INFLUENCE OF DESIGN DATA OF INDUCTION MOTOR ON EFFECTS OF CAGE ASYMMETRY

Transcription

1 Pace Nauowe Intytutu Mazyn, Naędów i Pomiaów Eletycznych N 66 Politechnii Wocławiej N 66 Studia i Mateiały N 3 1 Alejando FERNANDEZ GOMEZ* Tadeuz J. SOBCZYK* induction moto, oto cage aymmety, cage moto diagnotic INFLUENCE OF DESIGN DATA OF INDUCTION MOTOR ON EFFECTS OF CAGE ASYMMETRY The ae eent eult of analyi of influence of choen aamete of induction cage moto on the comonent (1 )f in tato cuent, which i commonly ued fo diagnoi of cage condition. The invetigation concentate on the influence of commonly available moto data uch a oleai and oto lot numbe, eectively, but alo on elationhi between eitance of cage ba and end ing. A educed model of moto with a faulty cage i ued, in which cage fault ae eeented by aymmety coefficient of a cage. The main intention of the ae i to ovide enginee with imle etimate of effect due to cage fault fo vaiou moto given limited infomation. 1. INTRODUCTION Nowaday diagnoi of induction moto cage fault bae on the Moto Cuent Signatue Analyi (MCSA). Many ae [1] [7] ae devoted to that oblem. Pediction of effect in tato cuent due to cage fault i ovided engaging cicuital o field model of Induction Moto (IM) that ae moe o le comlicated. They equied detailed infomation on deign data of a moto, which uually ae not available fo enginee in the induty. Theefoe, it i equeted to etimate effect of cage fault uing only baic data of a moto. Thi ae i an attemt to anwe to that oblem given limiting neceay infomation to the ole-ai numbe and the oto lot numbe N. Commonly, the comonent with the fequency (1 )f in tato hae cuent i ecognized a a baic fundamental effect of cage fault. The effect can be edicted by a baic model of induction moto accounting fo the cage aymmety. One uch model wa eented in [8]. It oeate with ymmetical comonent of tato and oto quantitie, and it i a imle extenion of the claical IM model. The cage * Intitute on Electomechanical Enegy Conveion, Cacow Univeity of Technology, ul. Wazawa 4, Kaów, Poland.

2 358 aymmety i eeented in the model by the aymmety facto a and. In the cae of a healthy cage thoe facto ae equal to zeo.. ESTIMATION OF EFFECTS IN CURRENTS DUE TO CAGE FAULTS Vaiou tudie [9], [11] eented a dynamic model of IM conideing the main MFF hamonic only and a cage aymmety. When uly voltage ae balanced and teady-tate ae conideed that equation ae educed to fou algebaic equation of the fom U 1 = X σ + X μ j X μ X σ + X μ X μ X μ X' σ + X μ X μ X' σ + X μ + R + R 1 ( 1+ ) a e jα jα ae ( 1+ 1 I I I' N I' ) (1) jω t whee I denote a value of the fit ymmetical comonent i ( t) = I e of the uly fequency Ω and I j(1 ) Ω t a value of the econd comonent i ( t) = I e with the li deendent fequency ( 1 ) Ω. Thoe equation could be eeented by the equivalent cheme eented in Fig I 1 U R jxσ, jxμ jx' σ, (1+ a) a jx' σ, jxμ jx σ, R 1 I' Fig. 1. Equivalent cheme of induction moto with faulty cage Fom that equivalent cheme a elationhi between the main cuent comonent 1 I and the comonent I, geneated by a cage fault, can be found. In [11] it ha been

3 359 hown that at nomal oeating condition of a moto, i.e. fo mall li, the magnetizing eactance X μ and the leaage eactance X σ,, X' σ, can be omitted, eectively, and neglecting the eitance R, the atio between I and I 1 can be exe by the cage aymmety facto a I' 1 = 1 a () I = In Figue the value of the atio facto 1 ae hown veu li at diffeent aumtion fo equivalent cheme aamete. The cuve a i obtained fom a full cheme, the cuve b wa develoed when omitting the magnetizing eactance X μ. The cuve c i obtained when leaage eactance ae omitted a well, i.e. fo a uely eitive cheme. The dahed line (cuve d ) how the value a. Thoe cuve wee calculated fo a moto with the following ated data: P n = W, n n = 98 m, U = 6 V, I n = 7 A, = 1, N = 36. Fig.. The atio 1 veu li at diffeent imlification of the equivalent cheme in Fig. 1 [11] It i evident that the atio 1 i vey cloe to aymmety facto a fo nea ated li. 3. ESTIMATION OF ASYMMETRY FACTOR BY POLE-PAIR AND ROTOR SLOT NUMBERS To detemine the aymmety facto a, the eitance of each cage element hould be nown [8] [11], i.e. eitance of cage ba R b and end-ing egment R e.

