Top Banner
Field computation with finite element method applied for diagnosis eccentricity fault in induction machine Moufid Mohammedi, Tahar Bahi 1 Electrical Department, Faculty of Science Engineering, Annaba University, Annaba, Algeria Laboratory of Automatic and Signal Annaba (LASA) [email protected]; [email protected] AbstractThis paper deals with analysis of the magnetic field by using FEM and numerical computation of the electromagnetic characteristics of Induction machine. The knowledge of electromagnetic characteristics is very important in performance analysis of electrical machines. The purpose of this investigation is to use the field computation by finite element model to evaluate, detect and diagnosis fault of the static eccentricity effect on the vector potential and field magnetic. The result of simulation of our model allows us to clearly see the effect of the eccentricity on the electromagnetic quantities of the induction squirrel machine. KeywordsInduction machine, modelisation, finite element methode, eccentricity, diagnosis, simulation. I. INTRODUCTION The sudden damage of the induction motors, which are generally used as part of the product line in the industry, can lead to stop the whole process. Therefore, the diagnosis of the lack of time is important to prevent the spread of the fault on the product range. Energy conversion in an induction motor (converting electrical energy into mechanical energy) is through the magnetic energy in the air gap. However, the displacement effect of the rotor (eccentricity) directly affects the course of the magnetic flux (magnetic reluctance) [1,2]. According to the model developed in this work, we could introduce and study the consequences of the eccentricity phenomenon on the magnetic quantities of the machine through the magnetic vector potential. The complexity related to the spatial distribution of local forces [3,4] to calculate a resultant force has been surmounted due to the flexibility of our program allows us to consider the effect of changing the rotor position by adjusting its coordinates in the program. In the following sections, we propose the problematic will be resolved by our proposed model in this paper. In the third section, we consider the development of the model using the formulation of magnetic vector potential. Next, we present the simulation results and their interpretations. II. STATEMENT OF THE PROBLEM Our study is to see the evolution of magnetic variable (magnetic field and vector potential) along the axis of movement (x) of the rotor for 25% of the value of the airgap. Comparing the simulation results in the default case (with eccentricity) with those of the healthy case, we can see the impact of eccentricity on the magnetic quantity of the asynchronous machine. Figure.1 Balanced of the rotor along x axis. y x Stator Rotor x Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016 ISBN: 978-9938-14-953-1 (196) Editors: Tarek Bouktir & Rafik Neji
5

Field computation with finite element method …journal.esrgroups.org/jes/icraes/CDICRAESFinal/ICRAES16...Field computation with finite element method applied for diagnosis eccentricity

Jul 09, 2020

Download

Documents

dariahiddleston
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Field computation with finite element method …journal.esrgroups.org/jes/icraes/CDICRAESFinal/ICRAES16...Field computation with finite element method applied for diagnosis eccentricity

Field computation with finite element method applied

for diagnosis eccentricity fault in induction machine

Moufid Mohammedi, Tahar Bahi

1Electrical Department, Faculty of Science Engineering, Annaba University, Annaba, Algeria

Laboratory of Automatic and Signal Annaba (LASA)

[email protected]; [email protected]

Abstract— This paper deals with analysis of the

magnetic field by using FEM and numerical

computation of the electromagnetic characteristics of

Induction machine. The knowledge of

electromagnetic characteristics is very important in

performance analysis of electrical machines. The

purpose of this investigation is to use the field

computation by finite element model to evaluate,

detect and diagnosis fault of the static eccentricity

effect on the vector potential and field magnetic.

The result of simulation of our model allows us to

clearly see the effect of the eccentricity on the

electromagnetic quantities of the induction squirrel

machine.

Keywords—Induction machine, modelisation, finite

element methode, eccentricity, diagnosis, simulation.

I. INTRODUCTION

The sudden damage of the induction motors, which are

generally used as part of the product line in the industry,

can lead to stop the whole process. Therefore, the

diagnosis of the lack of time is important to prevent the

spread of the fault on the product range.

Energy conversion in an induction motor (converting

electrical energy into mechanical energy) is through the

magnetic energy in the air gap. However, the

displacement effect of the rotor (eccentricity) directly

affects the course of the magnetic flux (magnetic

reluctance) [1,2].

According to the model developed in this work, we

could introduce and study the consequences of the

eccentricity phenomenon on the magnetic quantities of

the machine through the magnetic vector potential. The

complexity related to the spatial distribution of local

forces [3,4] to calculate a resultant force has been

surmounted due to the flexibility of our program allows

us to consider the effect of changing the rotor position

by adjusting its coordinates in the program.In the following sections, we propose the problematic

will be resolved by our proposed model in this paper.

In the third section, we consider the development of the model using the formulation of magnetic vector potential. Next, we present the simulation results and their interpretations.

