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Characterization of topographical changes during lubricated wear
Wear, 98 (1984)
101
101 - 116
CHARACTERIZATION LUBRICATED WEAR
OF TOPOGRAPHICAL CHANGES DURING
JOICHI SUGIMURA and YOSHITSUGU KIMURA Institute of Interdisciplinary Research, Komaba Campus, Faculty University of Tokyo, 4-6-l Komaba, Meguro-ku, Tokyo 153 {Japan)
of Engineering,
The
(Received June 1, 1984; accepted October 8,1984)
Summary Experiments on lubricated wear are conducted and profiles of the wearing surfaces are studied. Two types of cross-correlation coefficient are introduced: one compares the profiles obtained at the same position before and after sliding for a fixed duration, and the other compares the profiles at different positions on the same wear track. It is found that the former represents a characteristic of the wearing mode, while the latter quantitatively gives the degree of two dimensionality of the topography. 1. Introduction Surface microtopography plays a significant role in almost all tribological problems. In particular, it is one of the most important factors in the wear of materials since it determines the state of microcontact between sliding surfaces. It is now widely accepted that the wear particles are generated as a result of fracture by the forces transmitted through the microscopic spots which form the area of real contact. However, it is only recently that such an idea has been brought into the stage of analysis. Halling [l] and Finkin [Z] applied the baron-Coffin relation of low cycle fatigue to the wear process and obtained linear wear equations. Suh [3,43 introduced fracture mechanics and established the delamination theory of wear which includes subsurface crack nucleation and propagation. These and other advanced analyses are noteworthy in that they have opened a path to be followed in pursuing essential mechanisms of wear. However, for analysing subsurface stresses, strains etc., they made rather simplified assumptions as to the actual forces working on the surface, ignoring the microscopic contact mechanics, which substantially undergo continuous changes due to wear. As wear proceeds, material removal and accompanying subsurface plastic deformation would bring about successive changes in surface microtopo~aphy, which might inevitably alter the shape and size of a real contact spot and thereby the direction and magnitude of 0043-1648/64&3.00
@ Elsevier SequoiafPrinted in The Netherlands
102
a force acting on it. Therefore the surface microtopography during the wear process must be followed in order to construct a proper model for analysis in which changes in the contact state are taken into account, providing variable boundary conditions. More specifically, investigation is needed to characterize the manner by which the surface topography changes during sliding wear and to characterize the topography produced by the process. Recently surface measurement has gained a great advantage by the application of digital techniques to the stylus instruments, and the analysis of surface profiles using a computer is now a usual practice. Together with this it has become common to employ stochastic methods for the characterization of surface profiles since the work of Peklenik [5] on manufactured surfaces. Various parameters and functions have been proposed for representing some characteristic features of a profile or further for analysing roughness effects in static contact [ 6,7], hydrodynamic lubrication [ 81 etc. As to the changes in surface topography associated with wear, most of the investigations carried out so far were concerned with the changes that occur during the so-called running-in period [9 - 141. These showed that wear took place only at the tops of asperities when a rough surface slid against a hard smoother surface under favourable conditions, and this was characof the height distribution of a terized by the occurrence of “truncation” profile, However, this is not always the case. During the sliding between a pair of surfaces having similar hardnesses, where what is called adhesive wear often offers problems, the changes in surface topography may not be so simple [ 15 - I$], even under lubrication. The investigations introduced above dealt with the two-dimensional aspects of surface topography, for the measuring instruments could provide only a profile along a particular section. Preferably, however, a surface should be treated three dimensionally, since actual surfaces are sometimes not isotropic. Techniques for a three-dimensional measurement by parallel traces are now available, but they are time consuming and, above all, it has not been established yet what information could be extracted from a vast number of data. In contrast, several investigators have attempted to describe three-dimensional features of a surface, especially its anisotropy, by some parameters obtained from ordinary profile measurement. For example, Peklenik [5] presented the cross-correlation function between two parallel traces and the correlation length obtained from its autocorrelation function. Patir and Cheng [ 191 used the ratio between the correlation lengths of two profiles taken at right angles to each other as a measure of anisotropy, and they discussed its effect on hydrodynamic lubrication. Nayak 120, 213 also proposed some parameters of anisotropy based on the statistical theory of gaussian random surfaces. Although there are a number of parameters which characterize the surface microtopography, the present paper introduces two types of correlation coefficient which can easily be determined from profile traces. One characterizes the changes in surface topography that occur during sliding, and the other measures its directional property.
103
2. Experimental
details
Wear experiments have been carried out on a three-pin-on-disk machine. Figure 1 shows diagrammatically an arrangement of its main part. The sliding system consists of a rotating upper specimen and a stationary lower specimen, either of which can be a disk or a three-pin assembly. Currently the three-pin assembly is used as the lower specimen so that wear debris generated at the sliding surfaces may easily escape from the interface. The disk specimen is fixed to the upper specimen holder, which is driven by an electric motor at a speed ranging from 0.1 to 1000 rev min-’ . The three-pin assembly is secured to the bottom of an oil bath, which is supported by a gimbal mechanism mounted at the top of a hydraulic piston. The gimbal mechanism ensures plane contact between the upper specimen and the lower specimen. The piston can freely rotate around its axis and move up and down. A normal load is applied to the contacting surface between the specimens by oil hydraulic pressure working on the bottom of the piston; this load can be varied from 0 to 600 N. A torque arm is secured to the gimbal 1 Rotating
Shaft
Disk Specimen Holder &
Fig. 1. Main part of the three-pin-on-disk
machine.
104
Fig. 2. The disk specimen and the three-pin assembly.
