Cite as: R. Camilleri, D.A. Howey, M.D. McCulloch, “Experimental investigation of the thermal contact resistance in shrink fit assemblies with
relevance to electrical machines”, IET Power Electronics Machines and Drives Conference (PEMD), 2014, DOI
http://dx.doi.org/10.1049/cp.2014.0472
Experimental investigation of the thermal contact resistance in
shrink fit assemblies with relevance to electrical machines
R. Camilleri, D.A. Howey*, M.D. McCulloch
Energy and Power Group, Department of Engineering Science, University of Oxford, UK,
*david.howey@eng.ox.ac.uk
Keywords: thermal contact resistance, shrink fit,
electrical machines, thermal modelling
Abbreviations
CFD
LPNA
computational fluid dynamics
lumped parameter network analysis
Roman Symbols
A
B,C
d
D
F
hc
HV
I
k
L
m
n
Q
r
Rth
T
u
V
x
y
area (m2)
constants
average diagonal length of the Vickers indent ( m)
cylinder diameter (m)
mass on Vickers Measurement (kg)
thermal contact conductance transfer (W/m2K)
Vickers Hardness (GPa)
current (A)
thermal conductivity (W/mK)
length (m)
surface asperity slope
no of samples
heat flux (W/m2)
total heat (W)
radius (m)
thermal resistance (oC/W)
temperature (oC)
uncertainty
voltage (V)
effective air gap (m)
vertical distance measured (µm)
Greek Symbols
D
linear thermal expansion (1/K )
change in diameter (m)
stress (MPa), RMS roughness ( m)
Subscripts
a
H
i
o
OH
R
RT
TC
air
hoop
inner cylinder
outer cylinder
oven hysteresis
radial
reference temperature
thermocouple
ambient air
Abstract
Thermal design and modelling in electrical machines is
important because it allows a proper choice of materials,
avoids de-rating of the machine and eliminates excessive
safety factors thus achieving higher current densities. In
high current density electrical machines, particularly those
making use of liquid cooled housing jackets for heat
removal, the stator to housing thermal contact resistance is
on the main heat removal path of the electrical machine. So
far it has always been assumed that this parameter is
dependent on the shrink fit manufacturing procedure of the
machine. However this paper provides experimental
evidence showing that the thermal contact resistance not
only varies with shrink fit pressure but is also affected by
heat flux and temperature. Hence the common notion that
the thermal contact resistance is a constant value set during
the machine assembly, and that during thermal design this
value can be applied across the whole operating range of the
machine is an over simplification. The paper presents
arbitrary correlations showing the variation of thermal
contact resistance with heat flux and shrink fit pressure and
compares the measured values with values quoted in the
literature.
1. Introduction
!
This paper provides an experimental investigation on the
thermal contact resistance of shrink fit concentric
geometries with particular relevance to electrical machines..
High power density electrical machines are becoming
popular in applications in which transient modes of
operation dominates, such as electric vehicles and wind
turbines[1, 2]. Hence in these circumstances, a transient
thermal model of the machine is important.
Thermal modelling in electrical machine design is typically
performed either through lumped parameter network
analysis (LPNA) or computational fluid dynamics (CFD).
While LPNA is quick to solve, it requires a number of
unknown thermal resistances that are either obtained from
experiments, CFD, or are guessed and later verified.
Conversely CFD models produce a better insight and more
detailed information, but may take a substantial time to
simulate [3]. These are hence limited to generating
parameters for particular components or locations, while
the overall machine thermal simulation is performed by
LPNA [4]. The difficulties in determining the thermal
resistances employed in LPNA have been highlighted in [5,
6] which categorized thermal resistances into convective
terms and contact terms. While there have been several
efforts to provide adequate convective resistances for
different machine topologies [7-9], the same cannot be said
for thermal contact resistances.
Thermal contact resistances such as that at the interface
between the stator and the housing are critical as they are
1
on the main thermal path of an electrical machine. Thus
they strongly affect the accuracy of model predicted
temperatures. This is particularly important in high current
density machines which make use of shrink fit liquid cooled
housing jackets as their main source of heat removal.
