4. Induction machines. 4.1 Significance and features of induction machines

Transcription

1 Moto develoment 4/1 nduction machine 4. nduction machine 4.1 Significance and featue of induction machine a Baic function and diffeent tye of machine: nduction machine ae in the owe ange of 100 W u to eveal MW the mot ominent moto alication, being the "woking hoe" of indutial dive ytem, but alo in dometic alication and in taction dive. Recently many induction machine ae ued a geneato in wind-mill alication in the owe ange of eveal 100 kw u to about 5 MW in off-hoe lant. nduction machine ae built uually in low owe ange u to about 3 kw with ingle-hae and fo inceaed owe with thee-hae AC winding. Roto winding i alway hot-cicuited. Synchonouly otating tato field excited by the tato cuent, which i diven by tato voltage uly - will induce accoding to Faaday law in hotcicuited oto winding oto cuent, a long a oto otate aynchonouly to tato field: n. Roto cuent oduce with tato field tangential oentz foce, thu geneating n yn diving toque, if n nyn (ub-ynchonou oeation = moto and baking toque, if n (ue-ynchonou oeation = geneato. That mean that fom tand-till n = 0 n yn u to ynchonou eed machine will otate by itelf a moto, wheea fo geneato a mechanical dive (tubine ha to dive the oto fate than the otating tato field. deal noload i at n n, a becaue in that cae no flux change in oto occu and theefoe no yn voltage i induced in oto, thu no oto cuent flow, hence yielding zeo toque. nevitable fiction caue alway ome mall load toque, o oto will alo at no-load otate lightly below ynchonou eed. Diffeence in eed i nomalized a li nyn n, (4.1-1 n yn which at tand till equal 1 and at ynchonou eed i zeo, being negative in geneato oeation. Roto winding i mot often a hot cicuited quiel cage (Fig.4.1-1, which i chea and obut, o ometime a hot cicuited thee-hae wie-wound oto winding. atte winding i uually ta-connected with the thee teminal connected to li ing, being hot cicuited thee. With thee li ing it i oible via liding cabon buhe a contact to connect additional oto hae eito. With thi atificial inceae of oto eitance it i oible to aie moto tating toque at = 1. a b Fig.4.1-1: Roto of induction machine: a Squiel cage, coniting of (hee kewed oto ba and two oute ing, hot cicuiting the ba. Ba ae ineted in lot in oto ion tack. Hee cage conit of die-cat aluminium. Note the additional "fan blade" on the outide of the cage ing to geneate additional ciculating ai flow fo oto cage cooling. b Wie-wound thee hae winding with li-ing e hae: 1: Roto ion tack, : oto winding, 3: bandage fixing winding ovehang, 4: winding connection to li ing, 5: li ing, 6: haft (Siemen AG. T Damtadt ntitute fo Electical Enegy Conveion

2 Moto develoment 4/ nduction machine Single-hae induction moto have tato winding, which conit of two hae a and b, dilaced by half ole itch, which ae fed by cuent i a and i b, hae hifted by 90. Thu again a otating tato field i geneated, in the ame way a it i done with thee-hae winding, whee the hae, V, W ae hae hifted by thid of ole ai itch, fed by thee cuent i, i V and i W, hae hifted by 10. So thi machine in eality i a two-hae machine. A no two-hae gid exit, moto ae oeated fom ingle hae gid N = a. Second hae voltage b i geneated by additional caacito C, which i hifting cuent i b by 90 with eect to i a (Fig A caacito C i connected in eie to tato hae winding b, thi hae hift i only oible at cetain li (uually ated li. At othe eed value (e.g. no-load o tating hae hift diffe fom 90, o otating field i not an ideal one. t change amlitude duing one evolution, thu cauing additional loe due to eddy cuent in tato and oto ion tack, and additional ulating toque, which caue the moto to vibate with twice line fequency (e.g. at 50 Hz line fequency thi i 100 Hz. Fo thi eaon thi o-called "caacito moto" i ued only at low owe below tyically 3 kw due to the athe low efficiency of about 70%... 75% in bet cae and due to the vibation, motly a - and 4-ole machine. a b Fig.4.1-: Two-hae induction moto: a Oeated fom ideal two hae gid (which uually i not available in eal wold, b oeated fom ingle hae gid, ued fo dometic alication at low owe below tyically 3 kw b Featue of tandad moto: A induction moto ae widely ued, thee low voltage thee-hae induction machine with quiel cage oto ae tandadized, indeendently fom manufactue, concening - haft height (= moto ize, - ditance of feet of moto houing o moto flange dimenion, - ated owe, - haft dimenion between haft height 56 mm and 315 mm (ee tandad EC 7. ow voltage i defined a le than 1000 V and i tandadized 30 V, 400 V, 690 V. Thee moto ae totally encloed, uface cooled with ai by haft mounted fan (TEFC: totally encloed fan cooled, Fig Pole numbe ae uually, 4, 6, 8. Moto with highe ole count ae aleady conideed ecial machine. Examle 4.1-1: Standadized haft height (mm: Standadized moto owe ( = mechanical haft owe = outut owe (kw: T Damtadt ntitute fo Electical Enegy Conveion

3 Moto develoment 4/3 nduction machine Fig.4.1-3: Standad induction moto: Moto element fo foot and flange tye totally encloed fan cooled quiel cage machine (Siemen AG Fig.4.1-4: Co ection of tandad induction machine (totally encloed fan cooled quiel cage machine, howing the main element fo foot (lowe half of dawing and flange tye (ue half: 1: houing, : endhield, 3: beaing lubication, 4: beaing, 5: fan hood, 6: haft-mounted fan, 7: haft, 8: teminal box, 9: tato winding ovehang, 10: tato ion tack, 11: oto cage, 1: oto ion tack (Siemen AG Examle 4.1-: Standad induction moto (TEFC: Rated data: 7.5 kw, 30 / 400 V, D/Y, 6.5 / 15. A, 50 Hz, 1455/min, co = 0.8 Shaft height 13 mm, fou ole = 4 Synchonou eed: f / 50 / 5 / 1500 / min n yn Rated li: ( n n / n ( /1500 3% N yn N yn T Damtadt ntitute fo Electical Enegy Conveion

4 Moto develoment 4/4 nduction machine Above moto fame ize 315 mm till main dimenion of moto houing ae tandadized in EC7 with haft height 355 mm, 400 mm, 450 mm, but coeonding owe ating vay with diffeent manufactue, lying in the ange of 355 kw kw fo 4-ole machine. Mot of the induction machine in the wold ae oeated diectly fom the gid. Roto i unning with ated li, which i uually only eveal ecent, o eed i nea ynchonou eed at load and nealy ynchonou eed at no-load (only fiction i then loading the oto. Concluion: ine oeated induction moto ae egaded a fixe eed dive, a ated eed i only a few ecentage below ynchonou eed, o eed vaiation between no-load and load i mall. c Stato winding featue: Note that on moto late alway ated voltage i line-to-line voltage and ated cuent i line cuent in moto cable. Fo delta connection line-to-line voltage i identical with hae voltage, but line cuent i lage by 3 than hae cuent. Fo ta connection line-to-line voltage i lage by (Fig than hae voltage, but line cuent and hae cuent ae identical a b Fig.4.1-5: Thee-hae tato winding can be connected eithe in a delta connection o b ta connection Examle 4.1-: Standad induction moto (TEFC: Rated data: 7.5 kw, 30 / 400 V, D/Y, 6.5 / 15. A, 50 Hz, 1455/min, co = 0.8 Winding connection delta ta Phae voltage 30 V 30 V line-to-line voltage 30 V 400 V Phae cuent 15. A 15. A ine cuent 6.5 A 15. A Fom that data we can calculate electic inut owe fo moto oeation at ated li with line value. Of coue thi inut owe i the ame fo delta o ta connected tato winding. Delta connection (D: P 3 co W e N N Sta connection (Y: P 3 co W e N N Electic inut owe can alo be calculated with hae value, which ae identical fo delta and ta connection: P 3 co W. e T Damtadt ntitute fo Electical Enegy Conveion

5 Moto develoment 4/5 nduction machine P 7500 Moto ated efficiency: out P m N 86.6% P P 8656 in n ode to change eed at line oeation (fixed fequency, accoding to e n nyn f /, numbe of ole ai ha to be changed. Thi i accomlihed eithe by two (o thee diffeent winding in tato lot with diffeent coil an and coil aangement, thu geneating tato field with diffeent ole itch and theefoe diffeent ole numbe (e.g. ole and 6 ole. Some ecial winding allow by changing coil connection oeation with diffeent ole count with one and the ame winding, e.g. Dahlande-winding: 1 : = 1:. Stato winding itelf i uually ingle laye ound wie winding, a it i chea. Themal oveload caability of winding i decibed by evice facto SF, which give the additional teady tate owe of the machine at the cot of an additional temeatue ie of 10 K. Examle 4.1-3: Sevice facto SF = 1.15, ated owe 7.5 kw, winding ha Themal Cla F, which mean that aveage temeatue of tato winding doe not exceed 105 K at maximum 40 C ambient temeatue accoding to EC Meaued temeatue ie at 7.5 kw: 90 K < 105 K. Temeatue ie at SF P kw: 100 K < 105 K. N d Alication of line-fed induction machine: d1 ine-fed machine (fixed eed dive: ndutial dive fo um, fan, oduction machine in diffeent banche uch a aw mill, mechanical tooling, alication uch a awing, dilling, milling, ginding, olihing etc. machine, o it i eally a multi-uoe dive. n chemical lant, oil dilling latfom, oil efining (eto-chemity,... thee moto ae available a exloion oof machine with the following diffeent featue: EEx e: Moto uface temeatue tay below cetain temeatue limit. n cae of oveheating moto i witched off. EEx : Ai eue in moto i lightly lage than that of ambient ai. Thu no exloive ga might intude into moto, hence avoiding exloion hazad. EEx d: Moto houing i vey tong deigned to withtand ove-eue, if exloion haen inide moto (EN EN5000 Duing aynchonou tating cuent of moto inceae u to time ated cuent, which i athe big. Thi cuent i educed (in likewie tating toque - by witching moto fit in Y, and then in D-connection o - by ecial at winding to educe tato hae voltage, - by thyito-contolled voltage eduction. d nvete-fed machine (vaiable eed dive: Accoding to n nyn f / eed can be changed continuouly by changing tato fequency with invete. Pecentage of invete-fed tandad induction machine i teadily inceaing, uhing back the thyito-contolled claic DC dive in diffeent alication uch a extuding latic, oduction of wie, even in ae and foil oduction, a mooth toque i alo oible with invete fed induction machine with ule width modulation of invete outut voltage (PWM. At low eed, fan i geneating only little ai flow, o due to that bad cooling toque ha to be educed. T Damtadt ntitute fo Electical Enegy Conveion

