Wear debris generated during high velocity sliding contact

Wear debris generated during high velocity sliding contact

189 Wear, 69 (1981) 189 - 204 0 Eisevier Sequoia S.A., Lausanne - Printed in The Netherlands WEAR DEBRIS GENERATED DURING HIGH VELOCITY SLIDING CONT...

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189

Wear, 69 (1981) 189 - 204 0 Eisevier Sequoia S.A., Lausanne - Printed in The Netherlands

WEAR DEBRIS GENERATED DURING HIGH VELOCITY SLIDING CONTACT P. C. CONOR and D. E. MCROBIE* Defence Scientific Zealand)

Establishment,

Auckland

Naval Base Post Office, Auckland

(New

(Received September 5,198O)

Summary Significant numbers of metal microspheres were found to be associated with tribological distress in two different engineering situations. In both cases the majority of the wear debris containing the spheroids appeared to have been generated by partially lubricated sliding wear. Existing explanations for wear spheroid formation seemed unable to account for these observations. A disc-rider apparatus was therefore used to examine some of the factors controlling the configuration of wear particles produced by the high speed sliding contact of hard steel surfaces under boundary lubrication conditions. Most of the debris produced in these circumstances consisted of fine plate-like metal particles which appeared to have been generated by localized shear processes. Debris produced during light normal load tests contained a substantial population of microspheres and support is provided for the conclusion that these particles were generated when contacting surface asperities melted.

1. ~trodu~tion Chemical methods for estimating the wear debris content of lubricating oil are widely used in machinery health monitoring programmes. The spectrometic analytical techniques which are most commonly employed have only a limited capability to determine the potential severity of given defect indications. For this r&son there is strong interest in developing wear debris microscopy to augment existing diagnostic procedures. The general correlation between the severity of the wear process and the configuration of the wear debris evolved appears to have been relatively well established. For example, fine platelets are usually taken to have been formed during normal service conditions whereas swarf-like cutting particles *Present address: Auckland Industrial Development Division, Department Scientific and Industrial Research, Auckland, New Zealand.

of

190

are seen to be indicators of severe abrasive wear [l, 21. However, practical observations show that large numbers of metal platelets can also be generated in situations of intense wear while cutting particles may be developed in small numbers by systems which are still in good mechanical condition, These seeming contradictions indicate that the successful application of debris microscopy for diagnosis requires an improved scientific understanding of the physical processes which are responsible for the development of wear particle characteristics. Studies of the frictional aspects of sliding metal surfaces have provided insights into some wear mechanisms [ 3 - 5 J . Aspects of the factors contributing to the shaping of particular wear debris species have also been examined experimentally [6 - 121 but because of its complexity this area seems to be generahy less well understood. For example, there have been observations that spherical particles are associated with bearing failures in gas turbines [ 1,131 and it has been suggested that these particles are formed within fatigue cracks in bearing elements [ 14 - 161. However, other studies have shown that spheroids are produced by high energy cavitation [ 171, in rubbing wear [l&19] and by the vacuum annealing of wear debris [ 201 and that large spheroids can be generated during abrasive grinding operations [ 21, 221 or by fretting [ 23, 241. There has been a further unsubstantiated proposal that microspheres are produced by local melting [ 211. The present work began as an investigation into the characteristics of microspheres generated by machinery in service. It later became an experimental examination of wear of a type which might occur in or near a distressed rolling element bearing in a gas turbine engine. The results of the initial investigation are summarized briefly, while those of the subsequent experimental work are reported and discussed in more detail.

2. Preliminary

investigation

of spheroidal

wear debris

Spherical particles were originally encountered in two engineering situations. In one instance smooth iron-rich microspheres (Fig. 1) in the size range 3 - 10 pm were found in the wear debris extracted from the lubricating oil of a gas turbine engine which had failed in service. Breakdown had occurred after partial starvation of the oil supply to a rolling element thrust bearing had eventually led to failure of the bearing by overheating. In the second case, excessive bearing wear in a high speed diesel engine prompted an examination of the wear debris. Once again, highly spherical particles were found in significant numbers. The spheres were relatively large in size (approximately 30 pm in diameter) and X-ray analysis indicated that they were composed of the lead-based antimony-rich journal bearing alloy. Some of the spheroids exhibited superficial figuring which was strongly suggestive of internal shrinkage during solidification from a molten state (Fig. 2). In order to provide a comparison, some metal spheres were generated by repeating a previous experiment [ 231 which involved the fretting of two

