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Effect of thermal contact resistance on the performance of transformer lamination stacks
E F F E C T OF T H E R M A L C O N T A C T R E S I S T A N C E O N THE P E R F O R M A N C E OF T R A N S F O R M E R L A M I N A T I O N STACKS
P. W. O'CALLAGHAN,A. M. JONES and S. D. PROBERT
School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Beds. (Great Britain)
SUMMARY
The ejficiency and life of a transformer may be increased by prestressing the lamination-to-lamination contacts o f its core to about I k N m -2. This permits a relatively high rate of thermal transmission without impairing the electrical insulation.
NOMENCLATURE
A C I N P R T A
cross-sectional area, m 2 thermal conductance per unit nominal area of contact, W m - 2 K number of lamination-to-lamination interfaces present in the stack total number of contact planes present in a stack of laminations ( = I + 2) applied loading on the considered contact, N m - 2 heat flux crossing unit nominal area of the contact, W m - 2 thermal resistance of unit nominal contact area, m 2 K W - 1 temperature, K difference between
Subscripts B
LL ML N TOT
bulk material lamination-to-lamination flux meter-to-lamination number of contact planes total 13
Applied Energy (3) (1977)--© Applied Science Publishers Ltd, England, 1977 Printed in Great Britain
14
P. W. O~CALLAGHAN,A. M. JONES,S. D. PROBERT INTRODUCTION
The temperature attained within an electrical machine usually dictates its efficiency of energy conversion by restricting the output which may be taken continuously from it: I f a fixed electrical power input is applied continuously to a transformer, its temperature will rise until a balance is established between the rate of heat generation by eddy current dissipation within the core laminations and the rate of heat lost to the surroundings. The transformer core, which comprises metallic layers, has a high intrinsic thermal resistance arising from its large number of solid-solid interfaces in series. Any measure which would reduce this resistance, without disrupting the electrically non-conducting surface coatings, would improve the rate of dissipation of heat, thereby lowering the equilibrium temperature and hence increasing the efficiency and durability of the transformer. In practice this 'waste' energy should be used for other low-grade heating purposes.
•7"l.U
J,, n
rr
<[ tw
LIJ
THERMOJUNCTION INDICATIONS
ACTUAL TEMPERATURE ~ PROFILE
r,-
ktJ
I---
AXIAL DISTANCE.i.e. PERPENDICULARTO INTERFACIALPLANE (LINEAR SCALE)
Fig. 1. Schematictemperaturedistribution in the neighbourhoodof a nominallyplanecontact between two semi-infinite solids. When two nominally-flat surfaces are brought together they touch only at discrete points. If the surfaces are at different temperatures the rate of heat transfer is a function of the distributions of actual contact areas, as well as the properties of the contacting materials and the interfacial fluid. The real contact area is dependent upon the applied mechanical load, the elastic and plastic properties of the contacting materials and their surface topographies. The conductance, C, per unit area of a
EFFECT OF T H E R M A L CONTACT RESISTANCE ON TRANSFORMER STACKS
15
contact is defined as: C =
q/AT=
1/R
(l)
where q is the steady-state rate of heat flow across unit nominal area of the contact, AT the difference at the interface between the extrapolated linear temperature distributions in the contacting materials (see Fig. 1) and R is the thermal resistance of unit nominal contact area. The conductance, C, includes contributions due to conduction across the asperity bridges and interfacial fluid, as well as radiation across those regions of the interface not in physical contact. APPLIED LOAD
1
F':I S,LVER-STEEL I L.~ "°AD'N° SHAFT PTFE BEARING--~ I [
NII
.-"
SUPPORTPLATE III SCREWED ~"
RODS
HEATING ,'/"ELEMENT t280W) STAINLESS-STEEL ~:;¢HEAT FLUX METERS [STACK OF LAMINATIONS '/UNDER TEST
i ./
//
HEAT SINK COOLINGWATER
f I- J
] ~.__5_.cm......