6 Moto develoment 4/6 nduction machine Futhe, ecial induction moto fo invete-oeation ae available, motly fo highe eed and fo wide field weakening ange, whee contant outut owe i needed. Tyically thee moto ae cooled by extenal fan, o that they can oduce full ated toque alo at tand till. Pole count ae - and mainly 4-ole, machine being ued in tooling machiney and othe ecial alication. 4. Fundamental wave model of line-oeated induction machine a Fundamental tato ai ga wave: Hee only the thee-hae machine i conideed, but by ubtituting tato hae count 3 by hae count m in the deived equation, model i valid fo abitay hae count. The thee inuoidal tato hae cuent i, iv, iw have all the ame amlitude Î and.m.. value ˆ /, ame fequency f, but ae hae hifted by 10 each ( f, e.g. in hae : i ˆ in( t. With ditibuted AC winding, each hae hifted by / 3, a exlained in Chate 1, a moving ai ga flux denity i excited by the thee hae cuent ytem. The hae of ai ga flux denity ditibution i te-like becaue of the coil ide concentated in lot and lot oening neglected (ai ga width (Fig Fouie analyi yield a inuoidal ditibuted ace fundamental ai ga flux denity wave (x : tato cicumfeence co-odinate x B ( x, t B co( t, (4.-1 moving with cicumfeence eed x dx t cont. vyn vyn f, (4.- dt which coeond with otational eed nyn f /. Amlitude of that fundamental wave i - with aumed infinite ion emeability, numbe of tun e hae N and definition of tato winding facto k w accoding to Chate 1 - B m 0 N k w ˆ. (4.-3 Fig.4.-1: Fundamental ai ga wave moving with eed v yn. Afte e.g. quate of eiod of tato cuent ocillation T/4 =1/(4f wave ha moved by half ole itch: v yn T/4 = f /(4f = /. Stato flux e ole i T Damtadt ntitute fo Electical Enegy Conveion

7 Moto develoment 4/7 nduction machine ( t l Fe 0 x B ( x, t dx l B co Fe t dx lfeb in( t, ( which i ulating with tato fequency and theefoe induce each hae of tato winding accoding to Faaday law with "elf-induced" voltage u kwn d ( t / dt kwn lfeb co(, (4.-5 i, t which may alo be decibed with elf-inductance h e.g. fo hae, a it wa aleady decibed in Chate 1 fo ynchonou machine, which ha identical tato winding aangement: u i, h di m l Fe / dt h 0( Nkw (4.-6 A all voltage and cuent vay inuoidal, the advantage of comlex calculu i uually ued, e.g. elf-induced voltage (with an abitaily choen hae hift u j t j t ˆ ( e Re e ( t ˆ co( i, i, t Re i, i,, (4.-7 whee intead of time function u i, ( t the comlex numbe i, i, e i ued with.m.. value of i,. Thu we get intead of (4.-6, conideing the 90 hae hift fom in( t of cuent to co( t of voltage by multilication with j 1 : j i, h. (4.-8 b nduced oto voltage and cuent: Roto cage may be conideed a a hot cicuited winding ytem with m = Q oto hae, a each oto ba i one indeendent oto hae with it ba cuent a oto hae cuent. Each oto hae conit only of one ba, which i a "coil" with a half-winding: N = 1/. Theefoe ditibuted winding e hae i oible, hence oto winding facto i k w = 1. nduced voltage e oto hae (= e oto ba i calculated in the ame way, defining mutual inductance M between tato and oto winding: u i, k w N j M d ( t M dt di / dt M N k 0 w N k w j m l Fe (4.-9 i,. (4.-10 Note that due to oto movement with eed n elative to tato ace fundamental wave eed n yn the oto fequency i f. (4.-11 f Roto induced voltage e ba caue oto ba cuent. The Q inuoidal oto ba cuent i, 1, i,,... i, have all the ame amlitude Î and.m.. value ˆ /, ame Q fequency f, but ae hae hifted by /( Q /, becaue one ole ai - coeonding with Q / oto ba - i tato flux wave ace eiod (Examle T Damtadt ntitute fo Electical Enegy Conveion

8 Moto develoment 4/8 nduction machine Examle 4.-1: Roto cage with Q = 8 oto ba, induced be 4 fou-ole tato wave. Phae hift between adjacent oto ba cuent i theefoe: /( / /(8/ / 7 Q Fig. 4.-: Squiel cage oto: a Roto cage with Q = 8 oto ba, induced by 4-ole tato wave. b Roto ba cuent ae hae hifted by /7. c Fundamental oto ai ga wave: Accoding to (4.-7 actual oto cuent value at each time intant i given by eal at of comlex oto cuent, which i e.g. fo Examle 4.-1 at t = 0 vetical at of cuent hao in Fig.4.-. With actual value oto cuent ditibution e.g. at t = 0 (Fig.4.-3 Amee law yield the oto ai ga flux denity B and it m.m.f. H ( B / 0 V again a te-like function with te at oto lot location. Comaing with Fig we note, that te-like oto flux denity ditibution fit much bette to inuoidal ditibution than tato flux denity te function. Thi i due to the much bigge hae numbe in oto. Fig. 4.-3: Ditibution of oto ba cuent and oto m.m.f. V (ootional to ai ga flux denity in cae of infinite ion emeability and contant ai ga along oto cicumfeence fo examle Q / = 14 at t = 0 Fouie analyi yield a inuoidal ditibuted ace fundamental ai ga flux denity wave (x : oto cicumfeence co-odinate, fixed with oto efeence fame x B ( x, t B co( t, (4.-1 moving with cicumfeence eed the amlitude v yn, f o nyn f /, elative to oto, having T Damtadt ntitute fo Electical Enegy Conveion

9 Moto develoment 4/9 nduction machine T Damtadt ntitute fo Electical Enegy Conveion w k N m B ˆ 0. (4.-13 Adding oto mechanical eed, thi flux wave otate elative to tato with ynchonou eed: yn yn yn n f f f n f n n / (1 / / (1 /,. Theefoe oto fundamental induce oto cage with oto fequency (elf-induction i, and tato winding with tato fequency (mutual induction i,, calculating the coeonding inductance value in the ame way a fo tato ace fundamental. Fe w h h i l m k N j 0, (. (4.-14 Fe w w i l m k N k N M M j 0,. (4.-15 d Stato and oto voltage equation: So finally e hae a tato and oto voltage equation i deived, conideing alo elfinduced voltage by tay flux of lot and winding ovehang (inductance, and voltage do due to eitance R R,. Stato hae voltage ae balanced by gid voltage and oto i hot-cicuited: = 0. h M j j j R (4.-16 h M j j j R 0 (4.-17 Both voltage equation emain unchanged, if the facto ü, ü ae intoduced in the following way: / ( ( h ü M ü j j j R (4.-18 h M ü j ü ü ü j ü ü ü j ü R ü ü ( ( ( ( 0. (4.-19 f thee two facto ae defined a w w w w k N m k N m ü k N k N ü,, (4.-0 a imle eult i achieved (comae (4.-9, (4.-14, (4.-15!, which i called main inductance h : h h h ü ü M ü ü M (4.-1 With that and the abbeviation ü ü R ü ü R ü,, / (4.- tato and oto equation ae much hote: ( 0 ( h h j j R j j R (4.-3

10 Moto develoment 4/10 nduction machine T Damtadt ntitute fo Electical Enegy Conveion Subtituting and dividing oto voltage equation by, only tato fequency emain at the cot of an "atificial" oto eitance R / : ( / ( 0 ( h h j j R j j R (4.-4 Thee two equation coeond with the equivalent T-cicuit (Fig.4.-4 with the eactance h h X X X,, and the "magnetizing cuent" m, which i given by the ueoition of tato and oto fundamental wave in ai ga a eulting ai ga flux denity. Fig.4.-4: Equivalent cicuit of induction machine, conideing fundamental ace hamonic and inuoidal tato and oto cuent and voltage e Cuent and toque of induction machine: Solution of (4.-4 fo tato and oto cuent i ( ( R X X R j X X R R jx R (4.-5 h jx R jx, (4.-6 uing a abbeviation the tay coefficient, which i the atio of tay flux veu total flux and lie in the ange of tyically %. h X X X 1 ( h X X X, h X X X (4.-7 The no-load cuent at ynchonou eed ( = 0 i neceay to magnetize the ai ga flux comletely by tato cuent, which induce back EMF X h 0 to balance tato voltage; it ange between % of ated cuent, and it i nealy eactive. X j jx R 0 ( 0 (4.-8 At tating (tand till, = 1 tating tato cuent i time lage than no-load cuent ( time ated cuent and nealy the ame a fo infinite li (Fig.4.-5: X j 1 1 ( 1 (4.-9

11 Moto develoment 4/11 nduction machine Concluion: Stato cuent in induction machine i aleady neceay at no-load to magnetize ai ga flux. At tand till (unity li equivalent oto cuent i nealy a big a tato cuent, but with ooite hae. Hence oto flux i ooite to tato flux. Theefoe a vey big tato cuent i needed to magnetize eulting ai ga flux equal to the value at no-load to induce neceay back EMF to balance tato voltage. The ame i tue fo big negative li in geneato mode. Powe balance of equivalent cicuit how fo moto oeation, that electical inut owe P e * 3 Re ( * : conjugate comlex numbe of (4.-30 minu tato coe loe P Cu, mut be the ai ga owe P, tanfeed to oto, whee it mut be equal to oto coe loe P Cu, and mechanical outut owe P m. Pe PCu, Pe mr PCu, Pm m R Pm mr Pm (4.-31 P Fom equivalent cicuit we ee that ( R / P m. (4.-3 Theefoe we get fo electomagnetic toque M e fom P m M ( 1 M (4.-33 m e yn e and the comaion of (4.-31 and (4.-3 the following exeion M e Pm (1 yn 1 1 mr (1 yn mr yn. (4.-34 By taking the abolute value of, fom (4.-5, (4.-6, aynchonou toque fom (4.-34 i deived, deending on the quae of tato voltage and deending on li : M e m ( R R (1 X X X X R ( R X X R (4.-35 Concluion: - Aynchonou toque deend on the quae of tato voltage. - At no-load ( = 0 toque i zeo. - At infinite oitive and negative li toque i alo zeo. - Between = 0 and = thee exit maximum moto and geneato toque (moto beak down toque M b,mot and geneato beak down toque M b,gen. f at moto oeation load toque uae beak down toque, oto i ulled down to tand till. With neglected tato eitance toque equation imlifie: T Damtadt ntitute fo Electical Enegy Conveion

12 Moto develoment 4/1 nduction machine M e m (1 X ( X R X R (R = 0 (4.-36 Maximum toque i deived by dm e / d 0, yielding beak down li b R (+: moto, -: geneato (4.-37 X and beak down toque R 0 : M b m 1 X (+: moto, -: geneato. (4.-38 ing M b and b, toque equation (4.-36 look vey imle (o-called Klo function R M e 0 : (4.-39 M b b b With R > 0 value of geneato beak down toque i bigge than moto beak down toque (Fig. 4.-5, but geneato and moto li have till the ame abolute value. Examle 4.-: Toque-eed and tato cuent-eed cuve of induction machine: Data: R /X =1/100, R /X = 1.3/100, = 0.067, X = X = 3Z N, Z N = N / N Due to n ( 1 f / toque and cuent may be deicted eithe in deendence of li o in deendence of oto eed n (Fig Fig.4.-5: Toque M e and tato cuent deending on li (R /X =1/100, R /X = 1.3/100, = 0.067, X = X = 3Z N, Z N = N, / N, T Damtadt ntitute fo Electical Enegy Conveion

