A Study of the Lubrication of EHL Point Contact in the Presence of Longitudinal Roughness

A contact is produced in an EHL ball-on-disc rig in which a steel ball is loaded against a glass disc (see Fig. 1). The ball and the disc are driven by two independent motors so that it is possible to achieve mixed rolling–sliding as well as nominally pure rolling conditions. The lower surface of the disc is coated with a 20-nm-thick semi-reflective chromium layer and a silica spacer layer of around 130 nm in thickness that enables very thin film measurements [26]. During tests, light is shone on the contact where approximately half of the incoming beam is reflected from the chromium layer, while the remainder travels through the spacer layer and the lubricant film before being reflected back by the surface of the ball. The difference in path length between the two parts of the incoming beam produces a difference in phase between them, which generates interference fringes when they recombine. The images obtained are interferograms of the contact which can be captured via a CCD camera. These interferograms can be subsequently analysed to generate maps of the lubricant film thickness.

The standard interferometry technique implemented on the ball-on-disc rig is designed to measure EHL film thickness in smooth contacts. To be able to study roughened ball surfaces, several modifications had to be made to the standard set-up. These are described below.

In order to avoid excessive blurring as roughness passes through the field of view, it is necessary to use a camera with fast shutter speed. This is not usually a problem with extremely smooth specimens. In this study, 800 × 800 pixel resolution interferograms were captured with a high-speed camera at a shutter speed of 10 μs. At 2.2 m/s, the surfaces travel 22 microns and in practice it has been found that above this speed the roughness became too blurred to be analysed in detail. The magnification of the lens was 5× so that each pixel covered an area of 1 μm × 1 μm on the ball.

To monitor lubricant film build-up at precisely the same location on the ball as the speed was increased, and thus study the same roughness features, the camera was triggered off a fixed ball position for the duration of a test. To do this, a 12-bit encoder (4096 positions) was added to the ball shaft allowing a circumferential resolution around the ball of 15 μm for a ball of diameter 19.05 mm.

For accurate calculation of the lubricant film thickness, the spacer layer thickness must be known. This is not perfectly constant around the disc. During these tests, the camera is triggered from the ball position rather than from the disc position, as is normally the case, so the spacer layer thickness may vary from one image to another. To prevent this, the disc spacer layer thickness was mapped using a smooth ball by taking interference images all around the disc. A circumferential variation in the coating thickness of about ±1 nm is usually observed. To eliminate the effect of this variation, the triggering system was set up so that the camera was triggered only when the exact selected roughness position on the ball was in contact with a portion of the disc lying in a tightly specified range of disc track within which the coating thickness variation was measured to be minimal. This “double triggering” also ensured that the image stayed focused since it minimised the effect of disc runout. The triggering set-up was validated using a smooth ball that had a 500-μm laser-textured square at one position on the surface. Figure 2 shows images triggered on the ball position at different speeds. Over a large range of speed, it is clear that the square barely moves with respect to the triggering position and is not blurred, indicating that the triggering system is working as expected.

Some researchers have used white light [2, 27] to generate interference fringes for film thickness mapping. However, white light sources are usually broad and have a poor coherence length, typically around 500 nm for a halogen lamp, which means that the intensity of the interference fringes decreases rapidly with increasing film thickness and it becomes difficult to measure any film thicker than 500 nm. To overcome this problem, more coherent light sources such as monochromatic LEDs or lasers can be used. In this study, a green LED (530 ± 15 nm) and a red LED (617 ± 8 nm) were used in combination. Such a duo-chromatic system has been employed in the past, for example by Wedeven [28] and Kaneta et al. [29], but has usually involved filtering a spectral lamp. Due to their high divergence, the LED light sources were collimated prior to being recombined with a dichroic mirror. The obtained light source has a coherence length of 2.8 μm which enables measurement of lubricant films that are over a micron thick.

When using optical interference techniques to map film thickness, two issues have to be addressed.

