Performance Prediction of the Single-Sided Linear. Induction Motors for Transportation Considers. Longitudinal End Effect by Using Analytic Method

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1 Contmporary Enginring Scincs, Vol., 9, no., Prformanc Prdiction of th Singl-Sidd Linar Induction Motors for Transportation Considrs Longitudinal End Effct by Using Analytic Mthod Ali Suat Grçk Univrsity of Gaziantp Vocational School Vdat M. Karslı Univrsity of Gaziantp Dpartmnt of Elctrical Enginring Abstract Having th finit lngth of th stator or rotor of th singl-sidd linar induction motors (SLIM) lads to ngativ affct on th prformanc. Ths lctromagntic ffcts occur ntry-nd and xit- nd of th SLIM. Th ntry nd wav rducs th synchronous wav at high frquncy oprations. An analytic tchniqu basd on th quivalnt circuit taking into longitudinal nd ffct and othr ffcts account (transvrs dg, saturation tc...) ar usd to prdict th prformanc of th SLIM. Howvr, in th high spd applications of SLIMs, such as transportation, th prformanc prdiction is vry important for dsign. Analytical tool is dvlopd to prdict th prformanc of th SLIM. This tool is validatd with th tst rsults in th litratur (Canadian Institut of Guidd Ground Transport LIM). Th simulation rsults, which ar producd by this analytic tool, ar obtaind for th dsignd and constructd SLIM. Rsults ar rportd. Kywords- Linar induction motor, quivalnt circuit approach, nd ffct

2 96 A. S. Grçk and V. M. Karslı 1. INTRODUCTION Singl-sidd linar induction motor has bn applid in th widly usd in industrial ara. Espcially, it is usd in transportation. Th rason why it is slctd th LIM for transportation is th low nrgy consumption, high spd, and low pollution. Elctrical nrgy convrts into mchanical nrgy and linar motion is achivd. In th dsign of th LIM, th dirct lctromagntic fild application is rstrictiv. Consquntly, th quivalnt circuit approach is convnint for dsign and analysis. In th quivalnt circuit approach, mutual and scondary paramtrs ar valuatd with th appropriat corrctd factor (dg ffct, nd ffct, saturation) for prformanc prdiction. In ordr to gt th high prcision rsult, spcially ths paramtrs should b calculatd corrctly. As furthr applications for SLIM s ar xamind, thr will b a growing nd for analytical tools which will allow th computr-aidd dsign of a machin to a givn st of spcifications [1-]-[6]. Svral analytical mthods that ar mainly th dirct mthod, th mthod of th layrs and th mthod of Fourir sris wr dvlopd in ordr to modl th linar induction motor. Ths mthods, on by on or combind, mad it possibl to trat thm problms of filds with 1D, D and 3D within th linar induction motors [4]. If th air gap flux dnsity is assumd constant, th on dimnsional (1-D) analysis mthod can also b usd [8]. In this mthod, th longitudinal nd ffct occurs in th air gap as scond wav. Consquntly, this wav rducs th synchronous wav producd by primary ovr th high spd rang [3]. Th problms associatd with linar induction motors ar rlativly difficult to analyz. Svral tchniqus wr dvlopd for this nd. Thy can b gathrd in two familis: analytical mthods and numrical mthods. All ths mthods (which ar analytical or numrical) start from a formulation of lctromagntic filds rsulting from th Maxwlls quations. Thos govrn all thos lctromagntic phnomna, within th lctromagntic dvics in a gnral way and of th linar induction motor in particular. In this papr, th influncs of th longitudinal nd ffct on th prformanc of th SLIM with doubl layr raction-rail undr constant currnt xcitation by using th quivalnt circuit ar invstigatd and prsntd for th dsignd and constructd SLIM at th diffrnt frquncy oprations by using LIMCAD.. END EFFECT EQUATIONS OF THE SLIM Th nd ffcts of a SLIM is du to th finishd longitudinal lngth of th machin and th influnc th spd on th nonuniform distribution of th induction of air-gap and th currnts inducd in th scondary. This ffct is takn into account by a corrct factor k givn on th basis of a distribution of induction in th air-gap of th linar induction motor mad up of a fild slipping (similar to

