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RESEARCH PAPERS

# A Combined Optical-Ultrasonic Method of Establishing the Compressibility of High-Pressure Oil and Grease Films Entrapped in a Ball on Flat Contact

[+] Author and Article Information
S. Kondo1

Department of Mechanical Engineering, Imperial College London, SW7 2BX, UK

R. S. Sayles, M. J. Lowe

Department of Mechanical Engineering, Imperial College London, SW7 2BX, UK

The acoustic impedance of air and sapphire are about five orders of magnitude different, with air at around $350Ns∕m3$ at atmospheric conditions and sapphire about $39×106Ns∕m3$. Thus the reflection coefficient from such a sapphire/air interface is effectively unity [see Eq. 3]. Hence dividing the sapphire/lubricant signal voltage amplitude, by the equivalent signal amplitude from the sapphire/air interface, gives a true value of the former’s reflection coefficient.

The refractive index of each lubricant was measured at atmospheric conditions to be around 1.49 and extrapolated to higher pressures by the method given in Gohar (26). The method of 26 relates refractive index to the fluid density, which in turn can be related to the pressure through equations such as the Dowson and Higginson density relationship. If this is done, it is also easy to show that the variation in the value of the refractive index is small at these high pressures. Over the likely pressure range involved of about 1.5–3.5 GPa, the variation is less than 2%, from $n=1.64$ at 1.5 GPa to $n=1.67$ at 3.5 GPa. This means that within any iterative solutions for establishing entrapped film properties, accounting for refractive index changes will have a limited effect on overall results.

As fluid density, pressure, refractive index, film-thickness, etc. are all interrelated, some iteration is seemingly needed, and in fact is used, to reach the final and therefore best estimates of results given. However, the interrelationships involved are argued and shown in the discussion to be relatively insensitive to each other over the pressure and film thickness range achievable with the test apparatus. Thus approximations based on simple extrapolations using the Dowson and Higginson’s density-pressure relationship and Hertz theories are in most cases sufficient to give reasonably accurate overall results.

Equivalent curves for a $2μm$ film can be obtained by scaling the horizontal axis $(×1.4∕2.0)$ such that values of IRLLI shown at 100 MHz represent values at 70 MHz for a $2μm$ film.

1

Now at KyodoYushi Co. Ltd., Tokyo, Japan.

J. Tribol 128(1), 155-167 (May 17, 2005) (13 pages) doi:10.1115/1.2125887 History: Received March 01, 2004; Revised May 17, 2005

## Abstract

The paper describes an experimental technique combining optical interferometry and ultrasonic attenuation to measure the bulk modulus (compressibility) and film thickness profiles of oil and grease films entrapped between a stationary steel ball and a sapphire plate. Results are presented for lithium- and urea-based greases, and their base oils alone, at contact pressures up to and around 3 GPa, and are compared with some models and results from other studies, extrapolated to the higher pressures achieved here. Results show that the bulk modulus of a particular grease and its base oil are found to be similar, at a given pressure, and largely dependent on the base-oil properties, which is demonstrated to be what is expected with the concentration levels of fillers and solid lubricants present. However, the film shapes measured for the grease and its base oil can be quite different. This is seemingly due to the manner in which the lubricant samples “solidify”, due to the high pressures, and also to the way in which the edges of the squeeze-film entrapped fluid are sealed. This latter sealing effect seems to be assisted by secondary phases, particularly with greases where fillers and solid lubricants are present, creating a very effective sealed contact where the entrapped lubricant samples could be observed to remain stable for several hours.

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## Figures

Figure 1

Variation of reflection coefficients with ultrasonic frequency for various thickness silicone layers between glass, from Pialucha (13)

Figure 2

Schematic diagram of the ball-on-flat rig used

Figure 3

Photograph of ball-on-flat rig

Figure 4

Pulse-echo trace from and through the sapphire plate, which is open to the air on its upper face, using the 50 MHz transducer submerged in a water bath. The first significant echo signal is from the water/sapphire interface and the second from the sapphire/air interface.

Figure 5

Urea grease fringe images for an entrapped sample at 612 N load. The images are about 1 mm wide. (The small roughly circular light blotch at about 9 o’clock at the outer edge of the wide black fringe is a water mark fault on the photograph and not a real feature).

Figure 6

Urea grease base-oil fringe images for an entrapped sample at 612 N load and at the same scale as the previous figure

Figure 7

Film profile for the urea-grease established from the fringe pattern of Fig. 5. The fringes were measured radially on a horizontal line from center to the left edge of Fig. 5. The points are plotted at the mean fringe radius, i.e., the radius of the middle of each black fringe.

Figure 8

Film thickness and numerically calculated pressure profiles for lithium grease samples

Figure 9

Reflection coefficient (IRLLI) relationship to bulk modulus at 50 MHz for a 2μm film of density 1170kg∕m3 separating a sapphire and steel contact

Figure 10

The numerically calculated contact pressure distribution (CP), from the combined surface deformation, represented by the entrapped film thickness (FT), for the Li-grease base-oil sample. The dry contact Hertz pressure (HP) for the same load (612 N) is also shown for comparison.

Figure 11

A plot of the bulk-modulus results of Table 3 in relation to pressure. The theory line is the simple equation of Ref. 1 extrapolated to these higher pressures. Extrapolating values given in Ref. 2 would give predictions slightly below the experimental points, at around 18 GPa. (However, it should be noted that the oils and greases involved with these comparisons are all different and agreement is not anticipated. They are compared on the basis of a rough comparison of typical lubricating oils and greases).

Figure 12

Reflection coefficient values predicted for a 1.4μm fluid film, between sapphire and steel at two different fluid densities (the top figure is for 900Kg∕m3 and the bottom 1500Kg∕m3). Values are plotted over a range of frequencies and film bulk modulii (the seven curves plotted in each graph represent 20, 40, 60, 80, 100, 200, and 300 GPa, from the top down, respectively.) Note how the reflection coefficient is relatively insensitive to density.

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