Thermal modelling for an induction motor

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Thermal modelling for an induction motorR. Glises, A. Miraoui, J. Kauffmann

To cite this version:R. Glises, A. Miraoui, J. Kauffmann. Thermal modelling for an induction motor. Journal de PhysiqueIII, EDP Sciences, 1993, 3 (9), pp.1849-1859. <10.1051/jp3:1993245>. <jpa-00249048>

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J. Phys. III Franc-e 3 (1993) 1849-1859 SEPTEMBER 1993, PAGE 1849

Classification

Physic-s Abstra<.ts

60.70 75.40M

Thermal modelling for an induction motor

R. Glises, A. Miraoui and J. M. Kauffmann

Institut de G6nie Energ£tique, 2 Avenue Jean Moulin, 90000 Belfort, France

(Re<.eiised 23 Mart-h J993, revised J4 June J993, accepted 24 June J993)

Rksumk. Les auteurs de cet article se proposent de rdaliser l'dtude du comportement therrnique

en rdgime permanent d'un moteur asynchrone de 4 kW h rotor bobin£. 66 thermocouples ant dt£

positionn£s en diffdrents lieux du stator tels que les milieux des bobinages, [es fonds d'encoches au

encore le milieu des tbles. Un modble a £td r£alis£ h l'aide du logiciel de calculs magndtostatiques

par dldments finis Flux2d converti en un outil de rdsolution de I'£quation de la chaleur. Une autre

originalitd de cette Etude a dtd d'introduire en certains endroits du moteur des zones oh la notion de

rdsistance therrnique de contact est particulidrement importante. L'introduction de parambtresthermophysiques les caract£risant s est avdrde ndcessaire pour obtenir la convergence expdrimenta-

tion-simulation.

Abstract. The authors of this paper intend to achieve the study of the thermal behaviour in

permanent rate of an asynchronous motor with a wounded rotor of a rated power of 4 kW.

66 thermocouples have been settled in the stator at different places like the centers and the bottoms

of the windings or the middle of the yoke. A design has been realized thanks to the magnetostaticmodulus of the computation software with the finite elements method Flux2d converted in a

resolution tool of the heat equation. Another originality of this study is to introduce areas including

a contact thermal resistance phenomenon in some places of the motor to characterize the motor

therrnophysical parameters and to obtain the experimentation-calculation convergence.

1. Introduction.

The analysis and the conceiving of the electrical machines in general, and of the asynchronous

in particular come necessarily through the study of their thermal behaviour. This study turns

out to be essential because a small temperature increase beyond the normal operating level,

may decrease the life duration for the windings with a factor 10 and for the ball bearings of the

mechanical axis with a factor 4.

The required quality of such studies can only be obtained thanks to powerful data processingtools. Indeed, the simulation coupled with some experimental testings seems to be one of the

most economical way, the fastest, and above all, the most flexible of use to determine and

forecast the temperature at each point with a great precision for different operating rates and

power supplies.

1850 JOURNAL DE PHYSIQUE III N° 9

Many studies have been conducted in the past and they mainly have used nodal resolution

methods, which limits partially the structure of the studied system [1, 2].

Recently powerful resolution software by finite elements has appeared and they permit to

consider and to resolve much more complicated geometrical models thanks to a high number of

computation nodes [3].

The authors of this paper develop an original thermal computation method iihich consists in

converting the magnetostatic modulus of the Flux2d software using a finite elements method,

in a resolution tool of the heat equation. The use of the heat equation for the whole machine can

be considered as valid. Indeed, experimental calculation temperature differences in the fluid

area are not very important because precise temperatures are exclusively wanted in the solid

areas of the machine like the windings and the ball bearings.The studied motor is an asynchronous wounded 4 kW motor. The cooling is achieved with

an external fan which is not connected to the driving shaft, so operating at constant speed. The

studied structure is a 2D radial view. The model is taken into account for an angular space of

15° which presents the minimum symmetry conditions concerning the heat flow.

The boundary conditions used for the temperature are the Dirichlet conditions and the

Neumann homogeneous conditions (aTlan=

0).

