THE USE OF ULTRASOUND TO MEASURE CONTACT
STIFFNESS AND PRESSURE IN LARGE CONTACTING
INTERFACES
C. Holmes and B. W. Drinkwater
Department of Mechanical Engineering, Queens Building, University Walk,
University of Bristol, BS8 1TR, UK
ABSTRACT. This paper describes a study on the use of ultrasound to measure the contact
pressure between a rocking graphite brick and its foundation. A hydraulic loading rig has been
developed to allow ultrasonic measurements to be made of the contact interface given specific
loading conditions. Ultrasonic reflection coefficient measurements have been used to obtain
calibration curves of reflection coefficient against pressure for a graphite-aluminum interface.
These calibration curves allow the ultrasonic data from the hydraulic loading rig to be converted
to contact pressure at the interface. Results are described which show the use of this ultrasonic
measurement procedure to investigate the effect of curvature and a reduction in the contact area
on the brick rocking stiffness.
INTRODUCTION
In a Magnox type (gas-cooled) nuclear reactor, graphite bricks which are used to
moderate the reaction are assembled in columns approximately 10 bricks high and 50 wide
[1]. Each brick has a square cross section of width 200mm and a height of 800mm. The
rocking stiffness of these columns is used to determine the natural frequency of the core for
seismic response analysis. Within the reactor, the top and bottom surface of each brick is in
dry contact with the one above and below it. It is this solid-solid contacting interface, which
plays an important role in the rocking behavior. Figure 1 shows a photograph of a graphite
brick, both full size and after machining.
Robinson et al [2] measured the interfacial stiffness of graphite-graphite joints due
to surface roughness with ultrasonic reflection coefficient measurements [3], where
reflection coefficient is defined as the proportion of the incident signal reflected. The
calculated stiffness values were used to model the effect of surface roughness on the
rocking behavior of a single graphite brick. It was concluded that although surface
roughness on a microscopic scale plays no significant role in the tilting behavior, long
wavelength surface variation might be a factor. Experiments were also carried out to
measure the load-deflection behavior of a single brick rocking on a rigid foundation. These
results have been compared with elastic beam bending, a rigid body analysis and a finite
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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0.2m
0.8m
Load (N)
FIGURE 1. Magnox graphite bricks.
FIGURE 1. Magnox graphite bricks.
-Rigid Body
Motion
Rigid Body
80
70
60
50
40
30
20
10
0
Motion
-Beam
Bending
Beam Bending
-FE Analysis
FE Analysis
- Experiment
Experiment
0
10
Top of brick deflection (pm)
20
30
40
50
FIGURE 2. Load-deflection behaviour
single
brick rocking
Topofofabrick
deflection
(µm) on a rigid surface.
FIGURE 2. Load-deflection behaviour of a single brick rocking on a rigid surface.
element analysis. It was found that the brick was up to four times more flexible than
predicted. Figure 2 shows the load-deflection behavior of a graphite brick on a rigid
foundation
under
loading.
element
analysis.
It horizontal
was found
that the brick was up to four times more flexible than
Most
rough
surface
contact
models, such
as theofwell-known
predicted. Figure 2 shows the load-deflection
behavior
a graphite Williamson
brick on aand
rigid
Greenwood
contact
model
[4],
are
used
to
model
rough,
nominally
flat
surfaces. It is
foundation under horizontal loading.
possible
that during
manufacture
will also have
some longand
Mosthowever,
rough surface
contact
models,engineered
such as surfaces
the well-known
Williamson
wavelength undulation or 'waviness'. Thomas and Sayles [5] defined a machine tool
Greenwood contact model [4], are used to model rough, nominally flat surfaces. It is
surface as a continuous band of wavelengths, with high frequencies representing the surface
possible
however,
during
manufacture
engineered
some long
roughness,
midthat
range
frequencies
representing
the surfaces
wavinesswill
andalso
lowhave
frequencies
wavelength
undulation
or
‘waviness’.
Thomas
and
Sayles
[5]
defined
a
machine
representing errors of form. These mid-range frequencies are thought to be important intool
surface
as a continuous
band behavior
of wavelengths,
with
high frequencies
representing
the surface
influencing
the rocking
of bricks.
Ultrasonic
measurements
have been
used
roughness,
mid
range
frequencies
representing
the
waviness
and
low
frequencies
previously to determine the interfacial pressure over small contact areas such as a ball
bearing-raceway
wheel-rail
system
[6, 7]. The
aim of thisare
paper
is to describe
a method in
representing
errors ofor form.