STEEL
BALL
lllm
~
V
BASE PLATE
Fig. 2. The experimental module, which is mounted within the experimental chamber (see Fig. 3). A solid-solid interface usually has a high electrical resistance because the free electrons are constricted predominantly to pass via the micro-asperity bridges (usually of oxide or some 'contaminant' film) between the surfaces. Nevertheless, as described earlier, it is desirable to satisfy the often conflicting requirement of having a low thermal resistance across the laminations of the transformer. The standard transformer laminations considered were thin metal strips having cla (centre line average) surface roughnesses o f < 0-1 pm with a layer of < 0" 1 pm thick electrically-
P. W. O ' C A L L A G H A N , A. M. JONES, S. D. PROBERT
16
insulating varnish on both sides. Existing theories of thermal contact ~' 2 were not pertinent to this situation, especially because the observations of the contact areas formed showed that they could be better described as ellipses with high ratios of major-to-minor axes rather than as the circular regions commonly assumed in analyses. The present study was therefore experimental in order to provide immediately useful information for designers.
E X P E R I M E N T A L DETAILS
The test module consisted of a heater, two identical flux meters, with the stack of transformer laminations mounted between them, and a water-cooled sink arranged in vertical sequence (Figs. 2 and 3). 3 The 70mm diameter specimens of the transformer laminations were punched from strips of (a) grain-orientated silicon steel (0.28 fiam thickness) and (b) non-orientated electrical steel (0.35 mm thickness). Care was taken to ensure that the punching operation did not produce burring of the disc peripheries. ;RUM
APPUED LOAD
~ [[ ]= " ~ -~
~
~m
GUIDE BOLT
I
LOAD CELL LOADING SHAFT PTFE BEARING
t
OVERLO.,~DCUT-OUT~ SUPPORT_ RODS THERMOELEMENT LEAD- THROUGH
]
~ -~
COOLING-WATER PIPES
i ! ~ ~ I
VACUUM BELLOWS HEATER SUPPLY LEAD- THROUGH
/
PTFE BEARING
EXPERIMENTAL-----~CHAMBER
--
SAMPLING TUBE
o 0-RING SEALS [ ~ ..... -20cm..... ~ Fig. 3.
>> t <<~
VACUUMPUMPS
~
SUPPORTPLATE UPPER FLANGEOF CHEVRON BAFFLEVALVE
The mechanical loading arrangement and evacuated experimental chamber.
17
EFFECT OF THERMAL CONTACT RESISTANCE ON TRANSFORMER STACKS
The determination of the total thermal resistance of the contacting assembly involved estimating the mean steady-state temperature drop between the neighbouring fiat faces of the two heat flux meters and the thermal current crossing the interfaces. The appropriate temperature difference was obtained from the thermojunction readings using a least-mean-squares straight line fit to the temperature/axial distance data for each flux meter (see Fig. 1). The heat flux was derived from the axial temperature gradients in the flux meters and the independently determined thermal conductivity of the stainless steel from which they were manufactured.
RESULTS
The total thermal resistances were obtained with one-, three-, five- and six-layer stacks of either type (a) or type (b) lamination material in air at atmospheric pressure as well as with the system in high vacuum ( ~ 7 x 10- 2 N m - 2) (see Table 1 and Figs. 4 and 5). A stack containing (N - 1) layers has N contact 'planes' and (N - 2) lamination-to-lamination interfaces present between the faces of the identical flux meters, two of the contact planes being between the flux meters and the ends of the
so
~r
Z
o
,=,
z
20
15
o=
~
9"~2
a: b
O0Z'~~ '
Io
Fig. 4. Total thermal resistances for stacks of grain-orientated silicon steel laminations. (The full and dotted lines are for data obtained in air at atmospheric pressure and at 7 x 10 -z N m -2, respectively.)