The validation of the software comes through the determination of therrnophysical

parameters which are the thermal conductivity coefficients of the materials. If their values for

the cast iron and the iron are given in handbooks, it is not at all the case for the windings made

of many elements like insulating materials and copper. Many air hollows are also present in the

slots, so it is necessary to consider equivalent global coefficients [4]. To determine these ones,

the addition of 66 thermocouples made of chromel-alumel in the stator, on the bottom and in

the center of the slots as well as in the middle of the yoke is very useful. Indeed, if the

temperature gradient between two points and the thermal flux value are known, it is enough to

particularize the material.

However, to obtain valid results, the introduction of particular areas in the machine where

the notion of thermal contact resistance is dominating has been made. These have been settled

around the windings, between the mechanical axis and the rotor iron as well as between the

stator iron and the cast iron surrounding the motor. These areas have been subject to different

studies [5]. They intervene systematically when two solids are joined side by side. Indeed, the

less or more important shortcomings of the area states often induce relatively weak contact

areas through which the heat flows are disturbed by the nature of the crossed environment. The

main consequence consists in strongly disturbed temperature fields.

For our structure, these areas have been assimilated to mixed materials. We gave thermal

conductivity coefficients values between that of the air (infavourable for the cooling) and that

of the surrounding materials. Only many computations coupled with tests have permitted to

determine the parameters with a good accuracy.

The first tests have been effected in direct current in the stator and in the rotor windings.Indeed, the determination of the parameters could be easier without heat generation in the

yoke. These tests have allowed to particularize each thermal conductivity parameter of the

machine thanks to the knowledge of the heat flux and the temperature.The validity of the software is shown through the responses of the thermocouples in

sinewave applied tests. The results are very satisfying because the temperature difference

between the tests and the calculation does not exceed 1.5 K.

If the sources coming from the losses by Joule effect are easily established, previous studies

in our laboratory, issued from a thermal measurement method permitted to locate and to

separate all the losses of the motor in the case of a sinewave supply [6].

N° 9 THERMAL MODELLING FOR AN INDUCTION MOTOR 1851

2. The motor and its environment.

The motor shown in figure has been surrounded by a cylindrical enclosure to keep the air

flow constant along the armature. It has been determined precisely by graphic integration and

by anenometric measurements. Temperature statements have been achieved by optical

pyrometry on the areas blackened before.

Cooling ruw Enclosum

Fig. I.

The inner structure of the motor is shown in figure 2.

Frame Q OStator yoke ~

.~

AW gap

Rotor yoke

Km

«

. o

~

.


66 thermocouples made of chromel-alumel of 50 ~cm diameter have been achieved and

tested before they have been settled in the stator, at the bottom of the slots, in the centers of the

windings and in the iron plates. These thermocouples have a very short time of response, in the

order of a few ms. Such a time is insignificant in front of the thermal inertia constant of the

machine (3 h to reach the permanent rate).

Moreover, it was important to insulate the thermocouples wires from the surrounding air

flows to avoid thermal gradient for the measurement validation. The radiation and the

convection heat transfer have been reasonably neglected in front of the low temperature levels

(65 °C mximum) and in front of the small hollows diameters in which the thermocouples have

been inserted. Such thermocouples are supposed to measure the ambient temperature to the

nearest 0.I °C, taking into account the data acquisition unit.

3. Studied structure.

A particular care has been considered to define the studied structure. Indeed, it is very

important to limit the geometry of the model to decrease the computation time. The studies

effected before in our laboratory have reinforced the opinion that a study in two dimensions is

enough to obtain good accuracy conceming the results of temperature calculation in the center

of the motor. It turns out, that without internal ventilation, the gradient temperature vector can

be considered as useless where are located the thermocouples [7]. It is established that the

acceptable angular space to consider to obtain the symmetry of the thermal flux lines is 15°

(Fig. 3).

_ iso

~

Fig. 3. -Studied radial view.

Each calculation needs boundary limits, those used for the study are as follows ;

. the ab and ac lines are submitted to Neumann homogeneous boundary conditions. The

temperature gradient is useless, conveying the absence of thermal flows (insulation con-

ditions) ;

. the line bc may be subject to two kinds of boundary limits, that is to say that of Dirichlet

implying the knowledge of the surface temperature or of Neumann not homogeneous for which

the radiative-convective phenomena must be perfectly known. So only the Dirichlet conditions

determined thanks to the optical pyrometer are used, giving the temperature within half a

degree.


