The piston ring and liner interface is a major source of friction loss in automotive combustion engines. This loss can be mitigated by learning from surfaces from nature that manipulate friction. In this study, novel fabrication and testing methods were developed and used to efficiently compare three-dimensional bioinspired surface designs to existing piston liner surface topographies. Surface designs inspired by frog toes were fabricated using two-photon lithography, and their frictional performance is compared to that of typical piston liner topography. These designs reduce surface friction by an average of 18%, and up to 39%, compared to a flat control. The developed fabrication and testing methods allow comparison with existing topographies without needing to transfer the designs to the original materials and provide an efficient approach for designing surfaces to meet the frictional challenges of the future.
As CO2 emission reduction becomes more critical to the automotive industry, there is an increased need to improve engine efficiency in which friction reduction plays an essential role. The interface between the piston ring and liner represents a significant portion of the energy lost through friction. This interface contributes half of the mechanical frictional loss in the total engine system, which can be as much as 10% of the total automotive inefficiency . Research in this area is often dedicated to understanding how friction is generated , how the hydrodynamic lubrication regime is maintained , and the improvement of friction and wear properties through modification of the piston ring or liner surfaces [4,5]. There is a study exploring the effect of lubricant modification , but this approach is less common compared to the modification of the surfaces themselves.
The honing technique applied during the manufacturing of cylinder bores produces a cross-hatching texture, which stores lubricant in valleys and helps in reducing friction when the piston passes against the bore. A secondary step is often added to flatten the peaks into plateaus, leading to the plateau/valley structure, which is now widely used today. These valleys are generally on the order of 10–30 μm wide, with depths of 2–10 μm [7,8]. While useful and highly scalable, this technique leads to rough and imperfect grooves on the liner, which affects the ideal flow of fluid. In addition, the liners require a “run-in” period during which the tall asperities of the liner texture are ground down by the sliding action of the piston ring against the cylinder, eventually reducing the friction coefficient and the fuel consumption of the system . Under this repeated reciprocation, the surface approaches an optimal topography, which minimizes the wear and friction compared to the break-in period.
There are three main considerations for defining piston rings and liner topographies. The first goal is minimizing the friction to reduce energy losses as heat. This is usually done by modifying the contact area through texturing . The real contact area is a function of the load and roughness of the surface and is likely to change during the reciprocating action. The second goal is that the surface must be able to retain a small amount of oil during the piston movement, but not so much as to leak into the combustion chamber . Therefore, a smooth, mirror-finish surface would not be ideal; the surface would quickly become oil-starved, and thus, the lubrication regime becomes primarily boundary rather than hydrodynamic, leading to high friction and surface seizure. The third goal is to increase the resistance of the surface to wear, which is achieved by engineering the surface material and, more generally, by reducing the boundary friction between the two surfaces.
Existing solutions to meeting these goals utilize simple textures such as dimples or straight-walled grooves [12,13]. However, it is desirable to explore complex and truly three-dimensional (3D) structures to fully investigate the potential of surface textures to reduce friction and interact with lubricant. This article demonstrates a method whereby various truly three-dimensional textures can be quickly fabricated with ultraviolet (UV)-sensitive polymers and compared to the frictional performance of an existing texture regardless of material.
The surface of the frog toe has attracted much interest in recent years. These surfaces enable the frog and other creatures with similar features, such as the bush cricket, to cling to a variety of surfaces. The morphology of the frog toe generates an adhesive capillary force from a secreted liquid, which flows through a series of hexagonal channels on the toe surface . Hexagonal structures are quite common in nature, appearing in places such as crab eyes , insect hives , snake scales , fish scales , and cricket feet . One explanation for this reoccurrence is the material efficiency and coverage density of the shape . The hexagonal layout of the grooves spreads the lubricant fully throughout the contacting surface . In the case of the frog, this action removes water from the surface to provide a drier contact to the toe . This effect can be seen in modern automobile tire surfaces, which take advantage of the drainage properties of macro-scale hexagonal textures by using grooves to prevent hydroplaning during vehicle operation on slick roadways . The driest contact occurs when the width of the channels is approximately the same as the fluid film thickness on the contacting surface . Thicker fluid films are likely a consequence of deeper grooves since a sufficiently deep groove recycles lubricant back up to the contacting plane .