191

Fig. 2. “White metal” spheroid amongst wear particles extracted lubricating oil.

from diesel engine

Fig. 3. Silver spheroid developed by the “onion skin” addition of successive layers of metal during non-lubricating fretting.

dry pieces of silver. The fretting action generated large irregular spheroids (Fig. 3) in less than 1000 cycles. These particles were clearly formed by the rolling-up process proposed by Hurricks [ 241 but were different in appearance from those produced in the two engineering cases described above. Additional tests showed that, if the silver surfaces were lubricated with mineral oil before fretting, sphere development was suppressed completely and instead only burnishing took place. Similar fretting tests carried out on steel surfaces in air and in oil did not produce spherical debris. High velocity abrasive grinding of steel in air produces fine metal fragments which in some cases are heated sufficiently to burn as they leave the wear zone. These burning particles are known to form globular droplets which can cool in spherical form [21, 221 and it was considered to be possible that the spheres formed in the gas turbine were generated in this way. Further experiments in which soft and hard steel surfaces were abraded against one another at high speed in air produced large numbers of spheroids.

Fig. 4. Spheroid air. The particle Fig. 5. Collapsed

produced during unlubricated was produced by combustion, hollow

spheres

on a corroded

sliding of mild steel against mild steel in melting and then resolidification. wear debris sample.

However, the particles produced in this way were considerably larger (Fig. 4) than those generated in the gas turbine. Spherical particles can also be developed by corrosion of wear debris. If fine steel wear particles are moistened, perhaps by water vapour condensation during specimen preparation, a relatively rapid chemical reaction takes place. Hollow spheres (Fig. 5) are often formed, apparently by precipitation of hydrated iron oxide around gas bubbles. Because these spheres do not always collapse, their presence in the wear debris can sometimes give misleading indications of microsphere numbers. The formation of these artefacts can be prevented by careful specimen preparation and precautions were taken to avoid wear debris corrosion throughout this investigation. The initial work seemed to indicate that the spherical wear particles generated in the gas turbine and diesel engine had not been formed either by fretting or by pyrophoric combustion. The actual processes by which these particles were developed remained unclear, but sliding wear at a high relative velocity was likely to have been a feature common to both mechanical systems. The subsequent experimental study was therefore designed to elucidate some of the factors contributing to the formation of wear debris under similar conditions.

3. Apparatus and test procedures Wear particles were generated by holding a hardened steel rider against the periphery of a spinning disc (Fig. 6). The disc, which was made of high speed steel (of the composition given in Table l), had been heat treated to a hardness of 780 HVP (approximately 63 HRC) and was enclosed in a casing which was partially filled with lubricating oil (Mobil Jet Oil 2). A balanced lever arm holding the rider was pivoted to allow the bearing surface of the rider to move through an arc approximately normal to the

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ROTATING DISC

CASING \

PIVOT

LUBRICATING

RIDER

OIL

Fig. 6. Schematic diagram of the disc-rider apparatus.

TABLE 1 Disc composition in weight per cent

c

Si

Mn

W

Cr

V

MO

Co

Fe

0.64

0.63

0.31

14.3

3.98

0.98

0.19

0.51

Balance

TABLE 2 Rider composition (core) in weight per cent C

Mn

Ni

MO

Cr

Fe

0.24

0.84

0.56

0.21

0.43

Balance

lower edge of the disc. The addition of weights to the free end of the lever increased the load across the sliding surfaces. Vibration in the lever was damped by means of an oil-filled dashpot connected to it and at low loads the rider was provided with an additional spring suspension. The rider was made of quenched and tempered low alloy steel (Table 2). This component had been case hardened to an effective depth of approximately 0.75 mm and had then been heat treated to provide a surface layer hardness in the region of 775 HVP. All tests were run at a sliding speed of approximately 56 m s-l.

194

For comparison purposes two widely different loading conditions were examined. In one series of tests the rider was held against the disc by the application of a normal force of 7.8 N and in the second series the load was reduced to approximately 0.2 N. The lesser force was selected to provide intermittent light contact between rider and disc whereas the contact at the higher load was hard and continuous. The wear debris was collected from samples of the lubricating oil by centrifugation and washing in ~uo~a~d hydroc~bon solvent (Freon TF). Finally, particles were deposited on an aluminium slide by magnetic separation and were coated with a thin sputtered layer of gold for observation by scanning electron microscopy.

