6. The squirrel cage induction machine

Transcription

1 6. The quiel cage induction achine TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/1 ntitut f Eletiche Enegieandlung FB 18

2 Squiel cage induction achine Coe quiel cage: fo big oe achine > W and fo taction achine: Maive non-inulated coe ba in oto lot. At both font end hot-cicuited by to coe end ing by elding. Soetie coe die cat oto fo alle achine to inceae efficiency. Aluiniu coe quiel cage: Die cat cage fo alle achine < W: The hole cage i cat a one iece ith liquid aluiniu. Additional fan blade fo cooling at the end ing and balancing bolt ae cat at the ae tie. To adjacent ba fo ith the in beteen ing egent oto loo hee tato otating field induce the oto voltage. Thi caue oto ba cuent & end ing egent cuent. Roto ba cuent togethe ith tato field ceate electoagnetic toque. TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/ ntitut f Eletiche Enegieandlung FB 18

3 Aluiniu die cat quiel cage induction achine Cage induction achine oen ventilated ai cooling Ai flo Shaft-ounted fan Cage end ing ith fan blade Fan hood fo guidance of ai Aluiniu die cat quiel cage oto eed by one tato lot to educe loe caued by lot haonic TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/3 ntitut f Eletiche Enegieandlung FB 18

4 nduced oto voltage e ba Stato fundaental ai ga ave (alitude ˆ ) ove elatively to the oto ith eed v yn = v yn - v. To oto ba ditanced by ole itch = oto loo". Magnetic flux e loo: l ˆ Magnetic flux e loo Φ B nduced voltage e loo induced ith fequency f = f : ˆ f lbˆ ( f ) l Bˆ v l Bˆ i c Pe ba = half loo: half voltage ˆ i ba = Roto ba voltage ˆ v Bˆ i ba yn l ˆ i c / B yn TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/4 ntitut f Eletiche Enegieandlung FB 18

5 Roto ba voltage fo egula bundle of hao Ditance beteen to ba = oto lot itch Q. t yield hae hift beteen adjacent ba voltage = = Roto lot angle Q Q Facit: Voltage hao of all oto ba fo on colex lane a egula bundle of hao. Exale: Fou ole cage oto ith Q /= 14 ba e ole ai. To adjacent ba voltage hao ae hae hifted by oto lot angle Q / 7 Q 8 Afte ole hae bundle i eeated: The ba voltage of ba 1 and 15 and 16 etc. ae in hae. TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/5 ntitut f Eletiche Enegieandlung FB 18

6 Ba cuent ba foce toque Roto ba cuent fo egula cuent hao bundle hich excite a oto ai ga field ave. Only fundaental futhe conideed. Togethe ith tato fundaental field it fo the eulting ai ga agnetic field. The ba cuent and the tato fundaental ai ga field ceate e ba e ba the tangential ORETZ-foce: F ˆ ba ˆ balb ˆ All ba foce fo ith the leve d / the electoagnetic toque M e. c) TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/6 ntitut f Eletiche Enegieandlung FB 18

7 Ring cuent Ring cuent flo in the ing egent: e. g. beteen ba o. (ba cuent ) and o. 3 (ba cuent 3 ) a ing ection cuent 3. KRCHHOFF node ule: Hence the ing ection cuent ae alo hae hifted by oto lot angle Q and fo a egula bundle of ing ection cuent. c) 1 in( Q / ) ba Ring in( / Q ) Reitance e ing ection R Ring : the equivalent eitance eitance R ba : P * R Ring i added to ba * Cu Q Rbaba QRRing Ring Q ( Rba RRing ) ba * RRing RRing 1/(in ( / Q )) TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/7 ntitut f Eletiche Enegieandlung FB 18

8 ntitut f Eletiche Enegieandlung FB 18 TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/8 Cage tanfe atio Each ba ay be egaded a a eaate hae: nube of inding e hae: 1/ nube of oto hae = Q inding coefficient = 1. Voltage and cuent tanfe atio ae diffeent: Roto elf and utual inductance e hae (= e ba): ith tanfe atio: Reult: Q ba h h l l 0 0 h l l M 0 0 h l l M 0 0 R R h h M M

9 ntitut f Eletiche Enegieandlung FB 18 TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/9 Equivalent cicuit fo cage induction achine e of tanfe atio in the tato and oto voltage equation: T-Equivalent cicuit e tato hae: Facit: We get the SAME equivalent cicuit a ith ound oto induction achine. h R j j M j ) / ( 0 ) / ( ) / ( ) / ( h R j j M j h h R j j j h h R j j j 0 ) ( h jx jx R ) ( 0 h jx jx R

10 Field line B of a cage induction achine Stato Main flux ORTH POE Main flux: in tato and oto inding; field line co the ai ga eaage flux (tay flux): only lined ith eithe tato o oto inding; field line DO OT co the ai ga Roto Ai ga Roto lot leaage flux Exale: Fou-ole edge ba oto: Field line at tand till (n = 0) - Roto fequency = Stato fequency - Roto cuent i EARY in hae ooition to tato cuent Stato lot leaage flux TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/10 ntitut f Eletiche Enegieandlung FB 18

11 Roto lot tay flux f oto cuent denity J ba ba / Aba i hoogeneouly ditibuted ove ba co ection then lot tay field hich coe lot eendicula to lot axi inceae linea ith ba height x! H d HQ ( x) C x bba ba x Q ( x) 0 J 0 b b hba AMPERE la: B b J x b 0 x h ba ba BQ 0 b ba o x > h ba TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/11 ntitut f Eletiche Enegieandlung FB 18