Groove microtextures have differing effects on friction based on their orientation to the direction of sliding. Grooves that are oriented perpendicular to the sliding direction reduce friction to a greater degree than those oriented along the sliding direction [26,27]. Hydrodynamic lift is generated inside the groove, reducing friction. However, this effect is heavily dependent on the depth of the groove: shallower grooves were shown to have roughly no difference between parallel and perpendicular orientation, while the hydrodynamic effect became more pronounced at higher depths . Perpendicular grooves may also contribute to greater wear due to the increased stress on the edge of the groove.
Current research on biomimetic surfaces based on frog toes generally concentrates on the adhesive aspects of the topography, specifically the static friction caused by the capillary forces . The intention of much current research is to increase the adhesion and friction of nonslip surfaces. Huang and Wang showed that hexagonally arranged grooves increase friction as speed increases .
The cross section of the frog toe groove varies in shape depending on the location on the toe . For example, the grooves on the subarticular tubercles appear rectangular and shallow, whereas the grooves on the toe-pad surface are much narrower and deeper, with a more triangular cross section. The cross section design affects the fluid drainage and adhesion properties; thus, it makes sense that different parts of the contacting surface would have different designs for optimal grip . In particular, the aspect ratio of the cross section (defined by the channel depth divided by channel width) was found to have a positive relationship with the coefficient of friction, i.e. as the aspect ratio increases, so does the friction .
The coefficient of friction can be lowered if the density of grooves is appropriately small . The ideal density was determined through numerical simulations by Zhong et al. to be approximately 25% . The density of grooves of the frog toe is only 8%, assuming a hexagonal radius of approximately 10 μm and a groove width of approximately 1 μm . However, hexagonal feature density was found by Murarash et al. to have little effect on the kinetic coefficient of friction when realized in elastomer forms, indicating that the behavior of the surface under sliding conditions is related to the elastic modulus of the surface material .
Much current research on the frog toe intends to increase friction; however, these studies can be still helpful if a reduction of friction is desired. Friction can be reduced by a deeper groove, allowing lubricant replenishment during sliding contact . This depth is determined to be approximately 10 μm. The groove depth effect is less significant for high loads and speeds.
Although simple two-dimensional textures have been extensively studied, a method is needed, whereby complex 3D texture designs can be quickly fabricated and tested against existing topographies to explore better designs for friction reduction. The objective of this study is to develop such a method to quickly design, fabricate, and test novel, truly 3D surface designs for friction reduction.
2 Methods and Materials
Hexagons can tessellate the Euclidean plane and are therefore suitable for tiling processes to create patterns in a much larger, arbitrarily sized area. Dimples are shown to have a friction-reducing effect [36,37], and they can also improve lubricant use efficiency by storing lubricant between reciprocations and recycling it back to the contacting surface during operation . However, dimples that are too deep can have the opposite effect, increasing friction, as lubricant can become trapped inside the dimples and gradually starved from the contact surface . Huang and Wang showed that this effect is dependent on speed as dimples can reduce friction at higher speeds . There have been several investigations on the addition of dimples to honed cylinder liners. Denkena et al. found a friction-reducing effect by adding elliptical dimples of approximately 100 μm by 5 μm and a depth of 30 μm to a honed cylinder . This effect varied based on the location of the dimple along the piston stroke, indicating that different texturing approaches would be more effective in different stroke regimes. Similarly, Koszela et al. studied the effect of circular dimples of 300 μm diameter and 5 μm depth added to honed cylinders . Again, the dimples had a desirable effect on the friction by providing reservoirs for lubricant storage and wear particle removal, particularly when combined with a hard coating. This study also revealed that dimples that are not fully flooded can have the opposite effect on performance by preventing the formation of fully hydrodynamic sliding. This investigation focuses on designs that combine hexagons with triangular cross sections and truly 3D dimples, which has not been studied earlier.
2.1 Texture Design.
Figure 1 shows the surface texture design consisting of dimples and grooves arranged in elongated hexagon shapes, the details of which are described later in this article. The grooves that are parallel to the sliding direction are denoted as the parallel sliding grooves (of length t). The grooves that are at an angle to the sliding direction are denoted as the crossing grooves (of length ℓ). Elongated hexagons (also called elongated rhombi, a subset of parallelogons) have uncoupled internal radius, r, and parallel sliding grove length, t. The angle between the crossing grooves is denoted θ. The angle between the crossing grooves and the parallel sliding grooves is denoted ϕ. The groove depth is denoted d, and the groove width is denoted w. If the groove is assumed to have a simple triangular cross section, the remaining groove geometry is easily derived.