4. Experiment

results

4.1. Wear debris 4.1.1. High load The wear debris generated by tests at the 7.8 N normal load consisted primarily of flake-like particles of thicknesses predomin~tly in the range 1 2 ,um (Fig. 7) but significant numbers were much thinner, in the region of 0.1 I.trn thick (Fig. 8). The thin flakes were usually smooth and even in finish (Fig. 9) but the thicker particles ranged in configuration from some with a relatively smooth surface (Fig. 10) through others showing an irregular pebbly surface (Fig. 11) to planar masses of agglomerated fines (Fig. 12). Cutting particles were rare and spheroidal debris was effectively absent. 4.1.2. Low load Low contact pressures led to very low wear rates but at the conclusion of these tests the lubricant contained small amounts of debris which although generally similar in size range and type (Fig. 13) to the high load particles also contained a few swarf-like cutting particles (Fig. 14) and appreciable

Fig. 7. Typical

debris generated

in wear under high load conditions.

Fig. 8. Edge-on

view of a thin flake.

Fig. 9. Perpendicular

view of a thin flake. Some electron

Fig. 10. Perpendicular

Fig. 11. Surface

pebbles

transparency

is evident.

view of a thick flake,

on a wear flake.

Fig. 12. A mass of fine particles

agglomerated

into a larger flake.

Fig. 13. Wear debris produced under light load conditions. Flakes of various present and there are several spheroids in the field of view. Fig. 14. Cutting

particle

in light load debris.

types are

Fig. 15. Spheroidal particle in light load debris. indicates that the particle has a dendritic internal Fig. 16. Smooth-surfaced

The pattern structure.

of surface

indentations

spheroid.

numbers of microspheres (Figs. 15 and 16). Most of the spheres were in the range 3 - 5 pm in diameter, but a few were as large as 10 km across or as small as 1 I.tm across. Variations in surface appearance were evident among the spheres. Some of the particles exhibited a surface pattern of relatively regular indentations (Fig. 15) but others appeared smooth and featureless (Fig. 16). 4.1,3. Particle ~ornpos~t~o~ A number of wear particles were subjected to energy-dispersive X-ray analysis using electron beam excitation and were found to consist primarily of iron although traces of tungsten and chromium were also detected. It therefore seemed that while a large proportion of the wear metal originated from the plain carbon steel rider, mechanical alloying at the wear interface also caused metal to be removed from the surface of the alloy steel disc. 4.1.4. Tests for particle corn bustion (low load) It was considered possible that the spheroids might have been formed by fine metal particles burning in the air behind the contact region and to test for this effect wear particles were generated while the air space in the disc casing was purged of oxygen by a stream of argon. The numbers and appearance of the spheroids in the debris samples produced under these conditions did not differ significantly from those formed when air was present. The other types of wear particle were also not affected by the change in atmospheric composition. 4.2. Contact surfaces 4.2.1. Wear rate At the high contact force the rate of wear (the ratio of worn volume to distance slid) of the rider surface was approxima~ly lo-” cm3 cm-‘. (The hardened case of the rider was not penetrated in the durations of these tests,)

Fig. 17. Wear surface of the rider after a high normal load test. The smeared surface Iayer and a craze fissure are evident. Fig. 18. Wear surface of the disc after a high load test. Surface fissuring and pitting are widespread.

The disc surface appeared almost uneroded with only light surface polishing being apparent after many tests. Low load experiments produced no measurable wear on the rider surface even after extended contact times. Surface bu~ishing was the only observable effect. 4.2.2. Rider surface The contact zones on the rider also appeared smooth and polished. There were no clear differences in the configurations of the wear surfaces left after high and low normal load tests. Even at high magnifications the majority of the area of each of the wear surfaces was essentially featureless with only light grooving or scoring being apparent. However, localized portions of all the contact zones contained fine microcracks (Fig. 17), although the effect was more common on the surfaces formed at high load. Light pitting of the surface was often evident near the fissured regions. Other localized areas displayed signs of metal smearing and redeposition and were often associated with thin deposits of the fine rubble-like particles which made up a significant proportion of the wear debris. 4.2.3. Disc surface Portions of the disc surface were examined after a high load run and the bunched areas were found at high mastication to be similar in appearance to the wear zones on the rider. Crazing was generally more frequent and more severe than on the rider and loss of some of the surface material was again indicated by the presence of shallow pits in many areas (Fig. 18). 4.3. Subsurface microstructures 4.3.1. Disc Metallographic cross sections of the disc rim showed that, where the high speed steel microstructure was exposed, deformation was limited to a