Applied nominal loading ( k N m - 2)
10 58 144 202 317 462 600 745 887 1090
TABLE 1
4.62 3.80 2.36 2.16 1.84 1.77 1.55 1.47 1.41 1.25
1
19.30 16.50 10.60 9.91 8.82 7.60 6.90 6.05 5.64 5.25
3
26.80 20.10 15.51 13.60 11.95 10-32 9.30 8.45 7.83 7.11
5
In air at atmospheric pressure
30.50 20.40 19.80 15-00 12-00 11.15 10-80 10.10 9.46 8-80
6
157.00 102.00 65.40 57.50 29.90 26-80 23-70 20-30 20-00 19.50
1
702-00 598-00 478.00 393.00 300.00 186.00 164.00 150.00 117.00 105.00
6
3.40 2.83 2.07 1.70 1.63 1.38 1.09 0.96 0-84 0.72
1
8.24 7.32 6.62 5.91 5.25 4.95 4-04 3.88 3.54 3-42
3
12.10 11.23 10.22 9.53 8.52 7-51 6.75 6-22 5-74 5.31
5
In air at atmospheric pressure
14-20 13-60 11-40 10.90 10.30 9.20 8-05 6.56 6.46 6.27
6
73.50 61.50 35.70 30.00 28-70 23.00 20.50 19-00 17.10 13-00
1
279.00 249.00 219-00 162-00 129.00 107.00 101.00 67.50 61.00 52.80
6
In vacuum of 7 × 10 -2 N m -2
(b) Non-orientated electrical steel
Number ( N - 1) of laminations in the stack
In vacuum of 7 × 10 2 N m - 2
(a) Grain-orientated silicon steel
TYPICAL V A L U E S O F T H E T O T A L T H E R M A L R E S I S T A N C E RTOT, ~ (IN 10 4rn2 K W -1 U N I T S ) F O R T H E C O N T A C T I N G A S S E M B L Y
,..q
m
©
~7
'7
E
> z >
r-
Q
OO
EFFECT
OF THERMAL
CONTACT
RESISTANCE
ON TRANSFORMER
19
STACKS
-f o
n
$
z z
",,o
I
5 ...i
..J
J
e
Fig. 5. Total thermal resistances for stacks of non-orientated electrical steel laminations. stack. Thus the total resistance is given by: RTOT, N = 2RML + (N -- I)R B + (N - 2)RLL
(2)
F o r a single layer, N = 2, and so:
RXOT, 2 = 2RML + RB
(3)
Hence, by eliminating RML.'
RLL-~(RTOT'N~-RToT'2)--RB2
(4)
Thus the resistance per lamination-to-lamination interface (see Figs. 6 and 7) can be deduced from the measured overall resistance and the bulk resistance o f the laminations. The latter was negligible ( ~ 10 - 6 m 2 K W - 1) for the two types of insert tested. The specimen assemblies were o f sufficient lateral size and the mechanical loadings high enough that even the six-layer system, at the lowest loadings used, experienced lateral heat losses of less than 5 ~o o f the axial heat flux, as indicated from the difference between the two flux meter observations. DISCUSSION
Initial decreases in resistance with increasing mechanical loading on the assembly
P. W. O'CALLAGHAN, A. M. JONES, S. D. PROBERT
20
:~ %
160
8
W t/3 U3
B
W
i,i
rr"
140 r,
7
~e Z
L,LI
FF
o ×
'Y LU
6
120
~n~
100 y
5
(:3_ ~'-
IT n--
iii (D
80
4
Z
- E w~" o o c~ uA
IT iii
6O z 13: iii rl
IT
w Z
2
\
G) LU IT
.I
w c~
20 Z 0
IN VACUUM
,,g,
I
I
200
400
I
600
I
I
800
1000
1200
LOAOING PRESSURE (Nm -2)
Fig. 6.
Contact resistance (RLL) per interface between grain-orientated silicon steel laminations, O : I
= 2 , × : •=4,
A, O: 1 = 5 .
are due to the pressing out of the slight buckle present in the laminations at low loadings. The characteristics of the data obtained are qualitatively similar for both environmental conditions. For most stacks tested, two regimes of deformation behaviour were encountered. Initially the effect of applied loading was to press out the buckle in the laminations. Under higher pressures, the resistance v e r s u s applied loading characteristics flattened out corresponding to the zone of asperity deformation for the contacting surfaces. The thermal resistances of the contacts increased by a factor of about 25 when the air pressure was reduced from atmospheric to less than 7 x 10 _2 N m -2. Thus conduction through the air in the narrow interstices provided the major contribution to the heat transfer between
EFFECT
OF THERMAL
CONTACT
RESISTANCE
ON TRANSFORMER
2.5r
STACKS
21
50 v
i
o iii cr
t.0 w cr (2_
o
\ \ \
uJ u'~ LU O: O_
E z o x
\
IJJ I
30 t'Y
\
0
_J
\
r7 (.o iii rt"
\ \ _z
\
20
4.H t..)
\
1.1.1 (_~ I.L rr" W I-Z
cr tll t--
\ \
i11 12.
\
re" (.U
W t..) Z
\
W
INVACUUM/////~\
Z
m
"o
I.u
itl cY
I-.--
I-(.3 z o (._)
Z 0 u I
0
I
200
Z.00 LOADING
Fig. 7.