Six dimples were placed at each corner of the parent hexagon. The dimple is modeled as a regular spherical cap with depth h and radius a. The angle of the tangent between the top of the parent hexagon and the dimple (α, also called the angle of approach) is approximately to reduce lubricant turbulence effects. The dimple depth is selected based on the geometrical constraints of the angle of approach and the radius of the dimples. This yields a depth of approximately 11.5 μm, which is similar to other dimple depths in the literature . For stability during printing and testing, a base of height b was extruded from the bottom of the parent hexagon such that the total height of the structure was at least 5 μm below the bottom of the dimple (b = 5 μm). Thicker bases required a longer fabrication time.
The use of sliding grooves to reduce friction is well studied [13,43]. However, if the grooves are oriented parallel to the sliding direction, they can increase friction instead . Therefore, the angle of the crossing groove to the sliding direction plays a role in the final frictional response. The crossing grooves are necessary to ensure the distribution of lubricant across the surface , and the elongated hexagon addresses these factors nicely.
In this study, three key texture parameters, d, w, and t, were varied, while other parameters were fixed as presented in Table 1. Table 2 describes the texture parameters that were tuned by varying the three key parameters, referencing literature values [34,35]. This table also shows the density of voids ρT and the void volume (normalized to the measurement area) Vvv, which are functions of w, t, r, and θ. The root-mean-square surface roughness of the samples Sq was also measured from a 250 μm × 250 μm area to maintain measurement consistency between samples; the textures repeat across the surface and a full unit cell for analysis is contained in an area of this size. The valley fluid retention index is calculated as Svi = Vvv/Sq and can be helpful for comparing the relative ability of two surfaces to retain lubricant during operation [44–46]. The designed surfaces all show a higher Svi than the measured liner, indicating that they have a higher potential for lubricant retention (Table 2).
The surface topography was designed in modeling computer-aided design software. In total, 13 surface textures were fabricated. Nine were based on combinations of the groove and dimple system illustrated in Fig. 1, two were dimpled surfaces without grooves but arranged in similar hexagonal layouts, one was an idealized honed surface based on parameters observed in the plateau-honed cylinder bore surfaces, equivalent to the groove and dimple system where a = 0, , and t = 0, and the last was a scanned replica of a piston liner surface. To create the piston liner replica, a high-resolution laser confocal scanning microscope was used to encode the surface height data of a 200 μm × 200 μm area of the plateau-honed cylinder bore. A tiling process was then applied to these data so that an area larger than the scanned portion could be fabricated . The transformed data were then converted to a printable file.
2.2 Surface Fabrication and Characterization.
The designed surfaces were printed using a 3D nanoprinter, which uses the two-photon lithography technique to print at high resolutions in three dimensions. Two-photon lithography is a fabrication technique whereby a laser polymerizes a UV-sensitive polymer at discrete points called voxels, allowing fabrication of high resolutions (140 nm) and truly three-dimensional textures [48,49]. After printing the textures in IP-S photoresist, polydimethylsiloxane (PDMS) molds were created and used to transfer each texture into IP-Dip photoresist. IP-S photoresist was used for the initial fabrication step because it contains a smoothing agent to eliminate rasterization effects. IP-dip (hardness: 152 MPa, ) was used for the PDMS molding step to replicate the texture with a high resolution.
Atomic layer deposition (ALD) was used to coat the surfaces with a 150 nm-thick layer of zinc oxide (ZnO). The ZnO ALD coating was deposited at 150 °C using diethylzinc (DEZ) and deionized H2O as precursors. Previously, it was demonstrated that the ZnO ALD could achieve a high growth rate of 2.6 Å/cycle at 150 °C with good crystallinity . The ZnO ALD was performed in a custom viscous flow, hot-walled ALD chamber. Before the deposition, the designed surfaces were first preheated in the chamber. Then, the precursors were alternatively dosed into the chamber. During the ALD process, a constant 20 sccm flow of ultrahigh purity (99.999%) Ar was used as the carrier gas. The ZnO ALD was performed with the following timing, 0.015 s–10 s–0.015 s–10 s, corresponding to the DEZ dosing, the first Ar purge, the H2O dosing, and the second Ar purge, respectively. The ZnO coating (hardness: 9 GPa, ) is expected to provide wear resistance and friction reduction for the softer polymer . As reported in the study by Cai et al., the deposited ZnO films are highly crystalline with a hexagonal wurtzite structure . High-resolution scanning electron microscope images of the surfaces before friction testing were captured. A scanning confocal laser microscope was used to acquire the 3D profiles of the surfaces before and after friction testing to determine if wear had occurred.
