the induction machine handbook chuong (12)

We will define first the elements of thermal circuits based on the three basic methods of heat transfer: conduction, convection and radiation.. In electric induction machines, the therma

12.1 INTRODUCTION

Besides electromagnetic, mechanical and thermal designs are equally

important

Thermal modeling of an electric machine is in fact more nonlinear than

electromagnetic modeling Any electric machine design is highly thermally

constrained

The heat transfer in an induction motor depends on the level and location of

losses, machine geometry, and the method of cooling

Electric machines work in environments with temperatures varied, say from

–200C to 500C, or from 200 to 1000 in special applications

The thermal design should make sure that the motor windings temperatures

do not exceed the limit for the pertinent insulation class, in the worst situation

Heat removal and the temperature distribution within the induction motor are

the two major objectives of thermal design Finding the highest winding

temperature spots is crucial to insulation (and machine) working life

The maximum winding temperatures in relation to insulation classes shown

in Table 12.1

Table 12.1 Insulation classes

Insulation class Typical winding temperature limit [ 0 C]

Practice has shown that increasing the winding temperature over the

insulation class limit reduces the insulation life L versus its value L0 at the

insulation class temperature (Figure 12.1)

T

baL

It is very important to set the maximum winding temperature as a design

constraint The highest temperature spot is usually located in the stator end

connections The rotor cage bars experience a larger temperature, but they are

not, in general, insulated from the rotor core If they are, the maximum

(insulation class dependent) rotor cage temperature also has to be observed

The thermal modeling depends essentially on the cooling approach

Figure 12.1 Insulation life versus temperature rise

12.2 SOME AIR COOLING METHODS FOR IMs

For induction motors, there are four main classes of cooling systems

• Totally enclosed design with natural (zero air speed) ventilation (TENV)

• Drip-proof axial internal cooling

• Drip-proof radial internal cooling

• Drip-proof radial-axial cooling

In general, fan air-cooling is typical for induction motors Only for very large powers is a second heat exchange medium (forced air or liquid) used in the stator to transfer the heat to the ambient

TENV induction motors are typical for special servos to be mounted on machine tools etc., where limited space is available It is also common for some static power converter-fed IMs, that operate at large loads for extended periods

of time at low speeds to have an external ventilator running at constant speed to maintain high cooling in all conditions

The totally enclosed motor cooling system with external ventilator only (Figure 12.2b) has been extended lately to hundreds of kW by using finned stator frames

medium and large powers

However, axial cooling with internal ventilator and rotor, stator axial channels in the core, and special rotor slots seem to gain ground for very large power as it allows lower rotor diameter and, finally, greater efficiency is obtained, especially with two pole motors (Figure 12.3) [2]

a.)

end ring vents

b.)

finned frame

externalventilator

b.) totally enclosed motor with internal and external ventilator

c.) radially cooled IM d.) radial – axial cooling system

The rotor slots are provided with axial channels to facilitate a kind of direct cooling

axial channel

internal ventilator

axial rotor channel

axial rotor cooling channel

rotor slots

Figure 12.3 Axial cooling of large IMs

The rather complex (anisotropic) structure of the IM for all cooling systems presented in Figures 12.2 and 12.3 suggests that the thermal modeling has to be rather difficult to build

There are thermal circuit models and distributed (FEM) models Thermal circuit models are similar to electric circuits and they may be used both for thermal steady state and transients They are less precise but easy to handle and require a smaller computation effort In contrast, distributed (FEM) models are more precise but require large amounts of computation time

We will define first the elements of thermal circuits based on the three basic methods of heat transfer: conduction, convection and radiation

12.3 CONDUCTION HEAT TRANSFER

Heat transfer is related to thermal energy flow from a heat source to a heat sink

In electric (induction) machines, the thermal energy flows from the windings in slots to laminated core teeth through the conductor insulation and slot line insulation

On the other hand, part of the thermal energy in the end-connection windings is transferred through thermal conduction through the conductors axially toward the winding part in slots A similar heat flow through thermal conduction takes place in the rotor cage and end rings

There is also thermal conduction from the stator core to the frame through the back core iron region and from rotor cage to rotor core, respectively, to shaft and axially along the shaft Part of the conduction heat now flows through the slot insulation to core to be directed axially through the laminated core The presence of lamination insulation layers will make the thermal conduction along the axial direction more difficult In long stack IMs, axial temperature differentials of a few degrees (less than 100C in general), (Figure 12.4), occur