These
mid-range
frequencies
thought
to be important
for mapping
the contact
pressure
the surface
of a rocking
graphite have
brick. been
This used
is
influencing
the rocking
behavior
of atbricks.
Ultrasonic
measurements
accomplished
using
a
hydraulic
loading
rig,
which
allows
the
load-deflection
behavior
to
be
previously to determine the interfacial pressure over small contact areas such as a ball
measured concurrently
with ultrasonic
bearing-raceway
or wheel-rail
system [6,measurements
7]. The aim of
ofthe
thisinterface.
paper is to describe a method
for mapping the contact pressure at the surface of a rocking graphite brick. This is
EXPERIMENTAL LOADING RIG
accomplished
using a hydraulic loading rig, which allows the load-deflection behavior to be
measured
concurrently
with ultrasonic measurements of the interface.
Experimental Set-Up
EXPERIMENTAL
LOADING
RIG
An experimental
rig has
been developed to allow the pressure distribution of a
graphite-aluminum interface to be mapped using ultrasound. The experimental rig is shown
Experimental Set-Up
An experimental rig has been developed to allow the pressure distribution of a
graphite-aluminum interface to be mapped using ultrasound. The experimental rig is shown
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Water Bath
Focussed
Ultrasonic
Transducer
Aluminium
Plate
Hydraulic
Actuator
FIGURE
FIGURE3.3.Schematic
Schematicofofexperimental
experimentalloading
loadingrig.
rig.
FIGURE4.4.Photograph
Photographofofexperimental
experimentalrig
rigfrom
from above
above showing
showing steel
steel support
FIGURE
support plate
plate and
and trapezoidal
trapezoidalscanning
scanning
areas.
areas.
Figure3,3,from
fromwhich
whichititcan
canbe
beseen
seenthat,
that, aa steel
steel support
support plate
plate provides
ininFigure
provides rigidity
rigidity and
and acts
acts
as
a
water
bath
for
ultrasonic
coupling.
The
desired
loading
condition
is
applied
via
as a water bath for ultrasonic coupling. The desired loading condition is applied via four
four
hydraulicactuators.
actuators.AAphotograph
photographofofthe
theexperimental
experimental rig
rig is
is shown
shown in
hydraulic
in Figure
Figure 4,
4, from
from which
which
the
water
baths
which
allow
constant
coupling
during
scanning
can
be
seen.
the water baths which allow constant coupling during scanning can be seen.
Experimental Method
Experimental Method
Before each test, the graphite and aluminum surfaces were polished using various
Before each test, the graphite and aluminum surfaces were polished using various
grades of abrasive paper. The surface profile was measured using a Taylor Hobson Talysurf
grades of abrasive paper. The surface profile was measured using a Taylor Hobson Talysurf
Profilometer. Linear Variable Displacement Transducers (LVDT's) were then mounted on
Profilometer. Linear Variable Displacement Transducers (LVDT’s) were then mounted on
the brick, and the brick positioned in the center of the rig. A 10MHz ultrasonic transducer
the
brick,
and the
brick
in the
center
of the of
rig.1.6mm)
A 10MHz
transducer
with
a focal
length
of positioned
203mm (-6dB
focal
diameter
was ultrasonic
then focused
on the
with
a
focal
length
of
203mm
(-6dB
focal
diameter
of
1.6mm)
was
then
focused
on the
back face of the aluminum plate and a reference scan taken. The amplitude of the reflected
back
face
of
the
aluminum
plate
and
a
reference
scan
taken.
The
amplitude
of
the
reflected
signal was recorded at 1mm intervals using a tri-axial ultrasonic scanning tank with the
signal
was recorded
at 1mm intervals using a tri-axial ultrasonic scanning tank with the
inspection
software Winspect™.
inspectionThis
software
Winspect.
reference scan was of an aluminum-air interface, at which almost all
This of
reference
scanwave
waswas
ofreflected.
an aluminum-air
at which
almost
(99.9995%)
the incident
In this case,interface,
the reflection
coefficient
is all
(99.9995%)
of
the
incident
wave
was
reflected.
In
this
case,
the
reflection
coefficient
equal to unity. The rocking load was then applied and at each load increment, the interface is
equal
to unity.once
The more.
rocking
loadscans
was then
and atbyeach
load increment,
interface
was scanned
These
wereapplied
then divided
the reference
to give the
reflection
was scanned once more. These scans were then divided by the reference to give reflection
1074
coefficient at the interface. This allowed the reflection coefficient to be mapped at each
load increment.
