2006 icem (gerling - dajaku)

7/22/2019 2006 ICEM (Gerling - Dajaku)

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ABSTRACT – The lumped-parameter thermal method (conventional lumped-parameter thermal method) has beenused for a long time for calculation of the temperature risesin electric machines. In spite of being popular, generallythis method is not applied correctly for elements with

distributed heat generation. To overcome the drawbacks of this method, in this paper, a novel thermal model for

electrical machines is developed. Using this model, the

thermal performances of a PM machine are analysed. Theaccuracy of this model has been verified by comparingwith FEM calculations.

I. INTRODUCTION

Permanent magnet synchronous machines (PMSM)

gain more and more importance for special driveapplications. Up to recent years, PMSM were known for small drives, e.g. for servo applications. In the last years,PMSM are increasingly applied in several areas such astraction, automobiles, etc. Therefore, development of

different machine types requires attention to the thermalaspects since, at the end, it is always the thermalconstraints that will determine the power rating of themachine. To insure a successful design of the electricalmachines, it is necessary to be able to predict an accuratetemperature distribution in the most sensitive parts of themachine to prevent the damages that can occur either by

breakdown of the stator winding insulation or by thedemagnetization of the magnets. Knowledge of thermal behaviour in different situations can prevent overheating, but can also improve the utilization of the system at normaloperation.

As is known, different calculation methods can be

used to analyse the thermal behaviour of electricalmachines: exact analytical calculation (“distributed lossmodel”), numerical analysis, and the lumped-parameter or nodal method (“concentrated loss model”). Compared withother methods, the lumped-parameter thermal method issimple and attractive which can give accuraterepresentation of the thermal conditions within the

machine. This method has been used for a long time bymany authors for calculation of the temperature rises inelectric machines, which solves the thermal problems byapplying thermal networks in analogy to electrical circuits.Generally, the lumped-parameter thermal model iscomposed of thermal resistances, thermal capacitances and

power losses inside the system. Such a model is based onthe hypothesis that the system, under the thermal point of view, can be divided into several parts that are connected

An Improved Lumped Parameter Thermal Model for Electrical Machines

G. Dajaku, D. Gerling

Institute for Electrical Drives, University of Federal Defense MunichWerner-Heisenberg-Weg 39, D-85577 Neubiberg, Germany, tel: +49 89 6004 3708, fax: +49 89 6004 3718,

e-mail: [email protected], [email protected]

to each other by means of thermal resistors and capacitors.In the equivalent thermal network, all the heat generationin the component is concentrated in one point. This pointrepresents the mean temperature of the component. In

many literatures [4]-[15], during calculation of thermalcharacteristics using the lumped-parameter method, as heatgenerators are taken the corresponding power losses in thecomponents. In spite of being popular, generally this

method is not applied correctly for elements withdistributed heat generation. From the thermal analysis presented in [1], [2] it is shown that solving the thermal

problems with this method leads to wrong results if thetotal power losses are taken as heat sources in the thermalnetwork (conventional lumped-parameter method). In the past, this systematic mistake was unknown, but instrinsiclyeliminated by the fitting procedure. Based on the analysis presented in [1], [2], the required change to theconventional lumped-parameter thermal method to omitthis systematic mistake is simple, but decisive:

• Calculating a single lossy element, half of the

losses should be applied as heat generator source,

• Calculating a more complex system composed of more than one lossy element, compensating

elements have to be introduced into thelumped-parameter thermal network,

• Transient calculations can easily be developed

from the described steady state analysis.

II. THERMAL MODELING OF ELECRICAL

MACHINES

During the thermal analysis with lumped parameter

method, the electrical machine is divided geometricallyinto a number of lumped components, each componenthaving a bulk thermal storage and heat generation and interconnenctions to neighbouring components through alinear mesh of thermal impedances. The lumped

parameters are derived from entirely dimensionalinformation, the thermal properties of the materials used in

the design, and constant heat transfer coefficients. Thethermal circuit in steady-state condition consists of thermalresistances and heat sources connected between thecomponent nodes. For transient analysis, the heat thermal

capacitances are used additionally to take into account thechange in internal energy of the body with the time.

Heat transfer in electrical machines is a combinationof conduction within solid and laminated components, and convection from surfaces which are in contact with air or

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other cooling fluids. This section describes the thermalmodelling procedure of electrical machines with differentrotor topologies. The axial cut of a PM machine withsurface mounted magnets in the rotor is shown in figure1.

