THE USE OF ULTRASOUND TO MEASURE CONTACTSTIFFNESS AND PRESSURE IN LARGE CONTACTINGINTERFACES

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 contactpressure between a rocking graphite brick and its foundation. A hydraulic loading rig has beendeveloped to allow ultrasonic measurements to be made of the contact interface given specificloading conditions. Ultrasonic reflection coefficient measurements have been used to obtaincalibration 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 convertedto contact pressure at the interface. Results are described which show the use of this ultrasonicmeasurement procedure to investigate the effect of curvature and a reduction in the contact areaon the brick rocking stiffness.

INTRODUCTION

In a Magnox type (gas-cooled) nuclear reactor, graphite bricks which are used tomoderate 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. Therocking stiffness of these columns is used to determine the natural frequency of the core forseismic response analysis. Within the reactor, the top and bottom surface of each brick is indry contact with the one above and below it. It is this solid-solid contacting interface, whichplays an important role in the rocking behavior. Figure 1 shows a photograph of a graphitebrick, both full size and after machining.

Robinson et al [2] measured the interfacial stiffness of graphite-graphite joints dueto surface roughness with ultrasonic reflection coefficient measurements [3], wherereflection coefficient is defined as the proportion of the incident signal reflected. Thecalculated stiffness values were used to model the effect of surface roughness on therocking behavior of a single graphite brick. It was concluded that although surfaceroughness on a microscopic scale plays no significant role in the tilting behavior, longwavelength surface variation might be a factor. Experiments were also carried out tomeasure the load-deflection behavior of a single brick rocking on a rigid foundation. Theseresults 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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FIGURE 1. Magnox graphite bricks.

-Rigid BodyMotion

-Beam Bending

-FE Analysis

- Experiment

Top of brick deflection (pm)

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 thanpredicted. Figure 2 shows the load-deflection behavior of a graphite brick on a rigidfoundation under horizontal loading.

Most rough surface contact models, such as the well-known Williamson andGreenwood contact model [4], are used to model rough, nominally flat surfaces. It ispossible however, that during manufacture engineered surfaces will also have some longwavelength undulation or 'waviness'. Thomas and Sayles [5] defined a machine toolsurface as a continuous band of wavelengths, with high frequencies representing the surfaceroughness, mid range frequencies representing the waviness and low frequenciesrepresenting errors of form. These mid-range frequencies are thought to be important ininfluencing the rocking behavior of bricks. Ultrasonic measurements have been usedpreviously to determine the interfacial pressure over small contact areas such as a ballbearing-raceway or wheel-rail system [6, 7]. The aim of this paper is to describe a methodfor mapping the contact pressure at the surface of a rocking graphite brick. This isaccomplished using a hydraulic loading rig, which allows the load-deflection behavior to bemeasured concurrently with ultrasonic measurements of the interface.

EXPERIMENTAL LOADING RIG

Experimental Set-Up

An experimental rig has been developed to allow the pressure distribution of agraphite-aluminum interface to be mapped using ultrasound. The experimental rig is shown

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Water Bath

FocussedUltrasonic

Transducer

AluminiumPlate

HydraulicActuator

FIGURE 3. Schematic of experimental loading rig.

FIGURE 4. Photograph of experimental rig from above showing steel support plate and trapezoidal scanningareas.

in Figure 3, from which it can be seen that, a steel support plate provides rigidity and actsas a water bath for ultrasonic coupling. The desired loading condition is applied via fourhydraulic actuators. A photograph of the experimental rig is shown in Figure 4, from whichthe water baths which allow constant coupling during scanning can be seen.

Experimental Method

Before each test, the graphite and aluminum surfaces were polished using variousgrades of abrasive paper. The surface profile was measured using a Taylor Hobson TalysurfProfilometer. Linear Variable Displacement Transducers (LVDT's) were then mounted onthe brick, and the brick positioned in the center of the rig. A 10MHz ultrasonic transducerwith a focal length of 203mm (-6dB focal diameter of 1.6mm) was then focused on theback face of the aluminum plate and a reference scan taken. The amplitude of the reflectedsignal was recorded at 1mm intervals using a tri-axial ultrasonic scanning tank with theinspection software Winspect™.

This reference scan was of an aluminum-air interface, at which almost all(99.9995%) of the incident wave was reflected. In this case, the reflection coefficient isequal to unity. The rocking load was then applied and at each load increment, the interfacewas scanned once more. These scans were then divided by the reference to give reflection

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coefficient at the interface. This allowed the reflection coefficient to be mapped at eachload increment.

ULTRASONIC REFLECTION COEFFICIENT CALIBRATIONMEASUREMENTS

Introduction

In order to convert the measured reflection coefficient values from the loading rigto contact pressure, the relationship between reflection coefficient and contact pressuremust be found. This was done using a series of calibration experiments on small graphiteand aluminum specimens. Table 1 shows the elastic and ultrasonic properties of PGAgraphite and aluminum.

When an ultrasonic wave is incident on the boundary between two perfectlybonded materials, the reflection coefficient is given by [8],

where, Zj and Z2 are the respective acoustic impedances of the two materials (defined as theproduct of the density and the wave velocity through the material [9]).

For non-similar materials, the perfect contact reflection coefficient is non-zero. Fora graphite-aluminum interface, this value is 0.68, which can be compared with 0.87 forgraphite- steel. However, if the surfaces are rough and the interface is between perfectlybonded and zero contact, the system becomes more complex. The interstices that formbetween asperities on the opposing surfaces cause scattering of the ultrasound, which ishighly frequency dependent. In this case, the reflection coefficient will vary depending onthe amount of contact between the surfaces and the frequency of ultrasound used tointerrogate the interface.

