Sonlu elemanlar yöntemi ile asenkron motor analizi ve motorun farklı kayma değerlerine göre momentinin matlab programlama dili ile hesaplanması

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*_{<D]ÕúPDODUÕQ\DSÕODFD÷Õ\D]DU Sevcan $\WDo.RUNPD], sevcanaytackorkmaz@gmail.com, Tel: 05067927759}

6RQOXHOHPDQODU\|QWHPLLOH asenkron motor analizi ve

motorXQIDUNOÕND\PDGH÷HUOHULQHJ|UH momentinin

matlab programlama dili ile hesaplanmasÕ

Sevcan AYTAÇ KORKMAZ1*

,

Hasan KÜRÜM2

1_{)ÕUDWhQLYHUVLWHVLMaden MYO, (/$=,ö}

2_{)ÕUDWhQLYHrsitesi, 0KHQGLVOLN)DNOWHVL Elektrik-(OHNWURQLN0KHQGLVOL÷L%|OP(/$=,ö}

Özet

Bu makalede, VRQOX HOHPDQODU \|QWHPL 6(< NXOODQÕODUDN DVHQNURQ PRWRUXQ matlab SURJUDPÕQGDQ \DUDUODQDUDN o|]P E|OJHVLQGH PDJQHWLN YHNW|U SRWDQVL\HO YH PDJQHWLN DNÕ \R÷XQOX÷XGH÷LúLPOHULLQFHOHQLSPDQ\HWLNE\NONOHUKHVDSODQPÕúWÕU Ek olarak, enerji ve moment GH÷HUOHUL KHVDSODQDUDN GHQH\VHO VRQXoODUOD NDUúÕODúWÕUÕOPÕúWÕU %XQXQ LoLQ 0DWODE SURJUDPODPD GLOLNXOODQÕODUDNELUSURJUDPJHOLúWLULOPLúWLU BXoDOÕúPDQÕQsonucunda GH÷LúLNND\PDGH÷HUOHULQH J|UHHOGHHGLOHQPRPHQWE\NONOHULQLQGHQH\VHOoDOÕúPDODUDoRN \DNÕQVRQXoODUYHUGL÷L, matlab SURJUDPÕ VD\HVLQGH J|UOPúWU <DSÕODQ OLWHUDWU WDUDPDVÕQGD QHVQHO WDEDQOÕ ELU SURJUDPODPD GLOL LOH \DSÕODQ DQDOL]OHULQ daha uzun NRPXW VDWÕUODUÕ\OD \DSÕOGÕ÷Õ J|UOS PDWODE LOH \DSÕODQ analizlerde daha NÕVDNRPXWVDWÕUODUÕNXOODQÕOPÕúWÕU.

Anahtar Kelimeler: Asenkron Motor, 6RQOX(OHPDQODU<|QWHPL Matlab

mühendislikdergisi

Cilt: 3-9

Dicle Üniversitesi Mühendislik Fakültesi .DV×P4, ,

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Calculating momentum with matlab

programming language according to

values of different slip of motor and

induction motor analysis with finite

element method

Extended abstract

In this article, we will focus on the analysis of

an induction motor with finite element method. By using finite element method (FEM) calculation of energy and moment of induction motor is described. Aspects of being robust, requiring little maintenance, the low cost, not being affected by environmental conditions and their power per unit volume induction motors are superior to other motors and can be used in almost every field. Motor analyzed have 18 stator and 22 rotor. The air gap between stator and rotor is 0.5mm. Enameled copper conductors have diameter 2*0.55mm and winded as 47 windings. The finite element method generally can be explained from these stages: Giving node and element numbers, Division of the solution area, solution area is separated to areas and element numbers are given, Generation of coefficient matrix, Put known values of vector potential and excitations (current etc.) into problem, Solution of systems of equation and finding potential at nod points, Calculation of other quantities from calculated potential values. In finite element method initially solution area is divided small triangle

elements. In numerical calculation it is essential and expresses approximate solution. In this study, the magnetic vector potential and magnetic flux density changes have investigated in the solution of the induction motor using finite element method (FEM). Additionaly, calculated energy and momentum values , are compared with experimental results. For this, a program is developed using Matlab programming language. The induction motor (6A, 380V) is designed and constructed for this study has 7.45 Nm torque value is obtained from experimental studies.

Half of the motor according to the study of symmetry is discussed, so calculated value of moment multiplied by 2. In this case, the moment was 7.78 Nm. About 4.4% of error derived from negligence in the finite element method, experimental errors in measuring device is used in this study and etc. The momentum sizes that obtained from this study have a high degree of accuracy than literature examination. In addition, MATLAB software provides easy programming and advanced graphics features. Ready function takes many lines in programming languages, but it can be prepared in only a few lines by MATLAB program than literature examination (Polat ve Kürüm, 2011). Because of these advantages MATLAB programming language should be used during the analysis of an induction motor. As a conclusion, designing induction motor by using finite element method, gives better result.