3 Prformanc prdiction of linar induction motors 97 th spinning fild pattrn of th rotary machin) and of an induction bing propagatd into th dirction of th principal fild and which is du to th longitudinal ffct nd [4]: x t π π B( x, t) = Bms sin( ω t x) + Bm sin( ωt x + δ ) (1) τ τ Th lctromotiv forc inducd in a phas of th primary is th suprposition of two lctromotiv forcs, on is du to th fundamntal fild and th othr with induction du to th nd ffct and it can b xprssd in th form: p ( t) = ( t) + ( t) = E cos( ωt) E cos( ωt) = E (1 k)cos( ωt) () s ms m Whr k is a factor which taks account of th nd ffct, its xprssion was stablishd in [4]: ms k k = k Whr: w w t 1 τ π π + τ f ( δ ) pτ t pτ sinh t τ p sinh t (3) 1 π f ( δ ) = sinδ + cosδ (4) t τ δ is dphasing btwn th fundamntal wav of induction in th air-gap and induction du to th nd ffct bing propagatd in th dirction of th slipping fild, with th ntry of th motor. It is approximatd in an mpirical way by [4]: δ = δ + bv (5) Whr t δ = π arctan π τ = And Vr V 1 t ; arctan b = π 15 τ = Vr V (6) V Vr V V = Vs if Vr V = Vs V V if Vr V = < (7)

4 98 A. S. Grçk and V. M. Karslı Whr V is th boundary spd and it is xprssd as, V s V =.5 (8) 15 τ and t rprsnt th pol pitch of th nd wav and attnuation factor rspctivly. It can b calculatd by using th following xprssions [4]: π τ = (9) D t c = (1) Cgk c gk V μ σ r Al D Al 1 C + D 4 = X + 16Y X (11) 1 4 = X + 16Y X (1) X μ Vr Ald = σ k c R ( g + D ) Al (13) Y = μ ωσ Ald k c R ( g + D ) Al (14) Whr d R. is th thicknss of a homognous layr out of aluminum quivalnt to th two layrs which constitut th conducting part of th scondary, it can b usd to valuat rsistanc modling th ddy currnts in th scondary. This thicknss is stimatd starting from th quivalnt impdanc of th scondary. Indd, th conducting layr out of aluminum and that of frromagntic of th scondary ar quivalnt (from lctric point of viw) to a layr out of aluminum thicknss d R, which has as impdanc (if it is nglctd th ffct of skin): W 1 Z sc = ( ar + ja X ) k z (15) τ sσ Ald R Whr a R = 1 and a x = 1 for a nonmagntic matrial such as aluminum. From whr d R can b xprssd th quivalnt thicknss by idntifying th two xprssions of (15) and (18).

5 Prformanc prdiction of linar induction motors EQUIVALENT CIRCUIT OF SLIM Equivalnt circuit for SLIM is shown in Fig1. Equivalnt circuit paramtrs, which obtaind from th lctromagntic -D fild quations taking into account th saturation, hystrsis, skin, transvrs dg, slot ffct and th raction of th ddy currnt of th scondary, ar as follows; jωμ μr z = (16) 1 z ( K D ) K 1 tanh 1 ir jωμ K tanh K D al ( ) k zv = (17) Rsc Xsc zz 1 1 L zsc = j = k tr s s z s 1 + z τ (18) z jx M jωμ = β tanh ( βg ) = (19) " Whr μ μ( μ jμ ) r = ; = a a R x " μ ; =.5( a ) μ R a x ; k tr = m( Nk ) w p ( μ r Th saturation factor ( k μ ) and quivalnt prmability of th back iron ) ar calculatd using simpl itrativ mthod. a R and a x dpnd on th lctromagntic fild on th surfac of th scondary stl and tak account of saturation and hystrsis ffct. Saturation ffct and slot ffct ( k c ) modify th air gap lngth. g = k c kμ g () R 1 X 1 R /s E(1-k) X m R f X /s Figur 1. Pr Phas Equivalnt circuit of LIM Elctromagntic thrust for th fundamntal spac harmonic is xprssd as

6 1 A. S. Grçk and V. M. Karslı mi ( sc) R sc Fx = (1) svs Whr I sc is th scondary currnt rfrrd to primary and xprssd as Ems(1 k) I sc = () abs( z ) sc Symbol dfinitions ar in appndix. 4. SIMULATION RESULTS Firstly, an analytic tool has bn dvlopd for th modl of th quivalnt circuit and validatd with th tst rsult of CIGGT [3] which is shown in Fig.. Thn it was applid to th dsignd motor using th dsign paramtrs prsntd in Tabl I and th simulation was carrid out. Tabl 1 SLIM Data Paramtrs LIM Motor lngth,lp (mm) 1 Stack width,l (mm) 5 Pol pitch, τ (mm) 5 No. of slot,z 1 No. of pol,p 4 No. of phas,m 3 Turn pr phas,n 8 Coil pitch,wc (mm) 49 Air gap lngth,g (mm) 1 Scondary width,w (mm) 98.5 Thicknss of conducting plat, Dal (mm) 4.5 Thicknss of th back iron Dir(mm)