198

zone approximately 1 pm in depth. Redeposited layers were present in other areas and were made up of a non-etching material, also in the region of 1 I.tm thick. 4.3.2. Rider The subsurface structures of wear zones of the rider were generally more complex in that distinct variations were evident along their length. The usual pattern was that relatively large pieces of non-etching material were often embedded in the surface close to the leading edge of the wear groove (Fig. 19). Downstream of this region was a zone in which shear deformation had occurred in the top micrometre of material (Fig. 20). Slight microstructural alterations were usually apparent below the surface of this region but the changes were rarely extreme. Further downstream a distinct non-etching layer developed. The extent of this layer increased relatively quickly to approximately 1 - 2 I.trn in thickness but then remained relatively constant in depth to the trailing edge of the contact zone. The underlying microstructure usually displayed little evidence of mechanical deformation but there was often a distinct stratified band of modification, apparently a heataffected zone, extending approximately 5 pm into the base material. The crazing on the wear surface was shown to correlate clearly with fissures in the non-etching layer (Fig. 21). The pits on the rider and disc surfaces were caused by loss of fragments of the surface layer induced when cracks turned parallel with the surface and ran along the interface with the substrate. In some places the non-etching layer was composed of flakes of partially redeposited material, some of which were occasionally in the process of delaminating from the surface (Fig. 22). However, the unevenness of the interface between the non-etching layer and the base material strongly

Fig. 19. Metallographic cross section of a wear groove on the rider at a point leading edge. Hard non-etching particles have been driven into the carburized (Nital etched.) Fig. 20. Etched cross section of the rider surface a short edge of the wear zone. Surface deformation is restricted evidence for strong heating.

near the steel matrix.

distance back from the leading to a thin band and there is little

Fig. 21. Etched section of the rider approximately 1 mm from the leading edge. A nonetching transformed layer has developed and a craze fissure has penetrated this layer and is propagating along the interface with the substrate (cf. Fig. 17). Fig. 22. A redeposited portion of the surface layer is delaminating to form a flake of wear debris.

suggested that a front of thermal substrate.

transformation

was progressing

into the

5. Discussion 5.1. Wear at high load

5.1-l. Wear rate Sliding contact at the higher level of normal load caused a relatively rapid loss of metal from the rider, indicating the presence of a lubricated severe wear regime. However, if the criteria used by Welsh [4] to classify wear on unlubricated surfaces are applied, the low wear rate (ratio of volume worn to distance slid) and the small debris size are evidence of the existence of a mild wear condition. The classification proposed by Reda et al. [ll] also indicates the existence of a mild wear regime. The flake-like form of the wear debris and the relatively smooth unploughed appearance of most of the abrading surfaces were both indicative of a delamination wear mechanism but it became clear that in the present system the delamination process outlined by Suh and coworkers [8, 91 for low speed wear did not operate. Instead, there was evidence that at high sliding speeds thermal effects exert an overriding influence on the wear process. Roseanu and Pneuli 1251 have proposed a localized-shear mechanism to account for the wear and frictional behaviour of two sliding surfaces making up a thermally asymmetric pair. When two steel surfaces first touch, the model indicates that intense localized shear develops at true contact points on the interface. Strain rates in excess of 10’ s-l are probable. The consequent instantaneous temperature rise reduces the shear strength of the surface