Figure 12.4 Heat conduction flow routs in the IM

So, to a first approximation, the axial heat flow may be neglected

Second, after accounting for conduction heat flow from windings in slots to

the core teeth, the machine circumferential symmetry makes possible the

neglecting of circumferential temperature variation

So we end up with a one-dimensional temperature variation, along the

radial direction For this crude approximation defining thermal conduction,

convection, and radiation, and of the equivalent circuit becomes a rather simple

task

The Fourier’s law of conduction may be written, for steady state, as

(−K∆θ)=q

conductivity (W/m, 0C) and θ is local temperature

For one-dimensional heat conduction, Equation (12.2), with constant

thermal conductivity K, becomes:

qx

transported along distance l of cross section A is

Alq

with q, A – constant along distance l

electrical resistance

[ C/W]

KAl

s

s

∆insfA

Figure 12.5 One dimensional heat conduction

Temperature takes the place of voltage and power (losses) replaces the

electrical current

For a short l, the Fourier’s law in differential form yields

[W/m2]

density flowheat f

;xK

∆θ

pcos in watts is the electric power producing losses and A the cross-section area

For the heat conduction through slot insulation ∆ins (total, including all

conductor insulation layers from the slot middle (Figure 12.5)), the conduction

;R

con con cos Cos

∆

=

=θ

In well-designed IMs, ∆Θcos < 100C with notably smaller values for small

power induction motors

The improvement of insulation materials in terms of thermal conductivity

and in thickness reduction have been decisive factors in reducing the slot

insulation conductor temperature differential Thermal conductivity varies with

temperature and is constant only to a first approximation Typical values are

given in Table 12.2 The low axial thermal conductivity of the laminated cores

is evident

Table 12.2 Thermal conductivity

Material Thermal conductivity

490

Micasheet 0.43 -

12.4 CONVECTION HEAT TRANSFER

Convection heat transfer takes place between the surface of a solid body

(the stator frame) and a fluid (air, for example) by the movement of the fluid

The temperature of a fluid (air) in contact with a hotter solid body rises and

sets a fluid circulation and thus heat transfer to the fluid occurs

The heat flow out of a body by convection is

θ

∆

= hA

where A is the solid body area in contact with the fluid; ∆θ is the temperature

differential between the solid body and bulk of the fluid, and h is the convection

heat coefficient (W/m2⋅0C)

The convection heat transfer coefficient depends on the velocity of the

fluid, fluid properties (viscosity, density, thermal conductivity), the solid body

geometry, and orientation For free convention (zero forced air speed and

smooth solid body surface [2])

( ) horizontal- W/( )m C67

.0h

Cm W/

down l vertica496

-.0h

Cm W/

- up l vertica158

.2h

0 25

0 Co

0 25

0 Co

0 25

0 Co

where ∆θ is the temperature differential between the solid body and the fluid

For ∆θ = 200C (stator frame θ1 = 600C, ambient temperature θ2 = 400C) and

vertical – up surface

(60 40) 4.5W/( )m C158

.2

When air is blown with a speed U along the solid surfaces, the convection

heat transfer coefficient hc is

( )u h (1 K U)

with K = 1.3 for perfect air blown surface; K = 1.0 for the winding end

connection surface, K = 0.8 for the active surface of rotor, K = 0.5 for the

external stator frame

Alternatively,

L

U77.1u

75 0

U in m/s and L is the length of surface in m

For a closed air blowed surface – inside the machine:

a

air Co

c

C U h 1 K U 1 a/2; ah

θ

θ

=

−+

θair–local air heating; θa–heating (temperature) of solid surface

In general, θair = 35 – 400C while θa varies with machine insulation class

So, in general, a < 1

For convection heat transfer coefficient in axial channels of length, L

(12.13) is to be used

In radial cooling channels, hc(U) does not depend on the channel’s length,

but only on speed

( )U 23.11U (W/m C)