First, a correspondence between the lubricant film thickness and the colour intensity has to be determined. To do this, one of two different calibration methods is usually employed. One uses a static contact between a smooth ball and the coated disc. When the light is shone into the contact, Newton’s rings are formed and the colour intensities are scanned radially and related to the film separation using either a contact model such as Hertz (see [27]) or the periodicity of the fringes (see [30]). The second calibration technique is explained in Choo et al. [31] and involves measuring central film thickness versus entrainment speed with a very smooth ball using ultrathin film interferometry [32] and then taking interference images over the same speed range to follow the evolution of the colour intensities in the central area. Ultrathin film interferometry is an absolute technique based on measurement of interference wavelength and does not require external calibration.

The second issue that has to be addressed is that, due to experimental error and the quasi-periodic nature of the calibration curve, it is possible for a given set of colour intensities to give several solutions for the film thickness. In practice, authors have either focused on film thickness values that fall in the first period of the calibration curve (i.e. below 250 nm) or have defined a range of film thickness and chosen the best match within it.

All the above techniques give the correct intensity variation trend of the interference fringes against film thickness, but they also assume that the surfaces studied are as reflective as smooth surfaces. However, when rough surfaces are considered, it is observed that reflected light is diffused as opposed to the specular reflection of smooth surfaces. Hence, for a given film thickness the corresponding intensity of the interference fringes will be lower for rough than for smooth surfaces.

To enable the measurement both of very thick films and from rough surfaces, a novel procedure for film thickness measurement was developed. This involves two steps.

Similar to Molimard [27], a smooth ball is loaded against the disc in the presence of lubricant and the intensities of the circular red and green fringes are scanned radially as shown in Fig. 3.

Using Hertz theory, the gap outside of the contact is calculated and related to the intensity of the fringes. This is shown in Fig. 4.

As evident in Fig. 4, due to factors such as the loss of coherence of the light and the curvature of the ball, the amplitude of the fringes decreases with the increasing gap. To eliminate this effect, the relative optical interference intensity (ROII) can be used (see [33]). This is defined as:where I _max and I _min represent the maximum and minimum intensities for each period of the curve. The effect of this transformation can be seen in Fig. 5 for the red fringes; the curve shown is a normalisation of the original curve by the adjacent minimum and maximum intensities and has a very similar form to a cosine function. The period of this curve is equal to the period of interference that would be produced by monochromatic light whose wavelength is equal to the average wavelength of the light source modulated by the camera’s spectral response. The initial phase shift corresponds to the contribution of the spacer layer thickness and the phase shift due to the chromium layer.

From Fig. 5, it is apparent that the normalised intensity curve can be modelled by a cosine. Consequently, provided that the order of interference is known, the film thickness h can be calculated using:

The red and green channels can be used independently to calculate the film thickness and were found to give almost identical results. In this study, the film thickness is taken as the average of the film calculated using the two channels to reduce the experimental noise.

For any particular point within the contact, the adjacent minimum and maximum intensities that need to be considered to calculate the ROII are not easily accessible. For example, when the surface is rough, the order of interference is not always known because of large variations in film thickness within the contact. Another parameter that may modify the amplitude of the fringes is the local orientation of the surface which is affected by the presence of asperities. Hence, a rough surface that is illuminated perpendicularly tends to diffuse the incident light, which reduces the amplitude of the interference.

To obtain the local values of the minimum and maximum intensities, a series of images is taken at different speeds, and the change in intensity of both colours is followed at each point. Assuming that the speed increase step is small enough that no order is missed, and that the film thickness monotonically increases with speed, it becomes possible to calculate the ROII everywhere. The high resolution of the ball shaft encoder and the fast shutter speed help to ensure that all images are taken near the same spot on the ball as illustrated in Fig. 2. However, despite these precautions, the contact tends to move by a few pixels from one image to another. To correct for this, a correlation algorithm is used to realign the images before analysis.

