth eccentrcty case), there s no symmetry n the evoluton plane of the magnetc feld. The effect of the eccentrcty of the magnetc feld s opposte wth respect to ther effect on the potental vector, when the reduced ar gap, therefore, the magnetc reluctance also therefore reduces the ampltude of the magnetc feld decreases. For aganst,, when the ar gap ncreases the magnetc reluctance also ncreases, therefore. the ampltude of the magnetc feld ncreases. VI. CONCLUSION a. healthy case The results of smulatons enables us to ntroduce and clearly see the mpact of eccentrcty on the magnetc behavor of the machne (magnetc feld and vector potental) for the rotor poston change of 25% from ts ntal poston, t s found that the effect of the eccentrcty nfluences frst places on the magnetc reluctance (the course of the feld n the ar gap), the ISBN: (199) Edtors: Tarek Bouktr & Rafk Nej
5 Proceedngs of the Internatonal Conference on Recent Advances n Electrcal Systems, Tunsa, 216 varaton of the latter, causes a varaton of the magnetc propertes (magnetc quanttes), mechancs (mechancal quanttes ) and electrcal (electrcal quanttes). VII. REFERENCES [1] M. Rgon, N. Sadowsk*, N. J. Batstela, J.P.A.Bastos, Detecton and Analyss of Rotor Faults n Inducton Motors by the Measurement of the Stray Magnetc Flux, Journal of Mcrowaves, Optoelectroncs and Electromagnetc Applcatons, Vol. 11, No. 1, June 212 [2] Jawad Faz, Hamd Tolyat, Fnte-Element Transent Analyss of Inducton Motors Under Mxed Eccentrcty Fault,IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 1, JANUARY 28 [3] Sang Bn Lee, Member, IEEE, Gerald B. Klman, Lfe Fellow, IEEE, Manoj R. Shah, W. Tony Mall, N. Kutty Nar, Lfe Senor Member, IEEE, and R. Mark Lusted, An Advanced Technque for Detectng Inter-Lamnar Stator Core Faults n Large Electrc Machnes, IEEE TRANS. ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 25 [4] M. J. DeBortol, S. J. Salon, D. W. Burow, C. J. Slavk Effects of Rotor Eccentrcty and Parallel Wndngs on Inducton Machne Behavor: A Study Usng Fnte Element, IEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 2, MARCH 1993 [5] T W Preston, A B J Reece, P S Sangha Inducton motor analyss by tme-steppng technques, IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 1, JANUARY [6] J. Shen and A. Kost, Modelng of the Idealzed Exctng Current Sources n the FEM, IEEE TRANSACTIONS ON MAGNETICS. VOL. 31, NO. 3, MAY 1995 [7] Chang-Chou Hwang*, S.J. Salon, R. Palma A fnte element pre-processor for nducton motor ncludng moton and crcut constrants, IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 6, NOVEMBER [8] M. Mohammed, T. Bah, Y. Souf Fnte Element Modelng Under Stress by the Nonlnearty of a Materal Ferromagnetc, Journal of Electrcal Engneerng (JEE), 212. [9] M. Mohammed, T. Bah, Y. Souf Integraton of the eccentrcty effect n the feld computaton by FE, EVER, Monaco,212. [1] M. Mohammed, T. Bah, Y. Souf Integraton of the eccentrcty effect n the feld computaton of reluctance machne, Journal of Electrcal Engneerng (JEE), 214. ISBN: (2) Edtors: Tarek Bouktr & Rafk Nej
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