To lighten the computation model, a structure without cooling fins is used. Complementarymodelization tests, where only these fins appeared have been effected to determine the

temperature at their feet in the middle of the materials. Such a structure permits to consider the

resolution of a 9 414 lines matrix with 6 terms per line in average.

THERMAL CONTACT RESISTANCE. Figure 4 shows a solid interface. The contact between

materials and 2 is not perfect and many small air volumes are present. Heat flux converge to

the real solid contacts because the air is an insulator. The thermal contact resistance is a

physical property which depends on thermal conductivities A and A~ and on the considered

thickness of the perturbed area.

Ti Tz Ti> T2

Jlluid

Pe«urI1ed area

~id1 ~

~~~ ----- ~ ~

Ti

T2 ------j-----~-------~

Fig. 4. -Thermal contact resistance between two solids.

Thermal contact resistances values are not very easy to foresee because they change from a

machine to another (influence of the materials cbntact pressure). Modelling permits us to

determine these values with a good accuracy. Paragraph 5 shows a comparison between

experimental values obtained with a flash method and values obtained with our method.

THE AIR-GAP- The air-gap has been the subject of a particular study. Indeed, it is not easy to

conclude immediatly on the thermal exchanges process existing in this annular space (Couette

flows).

The expression of the Nusselt Number adopted in the absence of an axial flow (no internal

fan) supplying realistic convection coefficients values is as follows

~f U5 hNu

= a (Re)~~ (Pr)[d

(Re lm,=

(p/7~ )mwd~/2

represents the number of Reynolds associated to the rotating movement

(p,i~=

(~c~iA i~


represents the number of Prandtl with

f air-gap length (m),

wrotation speed (rad/s),

d rotor diameter (m),

7~air dynamic viscosity (kg/m.s),

C~ air specific heat ratio (J/kg K),

A air thermal conductivity coefficient (W/mK),

p air density (kg/m3),

a, b, c constant values which depend on (Re)~, value.

The fluid characteristics are computed for an average temperature equal to the arithmetic

average of the area temperatures at the rotor and at the stator. The validity domain

corresponding to the ge6metry and to the temperature levels leads to respective values for a, b,

c of 2, 0, 0. Nu takes 2 for value and corresponds to a heat transfer process assimilated to the

pure conduction. This result was more or less expected taken into account the small size of the

air-gap (f=

0.35 mm).

4. Magnetostatic~thermal analogy.

Steady state equatlons TAT= =

Dlrlchlet T KBoundarylayers Homogeneous dT/dn

=0 dAz/dn

=0

Neumann

I: lsotroplc conducth/ty p~: Mater~aJ magnetlccoefficient In W/mK perrneabllty

Q: Power v~ume pa: Vacuum perrneablltyproduction In W/m~ 4«.10'~

A: Laplace function J: Current denstyT: Temperature (A/mm~

A: Laplace functlon

PotenthJ vector scalar

The sources constitute the most important problem to fit the analogy of these two equations.Considering the figure 5 in which the plan XOY is really represented by Flux2d.

In magnetostatics, the current densities J, represent the sources and are integrated in Flux2d

in A/mm2. These densities are expressed by vectors which are normal to the plan XOY

L

o x

Fig. 5. Studied volume.


represented in figure 5. For thermal problems, the sources P are power productions in watt

created in the middle of the volume I, which are crossing the area (S) (hypothesis of onlyradial thermal flux). It is necessary to convert these flows in flux densities (W/mm2) dividing P

by (S). The software multiplying J by po, the obtained entity is divided by po. It will then be

multiplied by the (S II (s) ratio because the current densities express themselves according to

(s).

Finally, during the results exploitation, to avoid isothermal field values in K/m, the area

(S) will be reset to a depth of I m. So the thermal sources Q wich will be integrated, will be

computed as follows.

~~

(s) ~

Ho~ (s) ~

i

or

~(P x 000 j

(s) x po x1

with

P power created in volume I (watt),

(s) area on which the current densities apply,

po vacuum permeability : 4 w x10~?,

1 structure depth.

5. Experiments with continuous and sinusoidal supplies.