Figure 1. The axial cut of the electrical machine

In general, the geometric complexity of an electricmachine requires a large thermal network if a solution witha high resolution of the temperature distribution isrequired. Instead of using a large, complex model, thegeometrical symmetries of the machine were used to

reduce the order of the model. The distributed thermal properties have been lumped together to form a small

thermal network, representing the whole machine. Thefollowing assumptions have been made during thisanalysis:

• The motor has the following symmetricalcharacteristics: cylindrical around the shaft and mirror-like concerning a plane perpendicular tothe shaft in the middle of the shaft length,

• Each cylinder is thermally symmetrical in theradial direction,

• The inner heat sources are uniformly distributed,

• The heat flux in the axial direction has beenconsidered only in the shaft. It has been neglected

in the rest of the machine. In this way, the thermalradial resistance can be computed using the

equations of the hollow cylinder.

Based on the above assumptions, the electric machineis divided geometrically into a number of components. The

number of the nodes is reduced to seven that providesthermal access to all key elements inside the machine. One

node (1) is placed in the stator frame. Two nodes (2, 3)were used for the stator core, which is the largest machine part usually exposed to high temperature gradients. The

placement of one node (2) is taken to be in the stator yokeand one in the stator teeth (3). Motor operation at hightorque is associated with large heat dissipation in themachine windings. Two separate nodes are assigned to thestator windings, making it possible to separately estimatethe temperatures of the coil sides embedded in the stator core and the end windings. Therefore, in the model presented, there are two nodes (4, 5) representing the

windings; one node (5) for the end windings and one for the coil sides (4). It is assumed that heat dissipated fromthe end winding enters the slots via the conductors. As theend winding reaches the slot, heat starts to flow into thestator iron core and further out to the stator frame.

Predicting the temperature of the rotor, especially of the permanent magnets (for a PMSM), is of great importance.The behaviour of the permanent magnet material at

increased temperature can involve risk for permanentdemagnetization. For this reason, two nodes (6, 7) wereused for the rotor. The placement of one node is taken inthe first rotor layer (bandage) (6) and the other one in the

magnets (7).According to [1], [2] and the above modeling

concepts, each element is identified by a node in the

equivalent circuit and is associated with a thermalcapacitance, a heat source and correspondingcompensation thermal elements. The nodes are put in the

middle of each corresponding component and are coupled to their neighbours by thermal resistances. Figure 2 showsthe improved thermal model for the i-th element.

Therefore, development of a thermal model can bedivided into four parts:

• Forming the thermal network for the electricmachine,

• Determining the thermal resistances and capacitances,

• Determining the compensation thermal elements,

• Determining the losses and their distribution inthe machine.

All these items are important for the calculation of thethermal performances of the electrical machines.

Figure 2. Lumped-parameter thermal model with compensationelements for the i-th element

II.1 THERMAL RESISTANCES

It is possible to distinguish between two types of

resistances, depending on the kind of thermal exchange between the surfaces of the concentric cylinders that theyrepresent: one is the conduction heat transfer inside solid masses, and the other one is the convection heat transfer through the surface separating a solid mass from the fluid.The conduction thermal resistance in radial direction for a

hollow cylinder can be calculated as follows [3]:

( )ln /

2

o i

conduction

r r R

k Lπ

=⋅ ⋅

(1)

where, with , , L, and k are denoted the cylinder

outside radius, inside radius, the axial length, and thermal

conductivity of the material.

or ir

If a temperature exchange due to the convection exists,

the heat-transfer rate is related to the overall temperaturedifference between the wall and fluid and the convectionarea A. The convection resistance is defined as [3]:

1convection R

h A= ⋅ (2)



The quantity h is called the convection heat transfer coefficient. An analytical calculation of h may be made for some systems. For a complex situation it must bedetermined experimentally. The heat transfer coefficient in

many literatures is called as film conductance because of its relation to the conduction process in this stationarylayer of fluid at the wall surface.