support; the torque arm presses against a load cell to provide a measure of the friction. A heater is mounted under the oil bath and a chromel-alumel thermocouple for monitoring the oil temperature is inserted in the bath. Figure 2 shows a general view of the specimens used in the present experiments. The disk specimen is 40 mm in diameter. The three pin specimens of 4 mm in diameter are rigidly secured to a cylindrical plate at regular intervals on a circumference of 30 mm diameter to form a three-pin assembly. Both the disk and the pin specimens are made of S35C carbon steel (which corresponds to AISI 1035 steel) annealed to 220 - 260 HV. The sliding surfaces of both specimens were finished by lapping with white alumina to an r.m.s. roughness of about 0.28 pm. The results for two separate experiments conducted under different conditions will be shown. They are designated experiment A and experiment B. A low viscosity paraffinic base oil is used as a lubricant in experiment A and a similar oil with the addition of ndodecyl mercaptan in experiment B. Testing conditions and the properties of the lubricant used in each experiment are given in Table 1. These conditions are selected so that the wear rate becomes relatively high and fully detectable. Having been washed thoroughly in benzine and then in trichloroethylene and dried in hot air stream, the specimens were set in the apparatus in the manner described above. The load, sliding speed and oil temperature TABLE 1 Experimental conditions Experiment
Lubricant kinematic
A
Hi-white 70 (17.4 cSt at 30 “C)
B -
and its viscosity
Oil temperature CC)
Normal load WI
Sliding velocity (m s-l )
30
166.7
7.85 X 1O-4 500 (50 m X 10)
Hi-white 70 + 1.0% 30 n-dodecyl mercaptan (17.8 cSt at 30 “C)
245.2
1.57
X
lO-3
Sliding distance (ml
500 (50 m X 10)
105
were held constant, and a run was continued for a predetermined duration which corresponds to a sliding distance of 50 m; this took about 1060 min in experiment A and 530 min in experiment B. After a run, the specimens were removed from the apparatus. They were washed as before and surface profiles were measured; details of this measurement will be described later. Then the same specimens were again mounted on the apparatus and the same lubricant was poured into the oil bath for the next run of 50 m. The process was repeated ten times until the total sliding distance reached 500 m. In addition to their surface profiles being taken, the specimens were weighed in a precision balance at each stop to determine the wear amount. Measurements of the surface topography were conducted using a Talysurf 4 profile-measuring instrument in conjunction with a microcomputer. The output signal from the Talysurf was fed to a transient converter (4K of ll-bit word store) which converted the data to digital form and stored them temporarily. Immediately after the completion of a traverse, the data were transferred to the microcomputer and recorded on a G in floppy disk. The transient converter was controlled by the computer, which was programmed in machine code to shorten the time required for the data storage. As schematically illustrated in Fig. 3(a), the profiles were taken perpendicular to the direction of sliding at four locations spaced 90” apart on the circular wear track on a disk specimen and also on each of the three pin specimens. Repositioning of the stylus with respect to the wear track was done manually using a slide table such that approximately the same sections were traversed each time. Because of the difficulty in determining a common origin for each profile, a starting point for data acquisition was placed somewhere outside the wear track. A sample interval of 2.5 pm and 2048 samples were employed, which represented a profile about 5.12 mm in length across the wear track. Before a profile was analysed, data outside the wear track were omitted and then the average line of the profile was made to coincide with the datum, or the abscissa, by applying the least-squares method. That is, a
X
X, .. .
.. . :‘. :. .. - *.*
.
Xi+1
REGRESSION
..* .%....* ..*. . . . . *._*“_ .’..... ..* . .. . . ‘.‘.
*.: ,
SAMPLING
(a)
DAT”M
INTERVAL
/: *. .. *.* _.’ :“.
.. . .J’ * . : .:
.. ..
::
LINE
. -
t
(b)
Fig. 3. Obtaining surface profile data: (a) measurement itized profile with its regression line.
with each specimen; (b) a dig-
106
regression line for the profile was calculated and the discrepancies between the measured values and the obtained regression line were taken as new profile ordinates (Fig. 3(b)). By doing this, the mean of the profile ordinates became zero and any linear trend of the whole profile was removed.
3. Experimental
results
The variations n the coefficient of friction and the wear amount measured are shown in Figs. 4(a) and 4(b) for experiments A and B respectively. Basically the wear rate, i.e. the gradient of the wear curve, for both experiments is initially high and in time decreased to a lower value; this reduction is more pronounced in experiment B than in experiment A. The coefficient of friction shows irregular fluctuations, and its general behaviour is shown in the figures by the upper and lower lines which roughly envelop its fluctuations. Closer examination of the original friction records reveals that, particularly for experiment A, its value is consecutively subjected to irregular rises and falls. This suggests that interactions between the sliding surfaces, which would lead to material removal or plastic deformation of surface layers, have taken place at various positions on various scales. In 50
Lx-----
01 1W
200
SLIDING
300 DISTANCE,
400
0
500
(a)
Fig. 4. Variations in the wear amount tance: (a) experiment A; (b) experiment
100
200
SLIDING
m
300 DISTANCE.
400
500
m
(b)
and the coefficient B.
of friction
with
sliding dis-
107
Fig. 4(a), the averaged value of the friction coefficient is almost settled at around 0.6 after a sliding distance of 150 m; this high friction indicates that the inert oil used has not provided effective lubrication. In addition, the wear rate appreciably decreases at 150 m. It is likely that the sliding wear has come into a steady state, in a sense, at the sliding distance of 150 m. The coefficient of friction in experiment B (Fig. 4(b)) behaves in a different manner. It first increases until it reaches a value of about 0.3 and then gradually decreases. In the sliding period after 100 m the friction coefficient settles down at around 0.16, although relatively high values appear for a short time at the beginning of every sliding period of 50 m, and also in the midst of the periods occasional short-term rises are seen. The fairly low friction compared with that in experiment A indicates effective boundary lubrication by the extreme pressure additive. This would be supported by the fact that the wear track in experiment B was tinged redbrown, which provides evidence of some chemical changes. The initial high friction at each sliding period may be attributed to the removal of the effective film by washing of the specimens and to the drop in temperature at the sliding surface during each stop, which would retard re-establishment of the film. Figure 5 shows a typical worn surface of the disk specimen after sliding; it is made up of a number of parallel furrows and ridges along the sliding direction. Although the original surface of the specimens had a random isotropic structure formed in the lapping process, this very different feature appeared as early as at the end of the initial heavy wear period of 0 - 50 m in both experiment A and experiment B. The r.m.s. roughness determined from the measured profiles also exhibits a great change from the initial value of about 0.28 pm to a value over 2.5 pm during that period; this initial roughening of the surface has been observed by other investigators under poor lubrication [ 15 - 181.
Fig. 5. A worn surface of the disk specimen after sliding 500 m in experiment B: the arrow indicates the sliding direction.
108
When viewed under an optical microscope, the furrows are dark and look relatively rough, suggesting that they are grooves produced by wear, while the tops of the ridges are shiny, or a little bit dull, and smooth with very fine streaks along their longitudinal direction. It seems that the relatively flat portion of the surface has been forming solid contacts with the opposite surface. Quinn [22] found a similar feature of the sliding surface from more detailed observations using an electron microscope. Figure 6 shows changes in the profile at a position on the same wear track of the disk specimen in experiment A. At early stages the profile consists of wedge-shaped deep valleys and intervening steep hills. It suffers considerable changes in shape during each sliding period of 50 m and, in particular, the formation of new deep valleys is recognized. By the sliding distance of 250 m, the small valleys or hills have aggregated to form a profile having relatively gentle slopes. After that the formation of large valleys becomes rare and the occurrence of material removal on a smaller scale from the hill portion of the profile is seen instead; the general configuration of the profile is not changed appreciably by sliding in each period. The profiles of the pin specimens show a similar tendency. For experiment B, the profiles change in a simpler manner; the changes are drastic for the initial three periods but become slight after 150 m. The pattern of profile
Fig. 6. Profiles at the same position the distances shown.
on the disk specimen
in experiment
A after
sliding
109
Fig. 7. Profiles at four positions on the disk specimen after sliding 250 m in experiment A.
changes in the present experiment is quite different from that seen during the so-called running-in process, in which the high peaks on the softer surface are cut off while the valleys are unaffected when slid against a smooth harder material under favourable conditions [ 9 - 11,141. A clearer picture of the pattern of the change in surface topography due to the wear process will be given in Section 4 in terms of the cross-correlation coefficient. In Fig. 7 are shown four profiles taken from the same wear track on the disk specimen at a sliding distance of 250 m in experiment A. The profiles resemble each other, demonstrating that the worn surface is not isotropic but has a nearly two-dimensional structure, as would be expected from Fig. 5. This similarity is seen among the profiles on the same wear track at all the other sliding distances and also among the profiles of the three pin specimens, except for the initial unworn surfaces. The cross-correlation between the profiles will be also used to investigate the variations in the topographical two dimensionality during the wear process in Section 4. 4. Correlation analysis 4.1. Cross-correlation coefficient A surface profile has been treated as a random function and a number of stochastic parameters (roughness parameters) have been proposed to characterize it. When comparing profiles, some of these parameters are determined for individual profiles and comparisons are made between them. However, these parameters are often insufficient to represent the differences between the profiles of present interest. Peklenik [5] investigated various engineering surfaces and proposed to employ the cross-correlation function and the correlation length to characterize the directional structure in surface microgeometry. An attempt is made in the present paper to utilize the crosscorrelation coefficient between profiles for describing the changes in surface topography due to sliding wear.