A replicated copy of an original liner surface (Sq = 279 nm) was also tested to provide a reference value using the same materials and conditions as the other textured surfaces. A plateau honed cylinder liner was imaged using a scanning confocal laser microscope with extra-long working distance 100 × objective to prevent collision with the curved surface during scanning (Fig. 8(a)). This is not a concern with the flat samples, but the 100 × objective was also used to image these surfaces for consistency. The scanning confocal laser microscope generates a high-quality heightmap of each surface that was used to mathematically derive surface parameters such as roughness and void volume.
2.3 Friction Testing.
Linear reciprocating friction tests were performed with a tribometer (Fig. 3, force resolution of 1 mN) on both ZnO-coated and uncoated (bare IP-dip) samples, textured as defined in Table 2. The stroke length was 0.5 mm, the reciprocating frequency was 3 Hz with 3 mm/s linear velocity, and the vertical contact force was 1 N (Fig. 2). SAE 5W-20 GF-5 oil was used as a lubricant (approximately 0.5 mL, following Ref. ) at room temperature (kinematic viscosity ν ∼ 99.63 cSt). The total testing time was 900 s or 2700 cycles. The reciprocating counterface was a section of a nitrided steel piston ring (Sq = 180 nm, hardness: 1170 HV). Figure 2 shows a diagram of the system setup. The piston ring had a thickness of 1.15 mm and an outer diameter of 92.5 mm. At least three separate tests were performed on different samples with each texture.
During testing, it was discovered that a normal load of 2 N and reciprocating frequency of 5 Hz resulted in destructive wear (the w2d2t50 ZnO sample tested was completely worn away down to the glass substrate), a clear indication of boundary lubrication. Based on the Hamrock–Dowson equation, the sliding velocity would need to be several orders of magnitude higher to reach the mixed lubrication regime [55,56]. A lower load of 1 N and reciprocating frequency of 3 Hz were selected to prevent destructive wear, understanding that the system will remain in the boundary lubrication regime, regardless of the lubricant temperature. The polymer textures proved to be quite fragile under higher load and longer test conditions. Since the system would remain in the boundary lubrication condition regardless of testing temperature and the polymer could only withstand up to about 100 °C, the tests are conducted at room temperature. Therefore, a shorter time was selected to acquire a friction analysis of the textures while avoiding destructive wear, approximately 2700 cycles. The testing conditions in this study are not intended to model the piston–liner interface directly. Rather, the techniques presented herein are intended to show a new method for testing complex surface textures and comparing them to existing liner texturing using replication. In this way, the plateau-honed structures on the liner surface can be compared to 3D printed structures in a different material.
3 Results and Discussion
Figures 4 and 5 show optical images of selected surfaces, captured with a laser scanning confocal microscope using a 20 × objective. The arrows indicate the direction of sliding, and the white box outlines indicate dimples chosen for higher magnification examination in Figs. 6 and 7. In addition, Figs. 6 and 7 are marked with dashed lines to aid in visualizing the dimple and groove system. The replicated liner surface heightmap is shown in Fig. 8. Plateau-honed piston liners do not have consistent groove dimensions, as the honing process introduces a significant amount of randomness into the surface, such that no area of the liner is exactly like another. The 3D printed surfaces, on the other hand, have a consistent and repeatable surface texture. Figures 9 and 10 show images of the selected surfaces after testing. Because the printed photopolymer is significantly weakened by posttest cleaning solvents (such as acetone), a substantial amount of oil can still be seen on the surface of textures (particularly Figs. 9(b) and 10(b)). The presence of the remaining oil makes quantitative analysis of the relative height of the structures difficult. Very little wear is observed, likely due to the low load and lubrication conditions. However, a comparison of these figures with Fig. 9(c) shows that one texture, w15d10t150, did in fact experience some optically visible wear. These wear lines are consistent with the removal of the top layer of photoresist, which is printed layer by layer. This texture was one of the worst frictional performers (Fig. 11(a)). This demonstrates that the ring-sample contact covered several textures at once (thus more adequately approaching the conformal nature of true ring-cylinder contact) with a contact area of approximately 70 μm × 600 μm, so the effect of the hexagonal texture is shown not to be isolated to a single feature.