During thermal modelling of the electric machines,the mechanical contacts are important, for example, between the winding and teeth as well as between the

stator core and frame. A poor mechanical contact has gas pockets which decreases the heat transfer across the joint.The temperature drop between two contact surfaces is theresult of a thermal contact resistance [3],

1contact

cont

Rh A

=⋅

(3)

where, is called the contact coefficient and A is the

contact surface area. The value of the contact coefficient,

, depends on different factors such as: contact surface,

thickness of the void space, thermal conductivity of thefluid which fills the void space, pressure etc. The contactcoefficient for different materials and surface types is

difficult to be calculated, and has to be determined experimentally.

cont h

cont h

II.2 THERMAL CAPACITANCES

In time dependent problems, a representation of thestored thermal energy in the system is introduced asthermal capacitances. Each node is assigned with a thermal

capacitance from the node to ambient. The thermalcapacitance of an element is derived from geometrical and

material data of the machine,

(4)thi i iC m= ⋅c

where is the mass and is the specific heat capacity

of the i-th element.i

mi

c

II.3 COMPENSATION THERMAL ELEMENTS

According to [2], some compensation thermalelements have to be used in the improved thermal network

to compensate the temperature error obtained from theconventional lumped-parameter method loaded with thetotal power losses. If the nodes of the thermal network areapplied to the middle of each corresponding machine

component (as is performed during the following thermalanalyis of the PM machine), the expression for the

compensation elements for this modeling case is [2]:

,

,4 2

, Losses i th i

comp i

P Rt = ⋅ (5)

In analogy to the basic reason for the error of theconventional lumped-parameter method, where the heatgeneration of the regarded element leads to the gradient

temperature error inside the own element, in some casesthe heat generation of one element leads to the temperatureerror in the neighbouring component. In electric machines

this effect appears in the slot-teeth region. The heatgeneration in the stator slot leads to the wrong temperaturein the teeth region, and afterwards it is reflected to allcomponents of the electric machines. Therefore, to

compensate this temperature error, additional compesation

temperature elements between the midpoint of the stator teeth and its corresponding end points have to be used.

II.4 HEAT SOURCES

The heat generation due to losses in the different

machine components was introduced with currentgenerator parallel connected to the thermal components of the machine parts that generate these losses. The losses of an electric machine consist of: stator iron losses, stator copper losses, rotor losses and friction losses. The power losses can be calculated analytically or using FE methods.

For each operating condition, the calculated losses of theelectric machine have to be used as the thermal model

inputs. Because the parameters of the electrical machines(winding resistance R and the magnet remanence Brem) aretemperature dependent parameters, there is a strong

interaction between the electromagnetic and thermalanalysis, i.e. the losses are critically dependent on thetemperature and vice versa.

III. A SIMPLIFIED THERMAL NETWORK

FOR ELECTRICAL MACHINES

Based on the modifications and improvements

proposed in [1], [2], in this paper, a novel lumped-

parameter thermal model (lumped-parameter model withcompensation thermal elements) for the thermal analysis of

electrical machines with different rotor topologies is

developed, figure 3. This model consists of a seven-node

network that captures all key machine temperatures. For

PM machines with different rotor topologies the only

resistances that will be different in the thermal model

presented in figure 3 are , , and .5th R 6th

R 10th R

Figure 3. A novel lumped-parameter model for electrical

machines.

Using the above expressions, the model parameters

can be derived from the entire dimensional information of



the electric machine, the thermal properties of the material

used in the design, and constant heat transfer coefficients.

In the following Tables the thermal resistances and the

compensation elements of the thermal network are

explained briefly.

TABLE I: Thermal resistances

TABLE II: Compensation thermal elements

IV. SIMULATION RESULTS

In the following analysis, the thermal model given inthe figure 3 is implemented to calculate the thermal performances of a PM machine with surface mounted

magnets in the rotor. It has a stator outer diameter of 280mm and an active length of 68 mm. The motor is designed for a wide operation speed range (0-6000 rpm). Figure 4shows the cross-section of the studied machine.

Meaning of the thermal resistances

0th R Forced convection thermal resistance between

stator frame and cooling channels

1th R Equivalent thermal resistance between the stator

yoke midpoint and stator frame

2th R Equivalent thermal resistance between the stator teeth midpoint and stator yoke midpoint

3th R Equivalent thermal resistance between the coil side

and the stator teeth midpoint

3th R′ Equivalent thermal resistance between the coil side

and the stator yoke midpoint

4th R Equivalent thermal resistance between the coil side

and the end-winding node

5th R Equivalent thermal resistance between the stator

teeth midpoint and the first layer midpoint6th R Equivalent thermal resistance between the first

layer midpoint and the second layer midpoint

7th R Equivalent thermal resistance between the second

layer midpoint and the stator frame

8th R Equivalent thermal resistance between the end-

winding node and the stator frame

9th R Equivalent thermal resistance between the end-

winding node and the second layer midpoint

10th R Equivalent thermal resistance between the second

layer midpoint and the ambient

Figure 4. Geometry of the analysed PM machine.