Whereas research in improving the effectiveness of the
cooling jacket itself has been very active [10-13], work that
provides an understanding of the thermal contact
resistances in electrical machines is still lacking. While
some modellers have applied fixed thermal contact
resistances, which are calibrated with experiments others
have attempted to use theoretical or semi-empirical
correlations from flat joints in contact. However in flat
contacts, the interface pressure can be controlled by the
torque setting and is independent of the heat flux through
the interface. Conversely, in coaxial cylindrical surfaces
the interface pressure is dependent on the initial degree of
fit and the differential expansion of the two cylinders. This
is in turn a function of the temperature, which is effected by
the heat flux through the interface [14].
Following a brief literature review about research in
thermal contact resistances on cylindrical joints, thermal
contact resistances within the context of electrical machines
are also examined. The paper describes the experimental
procedure and discusses the developed correlations of
thermal contact resistance with contact pressure and heat
flux.
2. Literature review
2.1 Thermal contact resistances in cylindrical joints
While the works on thermal contact resistances in flat joints
is substantial (in the order of 200 publications [15]), studies
on cylindrical joints is much more limited (about an order
of magnitude less). Four main thermal contact resistance
models for flat joints have been developed and are known
as the Shlykov model [16], the Ross and Stoute model
[17], Veziroglu model [18] and the Cooper-MikicYovanovich model [19]. A comparison of these models
has been presented in [20-22] and is now generally
accepted that the Cooper-Mikic-Yovanovich model offers
better predictions.
[23] shows that the Cooper-Mikic-Yovanovich model can
be adapted for curved surfaces if the heat transfer is
coupled to classical thermo-elastic stress analysis. His
model was found to achieve accuracy within 5% of
experimental data by [24]. The authors also compared
alternative models and showed that they grossly
overestimate the contact resistance with errors in the range
of 25%-100% for the Ross and Stoute model and the
Shlykov Model, while 100%-200% by the Veziroglu
model. [14] proposes an extension to this work in which he
shows that the thermal contact conductance in coaxial
cylindrical joints not only depend on the contact pressures
and the surface and material properties of the cylinders, but
is affected also by the heat flux and the resulting maximum
temperatures. The analysis takes into account the
differential expansion of concentric cylinders due to the
temperature gradients caused by the heat flow. This
consequently changes the contact pressure at the interface.
An iterative solution to solve the contact pressure during a
heat load was proposed. The paper uses the model to
investigate the effects of surface parameters. However the
need for more experimental work with clear information on
the material properties, surface properties and temperatures
reached is highlighted in [14, 23].
2.2 Thermal Contact Resistances in Electrical Machines
[25] measured the thermal contact resistance of three
totally enclosed fan cooled electrical machines and
compared the results to the Shlykov flat joint model. The
model was extrapolated to predict the component
temperatures in a LPNA model. Conversely [26] designed a
series of experiments to obtain values of the thermal contact
resistances between a silicon steel stator and a shrink fit
mild steel housing used in a liquid cooled generator applied
in a wind turbines. A number of assemblies were developed
with shrink fit pressures varying up to 39 MPa. The authors
offer a series of guidelines in which the thermal contact
resistances is found to decrease with increasing contact
pressure, improved surface finish and with the application
of thermal interface material. However the paper does not
provide any values of heat loads, motor dimensions and
surface finish. Hence results cannot be replicated or
compared to. The paper fails to provide a correlation that
can be used for thermal modelling and assumes that the
thermal contact resistances are independent of heat flux and
only dependent on the initial shrink fit pressure.
Conversely, [4, 6] investigates unknown thermal contact
resistance values in LPNA models by introducing a small
effective interface air gap between the stator and the
machine housing. While suggested values of the effective
air gap are also quoted in [27, 28] the authors found that
real machines often require effective gaps that are an order
of magnitude larger than those suggested. With this
method, the modeller will be required to perform an initial
calibration with experimental results in order to determine
the correct size of the effective gap. Despite its
effectiveness during steady state machine operation, this
technique also assumes that the thermal contact resistances
is fixed and hence may lead to inaccuracies in the
temperature prediction when applied during transient
operation.
3.