The first kind of experiments consisted in supplying the motor in direct current at the stator and

at the rotor, which is open. This test is producing only thermal losses by Joule effect in the

windings and is very useful to particularize the thermophysical parameters of the materials and

of the flowing zones component of the motor. These thermal conductivity coefficients in the

solid points of the machine as well as in the mixed transfer zones are, a pt.iori, easier to

determine when there are no iron losses, if it is admitted that they are not uniformly distributed

in the stator iron.

The knowledge of the flux, (thermal sources), of the geometry and of the thermocouplesexperimental answers permits, after many tests, to surround precisely these parameters.

The Fourier law that is detailed hereafter in vectorial form is also exploited :

~~=-A dS.VT.n

dqI is the power exchanged across the ds area in watt,

dS exchange area,

n vector normal to the surface (or area),

VT temperature gradient vector.

During a test supplying a current of 15 A at the stator and of 5 A at the rotor, with boundaryconditions ranging from 300 K to 302 K, the following values have been considered :

Iron Rotor Cast Air Wnd~gs WlhdIng lto~ads Iron' (80°C) -lron cast

bound, bound,

1 67.6 45.82 55.8 0.03 0.5 0.1 0.07$ilrn.K~


Next table shows comparative values of the thermal contact resistances obtained with an

experimental method (flash method) for a similar motor [8] and ours obtained by simulation.

Method Thickness e (mm) Thermal contact reslstancecf the area i ( f~

m ~~

* jlS

0.4 0.2 2.0 10~

Slmulatlon 0.2 0.07 2.8 10~

Computations are made for a unit exchange surface S. It is a priori~ very difficult to say

where the difference of thermal contact resistance value comes from. Many parameters like the

contact pressure, the thermocouples responses or the localization of the heat flux influence the

final result. The 30 fb difference between these two values shows that the determination of that

thermophysical parameters of a computation method is very promising, especially in front of

the heavy experimental methods. In fact, these last methods are very useful to orientate and to

confirm the calculations.

Figure 6 shows the isothermal fields in the adopted structure as well as temperatures on two

lines of which the results appear in figure 7. These results have been obtained for surface

temperatures ranging from 299 K to 304 K.

T(wit 307.48

298.23 12 308.33

2 300.00 13 309,14

3 300.83 14 309.88

4 301.26 15310.81 j

5 302." 16311.94

6 303.32 17 312.47'~ ~~

7 304.15 18313.30

8 304.38 19 314.13~

9 305.82 20 314.89

lo 306.85 21 315.80

Fig. 6. Isothermal fields (direct current supply).

After having determined the thermophysical parameters, the modelling with sinusoidal

power supply is realized to confirm these values. The test has been performed under a 225 V

voltage between the stator phases and for a resistant torque on the driving shaft imposed by a

powder brake. The rotor rotating speed is of 450 tr/mn at permanent rate, that is to say after

3h operating. The useful sources for this handling have been separated during previous

experiments. Their values are as follows : 237 W for the stator copper losses, 118 W for the

rotor copper losses and 2 lo W for the stator iron losses. It has to be noticed that the rotor iron

losses have been neglected if we take into account the low frequency of the induced currents.

The value of the slip is 4 fl.


AT(K)

"~'/

/

331.6~~~ ~~r~nt supply

( is A stator / 5 A rotor)

Way no. 1

Way no. 2

321.6 ,

r(non)

316.6

20 60 100

Fig. 7. Radial temperature lines (overheating for a direct current supply).

The experiment-modelling convergence is really acceptable because, as it is shown in

following table, the obtained temperature differences do not exceed 1.5 K. It must be noticed

that the rotor winding temperature has been collected by a resistance measurement immediatlyafter the test. These results have been obtained for the Dirichlet boundary conditions between

307 K and 309 K.

temp. flQ Model,

35g.85 360.66 o-U

Mlddla Statof Wind. 333.53 335.11 1.57

Bottom SWOr wind. 328.87 327.43 1.44

Mlddle Stator Iron 325.31 324.02 1.29