All the images are then stacked and the evolution of the red and green intensities against speed is observed at every point independently. The ROII is then calculated for each point of the contact at every speed following the method described previously. Figure 6a, b, respectively, show an example of recorded red and green intensities and the calculated ROII.

Using these data and Eqs. 2 and 3, it becomes possible to calculate quite reliably the film thickness for each speed everywhere in the contact (Fig. 5a). Equally, at each speed considered, a map of film thickness can be obtained. An example of calculated film thickness at a selected point and a complete film thickness map are shown in Fig. 7a, b, respectively.

Unlike in smooth contacts, in rough contacts considered here there is no one single value of minimum or central film thickness. In order to be able to extract representative values of film thickness from the obtained maps, a rectangular area equivalent to the flat central area of the smooth contact is selected inside the contact, avoiding the constriction. Maps are generated for a range of entrainment speeds, and then the following values are calculated:

The disc, ball specimens, ball shaft, ball carriage and lubricant pot are consecutively soaked in toluene and isopropanol. They are then dried with a heat gun in order to eliminate any trace of solvent.

The pot is filled with the test lubricant and left for 30 min in order to allow the set temperature (disc + ball specimen + oil) to stabilise. A particular ball position is chosen from which all the measurements of film thickness are subsequently taken. The position of the disc is also logged to enable the partial triggering.

The specimens are drilled AISI 52100 steel balls with a diameter of 19.05 mm (3/4″). The geometry and the material properties are summarised in Table 1.

Smooth balls and discs had RMS roughnesses of 20 and 5 nm, respectively. Roughened balls with three different roughness structures were tested in this study. The textures were produced by careful roughening of the ball on a lathe to achieve periodic circumferential ridge-valley texture (parallel to the rolling/sliding direction). By varying parameters such as the feed rate and the radius of the cutting tool, it was possible to obtain surfaces with different dominant wavelength and peak-to-valley heights. The topographies of the three selected roughnesses are shown in Fig. 8.

Using a dedicated jig with angular positioning, it was possible to precisely locate the roughness and then capture the film thickness in this position. The measured roughness properties of the three selected rough specimens are listed in Table 2.

The specimens were tested in the ball-on-disc rig at the conditions listed in Table 3.

In all the tests, a load of 20 N was applied, giving a nominal Hertz pressure of 0.527 GPa and a contact diameter of 269 μm based on smooth surface calculation. In the case of rough surfaces and this film conditions, the load is mostly born by the asperities so the local pressure is expected to be higher. The overall size of the contact zone did not seem to be significantly affected by roughness, suggesting that the important parameter controlling this was the radius of curvature of the ball and not of the asperities. In each test, the entrainment speed was increased in steps while maintaining a fixed slide-to-roll ratio (SRR), where the entrainment speed is the mean speed of the surfaces while the SRR is defined as:

In all tests, the SRR was positive, i.e. the disc surface moved faster than the ball surface.

The oil tested was Shell Turbo 68, a Group II base oil with antioxidant additives, whose properties were measured and are listed in Table 4. The test temperature was 40 °C.

This lubricant and temperature were chosen to enable a full span of the lubrication regimes over the chosen entrainment speed range using just one oil. As seen in Fig. 9, for a smooth ball, film thickness varied from 10 nm (boundary conditions) to 1000 nm (fully flooded conditions) over the speed range available.

As shown in Molimard et al. [22], when accurate film thickness maps are available it is possible to use them as inputs to estimate the pressure distribution, assuming the undeformed surface is known. In our case, this requires the out-of-contact topography to be measured using white light interferometer (WLI) and matched to precisely the same location from which the film thickness maps are obtained in the ball-on-disc rig. To achieve this, an indent was made on the ball using a diamond cone (Rockwell C indenter). Figure 10 shows an interference image of a static rough contact and a corresponding surface topography map observed under the WLI. It can be seen that the two surfaces are closely aligned.