Contact
resistance
I
I
I
600
800
1000
PRESSURE
120,
(Nm-2)
(RLL) per interface between non-orientated = 2, x : I = 4 , ~., []: I= 5.
electrical
steel laminations,
O:
I
22
P. W. O'CALLAGHAN, A. M. JONES, S. D. PROBERT
adjacent laminations under small temperature differences near ambient temperatures. The application of interfacial loading is usually employed to promote greater numbers and sizes of solid-to-solid contact areas. Although this would not seem to be necessary because the air conductance contribution is much higher than the solid component, the resistance per interface still decreased (tenfold by applying 1090 N m- 2 normal loading) because the air gaps became smaller. No disruption of the electrically insulating surface films was observed within the loading range applied. The use of higher normal stresses for the transformer application is not recommended in view of the 'law' of diminishing returns with respect to improving the thermal conductance yet increasing the possibility of electrical shorting.
CONCLUSIONS
Although stacks containing one, three, five and six transformer laminations were examined, the measurements have been presented in terms of thermal resistance per interface to permit predictions to be made in practice for stacks containing a greater number of layers. The resistance per lamination-to-lamination interface was independent of the number of layers but approached asymptotically a constant value with applied loading. A law of diminishing returns was exhibited by which the marginal decrease in thermal resistance for an increment of loading diminished as the load was increased. Thus there appears to be little further to be gained with respect to improving thermal conductance by compressing the stacks under loadings greater than about 1 kN m-2. Below 1090 N m-2 (the maximum loading applied during testing) no electrical breakdown of the insulating surface films was observed. Thus, to reduce equilibrium temperatures and hence increase transformer et~ciency, the laminations should be appropriately tension-wound during assembly.
ACKNOWLEDGEMENTS
The authors wish to thank the Science Research Council for financial help with this project, and Delta Metals Ltd for suggesting this particular line of enquiry and for supplying the transformer laminations.
REFERENCES 1. H. FENECHand W. M. ROHSENOW, Prediction of thermal conductance of metallic surfaces in contact, Trans. ASME, 85C (1963) pp. 15-24. 2. J. J. HENRY, Thermal conductance of metallic surfaces in contact, USAEC Report No. NYO-9459, 1963. 3. P.W. O'CALLAGHANand S. D. PROBERT,An improved thermal contact resistance rig, J. Measurement and Control, 5(8) (1972) pp. 311 15.
P. W. O'CALLAGHAN,A. M. JONES and S. D. PROBERT
School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Beds. (Great Britain)
SUMMARY
The ejficiency and life of a transformer may be increased by prestressing the lamination-to-lamination contacts o f its core to about I k N m -2. This permits a relatively high rate of thermal transmission without impairing the electrical insulation.
NOMENCLATURE
A C I N P R T A
cross-sectional area, m 2 thermal conductance per unit nominal area of contact, W m - 2 K number of lamination-to-lamination interfaces present in the stack total number of contact planes present in a stack of laminations ( = I + 2) applied loading on the considered contact, N m - 2 heat flux crossing unit nominal area of the contact, W m - 2 thermal resistance of unit nominal contact area, m 2 K W - 1 temperature, K difference between
Subscripts B
LL ML N TOT
bulk material lamination-to-lamination flux meter-to-lamination number of contact planes total 13
Applied Energy (3) (1977)--© Applied Science Publishers Ltd, England, 1977 Printed in Great Britain
14
P. W. O~CALLAGHAN,A. M. JONES,S. D. PROBERT INTRODUCTION
The temperature attained within an electrical machine usually dictates its efficiency of energy conversion by restricting the output which may be taken continuously from it: I f a fixed electrical power input is applied continuously to a transformer, its temperature will rise until a balance is established between the rate of heat generation by eddy current dissipation within the core laminations and the rate of heat lost to the surroundings. The transformer core, which comprises metallic layers, has a high intrinsic thermal resistance arising from its large number of solid-solid interfaces in series. Any measure which would reduce this resistance, without disrupting the electrically non-conducting surface coatings, would improve the rate of dissipation of heat, thereby lowering the equilibrium temperature and hence increasing the efficiency and durability of the transformer. In practice this 'waste' energy should be used for other low-grade heating purposes.