II. STATEMENT OF THE PROBLEM

Our study is to see the evolution of magnetic variable

(magnetic field and vector potential) along the axis of

movement (x) of the rotor for 25% of the value of the

airgap. Comparing the simulation results in the default

case (with eccentricity) with those of the healthy case,

we can see the impact of eccentricity on the magnetic

quantity of the asynchronous machine.

Figure.1 Balanced of the rotor along x axis.

y

x

Stator

Rotor

x

Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016

ISBN: 978-9938-14-953-1 (196) Editors: Tarek Bouktir & Rafik Neji

Page 2: Field computation with finite element method …journal.esrgroups.org/jes/icraes/CDICRAESFinal/ICRAES16...Field computation with finite element method applied for diagnosis eccentricity

HrB ×= mm0

( )( ) W×=Wúû

ùêë

é÷÷ø

öççè

æ

¶×+×òò òò

W W

®dJd

t

AAcurlcurl sii 00 mwsmw

å= ii AA .w

[ ] [ ] [ ] [ ]FAMt

AK =×+ú

û

ùêë

é

¶×

ïïïï

î

ïïïï

í

ì

W×××=

÷÷ø

öççè

æ

¶×

¶+

¶×

¶=

W=

òò

òò

òò

W

W

W

dJF

yyxxM

dK

sii

jijiji

jiji

0

0

mw

wwww

wwms

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Figure 3 Grid of the domain

( ) )1(1

0sJAcurlcurl

t

A=÷÷

ø

öççè

æ×+

¶×

ms

III. MODEL OF INDUCTION MACHINE

To determine the field distribution at each time-step, a two dimensional transverse section of the induction motor is represented, in reducing the problem to two dimensions [5,6]. The transient magnetic field in terms of magnetic vector potential (A); The permeability of airis defined by µ0 = 4.p.10-7

H/m; Conductivity (σ) and current density (Js), can be expressed as:

The constitutive linear relationship of ferromagnetic

material is:

(2)

Where,

B: flux density;

H: magnetic field;

µr: permeability relative.

To solve the general diffusion equation (1) a classical weighted residual method with first order shape functions we obtain the following integral form [7,8]:

(3)

ωi : ponduration function.

With the following linear approximation for the vector potential:

(4)

Then, we obtain the following algebraic form:

(5)

(6)

IV. SIMULATIONS AND DISCUTION

The finite element model described above to evaluate the

effects of rotor eccentricity in the air gap on the vector

potential magnetic and the magnetic field [9,10].

The figure 2 shows the geometry of the induction

machine with four poles, 36 slots in the stator and 32

rotor bars.

The discretization of the geometry with finite element is

shown in figure 3.

The equipotential of potential vector magnetic is shown

by the figure 4.

Figure 2 Induction machine geometry

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Figure 4 Equipotentiel of potential vector magnetic

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016

ISBN: 978-9938-14-953-1 (197) Editors: Tarek Bouktir & Rafik Neji

Page 3: Field computation with finite element method …journal.esrgroups.org/jes/icraes/CDICRAESFinal/ICRAES16...Field computation with finite element method applied for diagnosis eccentricity

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2-0.06

-0.04

-0.02

0

0.02

0.04

0.06

x(m)

spatial distribution of potentiel magnetic

y(m)

A(A

.m)

Figure.5 Spatial distribution of potential vector

V. EFFECT OF THE ECCENTRICITY

A) Potential vector magnetic

The figure.5 shows the spatial distribution of the

potential vector magnetic for each element of the

geometry.

The projection of the spatial distribution of magnetic

vector potential presented in Figure.5 on the plane “zx”

allows us to obtain the potential vector magnetic in the

healthy case (figure6.a) and with fault, that is to say that

the rotor is balanced along the “x” axis (figure 6.b) is

illustrated by figure 6.

In the healthy cases (Figure 6.a) we find that the shape of

the spatial distribution of the magnetic vector potential is

symmetrical. Furthermore, the same figure shows that we

have the same absolute amplitude on the four poles of the

induction machine.

Against by, in the case with defect (Figure 6.b), the

thickness of the air gap is not uniform, then the shape of

the magnetic potential is not symmetrical and the

absolute value of magnetic potential is not uniform in the

four poles.The change in the position of the rotor (eccentricity)

occurs with the change of magnetic reluctance. Indeed,when the air gap reduces, so, the magnetic reluctance also reduces, therefore the amplitude of the magneticvector potential increases.

By against, when the air gap increases we see the opposite effect.