To estimate the pressure distribution, the elastic displacement map of the surfaces is needed. This is the difference between the loaded and the unloaded surface topographies plus a penetration value, the approach of centres of the two bodies. The latter is an unknown constant, and to obtain it, the displacement was approximated as Hertzian outside of the contact area and the constant was found by determining at the difference between the two solutions at the edge of the contact. Figure 11 shows the transverse profile of the displacement field before and after this operation. One disadvantage of this method is that it assumes that the pressure outside of the contact is zero. This is valid for static and low speed contacts, but is not the case in the inlet of lubricated contacts at high speeds. To evaluate the inlet pressure, it is possible to extrapolate the film profile around the contact and this was explored, but was found not to significantly affect the calculated pressure distribution within the contact area. Thus, it was not implemented in the results shown in this paper.

The pressure field P and the displacement field W are linked by the influence coefficient matrix K which is a function of the material properties and the dimensions of the mesh [23].where conv is the convolution operation. The problem can easily be inverted by considering the fast Fourier transform (fft) of the matrices:where ifft is the inverse fast Fourier transform that enables conversion into the spatial domain.

As well as the predominant longitudinal ridge texture, the ball surfaces also had much finer roughness features, predominantly along the rolling direction, with wavelength ca 1–5 μm and amplitude 10–20 nm. Since the focus of this study was the impact of the ridges on pressure, the displacement was smoothed prior to being used as input to calculate the pressure distribution. To do so, the macro-curvature was first extracted using a discrete cosine transform, and then the result was smoothed with a simple averaging. The kernel used was a 9 by 9 points square window, which represented a 9 μm by 9 μm area. This was found to be adequate to smoothen the lower frequencies without excessively attenuating the higher frequencies. Yet it was observed that the smoothing led to a slight reduction in the ridge amplitude; to compensate for this, the profile was multiplied by a constant. Finally, the macro-curvature was re-added to the profile.

During a test, the speed was slowly increased and images were taken in the same position on the rough ball. Figures 12 and 13 compare interferograms from a lubricated contact of a smooth specimen and rough specimen 1 in pure rolling at six entrainment speeds. It is evident that as the entrainment speed increases the colour changes, indicating lubricant film build-up. In the rough specimen case, the changes in colour occur faster in the valleys between the asperities, showing that the film build-up primarily occurs in these regions while the tops of the asperities remain in contact.

As the speed increases, the horseshoe shape becomes more and more visible in Fig. 13. Figure 14a shows the transverse profile of film thickness for a selected set of speeds for specimen 1. At low speeds, the surface features are very compressed, leading to an almost conformal contact. As the speed increases, the lubricant film thickness increases and the asperities start to recover. For comparison, the film profile for a smooth case at 1.1 m/s was added to the chart. This shows that the film shape in smooth and rough cases follows the same general trend. The profile in the rough case varies around a centreline that is well represented by the smooth profile. In the centre of the contact area, the asperities are more squashed than at the edge. This is similar to what happens in the smooth case, where the deformation is larger in the centre.

At the top of the ridges, a micro-EHL phenomenon becomes visible. A ridge was selected from the interferograms as shown in Fig. 13, and the evolution of the average film thickness profile along the top of this ridge is shown in Fig. 14b. In this figure, the contact inlet is to the left and the exit to the right.

As shown in Fig. 13, a square area was selected on each interferogram and the mean values described in Sect. 2.4b were calculated. The area of analysis was chosen to avoid the constriction region so that the measurements could be compared to the central film thickness region measured on a smooth specimen. The specimens were tested under both pure rolling and rolling–sliding conditions at SRR = 50 % over a range of entrainment speeds varying from 0.02 to 2.2 m/s. Figure 15 shows the minimum, the maximum and the average film thicknesses (as defined in Sect. 2.4b) over the selected area in the case of rough specimen 1. The central film thickness measured with a smooth specimen under the same conditions is also plotted for comparison. It is evident that there is very little difference between the nominally pure rolling and 50 % sliding cases.