200

material and so localizes the deformation in a thin layer. If the temperature gradients in the two bodies are not symmetrical (and under steady state conditions the subsurface material of the rider will be signific~tly warmer than that of the disc) the thermal peak and so the plane of maximum shear are displaced into the warmer body. The result is that a thin film of steel is skimmed off the rider surface. Thin (0.1 pm) and smooth wear platelets were found in significant numbers in the wear debris and it is difficult to offer any alternative wear process which could be responsible for their formation. Roseanu and Pnueli used equations of viscous shear in their calculations but, as has been suggested elsewhere [3, 261, thermally localized surface sliding has a number of similarities to adiabatic shearing in bulk materials. The essential requirement for adiabatic shear is that thermal softening induced by the temperature rise from local mechanical deformation should exceed the concurrent work-hardening rate [ 271. In high speed sliding this condition can be achieved relatively easily since the initial frictional energy input occurring when the surfaces first touch can reach extremely high values and is already localized to a planar surface. Unlike the situation of adiabatic shear in bulk materials the plane of instability is already present and does not have to be developed by shear band propagation. At the same time, the fact that true contact is achieved at only a few points on the wear surface means that the extent of adiabatic shear is reduced and as a result is modified. The effect was seen in the experimental situation where in the leading areas of the rider the cooling and separating effects of the residual oil film combined with the comp~atively low temperature of the disc were such as to prevent widespread transformation of subsurface material. Visible shear deformation extended into the base microstructure of both disc and rider and there was little evidence of the develop ment of a significant band of transformed material in this region. The deformation was therefore akin to untransformed adiabatic shear processes in bulk systems [ ZS] . 5.1.2. Contact of thermally softened surfaces The situation changed quickly as disc surface elements penetrated deeper into the wear zone. Continued frictional contact maintained the increase in temperature which assisted surface softening and increased the area of true contact. The result was that a layer of steel transformed to austenite [ 29 - 311 covered the entire centre and trailing area of the wear zone on the rider. After its initial appearance the transformed layer increased in thickness relatively quickly until.it reached a limiting depth of approximately 2 @rn. This dimension then remained approximately constant to the trailing edge of the rider. It must be assumed that at this thickness the strain rate in the austenite layer was such that the rate of work hardening was in balance with the rate of thermal recovery induced at the maintained temperature level, Taken with the metallographic evidence that there was no gross shearing of the substrate material beneath the transformed layer, this

observation provides a clear indication that the conditions for transformed adiabatic shear were satisfied. 5.1.3. Debris generation It is not possible to determine the details of the deformation mechanisms taking place within the austenite layer but the surface appearance suggested that shear flow was not laminar. The effect of prow formation has been demonstrated as a si~ific~t means of material transfer [lo] and while there was no evidence of large-scale prow development on either disc or rider the operation of short-lived shallow prows on both surfaces may have assisted the exchange of au&mite between them. In the experimental system the large ratio of total surface area to wear contact area of the disc in comparison with that of the rider was such as to ensure that the disc was cooler. The result was again a net transfer of steel from the rider to the disc, which consequently became coated with a layer of hot austenite as it was rotated towards the rear of the wear zone, As soon as the material on the disc moved out of contact with the rider, frictional heating stopped and the austenite quenched very rapidly, inducing craze fissures and spall cracks which in turn detached small platelike particles from the disc. A similar process also occurred on the rider surface when contact ceased. The majority of the wear particles in the debris showed signs of having been formed in this way. The enhancement of thermal shock induced by phase changes in the transformed layer is clearly important in this mechanism and the consequent high rate of metal loss from the disc may account for the successful application of high speed friction sawing to steel f32] . Retention of transferred material on the disc surface was common and its reintroduction into the wear zone after a revolution of the disc was a normal part of the wear process. Reinforcement of the leading edges of the wear zones of the rider by hard particles detached from the disc and driven into the base material may have had some si~ific~ce in reducing the general wear rate. In addition, the configuration of a substantial portion of the wear debris indicated that many particles were mechanically broken up as they passed between the two sliding surfaces before being released from the wear zone. The rebuilding of platelets by mechanical agglomeration of finer particles also seemed frequent. 5.1.4. Lubrication The role of the lubricant in inhibiting wear in the high load case cannot be determined with any certainty. Although there was continuous contact between the metal surfaces the oil must still have had some effect in reducing the amount of true contact. At the same time the evidence that very high temperatures existed in the contact zones suggests that the hydrodynamic effects can only have been transient. In general it seems that in these conditions the lubricant acted primarily as a coolant in the early stages of contact and also reduced oxidation in the high temperature regions.