Keywords: Induction Motor, Finite element

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GLULú

Bu makalede, bir asenkron motorun sonlu elemanlar yöntemi ile analizi üzerinde GXUXODFDNWÕU$VHQNURQPRWRUXQVRQOXHOHPDQODU \|QWHPL 6(< NXOODQÕODUDN magnetik enerji ve PRPHQWKHVDEÕ DQODWÕOPÕúWÕU%XNRQXGD0DWODE programlama dilinde bir bilgLVD\DU SURJUDPÕ JHOLúWLULOPLúYHEXSURJUDPLOHPRWRUXQHQHUMLYH PRPHQW GH÷HUOHUL KHVDSODQDUDN ELU DVHQNURQ PRWRUXQSHUIRUPDQVDQDOL]L\DSÕOPÕúWÕU

Asenkron motor

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Sonlu elemanlar yöntemi teorisi

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Bu deneme fonksiyonunun birinci dereceden SROLQRP NÕVPÕ denklem (3) oR÷X SUREOHPGH \HWHUOLKDVVDVL\HWLVD÷ODU y x y x, ) ₀ ₁ ₂ ( D D D I (3) Bu deneme fonksiyonunda I[YH\\HJ|UH GR÷UXVDO ELU úHNLOGH GH÷LúPHNWHGLU (÷HU oJHQLQ N|úHOHULQGHNL SRWDQVL\HOOHU Ii ,Ij ,Im LVHGHQHPHIRQNVL\RQXEXN|úHQRNWDODUÕQGDEX GH÷HUOHUL VD÷ODPDN ]RUXQGDGÕU %X QHGHQOH DúD÷ÕGDNLLIDGHOHU\D]ÕODELOLU i i i D0 D1x D2y I j j j D0 D1x D2y I m m m D0 D1x D2y I (4) (OH DOÕQDQ GHQHPH IRQNVL\RQXQX oJHQOHULQ N|úH I_i ,I_j ,I_m GH÷HUOHUL LOH GHQNOHP 4)¶GH YHULOGL÷L úHNLOGH LIDGH HWPHN LoLQ Ni ,Nj ,Nm úHNLOYH\DHQWHUSRODV\RQIRQNVL\RQODUÕNXOODQÕOÕU (Chari, 1973).

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ve bu matrisi düzenlersek » ¼ º « ¬ ª » ¼ º « ¬ ª » ¼ º « ¬ ª mi i ji i m j mm mj jm jj S g S g S S S S I I (9) elde edilir (Demirchian vd., 1976).

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x,y rotA

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P * 2 * * 2 _Alan _Yükseklik B Enerji Magnetik (28)

Denklem (¶GHNL HúLWOLNWHQ ID\GDODQDUDN \DSÕODQ KHVDSODPDODUD J|UH WRSODP PDJQHWLN eneUMLEHOOLROGXNWDQVRQUDPRWRUGDQJHoHQDNÕP GH÷HULQH J|UH LQGNWDQV GH÷HUL 'HQNOHP (29)¶GDn kolayca hesaplanabilir. 2 * 2 I Enerji Magnetik L (29)

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0RPHQW+HVDEÕ

Asenkron motorlarda moment biri stator ]HULQGH GL÷HUL GH URWRU ]HULQGH ROXúDQ LNL HOHNWULNDODQÕQÕQHWNLOHúLPLVRQXFXRUWD\DoÕNDU 6DELW ELU PRPHQWLQ UHWLOHELOPHVL LoLQ EX LNL DODQÕQ PRWRUXQ KDYD DUDOÕ÷ÕQGD Hú ]DPDQOÕ ELU GXUXPGDROPDVÕJHUHNLU%XoDOÕúPDGD0D[ZHOO VWUHVV PHWRGX NXOODQÕODUDN PRPHQW hesaplanPÕúWÕU (KüUP, 2002).

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Sonuçlar

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(8)

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Kayma=0.03 iken; Moment=3.8930 Nm Kayma=0.049 iken;

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Kaynaklar

Chari,M.V.K.,Silvester,P., (1970). Finite Element Solution of Saturable Magnetic Field Problems, IEEE Transactions on Power Apparatus and Systems, Vol pas-89, No:7 (1642-1650)

6HOoXN $ +., (2003). Lineer Asenkron 0RWRUODUGD 8o (WNLOHULQLQ 6RQOX (lemanlar <|QWHPL\OH øQFHOHQPHVL, Doktora Tezi )ÕUDW hQLYHUVLWHVL(OD]Õ÷

Silvester, P., Cabayan, H.S., Browne, B.T., (1973). Efficient Techniques For Finite Element Analysis Of Electric Machines, IEEE PES Winter Meeting, New York.

Chari, M.V.K., (1973). Finite Element Solution Of The Eddy Current Problem In Magnetic Structures IEEE PES Summer Meeting And EHV/UHV Conference, Vancouver, B.C. Canada.

Demirchian, K. S., Chechurin, V., Sarma, I., S., Boldea, A., (2002). Nasar, The Induction Machine Handbook, CRC Pres LLC, Washington D.C., 133 159.

Cathey, J., J., (2001). Electric machines analysis and design applying matlab, Mc Graw Hill, Singapore, 317-420.

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