Experimental Work
An experimental approach was taken with the aim to
provide a better insight on thermal contact resistance and
providing the thermal designer with better correlations that
can then be applied to thermal models. In order to allow
the thermal designer to replicate results, material and
surface properties that are also key players in thermal
contact resistances, such as the hardness and the surface
roughness were also measured and the results are presented.
2
3.1 Manufacturing
Four pairs of concentric cylinders were manufactured. The
materials were chosen so as to replicate the interaction
between the shrink-fit aluminium housing onto the stator.
Hence for each of the manufactured pairs, the inner
cylinder was made of mild steel while the outer cylinder
was made of aluminium. Despite some minor differences
in the thermal properties between silicon steel and mild
steel as shown in Table 1, mild steel was was still used due
to its ease of manufacturing.
Material
Silicon steel HF10
Silicon Steel Arnon 5
Silicon Steel Arnon 7
Silicon Steel M1924GA
Silicon Steel M1926GA
Silicon Steel M1929GA
1% Carbon Mild Steel
Aluminium Alloy
*Thermal
conductivity
[W/mK]
20.5
21.7
22.3
25.0
23.0
22.0
43.0
150
*Specific
heat capacity
[J/kgK]
4550
5000
5000
4600
4600
4600
4900
910
Table 1: Comparison of thermal properties of different types of silicon
steel with carbon steel as from [29]. *properties at 25oC.
Each pair was machined so that it contains an interference
fit, thus enabling to test a range of shrink fit pressures. Each
cylinder height was kept at 50 mm thus keeping a cylinder
height/thickness ratio to approx. 10. The geometrical
dimensions are listed in Table 2. The locations for
thermocouple temperature sensors were also machined.
This allows end effects caused by thermo-mechanical
stresses to be kept to a minimum.
between 20 kg and 40 kg. The diagonal lengths of the
indent were measured and the hardness was determined
using [30]:
eqn. 1!
Indents whose diagonal lengths varied by more than 10%
from each other were discarded so as to avoid skewed
deformations. The mean and standard deviation of the
measured hardness values for the two materials is shown in
Table 3.
Material
Hardness
[GPa]
Mild Steel Inner Cylinder
Aluminium Outer Cylinder
Table 3: Hardness values for the inner and outer cylinders.
3.3 Surface Roughness Measurement
The outer aluminium cylinders were machined using a 19
mm precision reaming tool while the interface surface of
the inner mild steel cylinders was machined on the lathe
using a carbide-tip tool.
The surface finish of a material is dependent on the material
itself and the process used for machining the component.
While machine surface finish charts [31] are available,
several verification tests were done using an Alicona
Infinite Focus Digital Profilometer. The measured RMS
roughness values were determined using:
eqn. 2!
3.2 Hardness Measurement
Six samples of each material were placed under a Vickers
Armstrong indenter and with the machine loaded an indent
was applied. In order to ensure that the effect of work
hardening during machining was accounted for, the
hardness tests were performed on the curved surfaces of
both the inner and outer cylinders. Loads were varied
Pair No
Cylinder
position
Material
1
Inner
Outer
Inner
Outer
Inner
Outer
Inner
Outer
Mild steel
Aluminium
Mild steel
Aluminium
Mild steel
Aluminium
Mild steel
Aluminium
2
3
4
Inner diameter
[mm]
where n is the number of equally spaced samples taken
along a trace and y is the vertical distance from the mean
line to the data point. Table 4 compares the measured RMS
roughness with suggested values found in the literature.
Outer diameter
[mm]
Interference
[mm]
-0.0033
Shrink fit
contact pressure
[MPa]
0
0.0120
35.2
0.0313
91.7
0.0495
145.0
Table 2: Dimensions of test geometry.
3
Description
Measured
RMS roughness
[µm]
Suggested
RMS roughness
[µm]
Mild Steel surface
machined with a
Carbide-tip lathe tool
1.83
0.4-6.3
[31]
Aluminium surface
machined with a
Reaming tool
3.27
0.8-3.2
[31]
Table 4: Comparison of the measured and suggested surface roughness
applied to improve the heat transfer between the heater and
the inner cylinder. T-type thermocouples were mounted on
each of the two cylinders and were also used to measure a
controlled ambient temperature.