The minimum and maximum film thicknesses in pure rolling for the three different rough specimens are shown in Fig. 16; the average film thickness is not shown because it was very similar for all the roughnesses and is well represented by the smooth surface curve. The three rough specimens all show similar trends:

However, it can be seen in Fig. 16 that, over the range of conditions tested, the surface separation (minimum film thickness) increases at a lower rate for the roughest specimen (specimen 3, RMS = 0.27 μm) compared with the smoother specimens (1 and 2, RMS = 0.15 μm). The wavelength of the roughness seems to have a marginal impact as the minimum and maximum film thicknesses measured with rough specimens 1 and 2, which have a 40 and 20 μm wavelength, respectively, but almost the same RMS.

Using the film thickness maps in the selected area the RMS of the separation was calculated. The practical significance of this RMS value is discussed later in this paper. Figure 17 shows how the ratio between this in-contact RMS and the undeformed RMS measured outside of the contact is affected by an increase in the entrainment speed. While it is greatly reduced at low speed compared with the unloaded out of the contact RMS, lubricant film build-up enables the roughness to partially recover at higher speeds. The RMS of the two specimens with the same undeformed RMS recovers at approximately the same rate, while the roughest specimen recovers more slowly.

Lift-off occurs when there is no more solid-to-solid contact. To characterise the speed at which this occurs, it is appropriate to look at the real contact area (solid to solid) rather than the minimum film thickness. This is defined as the number of points where the film is zero (or appears negative due to local spacer layer compression). Figure 18 shows the evolution with speed of the fractional real area of contact over the area analysed. For each rough surface, the real area of contact falls to zero at a quite well-defined entrainment speed.

At low speeds, the rough specimen with the smallest wavelength (specimen 2) has the largest solid-to-solid area of contact. Specimen 1, with the same roughness but a higher wavelength, has a slightly smaller area of contact, while the roughest specimen has an even smaller area of contact. As the entrainment speed increases, the surfaces start to separate and the solid-to-solid contact diminishes.

However, this diminution evolves at a different rate depending on the specimen considered. As with the film thickness measurements, the two rough specimens with the same RMS show lift-off occurring at about the same speed, between 0.150 and 0.20 m/s, while the roughest specimen lifts off more slowly and there is still solid to solid up to 0.50 m/s.

As was observed in previous work [8, 16], at low lambda ratio the roughness dramatically affects the film distribution. For example, at 0.150 m/s, the constriction is well defined in the smooth case but indistinguishable for rough specimen 1. At this low speed, the asperities are apparently much squashed and the conformity of the surfaces (seen in Fig. 14a) implies that they bear a large part of the load. As the speed increases, the lubricant film increases in the valleys, the roughness starts to recover and the real area of contact is reduced.

At higher speeds (over 0.5 m/s), contrary to what has been observed in other studies [16], a horseshoe shape becomes visible. This difference from previous work can be explained by the higher speeds reached and the higher viscosity of the lubricant employed in the current study, which leads to much thicker nominal films. It is clear from the interferograms of Figs. 13 and 14b that as the film becomes thicker a constriction appears at the exit of the contact. While micro-EHL features are particularly visible at the top of the ridges, a macro-horseshoe shape can also be seen over the contact as a whole. In Fig. 14a, the transverse film profiles are shown for rough specimen 1 along with the profile of a smooth ball at 1.1 m/s. As the speed increases, the asperities partially recover; however, the macro-curvature of the surface (i.e. when the roughness is ignored) follows closely that of the equivalent smooth case: the ridges in the central area are more compressed (more flattened), and a film reduction occurs at both edges of the contact (horseshoe). The rough contact behaves as if the roughness has been added to the smooth case deformation. Thus, the deformation seems to be far more influenced by the macro-geometry (i.e. the curvature of the ball) than the roughness.