110
(b)
(a)
Fig. 8. Correlation between profiles: (a) two surface profiles which are similar to each other with a lag existing between them; (b) the corresponding cross-correlation function with a sharp peak.
The cross-correlation coefficient gives a quantitative expression of the similarity between two profiles. In Fig. S(a) two typical surface profiles are illustrated. Let X(t) and Y(t) be the profiles, for example, taken at the same position after different sliding distances, or otherwise taken at different positions on the same wear track on a specimen; t is the coordinate taken in the transverse direction. As mentioned previously, the average line of each profile is taken to be the abscissa, i.e. X = 0 and Y = 0. The profile Y is similar to the profile X, but a delay may be present which is attributed to the difficulty in finding the common starting position of the profiles. When these profiles are presented in digital form, the normalized cross-correlation function is defined by n---7 Y(7)
=
2 i=l
n---7
xiYi+r
ii
l/2
n-7
Z: Xi2
C
i= 1
i=l
yi+r2
i
(1)
where Xi and Yj are the ith ordinates of the profiles X and Y respectively, T is the lag expressed as the number of ordinates and n is the total number of sampled data of each profile. As seen from eqn. (l), y is a function only of the lag r. Figure 8(b) exemplifies the cross-correlation function. When two profiles are closely correlated with each other, the cross-correlation function takes a maximum value of nearly unity at a certain lag. If the starting position of their traverse happens to be identical relative to the wear track, the maximum value occurs at zero lag. Although the cross-correlation function involves the length information, or the information about the periodic components in the random profiles, its maximum value can be representative of the similarity between the two profiles. Therefore only the maximum value will be evaluated here, and in the following it is called the correlation coefficient between profiles. Two types of correlation coefficient between profiles will be discussed. A correlation coefficient is computed between the profiles obtained at the
111
same position on a wear track before and after sliding for a fixed duration. This provides information about successive changes in a surface profile with wear, and will be called the type 1 correlation coefficient. The other correlation coefficient is computed between the profiles taken at different positions on the same wear track. This describes the directional structure of the worn surfaces, and will be called the type 2 correlation coefficient. 4.2. The type I correlation coefficient Figure 9(a) shows the type 1 correlation coefficient for the disk specimen in experiment A. In the figure are plotted the results which correspond to changes in the profile at the position shown in Fig. 6, together with those at the other three positions on the same wear track of the disk specimen. Each plot represents a value of the correlation coefficient between the profile taken at the designated sliding distance and the profile at the same position but taken before the preceding sliding of 50 m. For example, the values plotted for a sliding distance of 200 m represent the correlation between the profiles at sliding distances of 150 and 200 m. They describe how the surface topography has changed during the specified sliding period. A curve fitted by hand shows the general trend. In Fig. 9(a), the type 1 correlation coefficient lies between 0.2 and 0.5 at a sliding distance of 100 m, and it gradually increases until the sliding distance reaches 300 m where the values are about 0.82. This initial increase is followed by a period in which the values are almost unchanged. A similar computation has been made for the pin specimens. The data, not shown, are scattered widely but the coefficient behaves generally in a similar manner to those for the disk specimen. It is of interest to relate the type 1 correlation coefficient to the wear behaviour. It is naturally expected that the correlation coefficient would take a smaller value if the wear rate is high, because a large amount of
OL 0
1oO
200
SLIDING (a)
300 DISTANCE.
400
0
500
m
100
m SLIDING
300 DISTANCE.
4Do
500
m
(b)
Fig. 9. The type 1 correlation coefficient computed (a) experiment A; (b) experiment B.
from profiles on the disk specimen:
112
material removal would change the surface texture almost completely; it would become larger if the wear rate is low. This is the case with the wear behaviour in experiment A (Fig. 4(a)). The wear rate is initially high and then lower. This accounts for the topographical changes presumed on the basis of the characteristic behaviour of the type 1 correlation coefficient, i.e. the initial periods of substantial changes and the subsequent settled periods. A closer examination, however, reveals that the same wear rate does not always lead to the same value of the type 1 correlation coefficient. The wear rate is higher until the sliding distance reaches 150 m and is almost constant at a lower value during the rest of the sliding, but this transition at a sliding distance of 150 m is obscured in the type 1 correlation coefficient whose change is rather gradual. Further, the coefficient drops slightly at a sliding distance of 350 m without an appreciable change in the wear rate. Thus the type 1 correlation coefficient is in general correlated with the wear behaviour, but it seems to be indicative of certain changes in the wear process which do not appear distinctly in the wear amount. The details of the manner in which the sliding surface undergoes topographical changes are now examined. This is mainly concerned with the wearing mode, i.e. which parts of the profile have experienced wear. In addition to the removal of materials, the wear process may include plastic deformation of the surface layer and material transfer between the opposing surfaces, which might also change the surface topography. Pairs of profiles selected from Fig. 6 are superimposed in Fig. 10; the left-hand and the right-hand ends of the profiles are made to coincide, while on the left-hand side of the profiles it can be seen that wear has lowered the mean line. Figure 10(a) shows the profile change during the sliding period of 100 - 150 m. Although the feature of the profile at 100 m remains partly in the profile at 150 m, the height reduction due to wear occurs non-uniformly along the direction of the profile. It should be noted further that a height increase also occurs at several positions, indicated by thick arrows, owing to plastic deformation. In the present case, this may
MEAN
HEKSIT
15Om’
Fig. 10. Two pairs of profiles from Fig. 6 superimposed showing during the sliding periods of (a) 100 - 150 m and (b) 400 - 450 m.