5 318.30

T(K~ 6 335.65

7 340.25

308.52 8 345.25

2 314.64 9 350.47

3 319.75 lo 355.12 2

4 324.27 II 360.70

5 6 2

7

Fig. 8. Isothermal lines (sinewave supply).


6. Interpreting the results.

The first remark concems the fact that the rotor position is not very important in that designcomputation. Indeed, it is established by comparison of the temperature on the two lines in

figures 7 and 9, that the temperature keeps nearly unvarying for the rotor. Only a light increase

is noted in the windings. A small temperature increase is however recorded.

AT(K>

384.5

Sinewave supplyU=225 V / C

=18 Nom

364.5 Way no. 1

Way no. 2~_ ~

i

344.5

32405~~~'~'~

20 6o 1M

Fig. 9. -Radial temperature lines (overheating fora sinewave supply).

This phenomenon does not implicate the machine rotating speed. Indeed, the computationshows clearly that the conductive heat transfer mode in the air-gap would begin to change only

for a minimum speed of 15 000 tr/mn where Taylor cells would appear, so, for any rotatingspeed of the structure, the air-gap remains an insulator when there is no intemal axial cooling.

The second remark which these tests do inspire, is that a great surface temperature precisionis not very useful, because the presence of the mixed transfer zone stator iron-cast makes

rapidly the isothermal lines parallel. In these zones, highest temperature gradients were

normally noted, as well as in all the zones with low conductivity coefficient.

7. Conclusions.

The hypothesis of a two dimension radial study centered in the middle of the iron seems to be

confirmed through the thermophysical parameters values reliability in the sinusoidal test. Even

if the results do not appear in this paper, other confirmations came into sight for many

continuous tests, in particular.

The magnetostatic software Flux2d has been easily converted in a heat equation resolution

tool, it means applicable to the conduction transfer modes. It is necessary to keep careful for

electrical machines for which such transfer modes are no more applicable, for large air-gaps


where the convective phenomena take precedence. In such cases, it would be necessary to

change the value of the air thermal conductivity parameter to conserve the heat flux as

constant. So the temperature values in the solid parts of the motor would be sure, even if the air

temperature measurements are not accurate. But the most important is to determine and

forecast the temperature levels in the solid parts.The computation has been largely simplified thanks to the addition of the Dirichlet boundary

conditions, obtained directly by optical pyrometry. The homogeneous Neumann conditions are

more complicated of use because it is necessary to determine the convection exchangecoefficients which are function of the air temperatures of the area and of the fluid speed.

References

II Roye D., Mod61isation thermique des machines dlectriques toumantes. Application h la machine ~

induction. Thdse d'Etat I.N.P. Grenoble (1983).

[2] Chamagne D., Sidibe M. D., Kauffmann J. M., Moddlisation therrnique d'un moteur sans balais.

Couplage avec Ie modme £Iectrique. Collcque Intemational sur les moteurs pas § pas. Nancy(Juillet 1992).

[3] Satiraman V., Saxena R. B., Steady state thermal analysis of electrical machines by E.F. method, J.

Jnsr. Eng. (JNDJA) Elect. Eng. Div. 64 (1984) 201-206.

[4] Weil L., Echanges thermiques. Notes de cours.

[5] Bardon J. P., Introduction h l'6tude des r6sistances therrniques de contact, Rev. Grin£rate Thermique

n 125 (Mai 1972) 429-447.

[6] Mohamed Ali Y., Glises R., Pham Huu Phut, Cartographic des temp6ratures dans le stator d'une

machine asynchrone alimentde par des convertisseurs de puissance, Joum6es S-F-T. (22-23 mai

1991) Belfort, France.

[7] Glises R., Mohamed Ali Y., Kauffmann J. M., Estimation des penes therrniques d'un moteur

asynchrone de moyenne puissance. Colloque S-F-T-, Sophia Antipolis (Mai 1992).

[8] Bertin Y., Analyse des transferts de chaleur dans un moteur 61ectrique asynchrone. D6veloppementd'un environnement C.A.O, et moddlisations therrnoa6rauIiques. Thdse de Doctorat de

l'Universit6 de Poitiers (1987).

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Thermal modelling for an induction motor