The rough specimens were also tested in rolling–sliding conditions with a positive SRR equal to 50 %. Over the range of conditions tested, the measured film thicknesses were the same, within experimental error, as the ones measured in pure rolling conditions, suggesting that this level of sliding does not have any impact on the film distribution. This is important since it suggests that pure rolling behaviour is representative of that likely to be present in most rolling bearing contacts where SRRs are generally low. It also has implications on damage accumulation mechanisms in rough rolling–sliding contacts, such as micro-pitting, as it suggests that any increased asperity interaction at higher sliding speeds is not due to film thickness reduction.

For all of the rough specimens, the minimum film thickness in the central region was significantly thinner than the central film thickness measured with a smooth specimen, as can be seen in Fig. 16. This can be explained by the gradient of pressure between the ridges and the valleys: at low speed, the higher pressure at the ridges forces the lubricant laterally into the valleys, where the pressure is lower. For rough specimens, the lift-off (i.e. when the surfaces fully separate) occurred at much higher speed than for smooth surfaces. It can be seen in Fig. 18 that for specimens 1 and 2, it starts at around 0.170 m/s, at which speed the film thickness in the central region is already above 100 nm for the smooth ball. Rough specimens 1 and 2 differ only in the wavelength of their roughness; they have the same RMS roughness and peak-to-valley height. Figure 16 shows that the maximum and minimum film thicknesses for the two specimens are very similar at all speeds. Specimen 3, which has greater RMS and peak-to-valley height, behaves differently in that the maximum film thickness is higher since valleys are deeper, and the surface separation increases more slowly with increasing entrainment speed. As the real contact area shows in Fig. 18, some residual contact remains up to a speed of 0.5 m/s. A very interesting result was that average film thickness in the central area was found to be reasonably close to the average film thickness, independent of the roughness considered.

All of the above suggests that the film build-up is only affected by the RMS of the surface and not significantly by the wavelength of the roughness for the range of roughness structures studied here.

Recovery of the roughness can be estimated by the RMS of the separation. It should be noted that the observed RMS is the composite roughness of the contacting surfaces. As the glass disc has much lower elastic modulus than the steel, it can be assumed that the observed reduction in roughness is almost entirely due to smooth glass surface being deformed as the ridges elastically indent it, rather than the steel asperities flattened. Roughness recovery is then due to the indentations in the glass being reduced as the rough steel surface lifts away from it due to the build-up of film pressure.

At low speeds, the effective roughness is reduced to below 20 % of the undeformed roughness. As the speed increases, the roughness partially recovers which shows that a growing part of the load is borne by the lubricant film.

The lift-off speed is the speed at which the load stops being supported in part by solid-to-solid contact and becomes wholly supported by hydrodynamic lift from the lubricant film. Since the contact is in the EHL regime, the surfaces are still elastically deformed when this occurs.

To understand the link between the recovery of the roughness and the lift-off speed, the “real lambda” ratio calculated as the ratio between the average film thickness in the area of analysis and the in-contact RMS is shown Fig. 19. It can be seen that full surface separation occurs at a real lambda ratio λ _Lift ≈ 3.5 for all three rough surfaces.

The fact that the surface separation occurs at a given value of the lambda ratio suggests that the transition between the mixed-lubrication and the full film regimes is mostly dominated by a balance between the roughness recovery and the lubricant film build-up in the contact.

The film thickness maps of specimen 1 were used to estimate the pressure distribution variation with speed. Figure 20a shows a calculated pressure map in the static contact and illustrates the high pressure regions along the ridges. Figure 20b compares a pressure profile transverse to the ridge direction in static conditions with the Hertz pressure for a smooth contact at the same load. Also shown in this figure is the corresponding normalised out-of-contact roughness profile (the actual amplitude of the asperities is about 0.5 μm). As expected, peaks of pressure can be observed at the asperity ridges.