4 36 Uually, cage fault ae modelled by inceaing the eitance of a faulty element u to time the nominal value. The aymmety facto a detemine a eitive couling between equivalent cheme fo the fit and the econd ymmetical comonent, which ae connected bac-to-bac (ee Fig. 1) in comaion to the value of the oto eitance in the equivalent cheme fo the ymmetical cae π = ( ν) Re + Rb in (3) N whee i a ole-ai numbe and N i a numbe of ba in a cage. The eitance R b and egment R e can be elated uing deign data of a moto. Knowing the elationhi between cuent in ba and end ing egment I = I in( α ), whee α = ( π ) N, and etimating the elationhi between the ba length L and the diamete of end ing D a L = ( λ π D) a well a uing the machine atio λ = L τ, whee τ i the ole itch, the elationhi between the eitance R b and R e i done by the fomula 4π Re = λ N π in N π N je γb j γ b e b 1 whee: j b, j e ae cuent denitie in ba and end-ing egment, γ b, γ e ae eective conductivitie and in i a facto fo detemining in effect in a ba. Baed on thi elation the aymmety facto a can be etimated by uing a oleai numbe and a numbe of cage lot only and, a a conequence, the atio 1. The value of the facto a deend on the fault tye. Thi ae how that it i an eential cae when one ba i boen becaue effect of multi-ba fault can be etimated by that elementay fault. in R b e (4) 4. INFUENCE OF END-RING SEGMENT RESISTANCE ON ASYMMETRY FACTOR Fom () it follow that elationhi between eitance R b and R e deend on the conductivity of a mateial ued fo cage and cuent denitie aumed fo ba and ending. Uually, mateial ued fo end-ing and ba ae the ame, o the atio γ b /γ e i equal to one. Fo mall li the in effect can be neglected a well. So, an influence of end-ing geomety on the aymmety facto can be tudied by changing the atio j e /j b. Reult of calculation of the aymmety facto a fo one boen ba ae efomed given the following aumtion: λ = 1.5, in = 1. and γ b /γ e = 1. ee Fig..

5 361 Thee ae fou gah in thi figue, when the quotient j e /j b i changing. The gah a how the facto a veu the value fo diffeent ole-ai numbe (fom = 1 till = 5) fo j e /j b = 1.. The cuve b how the ame data fo j e /j b =. and gah c fo the atio j e /j b =.5. In the gah d the eitance of end-ing egment i aumed to be zeo (R e = ). Such aumtion i ometime ued when analyzing the cage aymmety. It can be een that fo eal value of the quotient j e /j b the aymmety facto a, and alo the atio 1, deend on the numbe of lot in a cage but alo on the ole-ai numbe. It can be tated that end-ing can be omitted fo highe lot numbe and then 1..7 Gah a.7 Gah b.6.5 a.4 j e / j b =1 j e / j b =.6.5 a Gah c Gah d.6.6 j e / j b =,5 R e =.5 a.4.5 a Fig. 3. Influence of end-ing egment eitance on the aymmety facto fo diffeent ole-ai numbe

6 36 5. ESTIMATION OF RATIO K 1 FOR MULTI-BAR FAULTS In the cae of multi-ba fault the atio 1 can be etimated by the aymmety facto fo one boen ba. In liteatue the elationhi 1 n/n i often ued, whee n i a numbe of boen ba. Howeve, thi elationhi i not valid even fo imle multiba fault. A fa moe exact etimation of the atio 1 fo multi-ba fault can be obtained by umming geometically the comonent (1 )f geneated by individual boen ba a it i exlained in Fig. 4 fo the cae of two ucceive boen ba. 1- γ 1 Fig. 4. Etimation of effect due to two adjacent boen ba It follow that fo n equent boen ba the atio 1 can be etimated by the following fomula γ in n = = (5) γ n in 1 a 1,a whee 1,a i the aymmety facto fo one boen ba and γ = α = (π ) /N. That etimation i much moe meaningful than 1 n / N. The change of atio 1 = a fo neighbou boen ba veu at diffeent ole-ai numbe ae hown in Fig. 5: gah a fo two ba and gah b fo thee ba. All cuve have been obtained fo λ = 1.5, in = 1., γ b/γ e =1. and j e /j b = Gah a.18 Gah b a.5.1 a Fig. 5. Aymmety facto at and 3 neighbou ba boen fo diffeent ole-ai numbe