changes
in profile
113
not be attributed to material transfer, because a similar height increase can be seen in the profiles at the other three positions of the same disk specimen. In the vicinity of the places where the height increase has occurred, deep grooves made by wear are seen. Thus it is likely that a large force which has generated wear particles has also acted to push the adjacent material laterally apart and has caused the plastic deformation. Vertical sections of the specimens were observed by optical microscopy after the wear experiment, and it was confirmed not only that there was shear deformation along the sliding direction but also that remarkable lateral displacement did occur. Many investigators have analysed the strain distribution or the rate at which a crack propagates in the subsurface layer during the wear process as a plane strain problem. However, the above discussion suggests that wear is accompanied by triaxial plastic deformation and, in particular, strain components out of the plane which is perpendicular to the surface and parallel to the sliding direction are no less significant. Figure 10(b) shows the change in the profile during the sliding period of 400 - 450 m. The height reduction is particularly remarkable around the centre of the wear track (indicated by a thick arrow) but as a whole the reduction is more uniform along the profile than for Fig. 10(a). In addition, a height increase is seldom seen, which suggests that substantial lateral displacement has not occurred during this period. From the above examples, it has become clear that the value of the type 1 correlation coefficient depends on the wearing mode rather than the wear itself. The coefficient is large when the amount of material removed is distributed along the whole wear track and is relatively uniform. For the limiting case when wear is completely uniform, surface profiles would not actually change in shape and the coefficient should be unity. Localization or non-uniformity of the formation of wear particles makes the value lower. Moreover, if the wear is accompanied by heavy lateral deformation or material transfer, changes in the profiles become more complicated and the type 1 correlation coefficient will be reduced further. Figure 9(b) shows the results for the disk specimen in experiment B, which has been conducted in the oil containing an extreme pressure additive. The type 1 correlation coefficients are small at the beginning, but then in a short time they become larger with some fluctuation remaining. The result for the pin specimens, not shown, behaves in much the same way. These results are reasonable in the light of the wear behaviour shown in Fig. 4. 4.3. The type 2 correlation coefficient Another correlation approach to the topography of wearing surfaces is provided by computing the type 2 correlation coefficient. This compares the different profiles on the same wear track and measures the similarity between them. More specifically, for the disk specimens, it is computed from a pair of neighbouring profiles taken 90” apart on the same wear track, and the computation is made for four pairs at every sliding distance. For
114
01
0
loo
200
SLlDlNG
300 DISTANCE.
4co
500
m
(b)
Fig. 11. The type 2 correlation coefficient (a) experiment A;(b) experiment B.
computed
from profiles
on the disk specimen:
the pin specimens, three pins positioned every 120” allow the computation to be made for three pairs of profiles. Figure 11(a) shows the type 2 correlation coefficient for the disk specimen in experiment A. Although the values are somewhat scattered, on the average they gradually increase as the sliding distance increases. This trend indicates that the profiles of different positions on the same wear track are becoming similar to each other, which means that the surface topography is slowly acquiring a two-dimensional parallel structure. Slight stepwise increases are seen at periods of 100 - 150 and 300 - 350 m, indicating that the changes are greater in these periods than in other sliding periods. The result for the pin specimens, not shown, is rather disappointing; the values are low and fluctuate extremely through the whole sliding period. For the disk specimen in experiment B, the coefficient behaves in a different manner, as shown in Fig. 11(b). It attains a high value of 0.8 by 50 m and remains almost unchanged after that, which suggests that the topography is highly directional both in the initial periods of high wear rate and in the subsequent steady periods. In contrast with the present experiments, unlubricated sliding [23] gives much lower values of the type 2 correlation coefficient in its earlier periods, although the coefficient also shows an increasing trend as in experiment A. It was observed in Fig. 5 that the worn surfaces consist of grooves and ridges, forming a highly directional structure. Although the type 2 correlation coefficient was determined between a pair of profiles taken 90” apart, an arbitrarily chosen interval, it demonstrates this feature quantitativejly. Moreover, it can be asserted that, so far as the present experiments are concerned, including the above-mentioned unlubricated experiment, the initial isotropic surfaces experience various modifications in their shape
115
and eventually acquire parallel directional topography. This process is promoted by favourable lubrication. Although in general the sliding surfaces tend to acquire directional structures, this seems not to be directly related to the amount of wear. For instance, the first stepwise increase in the coefficient at 150 m for the disk specimen in experiment A certainly corresponds to the change in the wear rate, while the second at 350 m is not accompanied by a change in the wear rate. For experiment B, the wear rate slightly decreases at 150 m without an appreciable change in the type 2 correlation coefficient. Nevertheless, it should be recognized that the appearance of the parallel directional property has a significant implication concerning the contact mechanisms. Stochastic approaches to the contact problem will be valid in the case where a parameter such as the type 2 correlation coefficient takes low values. In contrast, if its value is nearly unity, the contact point is no longer circular or elliptical but should be in the form of a strip with high aspect ratio. Thus forces are transmitted between mating surfaces through the very narrow contact strips that form on the smooth ridges on the wear track as seen in Fig. 5, and they produce flake-like wear particles; the relation between surface topography and loose particles is discussed in a separate paper [24]. Such a mechanism predominates almost from the outset in experiment B. 5. Conclusions In the present paper an attempt has been made to introduce two types of cross-correlation coefficient between surface profiles to characterize the topographical changes of sliding surfaces in wear processes. The type 1 correlation coefficient is found to be a parameter which describes the characteristic wearing mode, i.e. whether material removal occurs on the wear track uniformly or not. Further, its value is influenced by additional modifications of the surface configuration by triaxial plastic deformation. The type 2 correlation coefficient gives the degree of two dimensionality of the worn surfaces. This cross-correlation analysis is applied to the wearing surfaces in the lubricated wear experiments. With the cases in which the wear rate is initially high and then lowered, the changes in surface topography are summarized as follows. In the early stage of the sliding process, material removal occurs randomly at various scales on the wear track, and wear is accompanied by heavy lateral plastic deformation. As wear proceeds, the sliding surfaces tend to have strongly twodimensional structures parallel to the sliding direction, and the wear occurs over the whole wear track. Acknowledgment The authors would like to thank Dr. E. F. Finkin for his helpful comments on this paper.