13 Moto develoment 4/13 nduction machine f Roto cuent dilacement fo inceaed tating toque: Fig.4.-5 how 5 time ated cuent a tating cuent, but tating even a little bit lowe than ated toque. How to inceae tating toque? Accoding to (4.-34 inceae of oto eitance will inceae toque at = 1: M e yn mr ( 1. (4.-40 Fo wie wound oto induction machine with li ing it i oible via liding cabon buhe a contact to connect additional oto hae eito to inceae oto eitance to aie moto tating toque at = 1. But how i thi oible with cage oto? f oto ba i made with big ba height h ba ("dee ba", the oto lot tay flux will be athe big. t ocillate with oto fequency, which equal tato fequency at tand till. Fig. 4.-6: Roto dee ba : a Roto lot tay flux line coing the ba, b oto ba cuent denity without cuent dilacement, c ditibution of oto lot tay flux denity With Amee law we get fo oto tay flux denity a linea ie within ba and contant value above ba: H d HQ( x b J x bba C B Q x b ( x x ba 0J 0 x hba b b hba ba BQ 0 hba x hq b 0 (4.-41 (4.-4 Fig. 4.-7: Eddy cuent Ft in dee ba excite additional lot flux denity ooite to lot tay flux B Q, which i excited by ba cuent T Damtadt ntitute fo Electical Enegy Conveion

14 Moto develoment 4/14 nduction machine Thi oto lot flux induce accoding to Faaday law u d i Q / dt an additional voltage in the ba, which caue eddy cuent Ft flow (Ft: Foucault-cuent in the ba. Due to negative ign in Faaday law diection of eddy cuent flow i a to excite an additional lot flux denity B QFt which i ooing the oiginal lot flux denity (Fig Sueoition of ba cuent and eddy cuent yield inceaed cuent denity at ue ba edge and eduction of cuent denity at bottom of lot (Fig a b c Fig. 4.-8: Cuent dilacement in dee ba at fequency f in comaion to DC cuent ituation (nea li = 0. a Slot and ba co ection with lot tay flux line, b ba cuent denity ditibution with/without cuent dilacement, c lot flux denity ditibution with/without cuent dilacement A cuent flow mainly in ue at of dee ba, thi act like an inceae of oto eitance, which i eaily undetood by the following imlified cuent denity ditibution. Aume that cuent flow only in ba ection height d E with inceaed denity J ~, then we get b ba h ba J b ba d E J l h Fe ba ~ R~ R (4.-43 debba de Concluion: lfe hba Roto ba eitance i inceaed fom DC value R by a facto k R 1. hbabba de The effect of cuent dilacement deceae with deceaing oto fequency. t i mot ominent at tand till and vanihe at ated li, whee oto fequency i below Hz. Thu inceaed loe due to inceaed oto eitance occu only at tating (big li, whee toque inceae i needed, but NOT at ated oeation. Although total tay flux i educed by eddy cuent, the dee ba caue a athe big oto tay flux and theefoe an inceaed tay coefficient. Accoding to (4.-38 beak down toque i deceaed by ( 1 /, o inceae of tating toque due to cuent dilacement caue deceae of beak down toque (Fig Reulting eed-toque cuve ae claified by o-called oto clae, which define the atio of tating toque veu ated toque and the addle of the toque-eed cuve. Toque need to be bigge than load toque to allow moto to un u. A voltage may vay by +/- 5% (voltage ange A accoding to EN , the toque may be lowe by about 10% in eality (Fig Examle 4.-3: Roto cla 16 mean, that at N -5% the moto i caable to tat againt load toque of 160%M N. T Damtadt ntitute fo Electical Enegy Conveion

15 Moto develoment 4/15 nduction machine Fig. 4.-9: nceae of tating toque and deceae of beak down toque due to cuent dilacement: No o low cuent dilacement: a ound ba, b oval ba Big cuent dilacement: c dee ba, d wedge ba, e te ba, f, g h: double cage bonze ue cage to inceae eitance i Coeonding toque-eed cuve i Fig : Examle of cage induction moto claified accoding to oto clae K T Damtadt ntitute fo Electical Enegy Conveion

16 Moto develoment 4/16 nduction machine 4.3 Voltage limit and emium efficiency machine a Voltage limit: nduction moto oeated diectly fom the gid hall comly with eveal oeational demand, which ae ecified in tandad EC , - and othe at of thi intenational electic machiney tandad. Some featue ae: - ufficiently high tating toque M 1 (exeed in e unit of ated toque, ee Chate 4. - ufficiently low tating cuent 1 (uually time ated cuent - ufficient oveload caability (beakdown toque at leat 1.6-time ated toque - ufficient minimum tat-u toque ("addle minimum" of M(n-cuve - good efficiency (= low loe - low acoutic noie Standad low voltage level, which i tato voltage, ulied by ublic gid, i 400 V (line-toline, which may vay within Euoean Community between +/- 10%. Examle 4.3-1: Gid voltage limit: 400V+/-10%: minimum: 360 V, maximum: 440 V f induction moto i fed with inceaed voltage, tato flux linkage i alo inceaed accoding to imlified tato voltage equation (R = 0: j j ( j (4.3-1 h A flux linkage i excited by tato and oto cuent, magnetizing cuent i inceaed by inceaed tato voltage. nceaed atuation will occu. ( (4.3- h h m Fig.4.3-1: Meaued no-load voltage * veu no-load cuent, which in that ecial cae i identical with magnetizing cuent (70 kw, high-eed ole induction moto, invete oeation at f = 70 Hz, winding in delta connection. * Fundamental hamonic line-to-line voltage veu m-value of no-load cuent. T Damtadt ntitute fo Electical Enegy Conveion

17 Moto develoment 4/17 nduction machine Due to ion atuation (Fig an inceae of 10% voltage, thu an inceae of about of 10% tato flux linkage, mean an inceae of magnetizing cuent of MORE than 10%. At no load thi inceae of magnetizing cuent can eaily be meaued jut by aiing tato voltage (Fig and coeond diectly with inceae of tato cuent, a oto cuent at no-load i zeo. Too low voltage caue a do of beakdown toque by quae of voltage. Examle 4.3-: Rated voltage: 400V, oeational voltage: 360 V, eduction in beakdown toque: M b / MbN ( / N (360 / Beakdown toque M b i educed by almot 0%. f moto i oeated with contant ated load toque M N, li inceae above ated li accoding to Klo function. Klo function in ange of ated (and theefoe mall li may be imlified: R M e 0 : (4.3-3 M b b b b Fo contant electomagnetic toque M e = M N a deceae of beakdown toque by 0.81 (o 19% mean an inceae of li by 1/0.81 (about +5%. Theefoe tato and oto cuent inceae in the ame way, thu inceaing moto winding loe. Concluion: At inceaed voltage tato cuent may ie damatically, if machine i highly atuated. Thi cuent inceae may oveheat moto winding. The inceae of flux caue inceaed ion loe. At educed tato voltage (and theefoe educed moto flux the moto, oeated a ated toque, will conume inceaed cuent, a toque i given by oduct of cuent and flux. nceaed cuent might oveheat winding. Otimum moto deign at ated voltage and ated toque i theefoe minimum cuent conumtion a a balance between flux (and theefoe magnetizing cuent and load cuent (o oto cuent. Accoding to EC moto mut be caable of oeating at ated voltage ±5% ("voltage ange A" and ated owe at a maximum ulu in moto temeatue ie of 10 K above the temeatue ie limit of the ued inulation mateial. At ated voltage ±10% ("voltage ange B" the winding will be oveheated much moe, theefoe no long tem oeation at thee voltage limit i ecommended. Examle 4.3-3: Rated voltage: 400V, Voltage ange A: 400 V ±5% = V. Themal cla of inulation mateial F (EC : Temeatue ie limit fo moto with ated owe below 00 kw: 105 K ove 40 C ambient temeatue. Allowable temeatue ie of winding at voltage limit: 115 K. b Pemium efficiency moto: ndutial electic dive conume a conideable amount of enegy all ove the wold. Examle 4.3-4: n Gemany i an examle fo an indutialized county. Powe conumtion in 004 wa: a Electical enegy conumtion: 18 % of total enegy conumtion = 504 TWh b ndutial electical enegy conumtion: 47 % of a = 37 TWh c Conveion to mechanical enegy: 69% of b = 163 TWh T Damtadt ntitute fo Electical Enegy Conveion

18 Moto develoment 4/18 nduction machine With an aveage efficiency inceae of 4% of electomechanical enegy conveion by e.g. emium efficiency moto, which could be ealized fo 50% of intalled dive owe, one get an enegy aving of TWh = 3.3 TWh e yea (= 8760 h, which amount to owe delivey of a owe lant with 3.3 TWh / 8760 h = 377 MW. Thi value i inceaing, a enegy conumtion inceae. Mot owe lant in Gemany ae themal owe lant. New lant have an otimum efficiency of 50%, e.g. if a combined cycle lant i ued. n thi cae aving of themal inut owe i 754 MW. n eality, many of Geman themal owe lant ae of olde tye with an aveage efficiency of only about 35 %. Theefoe aving would even lead to a eduction of 1077 MW themal inut owe. Concluion: Efficiency imovement of indutial moto ha not only an economical, but alo an envionmental imact. Fig.4.3-: Tyical catalogue efficiency and haft height AH of fou ole induction moto: tandad with nomal efficiency ( , moto with inceaed efficiency ( -moto ( n nited State the Enegy Policy Act (EPACT wa etablihed (1997, demanding that manufactue of tandad induction moto (TEFC elling moto on the S Ameican maket, mut offe -ole and 4-ole quiel-cage induction moto with inceaed efficiency value u to a ating of 90 h.. with edefined value of efficiency at ated oeation. By aiming at - and 4-ole moto in that owe ange the main at of tandad moto alication i included. The meauement of efficiency mut be done accoding to intenational tandad by cetified laboatoy to enue quality tandad. n Euoe eveal moto manufactue had offeed tandad induction moto with inceaed efficiency fo long (Fig. 4.3-, but no legilative act u to now i focing all manufactue to do o. Shotly afte the EPACT the Community of Euoean Moto Manufactue (CEMEP ha ageed on a voluntay ageement with the Commiion of Euoean Community (EC to offe fo the Euoean maket - and 4-ole moto with inceaed efficiency in a imila way a the EPACT demand. Due to the diffeent tandad owe and voltage ating in SA and Euoe (e.g. SA: 460 V, 60 Hz, EC: 400 V, 50 Hz the moto tye with and thei edefined inceaed efficiency value ae lightly diffeent fom EPACT demand. Accoding to thi voluntay CEMEP ageement -and 4-ole moto in owe ange between kw ae available in thee efficiency clae (Fig : T Damtadt ntitute fo Electical Enegy Conveion