12.5 HEAT TRANSFER BY RADIATION

Between two bodies at different temperatures there is a heat transfer by

radiation One body radiates heat and the other absorbs heat Bodies which do

not reflect heat, but absorb it, are called black bodies

Energy radiated from a body with emissivity ε to black surroundings is

2 2 2 1 2 1 4

2 4 1

σ–Boltzmann’s constant: σ = 5.67⋅10-8 W/(m2K4); ε – emissivity; for a black

painted body ε = 0.9; A–radiation area

In general, for IMs, the radiated energy is much smaller than the energy

transferred by convection except for totally enclosed natural ventilation (TENV)

or for class F(H) motor with very hot frame (120 to 150°C)

For the case when θ2 = 40° and θ1 = 80°C, 90°C, 100°C, ε = 0.9, hrad = 7.67,

8.01, and 8.52 W/(m2 °C)

For TENV with hCo = 4.56 W/(m2,°C) (convection) the radiation is superior

to convection and thus it cannot be neglected The total (equivalent) convection

coefficient

h(c+r)0 = hCo + hrad ≥ 12 W/(m2,°C)

The convection and radiation combined coefficients h(c+r)0 ≈ 14.2W/(m2,°C)

for steel unsmoothed frames, h(c+r)0 = 16.7W/(m2,°C) for steel smoothed frames,

h(c+r)0 = 13.3W/(m2, °C) for copper/aluminum or lacquered or impregnated

convection radiation coefficient

It is well understood that the heat transfer is three dimensional and as K, hcand hrad are not constants, the heat flow, even under thermal steady state, is a very complex problem Before advancing to more complex aspects of heat flow, let us work out a simple example

Example 12.1 One – dimensional simplified heat transfer

In an induction motor with pCo1 = 500 W, pCo2 = 400 W, piron = 300 W, the stator slot perimeter 2hs + bs = (2.25 + 8) mm, 36 stator slots, stack length: lstack

= 0.15 m, an external frame diameter De = 0.30 m, finned area frame (4 to 1 area increase by fins), frame length 0.30m, let us calculate the winding in slots temperature and the frame temperature, if the air temperature increase around the machine is 10°C over the ambient temperature of 30°C and the slot insulation total thickness is 0.8 mm The ventilator is used and the end connection/coil length is 0.4

Solution

First, the temperature differential of the windings in slots has to be calculated We assume here that all rotor heat losses crosses the airgap and it flows through the stator core toward the stator frame

In this case, the stator winding in slot temperature differential is (12.3)

( ) 2.0 0.36 0.058 0.15 3.83 C

6.0500108.0l

bhNK

l

l1p

0 3

stack s s s ins

coil

endcon 1

Co ins

Then all these losses are transferred to ambient through the motor frame through combined free convection and radiation

( )

( )4/1 74.758 C3

.030.02.14

300400500A

h

frame 0 r c

total air

⋅

⋅

⋅π

⋅

++

=

=θ

12.6 HEAT TRANSPORT (THERMAL TRANSIENTS) IN

A HOMOGENOUS BODY

Although the IM is not a homogenous body, let us consider the case of a

homogenous body – where temperature is the same all over

The temperature of such a body varies in time if the heat produced inside,

by losses in the induction motor, is applied at a certain point in time–as after

starting the motor The heat balance equation is

radiation , conduction , convection through heat transfer from thebody

0 ) conv (condbody

in theaccumulationheat

0 t

in W timeper unit

lossesloss

TThAdt

TTdMc

M–body mass (in Kg), ct–specific heat coefficient (J/(Kg⋅0C))

A–area of heat transfer from (to) the body

h–heat transfer coefficient

;Ah

1R and Mc

(rad) t

equation (12.17) becomes

t 0 0

t loss

RTTdtTTdC

(12.19)

This is similar to a Rt, Ct parallel electric circuit fed from a current source

Ploss with a voltage T – T0 (Figure 12.6)

t

Figure 12.6 Equivalent thermal circuit

circuit (Figure 12.6)