The stator of the PM machine is mounted along itsouter periphery in an aluminium cylinder, which is cooled by forced water flowing through serial-circumferentiallycooling channels. Furthermore, water-cooling of the stator

frame was chosen to achieve a compact motor construction, and by making the cooling channels spiralshaped, the temperature differences along the framesurface can be kept small. Table III shows the calculated steady-state temperatures for different operation conditionswhen the stator frame temperature is 90 ˚ C .

TABLE III: Steady-state temperature Meaning of the thermal compensation elements

-Y Fr t Stator yoke – frame

-Y T t Stator yoke – teeth

-Y Cst Stator yoke – coil side

Stator yoke compensation

thermal elements due to

losses

YokeP

T-Yt Stator teeth – yoke

T-Agt Stator teeth – air gap

Stator teeth compensation


losses

TeethP

S

Teetht Stator teeth compensation thermal elements due to

losses-Coil sideP

Cs-Yt Coil side – stator yoke

Cs-Tt Coil side – stator teeth

Cs-Ewt Coil side – end

winding

Stator coil side compensation


losses

-Coil sideP

Ew-Cst End winding – coil

side

End-winding comp. thermal

elements due to - End wind P losses

L1-Agt Layer 1 – stator teeth

L1-Rct Layer 1 – rotor core

First layer compensation

thermal elements due to 1 Layer P

losses

Rc-L1t Rotor core – first layer Second layer compensation

thermal elements due to 2 Layer P

losses (magnets)

Speed [rpm] 500 3000 6000

-Frame [ C̊]1T 90 90 90

-Yoke [ C̊]2T 104.07 105.56 103.08

-Teeth [ C̊]3T 140.03 145.28 136.27

-Coil side [ C̊]4T 195.83 199.67 161.53

-End winding [ C̊]5T 203.1 206.4 164.85

-Layer 1 [ C̊]6T 122.12 163.93 181.8

-Rotor [ C̊]7T 121.69 163.9 183.18

IV.1 SENSITIVY ANALYSISIt must be denoted here, that the above calculations

are made for an ideal case. The equivalent thermal

conductivity and the thickness of the insulation layer in the

stator slot is taken to be W/(m˚ C) and 0.25eq

k = 0.5eq

x =

mm, respectively. In addition, the frame temperature is

taken to be constant for different operation conditions of

the PM machine. The effect of these parameters on the

thermal performances of the electric machine is discussed

below.

IV.1.1 COOLING EFFECTGenerally, for the water-cooled electric machine in the

stator frame, the total heat generated in the electric



machine flows throughout the components of the electricmachine to the frame and then by the convection the heat istransferred away to the coolant. In the figure 3, the heattransfer from the stator frame to the coolant is presented

with a convective thermal resistance . This parameter

depends on many factors, such as geometry of the coolingsurface, cooling effectivity etc., and requires a careful

consideration because of its position in the main heat flow path of the stator losses to the ambient. To show theinfluence of the stator frame convection heat transfer coefficient in the thermal performances of the PMmachine, the temperature is calculated for the differentstator frame cooling conditions. The following calculations

are done for the case when the coolant temperature is 90ºC , and the PM machine operates at 500 rpm. The other parameters of the thermal model are taken to be the sameas in the previous calculation. Table IV shows thetemperature variation in the PM machine for differentconvection heat transfer coefficients.

0th R

TABLE IV: Influence of the stator frame cooling

h 2

/( C)oW m⎡ ⋅⎣ ⎤⎦1000 6000 12000

0th R [ C̊/W] 0.0128 0.0023 0.0012

-Frame [ C̊]1T 156.8 102.13 96.33

-Yoke [ C̊]2T 170.69 116.16 110.38

-Teeth [ C̊]3T 206.06 152.02 146.29

-Coil side [ C̊]4T 262 207.84 202.12

-End winding [ C̊]5T 269.17 215.1 209.36

-Layer 1 [ C̊]6T 159.78 128.96 125.69

-Rotor [ C̊]7T 158.82 128.42 125.21

Table IV shows that the frame temperature (and as aconsequence the temperatures at the other parts of the PMmachine) varies with the variation of the heat transfer coefficient. Increasing the cooling intensity (using an

effective cooling method), clearly decreases thetemperature in all components of the machine.