Experimental Apparatus and Method

The calibration measurements were carried out using the experimental set-updeveloped by Drinkwater et al [10]. Figure 5 shows a schematic the apparatus used. Thegraphite specimens used, were 20mm in diameter and 20mm high. The top 5mm wastapered to ensure that the applied load was evenly distributed. The compressive load wasapplied via a Zwick 1478 mechanical loading machine. The apparatus was designed suchthat 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 appliedload, i.e. zero contact between the surfaces. As the load was increased, the reflection fromthe interface was recorded and divided by the initial reference (in the frequency domain) togive the reflection coefficient. The load was then decreased and finally, an end-referencewas taken when the load had been fully removed. The end-reference was used to check thatthe reflection coefficient returned to unity, indicating a good test. The reflection coefficientat the center frequency of the transducer was used to provide the reflection coefficientagainst pressure curve for the interface.

Figure 6 shows a best-fit to the loading data from three separate tests on graphite-aluminum surfaces. This curve provides an empirical relationship between reflection

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GraphiteAluminium

WaterBath

TransducerHolder

FIGURE 5. Schematic of experimental calibration rig.

coefficient and contact pressure for a graphite-aluminum surface prepared to the samesurface roughness. It was found using a linear regression technique that the best-fit linefollowed the empirical equation,

P[=aRC2+bRC + c (2)

Where, Pn is the pressure calculated from the nominally applied load, RC is themeasured reflection coefficient and a, b and c are constants equal to 42.86, -109.94 and67.08 respectively.

RESULTS AND DISCUSSION

Example: 3 Region Contact

In order to validate the measurement technique and allow comparison with simpletheory, a brick was prepared such that it rocked with only three regions in contact. The

A Experimental Data j

0.5 1 1.5 2 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 weremanufactured using abrasive paper and were spherical to allow comparison with Hertziancontact theory [11]. Figure 8 shows the surface profile of region number 1 along a singletraverse. Using the experimentally measured values of amplitude and width, it was possibleto calculate the effective radius of curvature. The radius of curvature of region 1 is 2.0m.

The rocking loads were then applied to rock the brick onto region 1. Figure 9shows a contour map of the reflection coefficient over this region. These reflectioncoefficient values were then converted to contact pressure, using equation 2. Figure 10shows a vertical (V) and horizontal (H) cross section of this point compared with Hertziancontact theory for a radius of curvature of 2.0m. It can be seen that the measured peakpressure is 25% lower than the predicted pressure, although the contact area is correct towithin 5%.

CONCLUSIONS

A method of measuring contact pressure and stiffness in large contacting interfaceshas been developed. A hydraulic rig has been used to measure the load-deflection behaviorof 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 forthe surface profile shown in Figure 8.

5 10 15 20

Traverse Length (mm)25

FIGURE 8. Horizontal surface profile of region 1, measured using a Talyor Hobson Talysurf Profilometer.

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Increasing pressure /decreasing reflection Lcoefficient

0 2 4 6 8 10 12 14 mDistance (mm) —

FIGURE 9. Contour plot of ultrasonically measured contact pressure over region 1.

-Hertz

-Exp(V)

-Exp(H)

- 6 - 4 - 2 0 2 4 6 8Distance (mm)

FIGURE 10. Contact pressure distribution over region 1.

measurements on graphite-aluminum interfaces have been used to convert the measuredreflection coefficient into contact pressure at the interface between the graphite brick andan aluminum foundation.

The contact pressure distribution has been compared with Hertz contact theory fora brick rocking on three spherical contact regions. The results show good qualitativeagreement with theory with an underestimate of load at the interface. The contact areameasured experimentally is within 5% of the theoretical value and the peak pressure isapproximately 25% lower than predicted. Further work is required to minimize the errorsassociated with the calibration curve at higher pressures.

ACKNOWLEDGEMENTS

This work is supported by BNFL Magnox U.K. through the IMC. We would liketo thank John Payne of BNFL Magnox for his assistance.

REFERENCES

1. Payne, J. F. B. and Steer, A., Nuclear Electric Internal Report.

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2. Robinson, A. M., Drinkwater, B. W., Dwyer-Joyce, R. S. and Payne, J. F. B., Proc.Inst. Mech. Engrs. Part C: Journal of Mechanical Engineering Science 215, pp. 167-178 (2001).

3. Drinkwater, B. W., Dwyer-Joyce, R. S. and Cawley, P., "Study of the Transmissionof Ultrasound across Real Rough Solid-Solid Interfaces," in Proceedings of the IEEEUltrasonics Symposium, edited, IEEE, Cannes, France, 1994, pp. 1081-1084.

4. Greenwood, J. A. and Williamson, J. B. P., Proc. Royal Soc. London 295, pp. 300-319(1966).

5. Thomas, T. R. and Sayles, R. S., JEngInd Trans ASME 99 Ser B, pp. 250-256(1977).

6. Quinn, A. M., Drinkwater, B. W. and Dwyer-Joyce, R. S., Ultrasonics 39, pp. 495-502 (2002).

7. Pau, M., Aymerich, F. and Ginesu, F., Proc. Inst. ofMech. Engrs. PartF: Journal ofRail and Rapid Transit 214, pp. 231-243 (2000).

8. Tattersall, H. G., JPhys D (ApplPhys) 6, pp. 819-832 (1973).9. Krautkramer, K. and Krautkramer, K., Ultrasonic Testing of Materials. Springer-

Verlag Berlin Heidelberg New York, 1983.10. Drinkwater, B. W., Dwyer-Joyce, R. S. and Cawley, P., Proc. Royal Soc. London 452

(1996).11. Johnson, K. L., Contact Mechanics. Cambridge University Press, 1985.

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