ULTRASONIC REFLECTION COEFFICIENT CALIBRATION
MEASUREMENTS
Introduction
In order to convert the measured reflection coefficient values from the loading rig
to contact pressure, the relationship between reflection coefficient and contact pressure
must be found. This was done using a series of calibration experiments on small graphite
and aluminum specimens. Table 1 shows the elastic and ultrasonic properties of PGA
graphite and aluminum.
When an ultrasonic wave is incident on the boundary between two perfectly
bonded materials, the reflection coefficient is given by [8],
where, Zj and Z2 are the respective acoustic impedances of the two materials (defined as the
product of the density and the wave velocity through the material [9]).
For non-similar materials, the perfect contact reflection coefficient is non-zero. For
a graphite-aluminum interface, this value is 0.68, which can be compared with 0.87 for
graphite- steel. However, if the surfaces are rough and the interface is between perfectly
bonded and zero contact, the system becomes more complex. The interstices that form
between asperities on the opposing surfaces cause scattering of the ultrasound, which is
highly frequency dependent. In this case, the reflection coefficient will vary depending on
the amount of contact between the surfaces and the frequency of ultrasound used to
interrogate the interface.
Experimental Apparatus and Method
The calibration measurements were carried out using the experimental set-up
developed by Drinkwater et al [10]. Figure 5 shows a schematic the apparatus used. The
graphite specimens used, were 20mm in diameter and 20mm high. The top 5mm was
tapered to ensure that the applied load was evenly distributed. The compressive load was
applied via a Zwick 1478 mechanical loading machine. The apparatus was designed such
that the 10MHz transducer was focused at the center of the graphite-aluminum interface.
A reference measurement was taken at the beginning of the test with no applied
load, i.e. zero contact between the surfaces. As the load was increased, the reflection from
the interface was recorded and divided by the initial reference (in the frequency domain) to
give the reflection coefficient. The load was then decreased and finally, an end-reference
was taken when the load had been fully removed. The end-reference was used to check that
the reflection coefficient returned to unity, indicating a good test. The reflection coefficient
at the center frequency of the transducer was used to provide the reflection coefficient
against pressure curve for the interface.
Figure 6 shows a best-fit to the loading data from three separate tests on graphitealuminum surfaces. This curve provides an empirical relationship between reflection
1075
Graphite
Aluminium
Water
Bath
Transducer
Holder
FIGURE 5. Schematic of experimental calibration rig.
coefficient and contact pressure for a graphite-aluminum surface prepared to the same
surface roughness. It was found using a linear regression technique that the best-fit line
followed the empirical equation,
P[=aRC2+bRC + c
(2)
Where, Pn is the pressure calculated from the nominally applied load, RC is the
measured reflection coefficient and a, b and c are constants equal to 42.86, -109.94 and
67.08 respectively.
RESULTS AND DISCUSSION
Example: 3 Region Contact
In order to validate the measurement technique and allow comparison with simple
theory, a brick was prepared such that it rocked with only three regions in contact. The
A
0.5
1
1.5
2
Experimental Data j
2.5
Contact Pressure (MPa)
FIGURE 6. Calibration curve showing experimental scatter and best-fit line.
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regions of contact were positioned as shown in Figure 7. The three regions were
manufactured using abrasive paper and were spherical to allow comparison with Hertzian
regions of contact were positioned as shown in Figure 7. The three regions were
contact
theory [11].
8 shows
the surface
profile to
of allow
regioncomparison
number 1 along
a single
manufactured
usingFigure
abrasive
paper and
were spherical
with Hertzian
traverse.
Using
the
experimentally
measured
values
of
amplitude
and
width,
it
was
possible
contact theory [11]. Figure 8 shows the surface profile of region number 1 along a single
to traverse.
calculateUsing
the effective
radius of curvature.
radius
of curvature
region
1 is 2.0m.
the experimentally
measuredThe
values
of amplitude
andofwidth,
it was
possible
The rocking
loadsradius
wereofthen
appliedThe
to radius
rock the
brick onto
region11.
Figure 9
to calculate
the effective
curvature.
of curvature
of region
is 2.0m.
shows a contour
map loads
of the
reflection
coefficient
this region.