IV.1.2 INFLUENCE OF THE SLOT INSULATION

MATERIAL

Various modelling strategies have been developed by

many authors to model the heat transfer and temperature

distribution within a winding. One of them is thecomposite thermal conductivity method [4] in which thecalculations of the thermal resistance perpendicular to the

winding conductors were made by considering theinsulated conductors and impregnation material ashomogeneous body of slot material. The slot region ismodeled with an homogeneous material (copper) at the slotcenter, insulated with an equivalent insulation layer. Thisinsulation layer is characterised by an equivalent thermal

conductivity , which takes into account the thermal

conductivity of:

eqk

- the slot insulation layer,

- air-gap between the slot insulation and thelaminations,

- the insulation varnish of the windings, and

- the air-gaps between the conductors.

The equivalent thermal conductivity is difficult to bedetermined analytically. For this parameter, a thermal test, proposed in [4], with a stator DC supply is simplyrequested. According to the experimental results made for an induction motor [15], the equivalent thermal

conductivity can be considered in the range of 0.06 to 0.09W/(m˚ C).In the above thermal analysis, an insulation material

with thermal conductivity W/(m˚ C) and

thickness

0.25eq

k =

0.5eq

x = mm is taken during the simulation. To

show the influence of the equivalent insulation layer on the

thermal performances of the electric machine, the

following calculations are made for different values of .

For stator frame convection

coefficient, the steady-state temperatures of the electricmachine at 500 rpm are presented in the Table V.

eqk

212000 /( C)o

h W m= ⋅

TABLE V: Influence of slot insulation material [W/(m C̊)]eqk 0.25 0.1 0.06

3th R [ C̊/W] 0.0148 0.0360 0.0597

3th R′ [ C̊/W] 0.0654 0.1574 0.2597

-Frame [ C̊]1T 96.33 96.33 96.33

-Yoke [ C̊]2T 110.38 110.21 110

-Teeth [ C̊]3T 146.29 148.45 148.57

-Coil side [ C̊]4T 202.12 291.95 387.98

-End winding [ C̊]5T 209.36 298.63 394.05

-Layer 1 [ C̊]6T 125.69 129.21 131.91

-Rotor [ C̊]7T 125.21 128.73 131.48

Table V shows that the equivalent thermalconductivity of the insulation layer has a significant effecton the stator windings temperature. To improve the

thermal characteristics of the electric machine, especiallyin the stator windings, the slot insulation material with

high thermal conductivity must be used.

From the above analysis it is shown that the stator frame temperature depends on the efficiency of the cooling

method and the generated power losses in the electricmachine. The variation of the convection heat transfer

coefficient in the stator frame alters the temperature rise inall components of the electric machine. Otherwise, the end winding temperature is of great importance since it is the part in the machine, which reaches the highest temperature.

As is shown in Table V, and affect the predicted

end winding temperature significantly. Focusing onregions with high temperature gradients is especiallyimportant here. In this case, the slot insulation and air pockets around the stator windings should be brought to

attention.

3th R 3th R′

IV.2 COMPARISON WITH FE METHODS

In this section the proposed thermal model isvalidated by comparison with FE methods. Figure 5 shows

the temperature distribution inside the PM machine. The



FE simulations are performed under the followingconditions: 500 rpm operating speed, 90 °C coolant

temperature, (coolant convection

coefficient), and W/(m˚ C) (thermal conductivity

of the slot insulation layer).

212000 /( C)oh W m= ⋅

0.25eq

k =

Figure 5: Temperature distribution inside the PM machine.

Under the same simulation conditions, Table VI comparesthe results obtained from the improved lumped-parameter thermal method, conventional lumped-parameter thermalmethod, and from ANSYS thermal analysis.

TABLE VI: Comparison of results.

As is shown in the Table VI, the calculation resultsobtained with the improved lumped-parameter method arein good agreement with the ANSYS results. Comparing theconventional lumped-parameter method and the ANSYSresults, it is shown that in some sections of the studied

electric machine such as in the stator teeth, coil side, and end winding, there is a relatively large discrepancy

between the results. Based on the expression for thecompensation thermal elements presented in the sectionII.3, the deviation of the results obtained with conventional lumped-parameter thermal method from an accurate

calculation method (FEM, improved lumped-parameter method) depends on the operation conditions of the studied machine (power losses), thermal characteristics of thematerials, and the operation temperature (thermalconductivity of the materials vary with the temperature).

