Application of lumped parameters and finite element methods to the ...

Application of Lumped Parameters and Finite Element Methods to the Thermal Modeling of an Induction Motor R. Ibtiouen S. Mezani 0. Touhami

N. Nouali

M. Benhaddadi

Ecole Nationale Polytechnique Laboratoire de Machines Electriques BPI 82 El Harrach 16200 Alger (Algeria) E-mail: [email protected]

Institut de Physique USTHB B.P 32 El- Alia Bab-Ezzouar, Alger 16 1 1 1 E-mail: [email protected]

Ecole Polytechniquede MontrCal, Dept. de Genie Electrique et lnformatique Case Postale 6079, Montreal Canada H3C 3A7 3214 Email :[email protected]

Abstract -The authors deal with the thermal modeling of an induction motor of Totally Enclosed Fan Cooled "TEFC" design. Applications of nodal method and 2-D finite element method to calculate the temperature distribution within the considered machine are described. The obtained results are compared to temperature measurements performed on an induction motor.

I. INTRODUCTION

.

Rotating electrical machines have achieved a high level of performances especially with conventional energy supplies (sinusoidal or dc feedings). The development of power semiconductors and the increased need for motors with high power to weight ratio require the prediction of the thermal behavior of electrical machines. To insure a successful design of electrical machines, it is necessary to be able to predict an accurate temperature distribution in the most sensitive parts of the machine to prevent the damages that can occur either by breakdown of the stator winding insulation or by mechanical distortion and fatigue of the rotor structure. The prediction of the temperature distribution also allows to track its influence on the machine performances [1,2]. Two main methods are usually used to analyze the thermal behavior of electrical machines: nodal method and finite element method (FEM) [2,3,4]. This paper intends to describe and to discuss the application of these two methods to calculate the steady state temperature distribution inside an induction motor. To corroborate the theoretical. results, experimental investigations have been performed on an induction motor.

11. MEASUREMENTS The tested machine is a standard 3-phase, 4-po1eY2.2 kW, 380V TEFC induction motor manufactured in Algeria by ELECTRO-INDUSTRIES. The temperatures at different stator and rotor points were obtained using thermistor sensors. The locations of the thermistors in the machine are shown in Fig. 1. The signal from the rotor sensors is obtained using a slip rings system. More details about the experimental procedure can be found in [5]. The temperature distribution inside the machine at full load is presented in Fig. 2.

0-7803-7091-0/01/$10~2001 IEEE

I ,

Fig. 1 . Axial view of the motor showing location of sensors.

111. EQUIVALENT THERMAL NETWORK The principle of the nodal method consists in dividing the machine into basic thermal elements that represent a combination of conduction, convection and radiation heat transfer processes. The conduction process is governed by a second order differential equation whereas the convective heat transfer is described by the Newton's law of cooling. Any radiation effect is neglected in the present study. The regular structure and the symmetry of the machine make it possible to divide the machine into elements that are concentric around the shaft. If the asymmetry of the axial temperature distribution, due to the presence of the external fan, is neglected then only half the machine needs to be considered, as shown in Fig. 2. In developing a heat transfer model in a machine, it is assumed that heat flows only in the axial and radial directions which are completely independent of each other [2,3]. The circumferential heat flow is neglected. Fig. 3 shows a 2-D section of a hollow cylinder and its equivalent thermal circuit that derives from the resolution of R2 and R,,J the heat equations in the axial (R3) and radial (RI, directions [2,3].

505

r

e1

1, I

_.-.-Z Fig. 3. Two dimensional section of a hollow cylinder with its equivalent thermal circuit

7

t J

-1

Rm= Fig. 4. Equivalent thermal network of the induction machine

Iv.FINITE ELEMENT MODEL With & , 1 the thermal conductivities in the radial (r) and axial (z) directions respectively and 01 the angle of the section of the hollow cylinder.

A single thermal resistance R =-

1

hA

, where h is the film

coefficient and A is the area of contact with the cooling air, is used to model the convective heat transfer. The film coefficients used in the thermal network have been obtained either experimentally or analytically. In addition, a thermal resistance that allows for the poor thermal contact between the stator laminations and the frame is included [2,3]. The equivalent thermal network (ETN) of the motor is presented in Fig. 4. The machine has been divided into I O components numbered as follow : 1- Frame including the endcap, 2- Stator yoke, 3- Stator teeth, 4-Stator winding, 5- Air gap, 6- End winding, 7- Endcap air, 8- Rotor cage, 9- Rotor iron and IO- Shaft. A homogeneous toroid structure is assumed for the end windings whose the model is weighted to estimate the peak hot-spot temperature rather than the mean, [3].