19 Moto develoment 4/19 nduction machine Chea tandad moto with uual efficiency value: Standad moto with inceaed efficiency: Pemium efficiency moto at inceaed moto ice: Efficiency cla eff3 Efficiency cla eff Efficiency cla eff1 t i the long tem aim that in the futue only two moto clae will exit: eff and eff1. Since 1999 and 003 aleady a conideable hift in old moto fom cla eff3 to cla eff wa exeienced in Weten Euoe. Fig.4.3-3: Definition of efficiency clae eff1, eff, eff3 fo fou ole tandad induction moto in owe ange kw accoding to voluntay ageement between CEMEP and commiion of EC oe in induction machine ae eaated into tato and oto loe o in no-load and load loe, mainly eddy cuent and hyteei loe in the ion tack, winding and cage loe due to electic cuent flow, fiction loe in beaing and ealing and windage loe due to owe conumtion of haft mounted fan. Stato loe Roto loe No-load loe Coe loe in winding P Cu,0 on loe in ion tack P Fe Additional no-load loe Fiction and windage loe P f+w Additional no-load loe Table 4.3-1: oe in induction machine at no-load and load (ated load oad loe Coe loe in winding P Cu, Additional load loe Cage loe due to oto cuent P Additional load loe Ditotion of ai ga flux denity ditibution by lot oening: - tato and oto tooth flux ulation loe at no-load, being inceaed at load Ste-like ditibution of ai ga flux denity due to aangement of winding in lot: - additional hamonic oto ba cuent, loe inceaed by cuent dilacement due to the athe high fequencie, - additional hamonic cuent in tato winding, - eddy cuent loe in oto uface, if the oto inulation between the ion heet i bidged by the tooling of the oto uface to enue mall mechanical ai ga, The additional hamonic oto ba cuent may flow a inte-ba cuent between adjacent oto ba, eecially when the oto i kewed, becaue thee i uually no inulation between oto ion tack and oto ba. on atuation caue alo deviation of ai ga flux denity fom ideal inu, mainly by intoducing an additional thid ace hamonic, which i inducing - additional hamonic oto cuent in the cage at load - ciculating tato cuent in delta connected tato winding, Flux denity leave ion tack at the tack end axially, enetating the end heet. Theefoe adial tack lamination cannot ue eddy cuent flow, thu - additional ion loe in the end heet due to axial flux comonent occu Magnetic flux i not contained only to ion tack and ai ga, but a cetain tay flux enetate alo maive metallic (conductive at uch a houing and haft, cauing - additional eddy cuent loe in maive metallic at Table 4.3-: Ove-view on main comonent of additional loe. T Damtadt ntitute fo Electical Enegy Conveion

20 Moto develoment 4/0 nduction machine n oto fequency at no-load i almot zeo and at load it i mall (e.g. ated li: 5%, tato fequency: 50 Hz, then oto fequency i f f Hz, o nealy no oto ion loe (eddy cuent loe and hyteei loe in oto ion tack will occu. Additional loe (tay load loe ae caued mainly by the fact that the ai ga flux denity i not ditibuted like an ideal inu flux denity wave, but athe te-like due to the aangement of winding and cage in lot. Thu additional high-fequency tato and oto cuent ae induced, cauing additional loe. Thee exit a lot of futhe eaon, why thee additional loe may aie and can become athe ignificant, eecially at high eed moto (Table Powe flow in moto i accoding to Chate 4. given by electic tato inut owe P in, which feed tato winding loe P Cu, and tato coe loe P Fe. Stato additional loe at no-load ae uually included in tato coe loe in tandad meauement accoding to EC Powe flow fom tato to oto via ai ga P = P in - P Cu, P Fe i feeding oto cage loe (li loe P and fiction and windage loe P f+w. Remaining owe may eaated into mechanical outut owe P out, diectly meaued via the haft toque e.g. with a toquemete and eed P n M and additional load loe P ad1 = P - P - P out. out Examle 4.3-4: Meaued lo balance of a.55 kw, 8-ole, totally encloed induction moto with haft mounted fan (EC : ambient temeatue 0 C, winding temeatue ie: 61.5 K Sli at ated owe.55 kw N = 4.44 % Seed / toque n / M 860 /min / 8.4 Nm Meaued electical inut owe P in 354 W Stato coe loe P Cu, 385 W (55 % Stato ion loe P Fe 133 W (19 % Roto cage loe P P 11 W (17 % Additional load loe P ad,1 47 W (7 % Fiction and windage loe P f+w 14 W ( % Total loe P d 700 W (100 % Outut owe P out 554 W Efficiency % Table 4.3-3: Examle of meaued lo balance and efficiency of a Themal Cla B 8-ole induction moto at 60 Hz, 440 V Y accoding to "diect" method a of EC at ated load Pleae note, that efficiency of on ecific moto vaie with load. At no-load outut owe i zeo, theefoe efficiency i zeo. Conideing no-load loe P d0 a indeendent fom load, and load loe P d1 a caued by coe loe in winding and cage: Pd 1 ~, ~, one get a imle lo model fo etimating change of efficiency with load (Fig.4.3-4: - Moto flux deending on voltage and fequency, which ae both fixed, o flux i contant - No-load loe P d0 indeendent of moto load M - Moto load M deend on flux and cuent, o vaie linea with cuent - oad loe P d1 mainly ohmic loe in tato and oto, deending on quae of cuent d0 cont Pd 1 ~ ~ P., M Pout Pout PN ( M / M N (4.3-4 P P P out d0 d1 T Damtadt ntitute fo Electical Enegy Conveion

21 Moto develoment 4/1 nduction machine d0 k0 PN Pd 1 k1 PN ( M / M N, Pd 1N k1 P, P (4.3-5 Otimum (maximum efficiency i given fo d / dm 0, yielding the eult: N M M N P ot d0 / Pd 1N / (4.3-6 At thi load oint the no-load loe and the load loe ae equal: Pd 0 Pd 1, yielding a maximum oible efficiency of Pd 0 / Pd 1N max. (4.3-7 P / P ( P / P d0 d1n d0 N Fig.4.3-4: Vaiation of loe P d and efficiency with outut owe P out. Hee it i aumed that no-load loe ae contant and 0.1P N, load loe at ated owe ae 0.14P N and vay with the quae of outut owe Examle 4.3-5: Efficiency vaie with vaying load: d 0 0 N d1 N N 0 1 Moto data: P.06 P, P 0. P ( M / M, k 0.06, k 0. m m m, m M / M N oad M/M N Efficiency % % % % Table 4.3-4: oad deending efficiency at contant voltage line uly Hee: M / M N 0.06 / , Pd 0 Pd PN, max ot 0.06 / / Concluion: n ode to inceae moto ated efficiency, moto utilization (Powe/volume mut not exceed a cetain limit in ode to get ated efficiency at the otimum value. At othe load oint (highe o lowe load efficiency will deceae. T Damtadt ntitute fo Electical Enegy Conveion

22 Moto develoment 4/ nduction machine How can maximum efficiency be inceaed fo a cetain moto? - By uing low lo ion heet ion loe ae be educed (e.g. 1.7 W/kg intead of.3 W/kg. - By uing coe intead of aluminium cage oto conductivity ie by 57/34 = 167%, thu educing oto eitance and loe. - By inceaing lot numbe e ole and hae q (e.g. fom 3 to 4 the numbe of te of the ai ga flux denity ditibution i inceaed by 4/3, but the te itelf get malle by 3/4. Hence the flux denity ditibution i moe inuoidal, and the additional loe ae educed. - nceae of lot numbe alo inceae the cooling uface of winding, a the winding uface towad ion i inceaed accoding to the lot uface. Thu the temeatue ie of winding i educed, and theefoe the winding eitance i lowe, leading to lowe loe (and a longe life an of inulation mateial. Concluion: A lot of ule exit to inceae efficiency, but uually all thee meaue inceae moto manufactuing cot. So moto with inceaed efficiency ae uually moe exenive. Examle 4.3-6: nfluence of winding temeatue on efficiency fo a 8-ole moto,.55 kw, 60 Hz, 440 V: Temeatue ie 60 K 105 K Wam hae eitance 4.11 Ohm 4.7 Ohm Sli at ated owe.55 kw 4.44 % 5.05 % Seed / toque 860 /min / 8.4 Nm 854 /min / 8.6 Nm nut owe 3198 W 368 W Stato coe loe 380 W 434 W on loe 133 W 133 W Roto cage loe 11 W 137 W Fiction and windage loe 14 W 14 W Outut owe 550 W 550 W Efficiency % % Table 4.3-5: Reduced efficiency due to inceaed temeatue ie caued by infeio cooling, ambient 0 C 4.4 Sace hamonic effect in induction machine Although time vaiation of tato voltage and cuent i inuoidal due inuoidal gid uly, atial ditibution of flux denity in ai ga i NOT, a winding i located in lot. So the atial ditibution of flux denity i NDEPENDENT of the kind of time vaiation of feeding winding cuent. t deend ONY on winding aangement in lot and ai ga geomety. n Chate only effect of fundamental ine wave of ai ga flux denity ditibution wa conideed. n eality alo the highe ace hamonic of tato and oto field ditibution have to be conideed to undetand meaued toque-eed cuve of induction machine. Fo imlification influence of lot oening will be neglected hee. With lot with infiniteimal mall lot oening the ai ga flux denity i te-like ditibuted, a exlained in Chate 1 fo tato and in Chate 4. fo oto field Field ace hamonic and cuent time hamonic at inuoidal tato voltage a Stato field atial hamonic: Sinu time-function of tato voltage caue inu time-function tato cuent to flow in tato winding. Fouie analyi of tato ai ga field of a m -hae (uually thee-hae T Damtadt ntitute fo Electical Enegy Conveion

23 Moto develoment 4/3 nduction machine tato winding concentated in tato cuent ytem with hae hift Q m q tato lot, fed by a time-inuoidal m -hae / m between hae, amlitude and fequency f, yield following eult: The te-like ai ga flux denity ditibution B ( x,, t along tato cicumfeence co-odinate x can be eeented by an infinite um of inu atial-ditibuted flux denity wave. Summing index i the odinal numbe. With inceaing wave length, wave eed v f and amlitude B, ae deceaing. B x, ( x, t B, co( t f 1 ( Fo m = 3: 1 m g = 1, -5, 7, -11, 13, -17,... ( (g: intege numbe: g 0, 1,, 3,... B, 0 m N k w, (no ion atuation conideed ( / ( The altenatively changing ign of odinal numbe indicate that wave move altenatively with fundamental in the ame diection (clockwie o in ooite diection (counte-clockwie. No even odinal numbe occu, a flux denity ditibution i ymmetical to abcia. Thi mean, the hae of noth and outh ole of flux denity ditibution i identical. No odd odinal numbe dividable by the hae numbe occu due to the ditinct numbe of hae. Winding facto k w, i defined by ditibution facto k d,, which conide how many lot e ole q ae occuied by one hae, and by itch facto k,, which conide if an e coil W equal ole itch o not. k k k ( w,, d, k d, in( m, q in( m q W k, in ( Examle : Fouie analyi of flux denity ditibution of a thee-hae, fou ole, two-laye winding with q =, W/ = 5/6. Winding and ai ga data: 1mm; tun e coil N c 5 ; all coil e hae connected in eie, o numbe of aallel winding ath i a = 1; boe diamete d i = 80 mm; hae cuent (.m.: = 30 A. We get: Q / = 1 lot e ole ai, ole itch: /( 6. 8 mm and tun e hae: N q N / a 4 5/1 40 c. Flux denity amlitude of fundamental: 7 0 m kw, B, 1 N d i 0.95T T Damtadt ntitute fo Electical Enegy Conveion