12 Cuent dilaceent in oto ba Slot flux denity i ulating ith oto fequency enetating the oto ba fo the ide. High oto ba fo a "aive hot cicuit loo". FARADAY la yield: B Q induce voltage u i = -d/dt in ba hich caue eddy cuent flo Ft. Self field of that eddy cuent B QFt i diected ooite to B Q due to EZ ule. Hence the eddy cuent Ft flo in ue ba egion diection of ba cuent ba and in loe ba egion OPPOSTE to ba cuent. Facit 1: Due to Ft the eulting ba cuent denity i HGHER in ue ba egion: Cuent dilaceent toad ue ba egion ( Sin effect ). Facit : The eulting lot tay flux denity B Q~ i due to B QFt educed. Cuent dilaceent CREASES ith inceaing oto fequency f ith inceaing electic ba-conductivity ith inceaing ba height h ba and ith inceaing eeability of conducto. (ote: Coe and aluiniu eeability i = 0!) TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/1 ntitut f Eletiche Enegieandlung FB 18

13 Effect of oto cuent dilaceent - At high oto fequency (e. g. = 1) ajo at of ba cuent flo in ue ba egion: o only educed ba co ection i ued fo cuent flo. Thu AC ba eitance R ba~ i highe than DC ba eitance R ba=. -Due to eduction of lot tay flux denity the lot leaage flux i educed. Hence the AC ba inductance ba~ i alle than the DC ba inductance ba=. R ba ~ RRba Rba ba~ ba ba - At lo oto fequency (e. g. = ) nealy O cuent dilaceent occu! TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/13 ntitut f Eletiche Enegieandlung FB 18

14 Reitance inceae R and inductance deceae Reduced conducto height : Pe-unit value containing all elevant aaete: R fo dee ba ( ectangula co ection") deend on: h ba f b b ba TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/14 ntitut f Eletiche Enegieandlung FB 18

15 Exale: Cuent dilaceent in dee ba Coe dee ba: - At 75 C ba teeatue coe conductivity i Cu = S/. - Ba idth = lot idth: ba b 7 - Peeability: Cu V/(A) - Stating of induction achine: = 1: Roto fequency f =50Hz - Ba height: h ba = 3 c h ba f b b ba b Fo cuve R () e get: R (3) = 3 and fo () follo: (3) = 0.5. Facit: - Roto ba eitance inceae u to 3-fold! - Roto ba inductance deceae don to 50%. Thub ule: At 50 Hz the inceae of eitance of coe dee ba i h c R.98 3 ba TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/15 ntitut f Eletiche Enegieandlung FB 18

16 nceae of tating toque by cuent dilaceent nceae of oto loe lead to inceae of tating toque M 1 : P PCu / PCu M e( ) M1 M e( 1) Ω Ω Ω yn yn Secial ba co ection fo all and big tating toque: yn SMA cuent dilaceent = M 1 all: a) Round ba b) Oval ba BG cuent dilaceent = M 1 inceaed: c) Dee ba d) Wedge ba e) -ba VERY BG cuent dilaceent = M 1 big: f) and h): Double ba g) altenating ba: Round ue bonze ba (high eitance) caue along ith cuent dilaceent fo loe in ue ba high oto loe M 1 i big. oe ba nealy ithout cuent (STARTG OF MOTOR = 1). At ated li all cuent dilaceent: Cuent flo ainly in loe ba: lo loe! TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/16 ntitut f Eletiche Enegieandlung FB 18

17 Toque chaacteitic of induction achine M(n)-chaacteitic of induction achine ith diffeent oto ba co ection n the figue toque i given e unit of ated toque eed e unit of ynchonou eed! Wound oto ith ound ie: Roto inding conit of any thin ie: no cuent dilaceent; iila: Round ba oto Wedge and dee ba oto: inceaed tating toque of about 40%... 80%M ; Double cage oto: Stating toque eache 160% M. Big cuent dilaceent need dee ba = high dc ba inductance = big leaage coefficient. Hence bea don toque deceae. 1 Mb X TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/17 ntitut f Eletiche Enegieandlung FB 18

18 Dee ba oto: nfluence of cuent dilaceent Calculated tato cuent and toque in deendence of eed: 550 W 4 ole thee hae dee ba oto cage 6.6 V 50 Hz With cuent dilaceent ( R ) in the oto ba Without cuent dilaceent ( = 1 R = 1): Toque and cuent ae alle at = 1. TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/18 ntitut f Eletiche Enegieandlung FB 18

19 nfluence of cuent dilaceent on cicle diaga nceae of eitance: Coefficient R : Shae of cicle eain unchanged but li cale i hifted to the left toad no-load oint P 0. Reduction of tay inductance: Coefficient : inceae cicle diaete! Facit: Each li value define by R () () a eaate cicle. Hence eulting cuent locu i no longe a cicle! TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/19 ntitut f Eletiche Enegieandlung FB 18

20 Flux denity line ithout / ith cuent dilaceent Wedge oto cage a) b) a) o-load: Roto fequency zeo: o oto cuent no cuent dilaceent. b) oced oto ( = 1): Roto fequency = tato fequency: Big cuent dilaceent. Roto cuent hae ooite to tato cuent; flo ainly in ue at of oto ba eule tato field to ai ga. TECHSCHE VERSTÄT Pof. A. Binde : Electical Machine and Dive 6/0 ntitut f Eletiche Enegieandlung FB 18