INFLUENCE OF BROKEN ROTOR BARS LOCATION IN THE SQUIRREL CAGE INDUCTION MOTOR USING FINITE ELEMENT METHOD

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1 Journal of Fundamental and Applied Science ISSN - Available online at INFLUENCE OF BROKEN ROTOR BARS LOCATION IN THE SQUIRREL CAGE INDUCTION MOTOR USING FINITE ELEMENT METHOD N. Halem*, S. E. Zouzou, K. Srairi, S. Guedidi Univerité de Bikra, département de génie électrique, BP,, Algérie. Received: Avril Accepted: June Publihed online: June ABSTRACT It i well known that the number of broken bar and varying load affect on the amplitude of pecific harmonic component k in the proce analyi of induction motor under broken rotor bar. The location of broken bar i an important factor which affect the diagnoi of the broken bar defect. In thi paper the imulation i determinate for different cae for ditribution of broken bar under induction motor pole in order to how the impact of broken bar location upon the amplitude of harmonic fault. The imulation reult are obtained by uing time tepping finite element (TSFE) method. The geometrical characteritic of motor, the effect of lotting and the magnetic aturation of lamination core are included in induction motor model. Key word: Induction motor, time tepping finite element (TSFE) method, broken bar.. INTRODUCTION Rotor fault of induction machine yield aymmetrical operation of thi one, cauing unbalanced current, torque pulation, increaed loe and decreaed average torque. The need for detection of rotor fault at an earlier tage, o that maintenance can be cheduled, ha puhed the development of monitoring method with increaing enitivity and noie protection. Author Correpondence, n_halem@yahoo.fr ICID:

2 N. Halem et al. J. Fundam Appl Sci., (), - For that, a model cloer to reality conidering fault condition mut be etablihed. An analytical analyi method baed on the rotating field theory and coupled circuit wa ued []. In work, where the machine inductance are calculated and the machine performance i tudied under faulty condition, the Winding Function Approach (WFA), i ued, where everal aumption and approximation of the actual machine layout are made, like the effect of tator teeth and lot, which are omitted in the calculation []. The modeling with finite element method repreent a high fidelity electromagnetic behaviour which lead to more precie reult than other model, a the actual geometry and winding layout of the machine are ued. The conideration of the behaviour of the local electromagnetic induction machine provide a more accurate modeling. The numerical olution of Maxwell' equation governing the behaviour of electromagnetic field and the conideration of the equation repreenting the electrical upply circuit of the machine reduce the implification made in the claical model. In analyi of induction motor, the input current, not the voltage, i uually ued. The voltage ource i more uitable than current ource. The external circuit that repreent the electrical ource and circuit component are coupled to the FEM. Only the terminal voltage applied to the motor are required a known input quantitie, and the total terminal current are the unknown to be evaluated. The ue of time-tepping finite element i the mot precie way, up to date, for modeling the coupled field-circuit and motion of induction motor, accounting for both aturation, time and pace harmonic. Indeed, the modeling of rotor mechanical motion and tator field ource variation imultaneouly allow coupling the intantaneou field of tator and rotor []-[]. Thi paper preent the tranient tate modeling of cage induction motor uing the coupled electric circuit with D finite element electromagnetic field analyi. The flux D magnetic analyi oftware i ued for calculating the magnetic field of an induction motor for the healthy rotor, and broken bar. In aim to how the influence of the broken bar location upon the amplitude of harmonic due to the fault, even for different poition are imulated at rated load.. TSFE ANALYSIS OF INDUCTION MOTOR BASED CIRCUIT-COUPLED METHOD Generally the induction motor i excited by an external voltage ource, from many model baed on finite element method, only the Circuit-Coupled Finite Element Method (Circuit- Coupled FEM) can cloe thi reality, here the external electric circuit which contain the three

3 N. Halem et al. J. Fundam Appl Sci., (), - voltage ource i coupled to the finite element domain which contain the magnetic circuit of the electric machine []-[]-[]. In table, pecification of the tudied induction motor. Table. Specification of tudied induction motor Number of pole Number of phae Rated power (kw) Rated voltage (V) Rated peed (rpm) Number of tator lot Number of rotor lot. For Preton [] the tranient magnetic field in term of magnetic vector potential A, the reluctivity, conductivity, and current denity J can be expreed a: A A A J () x x y y t The lat term repreent current induced in conducting material when flux change with time. For Salon [] and Lombard [] the full tranient performance can be obtained by accounting for the mechanical equation of the motor and the tranient motional induced eddy current in the rotor bar can't be neglected a in equation (), the complete ytem i baed on the differential equation in compact form: A t A E V A Where V i the peed of the moving part, E i the electrical calar potential applied by the external circuit. So the problem i conidered a tranient alike. When the motor i loaded the voltage time tep mut be accompanied by rotor motion correponding to the lip. The time tep mut be ufficiently mall to enure that the effect of lotting and tatic air gap eccentricity are accurately modeled, alo to obtain a uitable frequency reolution for the application of Fat Fourier Tranform (FFT) []. (). SIMULATION RESULTS

4 N. Halem et al. J. Fundam Appl Sci., (), - In thi paper, the induction motor i imulated under rated condition. An induction machine rotor aymmetry introduced by broken bar produce pectrum line of tator current at frequencie: Where f bb k f i the electrical upply frequency, i the lip, k=,,,... Figure a, b how the tator current pectrum of healthy and faulty rotor. According to fig. a it can be clearly hown that the tator current pectrum for healthy tate i very rich by the expectation harmonic component [] uch; principal lot harmonic at.hz and.hz, aturation harmonic ( Hz, Hz, Hz,...) and aturation related harmonic (.Hz,.Hz,.Hz,...), the appearing of thoe harmonic component ignifie that the finite element model ued in thi paper cloer the reality of the induction motor. () (a) (b) Fig.. Stator current pectrum at teady tate: a healthy rotor; b one broken bar