Temperature sensor
location holes were also filled with thermal interface
material to ensure a good contact between the sensor and
the component. Temperature sensors were recorded using
TC-08 Pico data loggers. The heater was connected to a
transformer so that the heat input could be regulated. A
current meter and a differential probe were connected to
PicoScope 3000 series and were recorded at 1s intervals.
The heat input was calculated as:
3.4 Shrink fit Assembly
eqn. 6!
Following machining, the interface diameters of all inner
outer cylinders were surveyed at 45o intervals, at various
cylinder heights. This ensured that the cylinders are paired
with the correct interference fit and that the desired range of
shrink fit pressure is achieved. The cylinders were
assembled by a shrink fit procedure in which the inner steel
cylinder was subjected to a thermal contraction at a
temperature of -5 oC while the aluminium outer cylinder
was placed in a Carbolite oven and subjected to a thermal
expansion at a temperature of 300 oC. The change in
diameter for each cylinder due to temperature difference
was calculated using:
The test setup is shown in Figure 2. The assembly was
placed between thick polystyrene blocks to reduce thermal
losses from the end surfaces.
eqn. 3!
The resulting contact pressure at the interface of each
assembly was determined by solving Lame’s equations
[32]:
eqn. 4!
eqn. 5!
The resulting contact pressures at the interface are also
shown in Table 1. An example of a final shrink fit assembly
is shown in Figure 1.
Figure 2: test setup with 1) temperature sensors (locations marked with a
red dot), 2) concentric assembly with 3) internal cartridge heater, 4)
variable transformer, 5) ac power supply
The variable transformer was used to regulate the voltage to
the heating element and the test was repeated for a number
of heat fluxes. For each heat flux, the experiment was left to
run for approximately 6 hours until a steady state condition
was reached, and a further 2 hours during steady state. The
temperatures and power for the steady state period were
averaged and the overall thermal resistance was calculated
using:
eqn. 7!
In order to eliminate the effect of the thermal conductivity
across each cylinder, and account only for the joint contact
conductance, the thermal resistance was defined as follows:
eqn. 8!
Figure 1: Example of a shrink fit assembly investigated
3.5 Temperature and Thermal Contact Resistance
Measurement
A 230 V, 150 W cartridge heater was mounted inside the
inner cylinder. Silicon based thermal interface material was
Hence the joint conductance could be calculated.
3.6 Calibration and Uncertainty Analysis
A calibration procedure was performed in which the test
setup was mounted with thermocouples and inserted into a
Carbolite oven. The thermocouples and data acquisition
4
system were calibrated against a reference PT100
o
temperature sensor with an accuracy of
C. The
calibration was made for a range of temperatures from 20
o
C to 180 oC. The oven hysteresis was measured at 0.1oC,
while the thermocouple offset was measured at 0.33 oC.
The temperature sensor uncertainty was calculated using:
eqn. 9!
The temperature uncertainty was calculated at 0.35 oC.
Conversely the uncertainty in the voltage and current were
measured at
and
respectively. The
uncertainty of the heat load supplied was calculated using:
eqn. 10!
The uncertainty of heat input was found to be 4mW at low
heat flux and up to a maximum of 33 mW at the higher heat
flux values.
The uncertainty of the heat flux was found to be between 1
W/m2 and 14 W/m2 and was estimated using:
eqn. 11!
4.
Test Results and Discussion
Test results showing the variation of thermal contact
conductance with heat flux and contact pressure are shown
in Figure 3. As expected, the thermal contact conductance
increases as the shrink fit pressure increases. However at a
constant shrink fit pressure the thermal contact
conductance was also found to increase with heat flux. An
arbitrary correlation of conductance with heat flux is
shown for various shrink fit pressures. Each setup was
found to reach a critical heat flux value, after which the
thermal contact conductance flattens out. It was also noted
how with larger the shrink fit pressures it takes a higher
heat flux before the thermal contact conductance flattens
out. For any particular shrink fit pressure, the critical heat
flux can be correlated to a quadratic equation as follows:
eqn. 14!
The variation of the maximum temperature (reached at the
inner cylinder) with heat flux is shown in Figure 4. The
component temperature is a result of the input power, the
thermal capacity of the assembly, the heat transferred from
the inner cylinder to the outer cylinder and the heat
transferred from the outer cylinder to ambient air by
natural convection. The heat flux and temperature were
correlated with a quadratic trend line as follows:
In which the u(A) is the absolute uncertainty of the area,
estimated as 7.8 m using:
eqn. 12!