24 Moto develoment 4/4 nduction machine Relative amlitude winding facto wave eed at f = 50 Hz B / B 1 (% k, k d, k w, v (m/ Table : Fouie analyi of tato atial ai ga flux denity ditibution, excited by a thee-hae, fou ole, two-laye winding with q =, W/ = 5/6, delive a um of tavelling flux denity wave in the ai ga Fig : Ai ga flux denity at t = 0 ( i, i i / and fundamental and fit lot hamonic wave fo q =, W/ = 5/6. V W Fig how the coeonding flux denity ditibution, Fig the one fo q =, but W/ = 1, which i the cae fo ingle-laye winding. Obviouly Fig fit bette to a inu than Fig , which i accomlihed by the choding (itching of the coil an. Due to thi choding the winding facto fo 5 th and 7 th ace hamonic i almot zeo, again fo 17 th, 19 th, and o on, wheea fo 11 th, 13 th, 3 d, 5 th, and o on, winding facto i the ame a fo fundamental. Theefoe thee wave amlitude (o-called "lot hamonic" dominate the wave ectum. Thei odinal numbe i 1 Q g (g: intege numbe: g 0, 1,, 3,..., ( T Damtadt ntitute fo Electical Enegy Conveion

25 Moto develoment 4/5 nduction machine yielding hee = -11, 13, -3, 5,... Thee hamonic ae caued by the te in ai ga ditibution (ee Fig , o the aveage value of wave length of the fit ai of lot hamonic i equal to lot itch (te length. Examle : Winding: q =, W/ = 5/6, lot itch / 1. Odinal numbe of fit ai of lot hamonic: = -11, 13 Wave length of fit ai of lot hamonic: /11, / 13 Q Aveage value of wave length: ( 13 / / Concluion: Wave ectum of ai ga flux denity ditibution i dominated in choded two-laye winding (aat fom fundamental by lot hamonic wave. n unchoded ingle-laye winding alo the 5 th and 7 th hamonic mut be conideed. b Roto cage field atial hamonic, excited by oto cuent : Stato fundamental field = 1 move with ynchonou velocity v yn f f (o 1 ynchonou eed n yn, eectively, wheea oto i tuning with eed n, defining li ( n n /. Theefoe tato fundamental flux linkage with oto cage change with yn n yn oto fequency f f, inducing inuoidal oto voltage i, accoding to Faaday law. Thi voltage, a hown in Chate 4., caue the inu time-function oto cuent, to flow in adjacent ba with hae hift / Q, exciting alo a te-like ai ga flux denity ditibution B, ( x, t along oto cicumfeence co-odinate x. t can in the ame way be eeented by an infinite um of inu atial-ditibuted flux denity wave. Summing index i the odinal numbe. With inceaing wave length and wave eed v f i deceaing, amlitude B ae alo deceaing with 1/. A each ba eeent a oto hae, (m = Q, coniting of 1/ tun e hae (N = 1/, winding facto i alway unity (k w, = 1. Thu, we adot ( fo oto cage: B x, ( x, t B, co( t f 1 ( ( / g (g: intege numbe: g 0, 1,, 3,... ( Q 0 Q 1 1 B, (no ion atuation conideed ( ( The altenatively changing ign of odinal numbe indicate again that wave move altenatively with fundamental in the ame diection (clockwie o in ooite diection (counte-clockwie. A each ba eeent a hae, each atial hamonic i a lot hamonic. Equation fo odinal numbe ( and ( ae identical. Wave velocitie with eect to oto ae T Damtadt ntitute fo Electical Enegy Conveion

26 Moto develoment 4/6 nduction machine v f f / v. ( , yn / With eect to tato we ee that oto co-odinate x lu the ditance of oto uface movement give coeonding tato co-odinate x. A oto uface velocity v m i given by li o oto eed n nyn ( 1 eectively: vm ( 1 vyn (1 f, we get x x v t ( m and B ( x vmt ( x, t B, co( t B, x co(, t Theefoe eed of oto ace hamonic with eect to tato i v ( (1. ( v v v (1 /. ( , m yn Examle : Fouie analyi of flux denity ditibution of a cage with 8 oto ba, exciting a fou ole field ditibution. Stato fequency i 50 Hz. Winding and ai ga data: 1mm; N c 1/ ; boe diamete d i = 80 mm; ba cuent (.m.: = 40 A, li: = 5%. We get: Q / = 14 lot e ole ai, ole itch: /( 6. 8 mm, v m = 5.97 m/. Flux denity amlitude of fundamental: B 7 0, 1 Q d i T elative winding facto wave eed with eect amlitude to oto to tato B B (% k w, v, (m/ v / Table : Fouie analyi of oto atial ai ga flux denity ditibution, excited by oto cuent, which i induced by fou ole tato fundamental field (tato fequency f = 50 Hz Concluion: All oto ace hamonic excited by oto cuent - ae lot hamonic, containing theefoe le hamonic than tato field. Roto field fundamental un indeendently of oto eed - ynchonouly with tato field fundamental, thu oducing the contant aynchonou toque M e at any eed. Thi i the toque decibed by Klo function in Chate 4.. Thi oto fundamental induce tato theefoe with tato fequency f with the voltage M i,. T Damtadt ntitute fo Electical Enegy Conveion

27 Moto develoment 4/7 nduction machine c Stato hamonic cuent, induced by oto cage field atial hamonic: Roto ace hamonic 1 induce tato accoding to ( with fequency f, f (1, ( cauing mall additional tato time-hamonic cuent to flow, which uually ae hamle and theefoe mot often ae neglected in futhe conideation. Nevethele, if aynchonou machine i ued a a geneato, thee cuent have to be conideed a they ditot total tato cuent and may caue electomagnetic intefeence with telecommunication line (EM. Only oto ace hamonic can induce the tato winding. Fo the induced tato voltage i zeo due to the tato winding aangement. Examle : Fequencie of hamonic tato cuent, induced by oto flux denity ace hamonic ditibution: 4-ole moto with data of Examle : Cage with 8 oto ba, tato fequency: 50 Hz, li Fequency of tato cuent hamonic tato winding induced? f, / Hz Ye: Ye: No: No: Ye: 9 Table : Fequencie of hamonic tato cuent, induced by oto flux denity ace hamonic ditibution (tato fequency f = 50 Hz Concluion: A oeational li i uually mall ( 0, fequency of tato hamonic cuent may be etimated fo zeo li, howing that thi fequency i ootional to oto lot numbe. f f f 1 g Q / f g Q, / Examle : Meaued tato cuent including hamonic tato cuent, induced by oto flux denity ace hamonic ditibution. -ole moto, 3 kw, 380 V Y, 50 Hz, 6. A, cage with oto ba, ated li Stato line-to-line eak voltage value: V (meaued: 535 V - Stato cuent eak value: A (meaued: 8.84 A Odinal numbe of oto ace hamonic: 1 / 1 /1 1, 3 Coeonding tato cuent hamonic fequencie: 1: 1: Thi ace hamonic doe not induce the tato winding! 3 : 3: f 50 3 ( Hz Q, T Damtadt ntitute fo Electical Enegy Conveion

28 Moto develoment 4/8 nduction machine Fig : oaded -ole 3 kw cage induction moto at inuoidal voltage uly: a Meaued tato line-toline voltage, b meaued tato hae cuent, howing tato hamonic cuent with 1095 Hz (oughly x50 Hz d Hamonic oto ba cuent, induced by tato atial field hamonic: Stato ace hamonic 1 move with velocity v f v yn / (o eed nyn, nyn / much moe lowly than oto. Sli of thee hamonic (hamonic li i nyn, n 1 (1 ( n yn, Thee tato ace hamonic theefoe induce oto cage with fequency f, f f 1 (1, ( cauing mall additional oto time-hamonic ba cuent, to flow. A ole numbe of the tato hamonic i ba cuent i / Q., hae hift between adjacent hamonic T Damtadt ntitute fo Electical Enegy Conveion

29 Moto develoment 4/9 nduction machine Examle : Cage induction moto, tato fequency 50 Hz, no-load = 0. Roto cage with 8 ba, induced by tato ace hamonic = ( Hamonic li 6 5 Roto cage hamonic fequency: f f Hz, 5 Phae hift between adjacent ba cuent: 360 / Q 360 ( 5 / Roto ba cuent: Ba 1 Ba Ba 3 Ba 4 etc. i ˆ co( t ˆ co( t ˆ co( t ˆ co( t 3... Roto ba cuent i / ˆ e.g. at t = 0: Ba Fig : The cage oto eact to 10-ole inducing tato field wave with a ten ole oto field: The 5 th tato hamonic ( = 10 ole e fundamental ole ai induce in the cage (7 ba/ole oto hamonic ba cuent with hae hift (5/7, which excite accoding to Amee law a 10-ole oto field ditibution. A numbe of ba e 10 ole i only 1.4, the aoximation of inu cuve by cage field i athe coae, but contain a 10- ole Fouie fundamental, which fit to the 10-ole tato inu field wave. Concluion: Roto hamonic ba cuent excite a te-like ai ga field with a fundamental of the ame ole numbe a the inducing tato field hamonic:. Amlitude of thi fundamental i calculated with the ame Fouie fomula ( , but now conideing a exciting cuent. 0 Q 1 1 B,, (no ion atuation conideed ( Q g g 0, 1,,... Roto ba hamonic cuent can be calculated by taking the ame oto voltage equation of Chate 4., but conideing now the aamete of the -th tato ace hamonic. T Damtadt ntitute fo Electical Enegy Conveion

30 Moto develoment 4/30 nduction machine u k N d, ( t M dt i, w di / dt ( Flux e ole of -th tato ace hamonic i mall, - a ole itch i malle by 1/ than fundamental, - a flux denity amlitude i malle by k w, / intead of kw than fundamental amlitude. Thu hamonic flux e ole, i malle by facto k w, /( k w than fundamental flux, theefoe alo mutual and elf inductance of ai ga field i deceaed by thi facto. M N k 0 w N k w, m l Fe ( i, j M. ( The Fouie ace fundamental of oto flux denity ditibution 5 (Fig induce oto cage with oto fequency due to elf-induction with voltage i,. i, j h h m l Fe 0( Nkw. ( So finally oto voltage equation i deived, conideing alo elf-induced voltage by tay flux of lot and winding ovehang (inductance, voltage do due to eitance R, and that oto i hot-cicuited: = 0. 0 R j j j M ( h With m Q, N 1/ and ( m Nkw / Q h M we get fo the oto hamonic cuent (m Nkw / Q j R / j ( h h, ( which coeond with an equivalent cicuit Fig a fo oto cage, which cloely eemble to T-equivalent cicuit, but whee now hamonic li i intoduced. But note: Fig how, that the actual te-like field ditibution diffe conideably fom the fundamental, o a moe thoough analyi conide alo the elf-induction in the oto cage not only fom the oto fundamental, but alo the elf-induction fom all othe Fouie ace hamonic of the oto field. Thu the elf-induction voltage ( i enlaged by a facto 1/ (which i not oven hee: in( / Q ( / Q Thi additional hamonic elf-induction voltage i, j h (1/ 1 i uually conideed in ( by adding it to the tay inductance (Fig b: T Damtadt ntitute fo Electical Enegy Conveion