7 Prformanc prdiction of linar induction motors 11 All simulation rsults wr obtaind at diffrnt frquncis (, 4,6Hz) undr constant currnt xcitation (I=1 A) for dsignd SLIM. Th analytic tool was conductd ovr a rang of spd. Thrust as a function of spd at constant currnt xcitation1 A is shown in fig.4. It was calculatd for th fundamntal spac harmonic using th T-typ quivalnt circuit shown in fig Hz 11 Hz 18 Hz 8 Hz 4 Hz 15 Thrust (N) Vr (km/h) Figur Simulation rsults of SLIM at diffrnt frquncy (CIGGT) [6] (brokn lin- without nd ffct, straight lin-with nd ffct) As xpctd, th nd ffct factor incrass at high frquncy shown in fig.3. This mans that th lctromotiv forc (EMF) inducd on th primary phas winding dcrass. Consquntly, th magntic flux producd by primary dcrass. It approachs th ngativ slop nar th synchronous spd for all applid frquncis. And it also shows th variations at low frquncis nar th synchronous vlocity Hz.5 End fffct factor (k) Hz 4 Hz Vr (m/s) Figur 3 End ffct factor at diffrnt frquncy (, 4, 6Hz)

8 1 A. S. Grçk and V. M. Karslı Hz 4 Hz 6 Hz 1 1 Thrust (N) Vr (km/h) Figur 4 Thrust (brokn lin- without nd ffct, straight lin-with nd ffct) Undr th constant currnt conditions (I=1A), th maximum availabl thrust was dcrasd as th input frquncy is incrasd du to th nd ffct and influnc th saturation of th magntic circuit and as shown fig CONCLUSION In this papr, th prformanc prdiction of th dsignd SLIM using dvlopd analytical tool which agrs with th litratur has bn prformd. Analytical curvs in Fig.3-4 hav bn invstigatd and valuatd for th prformanc prdiction taking into account nd ffct. Th dsign considration agrs with th xpctd thrust for dsignd SLIM at 4 Hz. Th dvlopd tool may conclud th prformanc prdiction of th SLIM with doubl layr ractionrail undr constant currnt xcitation ovr wid rang applications. 6. ACKNOWLEDGMENT All simulations wr carrid out MATLAB softwar packag rlas 14. Dsignd SLIM was constructd in th lctric machin laboratory in Univrsity of Gaziantp and supportd by TUBITAK.

9 Prformanc prdiction of linar induction motors APPENDIX Symbol μ r μ rs g g k μ kc O W Lp L hp τ d h l d Physical Quantity Equivalnt prmability of scondary iron Surfac prmability of scondary iron Mchanical claranc Effctiv air gap Saturation factor Cartr cofficint Slot width Scondary iron width Primary lngth Primary width Hight of th primary cor Slot pitch Slot hight Tooth width REFERENCES [1] J. F. Giras, A. R. Eastham and G. E. Dawson, Prformanc Calculation for Singl-Sidd Linar Induction Motors With a Solid Stl Raction Plat Undr Constant Currnt Excitation, In IEE Procdings, 13, (1985), [] J. F. Giras,Graham E. Dawson,Anthony R. Eastham, Prformanc Calculation of th Singl Sidd Linar Induction Motors wiyh a Doubl Layr Raction Rail Undr Constant Currnt Excitation, IEEE Transactions on Magntics,, (1986). [3] J. Faiz, H. Jafari, Accurat Modlling of Singl-Sidd Linar Induction Motor Considrs End Effct and Equıvalnt Thicknss, IEEE Transactions on Magntic, 36, (). [4] J. F. Giras, G. E. Dawson and A. R. Eastham, A Nw Longitudinal End Effct Factor for Linar Induction Motors, IEEE Transactions on Enrgy Convrsion, EC-., (1987), [5] M. Mirsalim, A. Doroudi,J. S. Moghani, Obtaining th Oprating Charactristics of Linar Induction Motor: A Nw Approach, IEEE Transactions on Magntics, 38, ().

10 14 A. S. Grçk and V. M. Karslı [6] R. M. Pai, Ion Bolda, A Complt Equivalnt Circuit of a Linar Induction Motor with Sht Scondary, IEEE Transactions on Magntics, 34, (1988). [7] R. M. Pai, S. A. Nasar and I. Bolda, A Hybrid Mthod of Analysis of Low- Spd Linar Induction Motors, IEEE Transactions on Magntics, 3,( 1987) [8] R. C. Crpp, J. A. C. Ulson, J. F. Rodrigus,Influnc of Dsign Paramtrs on Linar Induction Motor End Effct, IEEE Transactions on Enrgy onvrsion, 3, (8). [9] S. Yamamura,, Thory of Linar Induction Motor, Tokyo Prss., (1978). Rcivd: August, 8

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