•7"l.U
J,, n
rr
<[ tw
LIJ
THERMOJUNCTION INDICATIONS
ACTUAL TEMPERATURE ~ PROFILE
r,-
ktJ
I---
AXIAL DISTANCE.i.e. PERPENDICULARTO INTERFACIALPLANE (LINEAR SCALE)
Fig. 1. Schematictemperaturedistribution in the neighbourhoodof a nominallyplanecontact between two semi-infinite solids. When two nominally-flat surfaces are brought together they touch only at discrete points. If the surfaces are at different temperatures the rate of heat transfer is a function of the distributions of actual contact areas, as well as the properties of the contacting materials and the interfacial fluid. The real contact area is dependent upon the applied mechanical load, the elastic and plastic properties of the contacting materials and their surface topographies. The conductance, C, per unit area of a
EFFECT OF T H E R M A L CONTACT RESISTANCE ON TRANSFORMER STACKS
15
contact is defined as: C =
q/AT=
1/R
(l)
where q is the steady-state rate of heat flow across unit nominal area of the contact, AT the difference at the interface between the extrapolated linear temperature distributions in the contacting materials (see Fig. 1) and R is the thermal resistance of unit nominal contact area. The conductance, C, includes contributions due to conduction across the asperity bridges and interfacial fluid, as well as radiation across those regions of the interface not in physical contact. APPLIED LOAD
1
F':I S,LVER-STEEL I L.~ "°AD'N° SHAFT PTFE BEARING--~ I [
NII
.-"
SUPPORTPLATE III SCREWED ~"
RODS
HEATING ,'/"ELEMENT t280W) STAINLESS-STEEL ~:;¢HEAT FLUX METERS [STACK OF LAMINATIONS '/UNDER TEST
i ./
//
HEAT SINK COOLINGWATER
f I- J
] ~.__5_.cm......
STEEL
BALL
lllm
~
V
BASE PLATE
Fig. 2. The experimental module, which is mounted within the experimental chamber (see Fig. 3). A solid-solid interface usually has a high electrical resistance because the free electrons are constricted predominantly to pass via the micro-asperity bridges (usually of oxide or some 'contaminant' film) between the surfaces. Nevertheless, as described earlier, it is desirable to satisfy the often conflicting requirement of having a low thermal resistance across the laminations of the transformer. The standard transformer laminations considered were thin metal strips having cla (centre line average) surface roughnesses o f < 0-1 pm with a layer of < 0" 1 pm thick electrically-
P. W. O ' C A L L A G H A N , A. M. JONES, S. D. PROBERT
16
insulating varnish on both sides. Existing theories of thermal contact ~' 2 were not pertinent to this situation, especially because the observations of the contact areas formed showed that they could be better described as ellipses with high ratios of major-to-minor axes rather than as the circular regions commonly assumed in analyses. The present study was therefore experimental in order to provide immediately useful information for designers.
E X P E R I M E N T A L DETAILS
The test module consisted of a heater, two identical flux meters, with the stack of transformer laminations mounted between them, and a water-cooled sink arranged in vertical sequence (Figs. 2 and 3). 3 The 70mm diameter specimens of the transformer laminations were punched from strips of (a) grain-orientated silicon steel (0.28 fiam thickness) and (b) non-orientated electrical steel (0.35 mm thickness). Care was taken to ensure that the punching operation did not produce burring of the disc peripheries. ;RUM
APPUED LOAD
~ [[ ]= " ~ -~
~
~m
GUIDE BOLT
I
LOAD CELL LOADING SHAFT PTFE BEARING
t
OVERLO.,~DCUT-OUT~ SUPPORT_ RODS THERMOELEMENT LEAD- THROUGH
]
~ -~
COOLING-WATER PIPES
i ! ~ ~ I
VACUUM BELLOWS HEATER SUPPLY LEAD- THROUGH
/
PTFE BEARING
EXPERIMENTAL-----~CHAMBER
--
SAMPLING TUBE
o 0-RING SEALS [ ~ ..... -20cm..... ~ Fig. 3.
>> t <<~
VACUUMPUMPS
~
SUPPORTPLATE UPPER FLANGEOF CHEVRON BAFFLEVALVE
The mechanical loading arrangement and evacuated experimental chamber.
17
EFFECT OF THERMAL CONTACT RESISTANCE ON TRANSFORMER STACKS
The determination of the total thermal resistance of the contacting assembly involved estimating the mean steady-state temperature drop between the neighbouring fiat faces of the two heat flux meters and the thermal current crossing the interfaces. The appropriate temperature difference was obtained from the thermojunction readings using a least-mean-squares straight line fit to the temperature/axial distance data for each flux meter (see Fig. 1). The heat flux was derived from the axial temperature gradients in the flux meters and the independently determined thermal conductivity of the stainless steel from which they were manufactured.