31 Moto develoment 4/31 nduction machine 1/ h 1. th hamonic leakage : 1/ 1 h ( (m Nkw / Q j R / j ( h h, ( a b Fig : Equivalent cicuit fo oto cage fo -th tato ace hamonic, to calculate oto cuent time hamonic a without and b with conideing elf induction of all oto ace hamonic excited by Examle : th hamonic leakage : Fou-ole cage induction moto, f = 50 Hz, oto cage with 8 ba, n yn = 1500/min (i How big i the inceae of oto elf induction voltage due to all oto ace hamonic? / (ii At which oto eed n i the oto cage NOT induced by-th tato ace hamonic? f f f 1 (1 0 11/ n n /, yn n /1/min Concluion: Neglecting elf induction of oto ace hamonic fo calculating oto hamonic cuent yield nealy no eo fo fundamental oto cuent of baic theoy Chate 4., but conideable eo fo highe hamonic; o it mut be conideed. n the low eed egion between +/ 0% ynchonou eed fo each tato field hamonic thee exit a oto eed, whee oto cage i not induced by that hamonic. f nfluence of main flux atuation on tato field atial hamonic: to now influence of atuation of ion on hamonic ha been neglected. natuated inu ace-function of tato fundamental B,=1 (x i ootional 1/. Magnetic field tength i H B / 0. When ion i unatuated, H Fe i zeo, o total amee tun of tato ae needed only to magnetize ai ga, yielding m.m.f. V H. n cae of ion atuation at high B magnetic field tength in ion along ion ath Fe i not any longe zeo, yielding V H HFe Fe. So ai ga field tength and ai ga flux denity do not ie any longe linea with inceaing V (Fig So if we conide only fundamental of tato ai ga field, coeonding with inuoidal ditibuted m.m.f. V ( x V co( x / t, T Damtadt ntitute fo Electical Enegy Conveion

32 Moto develoment 4/3 nduction machine the ai ga flux denity ditibution i flat-toed, which may be decibed by a um of a fit and 3 d hamonic. Concluion: on atuation caue a ditotion of ai ga flux denity ditibution, geneating a thid hamonic field wave. B 3x 3( x, t B, 3 co( 3 ( , t Thid "atuation hamonic" move with ynchonou eed a fundamental, theefoe it induce tato winding with 3-time tato fequency, which i N PHASE in all thee hae. n ta connected winding only hae voltage will how a 3f voltage comonent, wheea in line-to-line voltage thi comonent i cancelling (ee Chate 1. Cuent with 3f cannot flow in ta connected winding, but in delta winding it will flow a a cicling cuent within then delta, cauing additional winding loe. a b Fig : Geneation of thid ace hamonic of ai ga field ditibution due to ion atuation With eect to oto ( x B x f (1 t thi wave i moving with 3x 3( x, t B, 3 co( 3, ( , t inducing the oto with additional loe. 3 f, cauing additional oto hamonic cuent 3 with 4.4. Hamonic toque a Aynchonou hamonic toque: Roto hamonic cuent oduce not only additional cage loe, but alo due to oentz foce with tato field hamonic B additional toque, which i called "aynchonou T Damtadt ntitute fo Electical Enegy Conveion

33 Moto develoment 4/33 nduction machine hamonic toque". Fo the ecial cae = 1 thi i the aynchonou toque of Klo function. With the ame mechanim of - tato (hamonic field inducing oto (hamonic cuent and - oto (hamonic oducing toque with tato (hamonic field the aynchonou hamonic toque i calculated. Powe balance of equivalent cicuit Fig yield hamonic ai ga owe P, tanfeed to oto, mut be equal to oto hamonic cage loe P Cu, and mechanical owe P m due to aynchonou hamonic toque M e. P P Cu, P ( m Fig : Aynchonou hamonic of 5 th and 7 th tato field hamonic, which ae ueimoed on fundamental aynchonou toque. Data: R /X =1/100, R /X = 1.3/100, = 0.067, X = X = 3Z N, Z N = N / N, 36 tato and 8 oto lot, 4 ole machine, ingle laye winding (unchoded coil, unkewed lot Fom equivalent cicuit Fig we ee: P ( R / Q, Cu, Q R P (4.4.- Theefoe we get fo aynchonou hamonic toque M e fom P m mme ( 1 yn, M ( and by comaion of (4.4.-, ( finally the toque itelf: M e 1 e 1 Q R P m Q R ( 1 yn, (1 yn, yn,. ( By taking the abolute value of, fom ( , aynchonou hamonic toque i given deending on the quae of tato cuent and on li : M e (m Nk Q w ( yn, h R ( ( R h ( T Damtadt ntitute fo Electical Enegy Conveion

34 Moto develoment 4/34 nduction machine Aynchonou hamonic toque follow a Klo function, deending in hamonic li. At = 0 thi toque i zeo. At > 0 toque i oitive and add to fundamental toque. At < 0 the toque i negative and i baking the machine. At hamonic beak down li b R ( ( h toque eache oitive and negative maximum value. A h R hamonic beakdown li i mall, maximum toque value ae neaby the zeo value. Hamonic aynchonou toque ae excited by each tato field hamonic and ae ueimoed the fundamental aynchonou toque (Fig b Synchonou hamonic toque: Roto field hamonic of te-like ai ga flux denity ditibution ( , excited by oto fundamental cuent, will alo oduce aaitic toque with tato field hamonic. ike aynchonou hamonic toque, the condition fo contant toque geneation i (i ame wave length, (ii ame velocity (mean alo: ame diection of movement of tato and oto field wave. Fo aynchonou hamonic thee two condition wee alway fulfilled, a oto cuent ditibution and it excited oto field wave wee induced (geneated by tato field wave, thu having the ame wave length and velocity. Fo highe hamonic of oto field Fig thee condition ae only fulfilled at cetain oto li = *: Stato hamonic field (excited by : Roto hamonic field (excited by : x x B, co( t B, ~ B, co( t B, ~ (i dentical wave length: (ii dentical velocity: (with eect to tato o v v vyn ( 1 / v yn / Fom v v one get: v yn / v yn (1 * * / condition fo li whee ynchonou hamonic toque occu: * 1/ 1, eulting in the 1/ 1 : : * 1 1 * 1 ( f tato and oto lot numbe i the ame, then lot hamonic of tato and oto have DENTCA odinal numbe =, yielding to big ynchonou hamonic toque at tand till of moto = 1, which i known a tand till cogging (Fig a. Theefoe fo electic moto uually it mut be Q Q. But even in thi cae fo cetain hamonic ( i fulfilled. At cetain li * 1and theefoe only at cetain moto eed n* tato and oto field hamonic will ceate a contant toque M e, with it amlitude ootional to amlitude of the two eacting field wave: M e ~ B, B, ~. A thi hamonic toque occu only a cetain eed whee tato and oto field hamonic move with identical T Damtadt ntitute fo Electical Enegy Conveion

35 Moto develoment 4/35 nduction machine eed (moving "ynchonouly", thi kind of hamonic toque i called ynchonou hamonic toque. f the hae hift (Fig b between the two wave i 0 o 180, both wave have aligned N- and S-ole, o no toque will occu. Thi i the ame ule a with ynchonou machine. Thu hae hift angle may be egaded a load angle, yielding fo ynchonou hamonic toque M ~ in ( e At = 90 toque i maximum oitive, o toque will add to aynchonou toque, at = -90 toque i maximum negative and act a a bake. A hae hift i an abitay value, deending fom which oition of oto elative to tato the machine wa tated, all oible toque value between M e, max... Me may occu., max a b Fig : a f tato and oto teeth numbe i the ame, cogging will occu, eeenting a ynchonou toque =, b Geneation of ynchonou hamonic toque by a -th tato and -th oto field hamonic, tavelling in ai ga with ame eed and having ame wave length Fig : nduction moto 15 kw, 4-ole, 36/8 lot numbe atio: With finite element calculated M(n- chaacteitic with aynchonou toque at 136/min and ynchonou toque at 15/min T Damtadt ntitute fo Electical Enegy Conveion

36 Moto develoment 4/36 nduction machine Examle : 4-ole cage induction moto, 380 V, D, 50 Hz, 15 kw, ated toque M N = 100 Nm, unkewed lot, Q /Q = 36/8, ai ga 0.45 mm, ion tack length 195 mm, tato boe diamete 145 mm, two-laye winding. Toque calculated with finite element: (i Aynchonou hamonic toque due to = -11 tato field hamonic with ynchonou hamonic li 0 at li 11/ 11/ , coeonding with eed n ( 1 n ( / min. yn (ii Synchonou hamonic toque at li Which field hamonic geneate thi toque? Analyi: Stato odinal numbe: 1 m g 1 6g 1, 5,7, 11,13, 17,19,... Roto odinal numbe: 1 ( Q / g 114g 1, 13,15, 7,9,... * 1 1 Condition fulfilled fo 13 : n* (1 * /min 1 14 c Satuation caue additional hamonic toque: The 3 d tato hamonic atuation wave caued an additional oto hamonic cuent to flow 3 with fequency 3 f, which excite itelf a oto field with oto hamonic with odinal numbe Q g, g 0, 1,,.... ( Thee additional oto hamonic may be ufficient big to geneate with tato field hamonic additional ynchonou hamonic toque. Condition ae again: Stato hamonic field (excited by : Roto hamonic field (excited by,=3 : x x B, co( t B, ~ B, co( 3 t B, ~, 3 (i dentical wave length: (ii dentical velocity: (with eect to tato o v v vyn ( 1 3 / v yn / Fom v v one get fo li, whee hamonic ynchonou toque occu, caued by atuation hamonic: * 1/ 1, : ( / 1 Examle 4.4.-: -ole cage induction moto, 380 V, D, 50 Hz, 11 kw, ated toque M N = 37 Nm, kewed lot, Q /Q = 36/8, inulated coe cage to avoid flow of inte-ba cuent, two-laye tato winding, winding itch 1/. Shaft toque meaued with acceleomete (Fig a; moto with additional inetia mounted to haft wa eveed fom 3000/min to 3000/min by changing two hae connection, thu allowing to meaue moto toque in li ange T Damtadt ntitute fo Electical Enegy Conveion

37 Moto develoment 4/37 nduction machine (i Aynchonou hamonic toque due to = -5 tato field hamonic with ynchonou hamonic li 0 at li 11/ 11/ 5 1., coeonding with eed: n ( 1 n ( / min. yn (ii Synchonou hamonic toque at li 1.07 and Which field hamonic geneate thee toque comonent? Stato odinal numbe: 1 m g 1 6g 1, 5,7, 11,13, 17,19, 3,5, 9,31, 35,37,... Roto odinal numbe of : 1 ( Q / g 1 8g 1, 7,9,... Roto odinal numbe of,=3 : 3 ( Q / g 3 8g 3, 5,31,... 11/ 5 11/ 9 Condition fulfilled: 5 : * , 9 : * / 5 11/ 9 11/ 31 31: * / 31 Fig : Meaued tating toque with acceleomete of induction machine with inulated coe cage, f = 50 Hz, 380 V: a -ole moto, 11 kw, M N = 37 Nm, 36/8 tato/oto lot, b 4-ole moto, 9.5 kw, M N = 64 Nm, 36/8 tato/oto lot Examle : 4-ole cage induction moto, 380 VD, 50 Hz/9.5 kw, ated toque M N = 64 Nm, kewed lot, Q /Q = 36/8, inulated coe cage (= no inte-ba cuent, unchoded tato winding. Shaft toque meaued with acceleomete like in Examle (Fig b. (i Aynchonou hamonic toque due to = -17 tato field hamonic with ynchonou hamonic li 0 at li 11/ 11/ (ii Synchonou hamonic toque at li 1.9 and Fom which field hamonic ae thee toque comonent geneated? Stato odinal numbe: 1 m g 1 6g 1, 5,7, 11,13, 17,19, 3,5, 9,31, 35,37,... Roto odinal numbe of : 1 ( Q / g 114g 1, 13,15, 7,9... Roto odinal numbe of,=3 : 3 ( Q / g 3 14g 3, 11,17, 5, /11 Condition fulfilled fo: 11: * /11 T Damtadt ntitute fo Electical Enegy Conveion