202

5.2. Wear at low load 5.2.1. Lubrication In contrast, in the light normal load situation the hydrodynamic effect of the lubricating oil was clearly important in separating the surfaces. In spite of this the primary wear processes, although occurring at a very low rate, appeared to be generally similar to those of higher contact loading. However, true contact between the surfaces would have been comparatively rare and would often have been confined to asperity interference events. This effect may provide an explanation for the formation of microspheres in light load sliding wear. 5.2.2. Microsphere generation Relatively extensive surface heating has already been indicated as a primary feature of high load, high velocity wear. Doyle [ 201 has shown that when steel wear debris is heated to temperatures in the region of 900 “C a solid state spheroidization effect can cause globular particles to be generated. This process cannot be excluded as a mechanism of microsphere development in the present case. However, the near absence of rounded particles from the high load debris, which was formed under very widespread frictional heating, reduces the likelihood that this was the primary mechanism for spheroid development in high speed sliding. Direct temperature measurements of surfaces sliding at much lower velocities [ 33, 341 have indicated that transient temperatures up to the melting point of the surface material can be attained without difficulty. At very high speeds, in the region of 500 m s-l, the energy of interaction is sufficient to melt the entire contact area [3, 35, 361. In the intermediate speed range, represented by the present tests, there is therefore every likelihood that, when asperities touch, local strain rates can be high enough to induce melting. Calculations by Roseanu and Pnueli [ 251 and by Archard [ 371 support this conclusion. Melting may have occurred during high load sliding but under these conditions the surfaces were close enough together to prevent the escape of molten metal. However, for a low normal load the indications are that momentary contact of asperities provided small volumes of molten steel and that the impact energy was sufficient to detach some of the liquid into the surrounding space. The resulting globular droplets chilled very quickly in the enveloping oil film. Internal crystallization during solidification left a characteristic pattern on many of the spheres and the close spacing of the dendrite arms is indicative of a high cooling rate. Other spheres were smooth and it seems possible that the combination of the small volume of the droplets and their rapid cooling was sufficient to suppress the nucleation of crystalline material, with the result that they solidified in a glassy state. 5.2.3. Cuttingparticles The most probable way in which the machining action necessary to produce cutting particles could have occurred is if quench-hardened fragments of material of suitable shape became embedded in one or other of the

203

abrading surfaces (381. The cutting action of protrusions of this kind would be relatively short lived because frictional heating would quickly reduce the strength of the cutting edge. However, the presence of tungsten in the wear debris and the likelihood that light oxidation of the cutting surface will reduce the heat transfer rate might together act to prolong the effective lives of any sharp protrusions acting as cutting tools. 6. Conclusions (1) Partially lubricated high velocity sliding contact of hard steel surfaces at moderate and low normal loads produced wear particles of a predominantly flake-like form. The experimental observations indicated that the energy of interaction between the two surfaces was extremely high. Consequently the wear mechanisms and therefore the configuration of the wear debris were controlled as much by thermal effects as by mechanical factors. (2) The majority of the debris platelets were formed when fragments of a transformed layer attached to the disc surface by an adiabatic shear process in the contact area were subsequently detached by quench spalling as elements of the disc slid clear of the wear zone. (3) A variation of this wear process appeared to operate in the leading portion of the wear zone where temperatures were lower. In this situation a highly localized shearing action generated wear flakes which were much thinner and smoother than those developed by the transformation and spalling mechanism. (4) Small steel microspheres with smooth surfaces appeared in wear debris formed during sliding at low normal loads. There is theoretical and practical evidence to indicate that these were formed when momentary contact of asperities on the opposing surfaces caused the interfering material to reach temperatures exceeding the melting point of the steel. This conclusion provides support for the suggestion of Broszeit and Hess [21] that microspheres can be a product of frictional heating. (5) There are strong indications that metal microspheres can be formed by any of several different physical and chemical processes including fretting, hot particle spheroidization, asperity melting and pyrophoric oxidation. All these mechanisms are associated with adverse wear conditions and a general practical conclusion is that an item of machinery which develops a high microsphere population in its lubricating oil is suffering from internal tribological distress. Detailed examination of the spherical particles and of the debris with which they are associated should provide useful information about the wear mode and so about the mechanical health of the system. Acknowledgments This paper is published with the permission of the New Zealand Ministry of Defence. The authors also acknowledge the support provided

by

204

Mr. H. Levinsohn and are grateful chemical analysis results.

to Mr. L. P. Judson

for supplying

the

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