The solution of this electric circuit is evident

t 0 t 0

The thermal time constant τt = CtRt is very important as it limits the

machine working time with a certain level of losses and given cooling

conditions Intermittent operation, however, allows for more losses (more

The thermal time constant increases with machine size and effectivity of the

cooling system A TENV motor is expected to have a smaller thermal time

constant than a constant speed ventilator-cooled configuration

12.7 INDUCTION MOTOR THERMAL TRANSIENTS AT STALL

The IM at stall is characterized by very large conductor losses Core loss

may be neglected by comparison If the motor remains at stall the temperature of

the windings and cores increases in time There is a maximum winding

temperature limit copper

max

should not be surpassed This is to maintain a reasonable working life for

conductor insulation The machine is designed for lower winding temperatures

at full continuous load

To simplify the problem, let us consider two extreme cases, one with long

end connection stator winding and the other a long stack and short end

connections

For the first case we may neglect the heat transfer by conduction to the

winding in slots portion Also, if the motor is totally enclosed, the heat transfer

through free convection to the air inside the machine is rather small (because

this air gets hot easily) In fact, all the heat produced in the end connection

(pCoend) serves to increase end winding temperature

tcopper endcon endcon

endcon Coend

∆

(12.21)

with pCoend = 1000 W, Mendcon = 1 Kg, ctcopper = 380 J/Kg/0C, the winding would

heat up 115°C (from 40 to 155°C) in a time interval ∆t

10003801115

Now if the machine is already hot at, say, 1000C, ∆θendcon = 1550 – 1000 =

550C So the time allowed to keep the machine at stall is reduced to

1000

380155

The equivalent thermal circuit for this oversimplified case is shown on

Figure 12.7a

On the contrary, for long stacks, only the winding losses in slots are

considered However, this time some heat accumulated in the core and the same

heat is transferred through thermal conduction through insulation from slot

conductors to core

T

Tinitialendcon

Figure 12.7 Simplified thermal equivalent circuits for stator winding temperature rise at stall

a.) long end connections; b.) long stacks

With pCoslot = 1000 W, Mslotcopper = 1 Kg, Cslotcopper = 380 J/Kg/0C, insulation

thickness 0.3 mm Kins = 6 W/m/0C, ctcore = 490 J/Kg/0C, slot height hs = 20 mm,

slot width bs = 8 mm, slot number: Ns = 36, Mcore = 5 Kg, stack length lstack = 0.1

m,

2361.0108202

103.0K

Nlbh

3 3 ins

s stack s s

⋅

⋅

=+

∆

=

C/J24504905cMC

C/J3803801cMC

0 tcore

core core

0 tcopper

slotcon slotcon

−+

τ++

Coslot ambient

core

t

con slotcon

2 t core slotcon Coslot ambient copper

e1tCC

PT

T

e1C

CC

tP

TT

(12.25)

with

condinsul core slotcon core slotcon t

condinsul slotcon

CCCC

;RC

+

⋅

=τ

=

As expected, the copper temperature rise is larger than core temperature

rise Also, the core accumulates a good part of the winding-produced heat, so

the time after which the conductor insulation temperature limit (1550C for class

F) is reached at stall is larger than for the end connection windings

The thermal time constant τt is

seconds2855.01068.83802450

The second term in (12.25) dies out quickly so, in fact, only the first, linear

term counts As Ccore >> Cslotcon, the time to reach the winding insulation

temperature limit is increased a few times: for Tambient = 400C and Tcopper = 1550C

from (12.25)

1000245038040155

Consequently, longer stack motors seem advantageous if they are to be used

frequently at or near stall at high currents (torques)

12.8 INTERMITTENT OPERATION

Intermittent operation with IMs occurs both in line-start constant frequency

and voltage, and in variable speed drives (variable frequency and voltage)

In most line-start applications, as the voltage and frequency stay constant,

the magnetization current Im is constant Also, the rotor circuit is dominated by

the rotor resistance term (Rr/S) and thus the rotor current Ir is 900 ahead of Im

and the torque may be written as

2 m 2 s m m 1 r m m 1

The torque is proportional to the rotor current, and the stator and rotor

winding losses and core losses are related to torque by the expression

||

m

2 m m 1 2

m m 1

e r 2

m m 1 e 2

m s

core 2 r 2 s Corotor Costator core dis

RIL3ILp

TR3ILp

TI

R

3

pIR3IR3pp

pP

ω+







+

=

=++

≈++

=

(12.29)

(12.29) remains a rather complicated expression of torque, with In = const

For medium and large power (and 2p1 = 2, 4, 6) IMs, in general Im < 30%Isn

and Im may be neglected in (12.29), which becomes

m m 1

e r s const core dis

ILp

TRR3p

Electromagnetic losses are proportional to torque squared For variable

speed drives with IMs, the magnetization current is reduced with torque

reduction to cut down (minimize) core and winding losses together