38 Moto develoment 4/38 nduction machine 11/ 5 5 : * / 5 11/17 17 : * /17 The ynchonou hamonic toque in thi examle can only be exlained by conideing ion atuation Roto kew and inte-ba cuent a Skewing of oto cage Slot hamonic effect can be ueed o educed by - two-laye tato winding with choded coil. f e.g. a choding of 5/6 of coil an i ued, then 5 th and 7 th tato hamonic ae educed tongly. - emi-cloed tato and oto lot, magnetic wedge in oen tato lot o cloed oto lot. - kewing of lot. A tato kew i exenive, uually oto cage i kewed. Fig : Due to kew of oto ba b k cetain tato field hamonic cannot induce oto Accoding to Faaday law induced voltage i in a ba with length l, moving in an extenal magnetic field B eendicula to field diection with velocity v v yn, v i given by m i v B l. ( f kew of oto ba b k i equal to wave length / of tato field hamonic, the fit half of oto ba will be induced by oitive field with oitive voltage /, and econd half by negative field and theefoe with voltage /, eulting in zeo voltage fo whole ba. Thu no hamonic cuent fo that -th hamonic will be geneated. Thi may be exeed by kewing facto in S b S k,, ( S which i zeo fo bk and multile of it. Thu oto hamonic cuent ae calculated by taking the fomula of Chate and multily it with kewing facto: T Damtadt ntitute fo Electical Enegy Conveion

39 Moto develoment 4/39 nduction machine (m Nkw / Q j R / j ( h h Concluion: f the oto cage i kewed by one tato lot itch induce the oto only negligibly. bk ( , then all tato lot hamonic will Examle : 4-ole induction moto with 36/8 tato/oto lot. Roto cage kewed by one tato lot itch: b / 9 k Stato field hamonic: Odinal numbe: 1 6g 1, 5,7, 11,13, 17,19, 3,5, 9,31, 35,37,... Slot hamonic: 1 (36 / g 1, 17,19, 35,37, Table : Skewing facto fo tato lot hamonic, if oto cage i kewed by one tato lot Fig : Skewing of oto ba b k lead alo to kew of oto field hamonic, excited by oto cuent. So hae hift between tato and oto field hamonic vaie along ba length and lead to cancelling of ynchonou lot hamonic toque. Hamonic ynchonou toque i alo educed tongly by kewing. The oto field hamonic of the oto field, excited by oto cuent, ae a exlained all of lot hamonic ode. f oto i kewed by one tato lot itch, alo the oto lot hamonic flux wave ae kewed in the ame way (Fig Fo tato lot hamonic theefoe hae hift angle vaie between along oto ba length. Aveage hamonic toque oduction i theefoe zeo. T Damtadt ntitute fo Electical Enegy Conveion

40 Moto develoment 4/40 nduction machine 180 M e ~ in d 0 ( Concluion: Skewing by one tato lot itch leave the fundamental field almot unaffected, but nealy cancel the inducing effect of tato lot hamonic. Theefoe aynchonou hamonic toque comonent due to tato lot hamonic ae minimized effectively. Skewing geneate alo vaiable hae hift between tato and oto field wave, thu allowing cancelling of ynchonou hamonic toque. n ode to avoid ditotion of fundamental aynchonou toque M(n-chaacteitic by hamonic toque effect, cage oto of line-tating induction machine ae alway kewed, uually by one tato lot itch. b oe due to inte-ba cuent: Roto ba ae uually not inulated, but have electical contact to ion tack. A numbe of tun e winding (= e ba i only 1/, induced voltage i low, o no big voltage diffeence between cage and ion occu. Along oto cicumfeence induced voltage vaie inuoidal, o total oto otential a aveage value of voltage inu ditibution i zeo. Moeove, only with coe ba, ineted manually in oto lot, cage inulation i oible, wheea with aluminium die cat cage uually not. By the way, between ion tack and coe o aluminium ba, oxidation of ion will caue additional contact eitance, which can be meaued a inte-ba eitance R q between adjacent ba accoding to Fig So by natue itelf, oto ba ae inulated to a cetain extent. f A denote the half-uface of a oto ba, the inte-ba eitance i malle, if A i bigge. R q lox A ox ( Neglecting the good conducting ion and coe o aluminium at, inte-ba eitance i detemined by thickne of oxidation laye l ox between ba and ion and conductivity of thi oxide ox. A tyical value fo aluminium die cat cage i q 6 l / 10 m, ( ox ox fom which inte-ba eitance i calculated by R A. q q / Fig : nte-ba eitance between adjacent ba R q i much bigge than ba o ing eitance, a it i detemined by oxidation of ion tack and ba uface. a nte-ba cuent flow via half ba-uface A duing oeation, b Duing meauement cuent flow via A, hence we obtain: R q = (/ R ba - R ing. T Damtadt ntitute fo Electical Enegy Conveion

41 Moto develoment 4/41 nduction machine a b c Fig : Effect of inte-ba eitance due to oxidation R q : a nkewed cage: inte-ba cuent i almot zeo, b Roto cage kewed by one tato lot, tato and oto lot numbe equal Q =Q : hamonic inte-ba cuent almot zeo, c a b, but Q =Q /1.5; hamonic inte-ba cuent may flow, a hamonic voltage add u. n unkewed oto cage voltage diffeence i1 along the oto ba i contant. So the two low-ohmic ing egment eitance R ing ae in aallel with high-ohmic inte-ba eitance R q. Cuent will flow fom one ba to next nealy only by ing egment a ing cuent. Nealy no inte-ba cuent via R q will occu (Fig a. n kewed oto with b k = hamonic voltage induced by -th tato lot hamonic - conideed along the loo of two ba and two ing egment, i zeo. No hamonic ba o ing cuent will flow. n eence of finite inte-ba eitance an additional cuent flow along dahed line in Fig b, c i oible. f tato and oto lot numbe i the ame (which i fobidden to avoid tand till cogging, of coue, total voltage along dahed loo i zeo, o again no inte-ba cuent will flow even at low inte-ba eitance (Fig b. nde eal condition with Q < Q in Fig c hamonic induced ba voltage along dahed loo um u to maximum value, o conideable inte-ba cuent flow i oible, cauing additional inte-ba loe P Q q q Q R. ( Concluion: Skewing (in non-inulated oto cage may give ie to inte-ba cuent, which caue additional loe and may inceae aynchonou hamonic toque. n cae of R q = 0 inte-ba loe ae zeo, but alo fo R q, a in that cae oto cage i inulated ideally. Theefoe additional oto cage loe, given by ohmic loe in ba and ing due to oto hamonic cuent and in inte-ba eitance due to inte-ba cuent q ad, Q ( R Rq q 1 P. ( vaie with vaying inte-ba eitance accoding to Fig with a maximum value fo cetain inte-ba eitance, which mut be avoided by moto deign to kee additional loe low. Examle : Moto data: 00 kw, 50 Hz, ole, tato/oto lot numbe 36/8, cloed oto lot, Aluminium cage, kewed by one tato lot itch. Half-uface of oto ba: A = 8570 mm, yielding "nominal" inte-ba eitance with m : R / A 10 /( m (Fig q qn q T Damtadt ntitute fo Electical Enegy Conveion

42 Moto develoment 4/4 nduction machine At "nominal" inte-ba eitance additional oto cage loe ae only 350 W ( = 0.18% ated owe. n wot cae at R* q = m thee loe may each 1 kw ( = 0.5% of ated owe. Fig : Calculated influence of inte-ba eitance on additional oto cage loe due to oto hamonic cuent at ated moto li = 0.01 (Moto data: 00 kw, 50 Hz, ole, tato/oto lot numbe 36/8, cloed oto lot, Aluminium cage, kewed by one tato lot itch Concluion: n the above examle due to R R * an inceae of inte-ba eitance will inceae qn q inte-ba loe, which none would have exected. With mall moto (below 5 kw uually "nominal" inte-ba eitance i R R *. Theefoe an inceae of inte-ba eitance qn q by e.g. heating u of oto in the oven to inceae oxide thickne uually deceae oto loe. Thi i eecially eential fo ingle hae induction moto, whee oto cage loe ae inceaed due to invee fundamental ai ga field comonent. a b Fig : a Simlified equivalent cicuit of one oto loo with ba and ing eitance and loo tay inductance, conideing inte-ba eitance to be concentated in middle of ba, b Vaiation of additional oto cage loe with vaiation of tato-oto lot atio. T Damtadt ntitute fo Electical Enegy Conveion

43 Moto develoment 4/43 nduction machine Q = Q : nkewed oto have nealy no inte-ba loe (Fig a. With kewed oto, inteba loe vay alo with atio Q /Q. At Q /Q = 1 thee loe ae minimum (Fig b. Q > Q : The athe low oto lot numbe caue a big deviation of te-like oto flux denity ditibution, excited by, fom ine wave fundamental, thu 1 / 1 h i athe big and limit oto hamonic and inte-ba cuent (Fig a. Q < Q : High oto lot numbe yield caue a malle deviation of te-like oto flux denity ditibution, excited by, fom ine wave fundamental, o facto i cloe to unity, i mall and hamonic cuent and elated loe will inceae (Fig b. Concluion: ine-tating cage induction moto have kewed oto cage to educe hamonic toque influence on tat-u toque. Roto lot numbe i choen SMAER than tato lot numbe to educe additional inte-ba loe. Examle : Exloion oof induction moto (EExe: Data: Moto ize 80 mm, ole numbe =, lot numbe Q / Q = 18 / 3, Q < Q (!, oto kewed by one oto lot itch. Moto wa oeated on tet-bench at ated load. Roto cage temeatue wa too high due to inceaed inte-ba loe, alo heating u tato winding too much. Afte changing oto againt a new one with Q = 14 (kewed, Q > Q (! with the ame ba and ing eitance loe went down ignificantly, o that tato winding temeatue tayed within themal limit. c Additional aynchonou hamonic toque due to inte-ba cuent: Conideing imlified equivalent cicuit Fig a, one can olve thi meh equation, getting the inte-ba cuent q e hamonic induced oto voltage. So in oto ba flow the ueoition of (valid fo infinite R q and of q. Fo unkewed cage induced voltage in ue and lowe meh half i imly /, o q in thi imlified equivalent cicuit i exactly zeo. Fo kewed cage one get inte-ba cuent q flow, o the ba hamonic cuent q geneate not only the hamonic aynchonou toque due to, a exlained in Chate 4.4., w yn, h (mnk ( R M e ( Q R ( ( h but alo an additional hamonic toque due to q M eq (m ( 4 Nkw ( R R h q q, ( Q ( R 4R ( ( yn, q h deending on facto q intead of. q in S / bk S. ( S / T Damtadt ntitute fo Electical Enegy Conveion