Figure 12(a) compares the average coefficient of friction for all types of textured surfaces, both coated and uncoated combined, versus the average coefficient of friction of the flat, untextured control, both coated and uncoated combined. Figure 12(a) shows that, overall, the textured surfaces (average μ = 0.28) showed a statistically significant, reduced coefficient of friction compared to a flat surface (average μ = 0.32, confidence interval CI = 0.95).
Figure 12(b) shows the comparison of the coefficient of friction for flat and textured surfaces with and without ZnO coatings, demonstrating that although the ZnO-coated textures have a slightly lower average, there are no statistically significant differences between the coated and the uncoated textured surfaces or the coated and uncoated flat surfaces (CI = 0.95).
Figure 11 shows the averaged coefficient of friction of all sample types, with both coated and uncoated surfaces combined within each sample type. Almost all tested textures showed a statistically significant reduction (an average of 18%) in the coefficient of friction when compared to the flat, untextured surfaces (CI = 0.95), except for the w0d0t50, w2d7t50, and w2d2t150 textures. The coefficient of friction of the “ideal” plateau-honed texture (w10d2t0) outperformed some hexagonal textures. The w0d0t150 texture, with dimples only, showed a higher coefficient of friction compared to the replicated piston texture, demonstrating that the presence of grooves to connect these dimples can further reduce the coefficient of friction. The w10d2t150 texture demonstrated an average of 22% reduction in the coefficient of friction compared to the flat surface, with one of the samples achieving 39% of reduction. It also significantly outperformed the replicated plateau-honed cylinder liner surface by a notable 10% (CI = 0.95).
The intercept term μ0 is not fixed at zero because friction is still present when d = w = t = 0. The following samples are excluded from the model: w10d2t0, because it contains additional modifications (the lack of dimples and a different crossing angle); and w15d10t150, because only one w = 15 sample was tested to explore the model’s geometrical limits.
Table 3 presents the parameters estimated by the linear factorial model according to a least-squares approach (R2 = 0.80, Fig. 13). The most significant parameters contributing to friction are the groove depth d and groove width w. Higher values of w and lower values of d lead to lower values of friction. Figure 13 shows a plot of predicted values of the coefficient of friction versus the actual measured values: it can be seen that the surfaces with the highest tested width (10 μm) and lowest tested depth (2 μm) performed the best, while the smallest tested width (2 μm) performed the worst. The frictional response is therefore dominated by the parameters that control the cross-sectional profile of the texture in the direction of sliding. At these sample space extremes, the sliding groove length t did not have much of an effect. The most influential parameters were related to the cross-sectional area in the direction of sliding (d, w, wd) and not the cross-sectional area in the transverse direction (t). Since the lubrication was in the boundary regime, the contribution of the converging gap and the resultant hydrodynamic lift is negligible. This left only the contribution of the lubricant directly underneath the contact, which is governed by the cross-sectional area, wd/2, most likely from lubricant storage and recycling. Literature reports that lubricant recycling is an effect of deeper grooves, not shallower (as the model indicates). However, a shallow groove can be beneficial at lower speeds because it can support a thicker film [28,57]. Given the experimental test conditions, it follows that a wide groove (allowing more lubricant) and a shallow groove (allowing a thicker film) would provide a better frictional response, and it is indeed the case. The surface void volume Vvv, surface roughness Sq, and density of textures ρT did not correlate well with the coefficient of friction. Void volume Vvv is a good indicator of how much lubricant can be stored in the surface below the contacting plane. In general, as the void volume increases, the coefficient of friction first decreases and then increases as the optimum lubricant volume is surpassed . Figure 14 shows the material bearing curve for the w15d10t150 sample with the void volume highlighted.