116
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13
14 15 16 17 18 19
20 21 22 23
24
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101
101 - 116
CHARACTERIZATION LUBRICATED WEAR
OF TOPOGRAPHICAL CHANGES DURING
JOICHI SUGIMURA and YOSHITSUGU KIMURA Institute of Interdisciplinary Research, Komaba Campus, Faculty University of Tokyo, 4-6-l Komaba, Meguro-ku, Tokyo 153 {Japan)
of Engineering,
The
(Received June 1, 1984; accepted October 8,1984)
Summary Experiments on lubricated wear are conducted and profiles of the wearing surfaces are studied. Two types of cross-correlation coefficient are introduced: one compares the profiles obtained at the same position before and after sliding for a fixed duration, and the other compares the profiles at different positions on the same wear track. It is found that the former represents a characteristic of the wearing mode, while the latter quantitatively gives the degree of two dimensionality of the topography. 1. Introduction Surface microtopography plays a significant role in almost all tribological problems. In particular, it is one of the most important factors in the wear of materials since it determines the state of microcontact between sliding surfaces. It is now widely accepted that the wear particles are generated as a result of fracture by the forces transmitted through the microscopic spots which form the area of real contact. However, it is only recently that such an idea has been brought into the stage of analysis. Halling [l] and Finkin [Z] applied the baron-Coffin relation of low cycle fatigue to the wear process and obtained linear wear equations. Suh [3,43 introduced fracture mechanics and established the delamination theory of wear which includes subsurface crack nucleation and propagation. These and other advanced analyses are noteworthy in that they have opened a path to be followed in pursuing essential mechanisms of wear. However, for analysing subsurface stresses, strains etc., they made rather simplified assumptions as to the actual forces working on the surface, ignoring the microscopic contact mechanics, which substantially undergo continuous changes due to wear. As wear proceeds, material removal and accompanying subsurface plastic deformation would bring about successive changes in surface microtopo~aphy, which might inevitably alter the shape and size of a real contact spot and thereby the direction and magnitude of 0043-1648/64&3.00
@ Elsevier SequoiafPrinted in The Netherlands
102
a force acting on it. Therefore the surface microtopography during the wear process must be followed in order to construct a proper model for analysis in which changes in the contact state are taken into account, providing variable boundary conditions. More specifically, investigation is needed to characterize the manner by which the surface topography changes during sliding wear and to characterize the topography produced by the process. Recently surface measurement has gained a great advantage by the application of digital techniques to the stylus instruments, and the analysis of surface profiles using a computer is now a usual practice. Together with this it has become common to employ stochastic methods for the characterization of surface profiles since the work of Peklenik [5] on manufactured surfaces. Various parameters and functions have been proposed for representing some characteristic features of a profile or further for analysing roughness effects in static contact [ 6,7], hydrodynamic lubrication [ 81 etc. As to the changes in surface topography associated with wear, most of the investigations carried out so far were concerned with the changes that occur during the so-called running-in period [9 - 141. These showed that wear took place only at the tops of asperities when a rough surface slid against a hard smoother surface under favourable conditions, and this was characof the height distribution of a terized by the occurrence of “truncation” profile, However, this is not always the case. During the sliding between a pair of surfaces having similar hardnesses, where what is called adhesive wear often offers problems, the changes in surface topography may not be so simple [ 15 - I$], even under lubrication. The investigations introduced above dealt with the two-dimensional aspects of surface topography, for the measuring instruments could provide only a profile along a particular section. Preferably, however, a surface should be treated three dimensionally, since actual surfaces are sometimes not isotropic. Techniques for a three-dimensional measurement by parallel traces are now available, but they are time consuming and, above all, it has not been established yet what information could be extracted from a vast number of data. In contrast, several investigators have attempted to describe three-dimensional features of a surface, especially its anisotropy, by some parameters obtained from ordinary profile measurement. For example, Peklenik [5] presented the cross-correlation function between two parallel traces and the correlation length obtained from its autocorrelation function. Patir and Cheng [ 191 used the ratio between the correlation lengths of two profiles taken at right angles to each other as a measure of anisotropy, and they discussed its effect on hydrodynamic lubrication. Nayak 120, 213 also proposed some parameters of anisotropy based on the statistical theory of gaussian random surfaces. Although there are a number of parameters which characterize the surface microtopography, the present paper introduces two types of correlation coefficient which can easily be determined from profile traces. One characterizes the changes in surface topography that occur during sliding, and the other measures its directional property.
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2. Experimental
details
Wear experiments have been carried out on a three-pin-on-disk machine. Figure 1 shows diagrammatically an arrangement of its main part. The sliding system consists of a rotating upper specimen and a stationary lower specimen, either of which can be a disk or a three-pin assembly. Currently the three-pin assembly is used as the lower specimen so that wear debris generated at the sliding surfaces may easily escape from the interface. The disk specimen is fixed to the upper specimen holder, which is driven by an electric motor at a speed ranging from 0.1 to 1000 rev min-’ . The three-pin assembly is secured to the bottom of an oil bath, which is supported by a gimbal mechanism mounted at the top of a hydraulic piston. The gimbal mechanism ensures plane contact between the upper specimen and the lower specimen. The piston can freely rotate around its axis and move up and down. A normal load is applied to the contacting surface between the specimens by oil hydraulic pressure working on the bottom of the piston; this load can be varied from 0 to 600 N. A torque arm is secured to the gimbal 1 Rotating
Shaft
Disk Specimen Holder &
Fig. 1. Main part of the three-pin-on-disk
machine.
104
Fig. 2. The disk specimen and the three-pin assembly.
support; the torque arm presses against a load cell to provide a measure of the friction. A heater is mounted under the oil bath and a chromel-alumel thermocouple for monitoring the oil temperature is inserted in the bath. Figure 2 shows a general view of the specimens used in the present experiments. The disk specimen is 40 mm in diameter. The three pin specimens of 4 mm in diameter are rigidly secured to a cylindrical plate at regular intervals on a circumference of 30 mm diameter to form a three-pin assembly. Both the disk and the pin specimens are made of S35C carbon steel (which corresponds to AISI 1035 steel) annealed to 220 - 260 HV. The sliding surfaces of both specimens were finished by lapping with white alumina to an r.m.s. roughness of about 0.28 pm. The results for two separate experiments conducted under different conditions will be shown. They are designated experiment A and experiment B. A low viscosity paraffinic base oil is used as a lubricant in experiment A and a similar oil with the addition of ndodecyl mercaptan in experiment B. Testing conditions and the properties of the lubricant used in each experiment are given in Table 1. These conditions are selected so that the wear rate becomes relatively high and fully detectable. Having been washed thoroughly in benzine and then in trichloroethylene and dried in hot air stream, the specimens were set in the apparatus in the manner described above. The load, sliding speed and oil temperature TABLE 1 Experimental conditions Experiment
Lubricant kinematic
A
Hi-white 70 (17.4 cSt at 30 “C)
B -
and its viscosity
Oil temperature CC)
Normal load WI
Sliding velocity (m s-l )
30
166.7
7.85 X 1O-4 500 (50 m X 10)
Hi-white 70 + 1.0% 30 n-dodecyl mercaptan (17.8 cSt at 30 “C)
245.2
1.57
X
lO-3
Sliding distance (ml
500 (50 m X 10)
105
were held constant, and a run was continued for a predetermined duration which corresponds to a sliding distance of 50 m; this took about 1060 min in experiment A and 530 min in experiment B. After a run, the specimens were removed from the apparatus. They were washed as before and surface profiles were measured; details of this measurement will be described later. Then the same specimens were again mounted on the apparatus and the same lubricant was poured into the oil bath for the next run of 50 m. The process was repeated ten times until the total sliding distance reached 500 m. In addition to their surface profiles being taken, the specimens were weighed in a precision balance at each stop to determine the wear amount. Measurements of the surface topography were conducted using a Talysurf 4 profile-measuring instrument in conjunction with a microcomputer. The output signal from the Talysurf was fed to a transient converter (4K of ll-bit word store) which converted the data to digital form and stored them temporarily. Immediately after the completion of a traverse, the data were transferred to the microcomputer and recorded on a G in floppy disk. The transient converter was controlled by the computer, which was programmed in machine code to shorten the time required for the data storage. As schematically illustrated in Fig. 3(a), the profiles were taken perpendicular to the direction of sliding at four locations spaced 90” apart on the circular wear track on a disk specimen and also on each of the three pin specimens. Repositioning of the stylus with respect to the wear track was done manually using a slide table such that approximately the same sections were traversed each time. Because of the difficulty in determining a common origin for each profile, a starting point for data acquisition was placed somewhere outside the wear track. A sample interval of 2.5 pm and 2048 samples were employed, which represented a profile about 5.12 mm in length across the wear track. Before a profile was analysed, data outside the wear track were omitted and then the average line of the profile was made to coincide with the datum, or the abscissa, by applying the least-squares method. That is, a
X
X, .. .