V. CONCLUSION

In this paper, an improved lumped-parameter thermal

model (lumped-parameter method with compensationthermal elements) for the thermal performances of

electrical machines is developed and analysed. This modelhas been applied to predict the thermal behaviour of a PM

machine. The influence of the equivalent slot insulationmaterial and the cooling efficiency on the thermal performances of the studied PM machine is investigated.Furthermore, a comparison with FEM is performed. It is

shown that the calculation results obtained with theimproved lumped-parameter method are in good agreement with the ANSYS results.

VI. REFERENCES

[1] Dajaku G., Gerling D., “Novel lumped-parameter thermalmodel for electrical systems”, EPE 2005, Dresden,

Germany, CD-ROM proceedings.[2] Dajaku G., Gerling D., “Thermal Calculation of Systems

with Distributed Heat Generation”, ITherm 2006, San

Diego, CA USA, CD-ROM proceedings.

[3] Holman J. P., “Heat Transfer”, McGraw– Hill Publishing

Company, 1990.

[4] Boglietti A., Cavagnino A., Lazzari M., “A Simplified

Thermal Model for Variable-Speed Self-Cooled Industrial

Induction Motor”. IEEE Transactions on Industry Application, 2003.

[5] Mellor H., Roberts D., Turner, R.: “Lumped parameter

thermal model for electric machines of TEFC design”,

IEE Proceedings on Industry Application, September 1991.

[6] Liu Z. J., Howe D, Mellor P. H., “Thermal analysis of

permanent magnet machines”, IEE Proceedings on

Electrical Machines and Drives, 1993, p. 359-364.

[7] Trigeol J.-F., Girault M., Bertin Y., “Estimation of the heat

losses in an electrical machine using an inverse method”,

International Conference on Electrical Machines (ICEM),

2004, Cracow, Poland.

[8] Parviainen A., Pyrhönen J., Niemelä M., “Modeling of

Axial Flux PM Machines Thermal Analysis”, International

Conference on Electrical Machines, 2004, Cracow, Poland.[9] Cho S. M., Jung S. Y., Jung H. K., “Thermal characteristics

and experimental validation in steel cored PMLSM

considering running condition”, International Conference

on Electrical Machines (ICEM), 2004, Cracow, Poland.

[10] Chin Y. K., Staton D. A., Soulard J., “Thermal Lumped

Circuit and Finite Element Analysis of a Permanent

Magnet Traction Motor”, International Conference on

Electrical Machines (ICEM), 2004, Cracow, Poland.

[11] Tang W. H., Wu Q. H., Richardson Z. J., “A Simplified

Transformer Thermal Model Based on Thermal-Electric

Analogy”, IEEE Transactions on Power Delivery, Vol. 19,

No. 3, July 2004.

[12] Lindström J., “Thermal model of a Permanent-Magnet

Motor for a Hybrid Electric Vehicle”. Licentiate thesis,

Chalmers University of Technology, Göteborg, Sweden,

April 1999.

[13] Neudorfer H., “Thermische Untersuchung und Berechnung

eines flüssigkeitsgekühlten Traktionsmotors mit

Getriebeölwellenkühlung”, Dissertation, University of

Technology, Vienna, Austria, 1998 (in German).

[14] Staton D. A., “Thermal Computer Aided Design –

Advancing the Revolution in Compact Motors”, IEEE

International Electric Machines and Drives Conference

(IEMDC), 2001, Cambridge, Mass., USA.

[15] Staton, D. A., Boglietti A., Cavagnino A., “Solving the

more difficult aspects of electric motor thermal analysis”.

IEEE International Electric Machines and DrivesConference, 2003, IEMD’03, Volume:2, 1-4 June 2003.

Temperature of the PM

machine at 500 rpm

ANSYS

2D

Improved

LPM

Conventional

LPM

-Frame [ C̊]1T 97.26 96.33 96.33

-Yoke [ C̊]2T 110.7 110.38 110.36

-Teeth [ C̊]3T 145.6 146.29 152

-Coil side [ C̊]4T 202.49 202.12 207.2

-End winding [ C̊]5T -- 209.36 222.35

-Layer 1 [ C̊]6T 124.6 125.69 125.78

-Magnets [ C̊]7T 124.01 125.21 125.32

2006 icem (gerling - dajaku)

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