5 N. Halem et al. J. Fundam Appl Sci., (), - In cae of broken rotor bar a preented in fig. b, the rotor i electrically aymmetric and the backward rotating field i created. The current pectrum reveal ideband expected around the upply frequency given by () []-[]. Figure a, b, c, d and e, f, g, h, how the tator current pectrum in teady tate according with the correponding magnetic flux ditribution for healthy and faulty rotor at the tranient tate. When the lip i large, the eddy current how a large value. Thi high value of lip i neceary to illutrate the effect of the broken bar on the field. The concentration of magnetic flux i oberved around the broken bar and create aymmetric magnetic flux ditribution []-[]. A hown in the fig. a, for healthy rotor; there are no index ignature of broken bar fault around fundamental harmonic. A expected in the fig. b, the fault ignature of one broken bar are appeared very clearly around fundamental harmonic. However when one bar break, it adjacent bar expoe more to the fault due to the larger tre on the bar. Following the breakage of the firt bar, the adjacent bar may break after a hort period []. Figure c chow the tator current pectrum for two adjacent broken bar under one pole, while the fig. d preent one broken bar on one pole and one broken bar on adjacent pole, the amplitude of harmonic component i increaed from -.db to -.db, alo the amplitude of harmonic component i increaed from -.db to -.db, Comparion of fig. b and c indicate that the amplitude of harmonic component are increaed when the number of broken bar increaed. Moreover comparion of fig. c and d indicate that the higher increaing of the amplitude of harmonic component occur when the two adjacent broken bar located at the ame pole. Figure e preent the tator current pectrum when the firt and the eight bar are broken; one broken bar on one pole and one broken bar on adjacent pole, the amplitude of harmonic component are -.db and -.db. Figure f preent the tator current pectrum when the firt and the fifteenth bar are broken; one broken bar on one pole and one broken bar on oppoite pole, the amplitude of harmonic component are -.db and -.db, it i clearly hown that the amplitude of harmonic component have no o much difference with the previou cae, only amplitude of harmonic component decreae from -.db to -.db.

6 N. Halem et al. J. Fundam Appl Sci., (), - (a) - - I o v a lu e R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- (b) (-)f - -.db (b) (+)f -.db I o v a lu e R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- (a) - - (c) (-)f -.db - (c) (+)f -.db (d) (-)f - -.db I o v a lu e R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- (d) (+)f -.db - I o v a lu e R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- - - Fig.. Stator current pectrum at teady tate and flux ditribution at tranient tate for different cae for ditribution of broken bar under pole: a healthy rotor; b one broken bar; c two adjacent broken bar on one pole; d two non adjacent broken bar, one broken bar on one pole and one broken bar on adjacent pole

7 N. Halem et al. J. Fundam Appl Sci., (), - (e) (-)f - (+)f -.db -.db - I o v a lu e R e u lt (f) (-)f - Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- (f) (+)f -.db -.db (e) - - (g) (-)f - -.db I o v a lue R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- (g) (+)f -.db (h) (-)f - -.db I o v a lu e R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- (h) (+)f -.db I o v a lu e R e u lt Ti m e (. ) :, Po ( deg) : -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E- -, E-, E-, E-, E-, E-, E-, E-, E-, E-, E- Fig.. Stator current pectrum at teady tate and flux ditribution at tranient tate for different cae for ditribution of broken bar under pole: e two non adjacent broken bar, one broken bar on one pole and one broken bar on adjacent pole; f two non adjacent broken bar, one broken bar

8 N. Halem et al. J. Fundam Appl Sci., (), - on one pole and one broken bar on oppoite pole; g three broken bar, two broken bar on one pole and one broken bar on adjacent pole; h three adjacent broken bar under one pole Figure g how the tator current pectrum when the firt, the econd and the eight bar are broken; it mean two broken bar on one pole and one broken bar on adjacent pole, the amplitude of harmonic component are -.db and -.db. Comparion of fig. e, f and g indicate an important increaing in the amplitude of harmonic component, thi increaing i caued by the added broken bar. It i neceary to note that ome reearch work witch baed on analytic method to modeling the faulty induction motor, affirmed that when two broken bar paced electrically of, the amplitude of harmonic component are very low []-[]. In thi paper, the imulation reult obtained from faulty induction motor model uing TSFE method (fig. e, f, and g) prove the contrary, the amplitude of harmonic component in all cae are very important. A hown in fig. h which preent the tator current pectrum of faulty induction motor with three adjacent broken bar, the ucceive breakage of three bar lead to more aymmetrical flux ditribution, and higher local aturation, more variation of the flux denity and larger harmonic component of the tator current are realized.. CONCLUSION Thi paper preent the circuit coupled finite element method ued to modeling the Three- Phae Squirrel Cage Induction Motor. For thi purpoe, the time-tepping finite element method (TSFE) wa propoed. The broken rotor bar fault i imulated for different poition under pole. It wa invetigated that the broken bar location affect upon the amplitude of harmonic fault. It wa hown that the amplitude of harmonic due to broken bar located on one pole are larger than the cae in which the broken bar are ditributed on different pole. Alo, the amplitude of harmonic due to broken bar are larger when broken bar are adjacent.

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