RESULTS
The total thermal resistances were obtained with one-, three-, five- and six-layer stacks of either type (a) or type (b) lamination material in air at atmospheric pressure as well as with the system in high vacuum ( ~ 7 x 10- 2 N m - 2) (see Table 1 and Figs. 4 and 5). A stack containing (N - 1) layers has N contact 'planes' and (N - 2) lamination-to-lamination interfaces present between the faces of the identical flux meters, two of the contact planes being between the flux meters and the ends of the
so
~r
Z
o
,=,
z
20
15
o=
~
9"~2
a: b
O0Z'~~ '
Io
Fig. 4. Total thermal resistances for stacks of grain-orientated silicon steel laminations. (The full and dotted lines are for data obtained in air at atmospheric pressure and at 7 x 10 -z N m -2, respectively.)
Applied nominal loading ( k N m - 2)
10 58 144 202 317 462 600 745 887 1090
TABLE 1
4.62 3.80 2.36 2.16 1.84 1.77 1.55 1.47 1.41 1.25
1
19.30 16.50 10.60 9.91 8.82 7.60 6.90 6.05 5.64 5.25
3
26.80 20.10 15.51 13.60 11.95 10-32 9.30 8.45 7.83 7.11
5
In air at atmospheric pressure
30.50 20.40 19.80 15-00 12-00 11.15 10-80 10.10 9.46 8-80
6
157.00 102.00 65.40 57.50 29.90 26-80 23-70 20-30 20-00 19.50
1
702-00 598-00 478.00 393.00 300.00 186.00 164.00 150.00 117.00 105.00
6
3.40 2.83 2.07 1.70 1.63 1.38 1.09 0.96 0-84 0.72
1
8.24 7.32 6.62 5.91 5.25 4.95 4-04 3.88 3.54 3-42
3
12.10 11.23 10.22 9.53 8.52 7-51 6.75 6-22 5-74 5.31
5
In air at atmospheric pressure
14-20 13-60 11-40 10.90 10.30 9.20 8-05 6.56 6.46 6.27
6
73.50 61.50 35.70 30.00 28-70 23.00 20.50 19-00 17.10 13-00
1
279.00 249.00 219-00 162-00 129.00 107.00 101.00 67.50 61.00 52.80
6
In vacuum of 7 × 10 -2 N m -2
(b) Non-orientated electrical steel
Number ( N - 1) of laminations in the stack
In vacuum of 7 × 10 2 N m - 2
(a) Grain-orientated silicon steel
TYPICAL V A L U E S O F T H E T O T A L T H E R M A L R E S I S T A N C E RTOT, ~ (IN 10 4rn2 K W -1 U N I T S ) F O R T H E C O N T A C T I N G A S S E M B L Y
,..q
m
©
~7
'7
E
> z >
r-
Q
OO
EFFECT
OF THERMAL
CONTACT
RESISTANCE
ON TRANSFORMER
19
STACKS
-f o
n
$
z z
",,o
I
5 ...i
..J
J
e
Fig. 5. Total thermal resistances for stacks of non-orientated electrical steel laminations. stack. Thus the total resistance is given by: RTOT, N = 2RML + (N -- I)R B + (N - 2)RLL
(2)
F o r a single layer, N = 2, and so:
RXOT, 2 = 2RML + RB
(3)
Hence, by eliminating RML.'
RLL-~(RTOT'N~-RToT'2)--RB2
(4)
Thus the resistance per lamination-to-lamination interface (see Figs. 6 and 7) can be deduced from the measured overall resistance and the bulk resistance o f the laminations. The latter was negligible ( ~ 10 - 6 m 2 K W - 1) for the two types of insert tested. The specimen assemblies were o f sufficient lateral size and the mechanical loadings high enough that even the six-layer system, at the lowest loadings used, experienced lateral heat losses of less than 5 ~o o f the axial heat flux, as indicated from the difference between the two flux meter observations. DISCUSSION
Initial decreases in resistance with increasing mechanical loading on the assembly
P. W. O'CALLAGHAN, A. M. JONES, S. D. PROBERT
20
:~ %
160
8
W t/3 U3
B
W
i,i
rr"
140 r,
7
~e Z
L,LI
FF
o ×
'Y LU
6
120
~n~
100 y
5
(:3_ ~'-
IT n--
iii (D
80
4
Z
- E w~" o o c~ uA
IT iii
6O z 13: iii rl
IT
w Z
2
\
G) LU IT
.I
w c~
20 Z 0
IN VACUUM
,,g,
I
I
200
400
I
600
I
I
800
1000
1200
LOAOING PRESSURE (Nm -2)
Fig. 6.