44 Moto develoment 4/44 nduction machine Beak down li, whee maximum hamonic toque occu, i much bigge fo M eq than fo M e (Fig : b R 4Rq intead of ( h b R. ( ( h Fig : Qualitative chaacteitic of aynchonou hamonic toque M e (at infinite inte-ba eitance and additional toque M eq due to inte-ba cuent with it much bigge beak-down li Examle : With oto cage kewed by one tato lot itch, kewing facto i almot zeo, o aynchonou hamonic toque diaea. But on the othe hand facto q diffe fom zeo fo fit / thid / fifth... ai of lot hamonic, o additional aynchonou toque M eq aea. Moto data: 4-ole induction moto with 36/8 tato/oto lot. Roto cage kewed by one tato lot itch: b / 9 k Stato lot hamonic: 1 (36 / g 1, 17,19, 35,37, q Table : Skewing facto and influence of inte-ba eitance fo tato lot hamonic, if oto cage i kewed by one tato lot Fig : Qualitative chaacteitic of total aynchonou toque a ueoition of the fundamental and of the hamonic toque M eq (hee: 5 th and 7 th hamonic due to inte-ba cuent T Damtadt ntitute fo Electical Enegy Conveion

45 Moto develoment 4/45 nduction machine Accoding to Table inte-ba cuent leave fundamental aynchonou toque almot unaffected, a q=1 i mall. Reulting aynchonou tat-u toque of induction moto with kewed oto cage i a ue-oition of fundamental toque and hamonic toque M eq. Theefoe the M(n-chaacteitic how a boad and dee addle in the egion 1 0 and an inceaed baking toque at 1. Examle : Exeimental comaion of inulated coe cage and non-inulated aluminium cage with ame ba and ing eitance (ee Examle and Cage kewed by one tato lot itch. Stato voltage 380 V, D, 50 Hz, Q /Q = 36/8. a -ole moto, 11 kw, M N = 37 Nm Fig b 4-ole moto, 9.5 kw, M N = 64 Nm Fig Fig Fig Fig : -ole induction moto, f = 50 Hz, 380 V, 11 kw, M N = 37 Nm, 36/8 tato/oto lot Fig : 4-ole induction moto, f = 50 Hz, 380 V, 9.5 kw, M N = 64 Nm, 36/8 tato/oto lot Meaued tating toque of cage induction moto: a inulated coe cage, b non-inulated aluminium cage of ame eitance. Additional aynchonou hamonic toque due to inte-ba cuent deceae tating toque fo and inceae baking toque at > 1. Note that due to inceaed baking and educed tating toque at b deceleating time fom = to = 1 i much malle and tat-u time fom = 1 to = 0 take longe than at a. n -ole moto the oto lot numbe e ole ai i with 8 twice of that of 4-ole moto. So facto fo -ole machine i cloe to unity than fo 4-ole machine, yielding a lowe 1/ 1 h. Theefoe oto hamonic and inte-ba cuent i bigge in -ole machine, yielding bigge hamonic toque M eq. Theefoe the addle haed toque eduction of tat-u toque of -ole machine i bigge than fo 4-ole machine. nfluence of lot numbe atio detemine not only loe, but alo hamonic toque. With Q > Q the athe big oto hamonic and inte-ba cuent will ditot M(n-chaacteitic much tonge than fo Q < Q. T Damtadt ntitute fo Electical Enegy Conveion

46 Moto develoment 4/46 nduction machine Examle : nfluence of lot numbe atio on M(n-chaacteitic: Moto data: Moto ize 160 mm, 11 kw, 380 V, D, 50 Hz, = 6, ai ga 0.35 mm, ion tack length l Fe = 170 mm, Q = 36, Single laye winding, emi-cloed tato and oto lot, oto aluminium die cat cage. Comaion of calculated ( q = m and meaued toque fo two diffeent oto: a Q > Q b Q < Q Q = 33 Q = 4 Roto ba kew: 1 oto lot itch. Calculated and meued eult ae hown in Fig Fig : Meaued and calculated toque chaacteitic between tand till and no-load of 6-ole induction moto, f = 50 Hz, 380 V, 11 kw, M N = 110 Nm, 36 tato lot, non-inulated aluminium cage: above: Q = 33, below: Q = calculated fundamental aynchonou toque calculated total toque including aynchonou hamonic toque meaued total toque T Damtadt ntitute fo Electical Enegy Conveion

47 Moto develoment 4/47 nduction machine Electomagnetic acoutic noie The hamonic field wave of tato and oto do not only inteact a tangential foce, leading to hamonic toque, but alo a adial foce due to the magnetic ull between tato and oto ion uface. Magnetic ull F n between two aallel ion uface (uface A, with magnetic field B n coing the ga in between eendicula, i accoding to Maxwell (Fig f n n Fn B. ( A 0 Fig : Magnetic field B n coing the ga between two aallel ion uface (uface A lead to an attacting foce, the magnetic ull F n The ace hamonic ai ga field wave of tato and oto mut be conideed a the total adial magnetic field, which exet a time-vaying magnetic ull on tato and oto ion uface. - Stato hamonic field wave, excited by tato cuent with tato fequency f : B x ( x t B f t, co, 1 m g, g 0, 1,,... ( Roto hamonic field wave, excited by oto fundamental ba cuent with oto fequency f f : B x ( x t B f t, co, 1 g Q /, g 0, 1,,... ( Conideing oto wave in tato fixed efeence fame, that mean intead of oto co-odinate x in tem of tato co-odinate x : x x v t x ( 1 v t x (1 f t ( yield m yn x B ( x, t B co f t ( (1. ( The magnetic ull due the hamonic wave i B ( x, t f ( x, t n ~ ( B B fn, ~ B B B B. ( , T Damtadt ntitute fo Electical Enegy Conveion

48 Moto develoment 4/48 nduction machine Mainly the mixed oduct B eult in adial foce, whoe ulating fequencie ae in B audible egion of about 100 Hz to 16 khz. We abbeviate x x f t, f t ( (1 ( and ue the tigonometic fomula 1 B co B co B B co( co(, getting x ( x ( f t ( 1 (1 f t ( 1 (1 0. ( A a eult, adial foce denity wave ae deived, which exet an ocillating ull on tato and oto ion tack. f ( x B B x, t co( fton ( n, t 0 The numbe of oitive and negative half-wave of foce denity along machine cicumfeence equal the numbe of node in between: ( The tonal fequency f Ton of foce wave vaiation i f Ton f ( 1 (1 fo ( f Ton f ( 1 (1 0 fo. ( The tato ion may be egaded a a teel ing, wheea the oto i a teel cylinde. Theefoe the tato i le tiff than the oto and i bent by the foce wave. A the ion uface i haken with thi fequency, the uounding ai i comeed and de-comeed with the ame fequency. So acoutic ound wave ae geneated with tonal fequencie, which may be head by e.g. human being. n Fig the foce denity ditibution along the ai ga cicumfeence i hown fo foce wave with diffeent numbe of node. Node occu alway in ai 0,, 4, 6, 8,.... ( At = 0 no node occu. The whole tato ing i exanded and hunken with tonal fequency. All uface element of tato ocillate in hae, o ai i comeed / decomeed in hae along tato cicumfeence. Theefoe tato uface act like a loudeake membane and acoutic ound wave i fa eaching (Fig a. T Damtadt ntitute fo Electical Enegy Conveion

49 Moto develoment 4/49 nduction machine At = the whole geomety i ocillating in a cetain diection. Theefoe the oto i bent. f tonal fequency coincide with natual bending fequency of oto, eonance with big bending amlitude may occu. At > mainly the tato ing-like geomety i bent. With inceaed node numbe zone of comeed and de-comeed ai altenate along tato cicumfeence, thu heling to equalize ound eue. Theefoe with inceaing node numbe ound wave deceae athe aidly in amlitude with inceaing ditance fom moto uface (Fig b. Fig : Foce ditibution along ai ga cicumfeence fo diffeent foce wave with diffeent node numbe a b Fig : Ocillating tato uface comee / de-comee ai and geneate acoutic ound wave. a Fo = 0 tato uface ocillate in hae along tato cicumfeence, o fa eaching ound wave i geneated. b With inceaed node numbe zone of comeed and de-comeed ai altenate along tato cicumfeence, thu heling to equalize ound eue. Theefoe with inceaing node numbe ound wave deceae athe aidly in amlitude with inceaing ditance fom moto uface. Stiffne of tato i defined mainly by tato yoke thickne and by tato houing tiffne. Moto with high ole count and theefoe mall flux e ole uually have thin tato yoke and theefoe ae not vey tiff. So the natual bending fequency i low. Concluion: Magnetic excited acoutic noie of line-oeated induction machine occu mainly, if a tonal fequency of exciting foce wave coincide with natual bending fequency of tato yoke, b the numbe of node of exciting foce wave coincide with numbe of ocillation node of natual bending mode of tato yoke. T Damtadt ntitute fo Electical Enegy Conveion

50 Moto develoment 4/50 nduction machine Examle : Exeimental modal analyi to detect natual bending mode and fequencie of induction moto: Data: 6-ole 11 kw induction moto, moto ize 160 mm, 36 tato lot, foot-mounted houing (intenational mounting M B3 a Moto wa excited with electomagnetic hake with adial vibation with fequency vaying fom 50 Hz to 750 Hz. Meaued ocillation amlitude, exeed a e unit value R (Fig , howed eonance behaviou at 390 Hz, 650 Hz, 975 Hz, 1495 Hz, 180 Hz. b n econd te oto wa emoved and natual bending mode wa examined at eonace fequencie 650 and 180 Hz. Due to oto emoval eonance fequency deceaed to 59 Hz and 1739 Hz. Exciting tato and houing with that fequency, a fou-node bending mode wa found at to be the natual bending mode at 59 Hz and a ix-node bending mode at 1739 Hz. An additional eonance wa found at 704 Hz with 8-node bending mode (Fig Fig : 6-ole 11 kw induction moto, moto ize 160 mm, foot-mounted houing, fan hood emoved. Meaued elative adial ocillation amlitude R of tato uface unde inuoidal adial foce excitation with vaying fequency, which i exhibiting eveal eonance tate. Examle : Calculation of tonal fequencie and meauement of ound eue level fo 6-ole moto of Examle (36 tato lot fo two diffeent oto, oeated fom 50 Hz gid. a oto with 33 lot, b oto with 4 lot Odinal numbe of tato field hamonic: 1 6g 1,-5,+7,-11,+13,-17,+19,-3,+5,-9,+31,-35,+37,.. Slot hamonic ae undelined. Odinal numbe of oto field hamonic, excited by oto cuent unde load: a 1 ( Q / g 111g = 1,-10,+1,-1,+3,-3,+34,.. b 1 ( Q / g 114g = 1,-13,+15,-7,+9,-41,+43,... Node numbe and tonal fequency of adial foce wave at ated li = 0.03: Only tato lot hamonic will be conideed, a they have conideable amlitude. T Damtadt ntitute fo Electical Enegy Conveion