7 363 Thoe figue illutate difficultie in diagnotic of multi-ba fault. The geometical um of (1 )f comonent geneated at individual boen ba can tae an abitay value and can even diaea at mall numbe of cage lot and bigge oleai numbe..5.4 Evolution of a =1 = =3.3 a Pai of ole Fig. 6. Aymmety facto fo veu oition of a ai of boen ba That effect can be obeved alo in Fig. 6, in which change of the aymmety facto ae hown fo two ba ae boen located at vaiou oition. In that figue the oition of a boen ba ai ae denoted a: 1, 1 3, 1 4 etc. The calculation wee efomed fo a moto with N = 36 ba fo ole-ai numbe = 1, = and = 3, and given λ = 1.5, in = 1., γ b γ e = 1. and j e /j b = 1.. Alo, it hould be noted that fo each ole-ai numbe thee ae ai fo which aymmety facto i cloe to zeo, meaning that the effect of cage aymmety i not obeved in tato cuent. Theefoe, it i athe evident that the atio 1 i not uniquely elated to a multi-ba fault tye. The final concluion of the eented analyi i that the diagnotic of cage fault baed on (1 )f comonent in tato cuent could be unatifactoy. In actice, diagnotic ytem hould attemt to identify the onet of cage damage becaue when multi-ba fault aie the analyi could be unatifactoy. 6. CONCLUSIONS In the ae a imle analyi of effect in tato cuent due to cage fault i eented. It ha been hown how to etimate effect of multi-ba cage fault baed on the effect of one boen ba. The lit of aamete equied fo that etimation ha been

8 364 limited to the numbe of ole-ai and the cage lot numbe. The influence of ending deign data on effect due to cage damage ha been alo dicued. Etimation eented in the ae can be ueful fo enginee fo cage diagnotic. Thi ae ha been eaed a a at of eeach oject Enegy SmatO in a fame of 7FP-ITN-PEOPLE-11. REFERENCES [1] BELLINI A., FILIPPETTI F., FRANCESCHINI F., SOBCZYK T.J., TASSONI C., Diagnoi of induction machine by d-q and i..c oto model, Poc. 5th IEEE Sym. on Diagnotic of Electic Machine, Powe Electonic and Dive, (SDEMPED 5), [] DIDIER G., TERNISIEN E., CASPAREY O., RAZIK H., Fault detection of boen oto ba in induction moto uing a global fault index, IEEE Tan. Induty Alication, 6, Vol. 4, [3] FILIPPETTI F., FRANCESCHINI G., TASSONI C., VAS P., AI technique in induction machine diagnoi including the eed ile effect, IEEE Tan. Induty Alication, 1998, Vol. 34, [4] JUNG J.H., LEE J.J., KWON B.H., Online Diagnoi of Induction Moto Uing MCSA, Tan. Indutial Electonic, 6, Vol. 53, No. 6, [5] KLIMAN G.B., STEIN J., ENDICOTT R.D., KOEGL R.A., Non-invaive Detection of Boen Roto Ba in Oeating Induction Moto, IEEE Tan. Enegy Conveion., 1998, Vol. 3, [6] KRAL C., KAPELLER H., GRAGGER J.V., HAUMER A., KUBICEK B., Phenomenon Roto Fault Multile Electical Roto Aymmetie in Induction Machine, Poc. 7th IEEE Sym. on Diagnotic of Electic Machine, Powe Electonic and Dive, (SDEMPED 9), IEEE Catalog Numbe CFP9DE-CDR, TF63. [7] MIRAFZAL B., DEMERDASH N., On innovative method of induction moto intetem and boenba fault diagnoi, IEEE Tan. Induty Alication, 6, Vol. 4, [8] SOBCZYK T.J., MACIOŁEK W., Aymmety facto of induction moto oto cage, Poc. 3d IEEE Sym. on Diagnotic of Electic Machine, Powe Electonic and Dive, (SDEMPED 1), [9] SOBCZYK T.J., MACIOŁEK W., Doe the comonent (1-)f o in tato cuent i ufficient fo detection of oto cage fault?, Poc. 5th IEEE Sym. on Diagnotic of Electic Machine, Powe Electonic and Dive, (SDEMPED 5), [1] SOBCZYK T.J., MACIOŁEK W., On Reduced Model of Induction Moto with Faulty Cage, Poc. 7th IEEE Sym. on Diagnotic of Electic Machine, Powe Electonic and Dive, (SDEMPED 9), IEEE Catalog Numbe CFP9SDE-CDR, TF1. [11] SOBCZYK T.J., MACIOŁEK W., Influence of Pole-Pai Numbe and Roto Slot Numbe on Effect Caued by Cage Fault, Poc. 8th IEEE Sym. on Diagnotic of Electic Machine, Powe Electonic and Dive, (SDEMPED 11), IEEE Catalog Numbe CFP11SDE-USB, ID54.