An additional metric, the maximum theoretical lubricant volume (Vtl) is helpful to understand the frictional behavior of different textures. Figures 15(a) and 15(b) show the cross-sectional area of the w10d7t150 and w2d2t50 textures, respectively, at each point in the sliding direction. Blueprints of the textures are added to help visualize the shape of the cross-sectional area (the shaded area) at each point in the sliding direction. Although the w10d7t150 texture had the largest designed cross-sectional groove area, it had an uneven distribution of the cross-sectional area along the sliding direction with some excessively large cross-sectional areas that could lead to lubricant starvation if there is not enough supply (Fig. 15(a)). Conversely, the shorter sliding grooves of the w2d2t50 texture ensured that the cross-sectional area varied much more consistently along the sliding direction with lubricant supply close to the interface (Fig. 15(b)). The discrete cross-sectional area is the largest in the region occupied by the crossing grooves (Fig. 15(a)). Vtl is then derived by sliding the piston ring face along the cross-sectional area curve, calculating the area under the curve at each point (shown as a shaded area in Fig. 15). The contact width in the sliding direction was taken to be 70 μm and the contact width in the transverse direction was taken to be 600 μm, based on examination of the wear scar from the w15d10t150 sample (Fig. 9(c)). This yields the total volume of the available space between the curved ring surface and the texture at each position of the piston ring, which may theoretically be filled by lubricant if there is enough lubricant supply.
Figure 16(a) shows the Vtl curves for the best-performing textures: w10d2t150 and w10d2t50, and Fig. 16(b) shows the Vtl curves for the worst-performing samples: w2d7t50 and w2d2t150. There are two main effects that act to increase friction in these samples. The first is the meniscus effect, which dominates where the lubricant volume (Vtl) is low. This can be observed by comparing w10d2t150 in Fig. 16(a) and w2d2t150 in Fig. 16(b). The w2d2t150 texture has a large sustained region of very low Vtl, as well as a very narrow groove width (Fig. 4(a)), allowing the meniscus force to dominate. Similarly, the w10d2t150 texture also has a sustained minimum Vtl, but it is much higher due to the larger groove width (Fig. 4(b)). The second is the lubricant starvation effect due to a very large theoretical Vtl, which may not be able to be fully filled with lubricant during operation. The best performing samples, w10d2t150 and w10d2t50, have a wide and shallow groove. This combination results in a Vtl that is not too high, like the wide and deep groove samples (w10d7t50 and w10d7t150) but is also distributed close to the interface. The importance of the wide groove is stressed by comparison of the Vtl curves of w10d2t50 (Fig. 16(a)) and w2d7t50 (Fig. 16(b)): the shapes of the two curves are very similar, but the narrow groove in w2d7t50 (only 2 μm wide, as shown in Fig. 4(a)) does not support a good lubricant supply and could also lead to high meniscus force, and so the benefit of the optimal Vtl was not realized. The wear on the w15d10t150 sample supports the hypothesis that a texture with a very large Vtl may not be able to be completely filled during operation, particularly under boundary lubrication conditions. This lubricant starvation contributes to higher friction compared to a texture with an optimized Vtl and results in the wear shown in Fig. 9(c).
Novel fabrication and testing methods were developed and used to efficiently compare novel, 3D bioinspired surface texture designs to existing piston liner surface topography. 3D printing using two-photon lithography enables quick fabrication of various surface 3D textures that cannot be easily accomplished by other techniques. The present investigation explored the effectiveness of surface materials and textures consisting of straight grooves and dimples on reducing the coefficient of friction. A few conclusions can be drawn from this investigation.
The surface textures resulted in a statistically significant reduction in the coefficient of friction at a low feature density under boundary lubrication conditions. Textured surfaces reduced the coefficient of friction by an average of 18% compared to flat surfaces. The highest performing texture, w10d2t150, reduced the coefficient of friction by an average of 22% with a maximum reduction of 39%. The w10d2t150 texture also outperformed a replicated plateau-honed cylinder liner surface by 10% without optimization, showing the great potential of this novel bioinspired texture design. The coating material was found to play little role in determining the textured surface performance. Therefore, the two-photon lithography fabrication technique and the testing methods presented here provide an efficient and versatile tool for texture optimization to achieve higher friction reduction.
Funding for this research was provided by the Ford Motor Company and the National Science Foundation (Grant No. OIA-1457888) from the Center for Advanced Surface Engineering, the Arkansas EPSCoR Program, ASSET III.
Conflict of Interest
There are no conflicts of interest.
- a =
- b =
- d =
- h =
- r =
hexagon internal radius
- w =
- t =
sliding groove length
- A =
discrete cross-sectional area
- Vtl =
theoretical lubricant volume
- α =
dimple approach angle
- θ =
- μ =
coefficient of friction
- ϕ =