.. . :‘. :. .. - *.*
.
Xi+1
REGRESSION
..* .%....* ..*. . . . . *._*“_ .’..... ..* . .. . . ‘.‘.
*.: ,
SAMPLING
(a)
DAT”M
INTERVAL
/: *. .. *.* _.’ :“.
.. . .J’ * . : .:
.. ..
::
LINE
. -
t
(b)
Fig. 3. Obtaining surface profile data: (a) measurement itized profile with its regression line.
with each specimen; (b) a dig-
106
regression line for the profile was calculated and the discrepancies between the measured values and the obtained regression line were taken as new profile ordinates (Fig. 3(b)). By doing this, the mean of the profile ordinates became zero and any linear trend of the whole profile was removed.
3. Experimental
results
The variations n the coefficient of friction and the wear amount measured are shown in Figs. 4(a) and 4(b) for experiments A and B respectively. Basically the wear rate, i.e. the gradient of the wear curve, for both experiments is initially high and in time decreased to a lower value; this reduction is more pronounced in experiment B than in experiment A. The coefficient of friction shows irregular fluctuations, and its general behaviour is shown in the figures by the upper and lower lines which roughly envelop its fluctuations. Closer examination of the original friction records reveals that, particularly for experiment A, its value is consecutively subjected to irregular rises and falls. This suggests that interactions between the sliding surfaces, which would lead to material removal or plastic deformation of surface layers, have taken place at various positions on various scales. In 50
Lx-----
01 1W
200
SLIDING
300 DISTANCE,
400
0
500
(a)
Fig. 4. Variations in the wear amount tance: (a) experiment A; (b) experiment
100
200
SLIDING
m
300 DISTANCE.
400
500
m
(b)
and the coefficient B.
of friction
with
sliding dis-
107
Fig. 4(a), the averaged value of the friction coefficient is almost settled at around 0.6 after a sliding distance of 150 m; this high friction indicates that the inert oil used has not provided effective lubrication. In addition, the wear rate appreciably decreases at 150 m. It is likely that the sliding wear has come into a steady state, in a sense, at the sliding distance of 150 m. The coefficient of friction in experiment B (Fig. 4(b)) behaves in a different manner. It first increases until it reaches a value of about 0.3 and then gradually decreases. In the sliding period after 100 m the friction coefficient settles down at around 0.16, although relatively high values appear for a short time at the beginning of every sliding period of 50 m, and also in the midst of the periods occasional short-term rises are seen. The fairly low friction compared with that in experiment A indicates effective boundary lubrication by the extreme pressure additive. This would be supported by the fact that the wear track in experiment B was tinged redbrown, which provides evidence of some chemical changes. The initial high friction at each sliding period may be attributed to the removal of the effective film by washing of the specimens and to the drop in temperature at the sliding surface during each stop, which would retard re-establishment of the film. Figure 5 shows a typical worn surface of the disk specimen after sliding; it is made up of a number of parallel furrows and ridges along the sliding direction. Although the original surface of the specimens had a random isotropic structure formed in the lapping process, this very different feature appeared as early as at the end of the initial heavy wear period of 0 - 50 m in both experiment A and experiment B. The r.m.s. roughness determined from the measured profiles also exhibits a great change from the initial value of about 0.28 pm to a value over 2.5 pm during that period; this initial roughening of the surface has been observed by other investigators under poor lubrication [ 15 - 181.
Fig. 5. A worn surface of the disk specimen after sliding 500 m in experiment B: the arrow indicates the sliding direction.
108
When viewed under an optical microscope, the furrows are dark and look relatively rough, suggesting that they are grooves produced by wear, while the tops of the ridges are shiny, or a little bit dull, and smooth with very fine streaks along their longitudinal direction. It seems that the relatively flat portion of the surface has been forming solid contacts with the opposite surface. Quinn [22] found a similar feature of the sliding surface from more detailed observations using an electron microscope. Figure 6 shows changes in the profile at a position on the same wear track of the disk specimen in experiment A. At early stages the profile consists of wedge-shaped deep valleys and intervening steep hills. It suffers considerable changes in shape during each sliding period of 50 m and, in particular, the formation of new deep valleys is recognized. By the sliding distance of 250 m, the small valleys or hills have aggregated to form a profile having relatively gentle slopes. After that the formation of large valleys becomes rare and the occurrence of material removal on a smaller scale from the hill portion of the profile is seen instead; the general configuration of the profile is not changed appreciably by sliding in each period. The profiles of the pin specimens show a similar tendency. For experiment B, the profiles change in a simpler manner; the changes are drastic for the initial three periods but become slight after 150 m. The pattern of profile
Fig. 6. Profiles at the same position the distances shown.
on the disk specimen
in experiment
A after
sliding
109
Fig. 7. Profiles at four positions on the disk specimen after sliding 250 m in experiment A.
changes in the present experiment is quite different from that seen during the so-called running-in process, in which the high peaks on the softer surface are cut off while the valleys are unaffected when slid against a smooth harder material under favourable conditions [ 9 - 11,141. A clearer picture of the pattern of the change in surface topography due to the wear process will be given in Section 4 in terms of the cross-correlation coefficient. In Fig. 7 are shown four profiles taken from the same wear track on the disk specimen at a sliding distance of 250 m in experiment A. The profiles resemble each other, demonstrating that the worn surface is not isotropic but has a nearly two-dimensional structure, as would be expected from Fig. 5. This similarity is seen among the profiles on the same wear track at all the other sliding distances and also among the profiles of the three pin specimens, except for the initial unworn surfaces. The cross-correlation between the profiles will be also used to investigate the variations in the topographical two dimensionality during the wear process in Section 4. 4. Correlation analysis 4.1. Cross-correlation coefficient A surface profile has been treated as a random function and a number of stochastic parameters (roughness parameters) have been proposed to characterize it. When comparing profiles, some of these parameters are determined for individual profiles and comparisons are made between them. However, these parameters are often insufficient to represent the differences between the profiles of present interest. Peklenik [5] investigated various engineering surfaces and proposed to employ the cross-correlation function and the correlation length to characterize the directional structure in surface microgeometry. An attempt is made in the present paper to utilize the crosscorrelation coefficient between profiles for describing the changes in surface topography due to sliding wear.
110
(b)
(a)
Fig. 8. Correlation between profiles: (a) two surface profiles which are similar to each other with a lag existing between them; (b) the corresponding cross-correlation function with a sharp peak.