On average, the pressure distribution seems to follow the Hertz distribution with local variations due to the presence of roughness. The highest pressure is observed in the centre of the contact, and the pressure drops in the outer parts. Figure 21a shows how the pressure evolves when the entrainment speed increases and the pressure builds up.

As the speed increase, the surfaces separate and they become less conformal. In the central area, this has the effect of redistributing the load support towards the top of the asperities that see the pressure rise, while it remains low and even diminishes in the valleys. At the outer edges, the pressure evolves in the opposite direction creating a low pressure “horseshoe” that can be seen in Fig. 21b similar to the one observe in a smooth contact. No pressure peak, known as the Petrusevich peak, could be seen at the exit, but it may be linked to the smoothing of the surfaces before they were used for the pressure calculations.

To explain the evolution of pressures at the peaks and the valleys, an analogy with a smooth contact can be drawn. A smooth specimen was tested using the same lubricant and under the same operating conditions. Similar to the rough specimen, the film maps were used to obtain the pressure distribution at different speeds. In Fig. 22, the pressure distribution in the transverse direction is shown at three different speeds.

As expected, at low speeds the pressure profile is almost Hertzian. As the speed increases, the pressure at the edges decreases, this is due to the formation of the constriction. Interestingly, the pressure in the centre of the contact increases with speeds, as if the loss of load support in the horseshoe is compensated by an increase in load support in the central area. The reduction in bearing capacity at the sides and exit is accompanied by an increase in the pressure in the inlet. However, as mentioned previously, this does not affect the pressure distribution in the contact area. This pressure increase compared with the static case can be seen in other studies (see [22, 34]) although this has not previously been formally identified.

For the rough case, if each ridge is considered as an individual micro-EHL contact, the same phenomenon would imply that as the speed increases, the pressure drops at the edges (i.e. the valleys) and increases in the centre of the contact area (i.e. the peaks), which is what is observed. The general horseshoe shape also seems to influence the pressure distribution as the pressure drop in the valleys located in the outer parts is much more dramatic than for the valleys located in the centre.

The results shown in this paper appear to contradict a number of previous studies that focused on localised roughness such as dents or transverse roughness. First, in these studies sliding was found to have an influence on the film thickness distribution, while such effects were not observed in the current study. For the case of transverse ridges, various authors [1, 3] have reported that, in the presence of sliding, a perturbation in the oil film was apparent when the ridges entered the contact. Analogous observations were made on dents (see [12, 35]) or bumps [14]. Secondly, it has been found in this study that the roughness recovery was primarily influenced by the RMS roughness rather than the wavelength of the texture. Again, this seems to contradict previous theoretical work [17] that predicts the contrary.

When considering the influence of roughness on EHD film thickness, it is very important to realise that the primary impact of localised roughness features such as dents or transverse ridges occurs in the contact inlet region, where a roughness feature has the effect of momentarily changing the combined radius of the surfaces and thus the rate at which the film gap converges. This causes a transient change in the quantity of lubricant being entrained and thus produces a momentary variation in film thickness. This “blip” or more formally “perturbation” in the film thickness then passes through the contact at the mean speed of the surfaces.

However, for longitudinal roughness, where the surface features are elongated precisely along the entrainment direction this does not occur. The ridges and valleys both have almost the same radius along the rolling/sliding direction as does the overall surface, so the system is essentially a steady-state one. In this case, uniquely, the main impact of the roughness occurs within the contact itself and results from the responses of the fluid to the local conditions generated by the varying pressure field therein, for example to the very high pressure along the ridges and to the difference in pressure between the fluid at the ridges and in the valleys. These differences in studied contacts may at least in part explain apparent discrepancies between results shown here and those found by previous studies.

This fundamental difference between longitudinal and all other forms of roughness explains why the results shown are quite different from that found by many previous authors.