Finally the uncertainty in thermal contact resistances was
found using:
eqn. 13!
eqn. 15!
The data has an R2 value of 0.99.
The experimental data was also compared to conductance
values used to simulate real machines in [6, 25]. The
effective air gaps shown in [6] were converted to a
conductance value by equating:
eqn. 16!
The uncertainty value of the thermal contact resistances
was measured as 0.0009 m2K/W. Hence the uncertainty in
thermal contact conductance measured 18 W/m2K.
The machine efficiencies and dimensions were obtained
from the manufacturer data [33] and are shown in Table 5.
The steady state heat flux was estimated by assuming that
the loss from each machine was distributed at 80% stator,
20% rotor.
Machine Description
4 kW TEFC IM MA112M4
7.5 kW TEFC IM MA132M4
15 kW TEFC IM MA160L4
30 kW TEFC IM MA200L4
55 kW TEFC IM M250M4
5.5 kW TEFC IM M132
Efficiency
85%
88%
90%
91%
93%
85%
Heat Flux q [W/m2]
3670.16
5704.48
4708.43
4957.10
4799.97
5229.11
Effective gap x [mm]
0.042
0.0762
0.077
0.016
0.037
-
75 kW TEFC IM M250
93%
6545.42
-
hc [W/m2K]
611.90
337.27
333.77
1606.25
694.59
1200
300
900
Table 5: Details of machines used to compare the thermal contact conductances.
5
While the lack of information on the shrink fit pressure of
the actual machines makes it difficult to make definite
deductions, the following remarks can be made:
•! All points fall beyond the critical heat flux line. This
matches expectations as these values correspond to the
steady state conductance values.
•! While it is noted that some points fall below the 0
MPa line, this could be due to a light press fit rather
than a shrink fit. The rest of the points fall within the
flattened conductance values of 0 MPa and 52 MPa.
The upper tensile stress of aluminium is approx. 50
MPa (depending on the type of alloy used for the
casing). However manufacturers may be cautious not
to exceed this limit.
•! The variations in values compared is likely due to the
variables that are unaccounted for in the chart such
such as the different properties of silicon steel and the
surface roughness. A better comparison could be
achieved through a non-dimensional conductance such
as proposed in [14, 15, 21, 23]:
eqn. 17!
In which , k and m are the effective surface
roughness, conductivity and the surface slope asperity.
However such a comparison would require more
detailed investigation on the material and surface
properties.
5.
Conclusion
In high current density machines, the stator-housing
thermal contact resistance is on the main heat path of the
electrical machine. Current lumped parameter network
models assume a fixed single value for the thermal contact
resistances across the whole machine operating range.
However this paper provided experimental evidence
showing that the thermal contact resistance not only varies
with contact pressure but is also affected by the heat flux
and the resultant component temperature. Hence the
common notion that the thermal contact resistances is a
single value, set during the machine assembly and can be
applied across the whole operation range of the machine is
oversimplified. When thermal modelling of a transient
application is required, the thermal contact resistances must
hence be set so that it is a function of heat flux. The paper
provides correlations of how the thermal contact resistances
in a shrink fit assemblies vary with contact pressure and
heat flux and compares them to values used in thermal
modelling of real machines. However we would caution
machine designers from the direct application of the values
presented, as more research to explore the effects of surface
and material properties on contact conductance is required.
Acknowledgements
The authors would like to thank Seifert-MTM Systems
Malta Ltd. for their generous funding. The support of Mr
Cleveland Williams, Mr Maurice Keeble-Smith, Dr Igor
Dyson, Dr Kalin Dragnevski and Mr Robin Vincent during
the various stages of the experimental work is also
acknowledged and appreciated.
Figure 3: Chart showing measurements of how the thermal contact conductance varies with contact pressure and heat flux.
!
6
Figure 4: Chart showing the variation of temperature with heat flux for all shrink fit assemblies.
!
Figure 5: Chart comparing the experimental results with thermal contact resistance from other machines
7
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