The cross-correlation coefficient gives a quantitative expression of the similarity between two profiles. In Fig. S(a) two typical surface profiles are illustrated. Let X(t) and Y(t) be the profiles, for example, taken at the same position after different sliding distances, or otherwise taken at different positions on the same wear track on a specimen; t is the coordinate taken in the transverse direction. As mentioned previously, the average line of each profile is taken to be the abscissa, i.e. X = 0 and Y = 0. The profile Y is similar to the profile X, but a delay may be present which is attributed to the difficulty in finding the common starting position of the profiles. When these profiles are presented in digital form, the normalized cross-correlation function is defined by n---7 Y(7)
=
2 i=l
n---7
xiYi+r
ii
l/2
n-7
Z: Xi2
C
i= 1
i=l
yi+r2
i
(1)
where Xi and Yj are the ith ordinates of the profiles X and Y respectively, T is the lag expressed as the number of ordinates and n is the total number of sampled data of each profile. As seen from eqn. (l), y is a function only of the lag r. Figure 8(b) exemplifies the cross-correlation function. When two profiles are closely correlated with each other, the cross-correlation function takes a maximum value of nearly unity at a certain lag. If the starting position of their traverse happens to be identical relative to the wear track, the maximum value occurs at zero lag. Although the cross-correlation function involves the length information, or the information about the periodic components in the random profiles, its maximum value can be representative of the similarity between the two profiles. Therefore only the maximum value will be evaluated here, and in the following it is called the correlation coefficient between profiles. Two types of correlation coefficient between profiles will be discussed. A correlation coefficient is computed between the profiles obtained at the
111
same position on a wear track before and after sliding for a fixed duration. This provides information about successive changes in a surface profile with wear, and will be called the type 1 correlation coefficient. The other correlation coefficient is computed between the profiles taken at different positions on the same wear track. This describes the directional structure of the worn surfaces, and will be called the type 2 correlation coefficient. 4.2. The type I correlation coefficient Figure 9(a) shows the type 1 correlation coefficient for the disk specimen in experiment A. In the figure are plotted the results which correspond to changes in the profile at the position shown in Fig. 6, together with those at the other three positions on the same wear track of the disk specimen. Each plot represents a value of the correlation coefficient between the profile taken at the designated sliding distance and the profile at the same position but taken before the preceding sliding of 50 m. For example, the values plotted for a sliding distance of 200 m represent the correlation between the profiles at sliding distances of 150 and 200 m. They describe how the surface topography has changed during the specified sliding period. A curve fitted by hand shows the general trend. In Fig. 9(a), the type 1 correlation coefficient lies between 0.2 and 0.5 at a sliding distance of 100 m, and it gradually increases until the sliding distance reaches 300 m where the values are about 0.82. This initial increase is followed by a period in which the values are almost unchanged. A similar computation has been made for the pin specimens. The data, not shown, are scattered widely but the coefficient behaves generally in a similar manner to those for the disk specimen. It is of interest to relate the type 1 correlation coefficient to the wear behaviour. It is naturally expected that the correlation coefficient would take a smaller value if the wear rate is high, because a large amount of
OL 0
1oO
200
SLIDING (a)
300 DISTANCE.
400
0
500
m
100
m SLIDING
300 DISTANCE.
4Do
500
m
(b)
Fig. 9. The type 1 correlation coefficient computed (a) experiment A; (b) experiment B.
from profiles on the disk specimen:
112
material removal would change the surface texture almost completely; it would become larger if the wear rate is low. This is the case with the wear behaviour in experiment A (Fig. 4(a)). The wear rate is initially high and then lower. This accounts for the topographical changes presumed on the basis of the characteristic behaviour of the type 1 correlation coefficient, i.e. the initial periods of substantial changes and the subsequent settled periods. A closer examination, however, reveals that the same wear rate does not always lead to the same value of the type 1 correlation coefficient. The wear rate is higher until the sliding distance reaches 150 m and is almost constant at a lower value during the rest of the sliding, but this transition at a sliding distance of 150 m is obscured in the type 1 correlation coefficient whose change is rather gradual. Further, the coefficient drops slightly at a sliding distance of 350 m without an appreciable change in the wear rate. Thus the type 1 correlation coefficient is in general correlated with the wear behaviour, but it seems to be indicative of certain changes in the wear process which do not appear distinctly in the wear amount. The details of the manner in which the sliding surface undergoes topographical changes are now examined. This is mainly concerned with the wearing mode, i.e. which parts of the profile have experienced wear. In addition to the removal of materials, the wear process may include plastic deformation of the surface layer and material transfer between the opposing surfaces, which might also change the surface topography. Pairs of profiles selected from Fig. 6 are superimposed in Fig. 10; the left-hand and the right-hand ends of the profiles are made to coincide, while on the left-hand side of the profiles it can be seen that wear has lowered the mean line. Figure 10(a) shows the profile change during the sliding period of 100 - 150 m. Although the feature of the profile at 100 m remains partly in the profile at 150 m, the height reduction due to wear occurs non-uniformly along the direction of the profile. It should be noted further that a height increase also occurs at several positions, indicated by thick arrows, owing to plastic deformation. In the present case, this may
MEAN
HEKSIT
15Om’
Fig. 10. Two pairs of profiles from Fig. 6 superimposed showing during the sliding periods of (a) 100 - 150 m and (b) 400 - 450 m.
changes
in profile
113
not be attributed to material transfer, because a similar height increase can be seen in the profiles at the other three positions of the same disk specimen. In the vicinity of the places where the height increase has occurred, deep grooves made by wear are seen. Thus it is likely that a large force which has generated wear particles has also acted to push the adjacent material laterally apart and has caused the plastic deformation. Vertical sections of the specimens were observed by optical microscopy after the wear experiment, and it was confirmed not only that there was shear deformation along the sliding direction but also that remarkable lateral displacement did occur. Many investigators have analysed the strain distribution or the rate at which a crack propagates in the subsurface layer during the wear process as a plane strain problem. However, the above discussion suggests that wear is accompanied by triaxial plastic deformation and, in particular, strain components out of the plane which is perpendicular to the surface and parallel to the sliding direction are no less significant. Figure 10(b) shows the change in the profile during the sliding period of 400 - 450 m. The height reduction is particularly remarkable around the centre of the wear track (indicated by a thick arrow) but as a whole the reduction is more uniform along the profile than for Fig. 10(a). In addition, a height increase is seldom seen, which suggests that substantial lateral displacement has not occurred during this period. From the above examples, it has become clear that the value of the type 1 correlation coefficient depends on the wearing mode rather than the wear itself. The coefficient is large when the amount of material removed is distributed along the whole wear track and is relatively uniform. For the limiting case when wear is completely uniform, surface profiles would not actually change in shape and the coefficient should be unity. Localization or non-uniformity of the formation of wear particles makes the value lower. Moreover, if the wear is accompanied by heavy lateral deformation or material transfer, changes in the profiles become more complicated and the type 1 correlation coefficient will be reduced further. Figure 9(b) shows the results for the disk specimen in experiment B, which has been conducted in the oil containing an extreme pressure additive. The type 1 correlation coefficients are small at the beginning, but then in a short time they become larger with some fluctuation remaining. The result for the pin specimens, not shown, behaves in much the same way. These results are reasonable in the light of the wear behaviour shown in Fig. 4. 4.3. The type 2 correlation coefficient Another correlation approach to the topography of wearing surfaces is provided by computing the type 2 correlation coefficient. This compares the different profiles on the same wear track and measures the similarity between them. More specifically, for the disk specimens, it is computed from a pair of neighbouring profiles taken 90” apart on the same wear track, and the computation is made for four pairs at every sliding distance. For
114
01
0
loo
200
SLlDlNG
300 DISTANCE.
4co
500
m
(b)
Fig. 11. The type 2 correlation coefficient (a) experiment A;(b) experiment B.
