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Submitted on 1 Jan 1993
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Thermal modelling for an induction motor
R. Glises, A. Miraoui, J. Kauffmann
To cite this version:
R. Glises, A. Miraoui, J. Kauffmann. Thermal modelling for an induction motor. Journal de Physique III, EDP Sciences, 1993, 3 (9), pp.1849-1859. �10.1051/jp3:1993245�. �jpa-00249048�
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 parambtres thermophysiques 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 magnetostatic
modulus 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 processing
tools. 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.
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].
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 O
Stator yoke ~
. ~
AW gap
Rotoryoke 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. Complementary
modelization 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
~id
1 ~ ~~~ --- ~ ~
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 h
Nu
= a (Re)~~ (Pr)[
d
(Re lm, = (p/7~ )m wd~/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),
w rotation 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 K
Boundary
layers Homogeneous dT/dn
= 0 dAz/dn
= 0
Neumann
I: lsotroplc conducth/ty p~: Mater~aJ magnetlc
coefficient In W/mK perrneabllty
Q: Power v~ume pa: Vacuum perrneabllty
production InW/m~ 4«.10'~
A: Laplace function J: Current densty
T: 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 only
radial 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 (SII(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 x 10~?,
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 thermocouples experimental 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
dq
I 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 boundary
conditions 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 reslstance
cf the area i ( f~
m ~
~
* j
lS
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(w
it 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 immediatly
after 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 design computation. 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 supply U=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 for a sinewave supply).
This phenomenon does not implicate the machine rotating speed. Indeed, the computation
shows 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 rotating speed 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 precision
is 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