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The 2-D study is done in an axial view. Because of radial and axial symmetries, only a quarter of the machine needs to be considered, Fig. 5. A geometrical simplification has been adopted for the end-windings. However, this simplification is done so the global volume of the real end-windings is maintained [2]. The axial plane may be either in the middle of a tooth or in the middle of a slot. To solve this problem and to take into account all sources in a 2-D axial study, the whole structure is replaced by concentric cylinders Fig. 5. To take into account the convective heat transfer in the air volumes (air-gap and endcap air), equivalent thermal conductivities "Artificial conductivities" obtained by experimental validation of the thermal model [6] is introduced. The standard finite element method is used to solve the heat equation in orthogonal coordinates. The boundary conditions considered in the present study are Dirichlet's condition that applies on lines OA and AB of Fig. 5 and Neumann's homogeneous condition that applies on lines OC and BC of Fig. 5 . The Dirichlet's condition is obtained by measuring the frame surface temperature (sensor "6",Fig. 1).

End-windmgs

Frame

TABLE I

Endcap

THERMAL CONDUCTIVITIES AND FILM COEFFICIENTS USED IN THE THERMAL MODELS

t a 1 w bark iron

air

I Thermalconductivitv I

I Endesp

Region

whn=.oc

Frame-ambient air

Ball bearing

Jt

End-ring

01

IC

Shall

Lx

Stator slot Stator end-winding Stator iron - frame boundary Air-gap Endcap air

v.RESULTS The values of the thermal conductivities and the film coefficients used in the two thermal models are listed in Table I. A comparison between measured and calculated temperatures is presented in Table 11. The underlined values in the FE model correspond to the teeth in contact with the air-gap. The calculated temperatures are in good agreement with the measured ones. Because of the compactness of the rotor structure where a good thermal contact exists between laminations and squirrel cage, there is an homogeneity of temperature distribution. This is also confirmed by the experimental results. The predicted shaft temperature is higher when using the finite element model. Highest temperature gradients are noted in the regions of low conductivity values (air-gap, endcap air, frame - stator iron boundary).

38 I38 3.5 13.5 5155 204 1204

Bearing Lamination Frame, endcap, rotor cage

Fig. 5. Studied structure for FE model

-

I

Film

386 10.9 386 10.9 0.07 10.07

416

0.5 10.5 0.25 10.25

132 28

TABLE I1

COMPARISON OF MEASURED AND CALCULATED TEMPERATURES AT FULL LOAD

I

Model Component

Shaft Rotor iron core Rotor bar End-ring Air-gap Endcap air Statorteeth

I

Measured I Calculatedtemaerature temperature (OC) ("C) FEM Em 109.65 109.20 78.83

101.40 102.52 103.59 101.27 104.04 84.28 104.50

I

93.45 114.01 114.38 114.38 99.42 83.54

VI. CONCLUSION A steady state thermal analysis of a 2.2 kW TEFC cage induction motor was successfully achieved. The application of finite element and nodal methods has been described and discussed. The predicted temperatures using these two methods are in close agreement with the measured ones, obtained by means of Thermistor sensors of the test motor. The described thermal models can be used as a tool for the design of unconventional machines, the improvement of the performances of a given structure and the online temperature estimation for the protection against thermal failures.

REFERENCES

[I] J. M. KaufFmann, B. Laporte, "Analyse des performances des machines dlectriques" RGE, No 8, Sept. 1994,pp. 36-40.

[2] D. Roye, Modelisation thermique des machines electriques tournantes. [3]

[4] [5]

ACKNOWLEDGEMENT The authors are very grateful to Electro - Industries Azazga (Algeria) for the financial support.

[6]

Application a la machine a induction, T h k de doctorat, I.N.P. Grenoble (France), Nov. 1983. P. H. Mellor, D. Roberts, D. R. Tumer, "Lumped parameter thermal model for electrical machines of TEFC design.",/EE Proc. 4 Vol. 138, No 5, Sept. 1991, pp. 205- 218. J. Driesen, R. Belmans, K. Hameyer, "Coupled magneto-thermal simulation of thermally anisotropic electrical machines", IEEE IEMDC'99, Seattle (USA), 1999, pp.469-471. M. Benhaddadi, R. Khaldi, M. Benghanem, "Experimental study of heating in induction motor fed by PWM inverter", IEEE Instr. and Measur. Tech. Conz, Ottawa (Canada), May 1997, pp. 335-338. R. Glises, "Machines dlectriques tournanteS. Simulation du comportement thermique", Techniques de I'Ingenieur, Traite Genie Electrique, 0 3 760.

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