These1. reflection
The rocking
were
then applied
to rockover
the brick
onto region
Figure 9
coefficient
values
were
then
converted
to
contact
pressure,
using
equation
2. Figure
10
shows a contour map of the reflection coefficient over this region. These
reflection
shows
a
vertical
(V)
and
horizontal
(H)
cross
section
of
this
point
compared
with
Hertzian
coefficient values were then converted to contact pressure, using equation 2. Figure 10
contact
for (V)
a radius
of curvature
of 2.0m.
It can
be point
seen that
the measured
peak
showstheory
a vertical
and horizontal
(H) cross
section
of this
compared
with Hertzian
pressure
is
25%
lower
than
the
predicted
pressure,
although
the
contact
area
is
correct
to
contact theory for a radius of curvature of 2.0m. It can be seen that the measured peak
within
5%. is 25% lower than the predicted pressure, although the contact area is correct to
pressure
within 5%.
CONCLUSIONS
CONCLUSIONS
A method of measuring contact pressure and stiffness in large contacting interfaces
A method of
contact
pressure
stiffness in
contacting interfaces
has been developed.
A measuring
hydraulic rig
has been
usedand
to measure
thelarge
load-deflection
behavior
been developed.
A hydraulic
rig has load
been and
usedcontact
to measure
the load-deflection
of has
a Magnox
graphite brick
under various
conditions.
Calibrationbehavior
of a Magnox graphite brick under various load and contact conditions. Calibration
FIGURE 7. Schematic of brick contact regions used in experiment. Horizontal line shows the scan line for
FIGURE 7. Schematic of brick contact regions used in experiment. Horizontal line shows the scan line for
thethe
surface
profile
shown
in in
Figure
surface
profile
shown
Figure8.8.
Amplitude (µm)
20
0
-20
-40
-60
0
55
1010
15
15
20
20
25
25
Traverse
TraverseLength
Length(mm)
(mm)
FIGURE
8. Horizontal
surfaceprofile
profileofofregion
region1,1,measured
measuredusing
using aa Talyor
Talyor Hobson Talysurf
FIGURE
8. Horizontal
surface
Talysurf Profilometer.
Profilometer.
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Increasing pressure /
Increasing pressure /
decreasingreflection
reflectionL
decreasing
coefficient
coefficient
0
2
4
6
8 10 12 14
m
—
Distance (mm)
Contact Pressure (MPa)
FIGURE
pressure over
over region
region 1.1.
FIGURE9.9.Contour
Contourplot
plotofofultrasonically
ultrasonically measured
measured contact
contact pressure
14
12
10
Hertz
-Hertz
8
6
Exp (V)
-Exp(V)
4
Exp (H)
-Exp(H)
2
0
-8
- 6-4 - -2
4 - 0 2 20 24 4 66 8
-6
Distance (mm)
(mm)
Distance
FIGURE10.
10.Contact
Contactpressure
pressuredistribution
distribution over
over region
region 1.
1.
FIGURE
measurements on
on graphite-aluminum
graphite-aluminum interfaces
interfaces have
have been
been used
measurements
used to
to convert
convert the
the measured
measured
reflectioncoefficient
coefficient into
into contact
contact pressure
pressure at
at the
the interface
interface between
reflection
between the
the graphite
graphite brick
brickand
and
aluminumfoundation.
foundation.
ananaluminum
Thecontact
contactpressure
pressuredistribution
distribution has
has been
been compared
compared with
The
with Hertz
Hertz contact
contact theory
theoryfor
for
a
brick
rocking
on
three
spherical
contact
regions.
The
results
show
good
qualitative
a brick rocking on three spherical contact regions. The results show good qualitative
agreement with
with theory
theory with
with an
an underestimate
underestimate of
of load
load at
at the
agreement
the interface.
interface. The
The contact
contact area
area
measured
experimentally
is
within
5%
of
the
theoretical
value
and
the
peak
measured experimentally is within 5% of the theoretical value and the peak pressure
pressure isis
approximately25%
25% lower
lower than
than predicted.
predicted. Further
Further work
work is
approximately
is required
required to
to minimize
minimizethe
theerrors
errors
associated
with
the
calibration
curve
at
higher
pressures.
associated with the calibration curve at higher pressures.
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
This work is supported by BNFL Magnox U.K. through the IMC. We would like
This work is supported by BNFL Magnox U.K. through the IMC. We would like
to thank John Payne of BNFL Magnox for his assistance.
to thank John Payne of BNFL Magnox for his assistance.
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1.
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1078
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Krautkramer, K. and Krautkramer, K., Ultrasonic Testing of Materials. SpringerVerlag Berlin Heidelberg New York, 1983.
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