Contact resistance (RLL) per interface between grain-orientated silicon steel laminations, O : I
= 2 , × : •=4,
A, O: 1 = 5 .
are due to the pressing out of the slight buckle present in the laminations at low loadings. The characteristics of the data obtained are qualitatively similar for both environmental conditions. For most stacks tested, two regimes of deformation behaviour were encountered. Initially the effect of applied loading was to press out the buckle in the laminations. Under higher pressures, the resistance v e r s u s applied loading characteristics flattened out corresponding to the zone of asperity deformation for the contacting surfaces. The thermal resistances of the contacts increased by a factor of about 25 when the air pressure was reduced from atmospheric to less than 7 x 10 _2 N m -2. Thus conduction through the air in the narrow interstices provided the major contribution to the heat transfer between
EFFECT
OF THERMAL
CONTACT
RESISTANCE
ON TRANSFORMER
2.5r
STACKS
21
50 v
i
o iii cr
t.0 w cr (2_
o
\ \ \
uJ u'~ LU O: O_
E z o x
\
IJJ I
30 t'Y
\
0
_J
\
r7 (.o iii rt"
\ \ _z
\
20
4.H t..)
\
1.1.1 (_~ I.L rr" W I-Z
cr tll t--
\ \
i11 12.
\
re" (.U
W t..) Z
\
W
INVACUUM/////~\
Z
m
"o
I.u
itl cY
I-.--
I-(.3 z o (._)
Z 0 u I
0
I
200
Z.00 LOADING
Fig. 7.
Contact
resistance
I
I
I
600
800
1000
PRESSURE
120,
(Nm-2)
(RLL) per interface between non-orientated = 2, x : I = 4 , ~., []: I= 5.
electrical
steel laminations,
O:
I
22
P. W. O'CALLAGHAN, A. M. JONES, S. D. PROBERT
adjacent laminations under small temperature differences near ambient temperatures. The application of interfacial loading is usually employed to promote greater numbers and sizes of solid-to-solid contact areas. Although this would not seem to be necessary because the air conductance contribution is much higher than the solid component, the resistance per interface still decreased (tenfold by applying 1090 N m- 2 normal loading) because the air gaps became smaller. No disruption of the electrically insulating surface films was observed within the loading range applied. The use of higher normal stresses for the transformer application is not recommended in view of the 'law' of diminishing returns with respect to improving the thermal conductance yet increasing the possibility of electrical shorting.
CONCLUSIONS
Although stacks containing one, three, five and six transformer laminations were examined, the measurements have been presented in terms of thermal resistance per interface to permit predictions to be made in practice for stacks containing a greater number of layers. The resistance per lamination-to-lamination interface was independent of the number of layers but approached asymptotically a constant value with applied loading. A law of diminishing returns was exhibited by which the marginal decrease in thermal resistance for an increment of loading diminished as the load was increased. Thus there appears to be little further to be gained with respect to improving thermal conductance by compressing the stacks under loadings greater than about 1 kN m-2. Below 1090 N m-2 (the maximum loading applied during testing) no electrical breakdown of the insulating surface films was observed. Thus, to reduce equilibrium temperatures and hence increase transformer et~ciency, the laminations should be appropriately tension-wound during assembly.
ACKNOWLEDGEMENTS
The authors wish to thank the Science Research Council for financial help with this project, and Delta Metals Ltd for suggesting this particular line of enquiry and for supplying the transformer laminations.
REFERENCES 1. H. FENECHand W. M. ROHSENOW, Prediction of thermal conductance of metallic surfaces in contact, Trans. ASME, 85C (1963) pp. 15-24. 2. J. J. HENRY, Thermal conductance of metallic surfaces in contact, USAEC Report No. NYO-9459, 1963. 3. P.W. O'CALLAGHANand S. D. PROBERT,An improved thermal contact resistance rig, J. Measurement and Control, 5(8) (1972) pp. 311 15.