North poles

South poles

North poles

South poles

a. healthy case

b. With fault

Figure.6 Effect of the eccentricity on the potential

vector magnetic

Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016

ISBN: 978-9938-14-953-1 (198) Editors: Tarek Bouktir & Rafik Neji

Page 4: Field computation with finite element method …journal.esrgroups.org/jes/icraes/CDICRAESFinal/ICRAES16...Field computation with finite element method applied for diagnosis eccentricity

Figure.7 Spatial distribution of magnetic field

B) Magnetic field

The figure.7 shows the spatial distribution of the

magnetic field (absolute values) for each element of the

geometry.

The projection of the spatial distribution of magnetic

field presented in Figure.7 on the plane “zx” allows us to

obtain the magnetic field in the healthy case (figure 8.a)

and with fault, where the rotor is balanced along the “x”

axis (figure 8.b), is illustrated by figure 8.

In healthy cases, the air gap is healthy, therefore uniform along the contour of the air gap. This is expressed by the symmetry of the shape of the magnetic field distribution observed in Figure 8.a.

By against, the figure 8.b (with eccentricity case), there is no symmetry in the evolution plane of the magnetic field.

The effect of the eccentricity of the magnetic field is

opposite with respect to their effect on the potential

vector, when the reduced air gap, therefore, the magnetic

reluctance also therefore reduces the amplitude of the

magnetic field decreases. For against, , when the air gap

increases the magnetic reluctance also increases,

therefore. the amplitude of the magnetic field increases.

VI. CONCLUSION

The results of simulations enables us to introduce and

clearly see the impact of eccentricity on the magnetic

behavior of the machine (magnetic field and vector

potential) for the rotor position change of 25% from its

initial position, it is found that the effect of the

eccentricity influences first places on the magnetic

reluctance (the course of the field in the air gap), the

Figure.8 Effect of the eccentricity on the magnetic field

a. healthy case

b. With fault

Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016

ISBN: 978-9938-14-953-1 (199) Editors: Tarek Bouktir & Rafik Neji

Page 5: Field computation with finite element method …journal.esrgroups.org/jes/icraes/CDICRAESFinal/ICRAES16...Field computation with finite element method applied for diagnosis eccentricity

variation of the latter, causes a variation of the

magnetic properties (magnetic quantities), mechanics

(mechanical quantities ) and electrical (electrical

quantities).

VII. REFERENCES

[1] M. Rigoni, N. Sadowski*, N. J. Batistela, J.P.A.Bastos, ” Detection and

Analysis of Rotor Faults in Induction Motors by the Measurement of the

Stray Magnetic Flux ”, Journal of Microwaves, Optoelectronics and

Electromagnetic Applications, Vol. 11, No. 1, June 2012

[2] Jawad Faiz, Hamid Toliyat, “Finite-Element Transient Analysis of Induction Motors Under Mixed Eccentricity Fault “,IEEE

TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 1, JANUARY

2008

[3] Sang Bin Lee, Member, IEEE, Gerald B. Kliman, Life Fellow, IEEE, Manoj R. Shah, W. Tony Mall, N. Kutty Nair, Life Senior Member,

IEEE, and R. Mark Lusted, “An Advanced Technique for Detecting

Inter-Laminar Stator Core Faults in Large Electric Machines,” IEEE

TRANS. ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5,

SEPTEMBER/OCTOBER 2005

[4] M. J. DeBortoli, S. J. Salon, D. W. Burow, C. J. Slavik “Effects of Rotor

Eccentricity and Parallel Windings on Induction Machine Behavior: A

Study Using Finite Element,”

IEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 2, MARCH

1993

[5] T W Preston, A B J Reece, P S Sangha“Induction motor analysis by time-stepping techniques,” IEEE

TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 1, JANUARY

1988.

[6] J. Shen and A. Kost, “Modeling of the Idealized Exciting Current Sources in the FEM,” IEEE TRANSACTIONS ON MAGNETICS.

VOL. 31, NO. 3, MAY 1995

[7] Chang-Chou Hwang* , S.J. Salon, R. Palma

“A finite element pre-processor for induction motor including motion

and circuit constraints,” IEEE TRANSACTIONS ON MAGNETICS,

VOL. 24, NO. 6, NOVEMBER 1988.

[8] M. Mohammedi , T. Bahi, Y. Soufi “Finite Element Modeling Under Stress by the Nonlinearity of a Material Ferromagnetic,”

Journal of Electrical Engineering (JEE), 2012.

[9] M. Mohammedi , T. Bahi, Y. Soufi “Integration of the eccentricity effect in the field computation by FE,” EVER, Monaco,2012.

[10] M. Mohammedi , T. Bahi, Y. Soufi “Integration of the eccentricity effect

in the field computation of reluctance machine,” Journal of Electrical

Engineering (JEE), 2014.

Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016

ISBN: 978-9938-14-953-1 (200) Editors: Tarek Bouktir & Rafik Neji