computed
from profiles
on the disk specimen:
the pin specimens, three pins positioned every 120” allow the computation to be made for three pairs of profiles. Figure 11(a) shows the type 2 correlation coefficient for the disk specimen in experiment A. Although the values are somewhat scattered, on the average they gradually increase as the sliding distance increases. This trend indicates that the profiles of different positions on the same wear track are becoming similar to each other, which means that the surface topography is slowly acquiring a two-dimensional parallel structure. Slight stepwise increases are seen at periods of 100 - 150 and 300 - 350 m, indicating that the changes are greater in these periods than in other sliding periods. The result for the pin specimens, not shown, is rather disappointing; the values are low and fluctuate extremely through the whole sliding period. For the disk specimen in experiment B, the coefficient behaves in a different manner, as shown in Fig. 11(b). It attains a high value of 0.8 by 50 m and remains almost unchanged after that, which suggests that the topography is highly directional both in the initial periods of high wear rate and in the subsequent steady periods. In contrast with the present experiments, unlubricated sliding [23] gives much lower values of the type 2 correlation coefficient in its earlier periods, although the coefficient also shows an increasing trend as in experiment A. It was observed in Fig. 5 that the worn surfaces consist of grooves and ridges, forming a highly directional structure. Although the type 2 correlation coefficient was determined between a pair of profiles taken 90” apart, an arbitrarily chosen interval, it demonstrates this feature quantitativejly. Moreover, it can be asserted that, so far as the present experiments are concerned, including the above-mentioned unlubricated experiment, the initial isotropic surfaces experience various modifications in their shape
115
and eventually acquire parallel directional topography. This process is promoted by favourable lubrication. Although in general the sliding surfaces tend to acquire directional structures, this seems not to be directly related to the amount of wear. For instance, the first stepwise increase in the coefficient at 150 m for the disk specimen in experiment A certainly corresponds to the change in the wear rate, while the second at 350 m is not accompanied by a change in the wear rate. For experiment B, the wear rate slightly decreases at 150 m without an appreciable change in the type 2 correlation coefficient. Nevertheless, it should be recognized that the appearance of the parallel directional property has a significant implication concerning the contact mechanisms. Stochastic approaches to the contact problem will be valid in the case where a parameter such as the type 2 correlation coefficient takes low values. In contrast, if its value is nearly unity, the contact point is no longer circular or elliptical but should be in the form of a strip with high aspect ratio. Thus forces are transmitted between mating surfaces through the very narrow contact strips that form on the smooth ridges on the wear track as seen in Fig. 5, and they produce flake-like wear particles; the relation between surface topography and loose particles is discussed in a separate paper [24]. Such a mechanism predominates almost from the outset in experiment B. 5. Conclusions In the present paper an attempt has been made to introduce two types of cross-correlation coefficient between surface profiles to characterize the topographical changes of sliding surfaces in wear processes. The type 1 correlation coefficient is found to be a parameter which describes the characteristic wearing mode, i.e. whether material removal occurs on the wear track uniformly or not. Further, its value is influenced by additional modifications of the surface configuration by triaxial plastic deformation. The type 2 correlation coefficient gives the degree of two dimensionality of the worn surfaces. This cross-correlation analysis is applied to the wearing surfaces in the lubricated wear experiments. With the cases in which the wear rate is initially high and then lowered, the changes in surface topography are summarized as follows. In the early stage of the sliding process, material removal occurs randomly at various scales on the wear track, and wear is accompanied by heavy lateral plastic deformation. As wear proceeds, the sliding surfaces tend to have strongly twodimensional structures parallel to the sliding direction, and the wear occurs over the whole wear track. Acknowledgment The authors would like to thank Dr. E. F. Finkin for his helpful comments on this paper.
116
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13
14 15 16 17 18 19
20 21 22 23
24
J. Halling, A contribution to the theory of mechanical wear, Wear, 34 (1975) 239. E. F. Finkin, An explanation of the wear of metals, Wear, 47 (1978) 107. N. P. Suh, The delamination theory of wear, Wear, 25 (1973) 111. N. P. Suh, An overview of the delamination theory of wear, Weor, 44 (1977) 1. J. Peklenik, New developments in surface characterization and measurements by means of random process analysis, Proc., Inst. Mech. Eng., London, 182 (3K) (1967 1968) 108. J. A. Greenwood and J. P. B. Williamson, Contact of nominally flat surfaces, Proc. R. Sot. London, Ser. A, 295 (1966) 300. D. J. Whitehouse and J. F. Archard, The properties of random surfaces of significance in their contact, Proc. R. Sot. London, Ser. A, 316 (1970) 97. H. Christensen, Stochastic models for hydrodynamic lubrication of rough surfaces, Proc., Inst. Mech. Eng., London, 184 (55) (1969 - 1970) 1013. G. W. Rowe, H. Kaliszer, G. Trmal and A. Cotter, Running-in of plain bearings, Wear, 34 (1975) 1. S. K. R. Chowdhury, H. Kaliszer and G. W. Rowe, An analysis of changes in surface topography during running-in of plain bearings, Wear, 57 (1979) 331. K. J. Stout, T. G. King and D. J. Whitehouse, Analytical techniques in surface topography and their application to a running-in experiment, Wear, 43 (1977) 99. T. G. King, W. Watson and K. J. Stout, Modelling the micro-geometry of lubricated wear, Proc. 4th Leeds-Lyon Symp. on Tribology, September 1977, Mechanical Engineering Publications, London, 1978, p. 333. T. R. Thomas, The characterization of changes in surface topography during runningin, Proc. 4th Leeds-Lyon Symp. on Tribology, September 1977, Mechanical Engineering Publications, London, 1978, p. 99. V. K. Jain and S. Bahadur, Surface topography changes in polymer-metal sliding, I, J. Lubr. Technol., 102 (1980) 520. E. F. Finkin, Surface roughness in wear, Wear, 6 (1963) 293. R. ostvik and H. Christensen, Changes in surface topography with running-in, Proc., Inst. Mech. Eng., London, 183 (3P) (1968 - 1969) 57. K. Endo and S. Kotani, Observations of steel surfaces under lubricated wear, Wear, 26 (1973) 239. M. A. Shafia and T. S. Eyre, The effect of surface topography on the wear of steel, Wear, 61 (1980) 87. N. Patir and H. S. Cheng, An average flow model for determining effects of threedimensional roughness on partial hydrodynamic lubrication, J. Lubr. Technol., 100 (1978) 12. P. R. Nayak, Random process model of rough surfaces, J. Lubr. Technol., 93 (1971) 398. P. R. Nayak, Some aspects of surface roughness measurement, Wear, 26 (1973) 165. T. F. J. Quinn, Dry wear of steel as revealed by electron microscopy and X-ray diffraction, Proc., Inst. Mech. Eng., London, 182 (3N) (1967 - 1968) 201. J. Sugimura and Y. Kimura, Wear behaviour and effects of lubrication on the topographical changes of wearing surfaces, Proc. 1 lth Leeds-Lyon Symp. on Tribology, September 1984, Butterworths, London, to be published. Y. Kimura and J. Sugimura, Microgeometry of sliding surfaces and wear particles in lubricated contact, Wear, 100 (1984) 33.