Biosurface and Biotribology 1 (2015) 270–277
Numerical study of surface texturing for improving tribological properties
of ultra-high molecular weight polyethylene
Y.L. Zhang
a,b,n, X.G. Zhang
b, G. Matsoukas
b aSchool of Mechanical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
b
School of Mechanical & Manufacturing Engineering, UNSW, NSW 2052, Sydney, Australia
Received 3 July 2015; received in revised form 20 November 2015; accepted 23 November 2015
Abstract
Ultra-high molecular weight polyethylene (UHMWPE) has been used in total joint arthroplasty for over 50 years. Conventionally, smooth UHMWPE surfaces are used for total joint replacements; however, smooth surface contacts have been shown to be inadequate in friction reduction and/or anti-wear. More recently, micro-textured surfaces have been investigated for reduction of the friction and wear of two contact interfaces. Unfortunately, the tribological behavior of textured UHMWPE surfaces requires further research to understand its tribological behavior. A numerical model is presented to understand the potential use of specially textured surfaces to improve the tribological properties of UHMWPE. A two dimensional, transient form of Reynolds equation was used to model the lubrication condition of the textured surfaces. The effects of area densities and pore depths over varying diameters were examined for several textured geometries including circle, rectangle, square and triangle. The simulation results show that the surface texturing can effectively be used to enhance hydrodynamic effects. More specifically, it was shown that the rectangular surface texture displayed superior characteristics over the other geometries investigated. The results provide a theoretical reference for the tribological design of surface texture on UHMWPE.
&2015 Southwest Jiaotong University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:Surface texturing; Hydrodynamic lubrication; Friction; UHMWPE
1. Introduction
Owing to its low cost, self-lubrication ability, excellent biocompatibility and high wear and impact resistance, UHMWPE has been widely used for the artificial joint prosthetics as well as other industrial applications since the 1960s [1]. However, tribological problems associated with micron and submicron sized wear particles of the material are a major obstacle that limits its service life in industrial and orthopedic applications [2–4].
Various methods, including inorganic filling (such as hydroxyapatite [5,6], zirconium oxide [7,8] and carbon black
[9–11]), cross-linking [12,13] and surface texturing [14–16] have been employed to enhance the tribological properties of UHMWPE. Among these, surface texturing has recently gained the research interest of triobologists. Designing special function orientated surface textures, such as micro-groove, micro-dimple and micro-convex geometries fabricated on contact surfaces, has been considered as a viable method to improve the tribological properties of mechanical components [17–19]. Surface texturing plays an increasingly important role as it can directly influence the friction and wear behaviors of contact surfaces in many ways. Firstly, micro-textures can improve the load-carrying capacity of the lubricant film through the enhanced hydrodynamic effect generated by the lubricants stored in the micro-textures[20–22]. Secondly, the lubricants stored in the micro-textures can provide increased space for extra lubricants which also improve the lubrication www.elsevier.com/locate/bsbt
http://dx.doi.org/10.1016/j.bsbt.2015.11.003
2405-4518/&2015 Southwest Jiaotong University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
nCorresponding author at: School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China.
E-mail address:[email protected](Y.L. Zhang).
condition [23]. Thirdly, wear debris can be captured by the micro-textures, which reduces abrasive wear between contact surfaces[16].
As the lubrication condition shifts to hydrodynamic lubrica-tion, the roles of lubricant pressure and load-carrying capacity of lubricantfilm formed by surface texturing become important [24]. Many researchers have investigated the effects of geometric parameters of textures, such as area densities and pore depths and diameters, on the lubricant pressure and loading capacity [25–28]. Ronen et al. [29] developed a simulation model to investigate influences of the aforemen-tioned variables on friction forces and found that a change in the area densities, in the range between 5% and 20%, affected the friction forces by less than 7%. An optimum value of the pore depth over diameter ratio was found, which varied between 0.1 and 0.18. A one-dimensional numerical model was used by Tomandik [30] to simulate effects of surface textures which considered both the full and partial texturing. The results indicated that micro-dimples were able to generate a significant hydrodynamic effect which improved its perfor-mance characteristics. In particular, partial laser surface texturing improved the friction and wear of hydrodynamic support near top dead center and at middle stroke by 50% and 90% respectively. However, existing simulations have not considered the effects of pore patterns, such as circle, square, rectangle and triangle on the tribological properties.
Experimental researches also confirm that tribological prop-erties of contact surfaces can be improved by selecting a propriety surface texturing. Kustandi et al. [31] fabricated nano-textures on the surface of UHMWPE by nano-imprint lithography whereby friction and wear tests were conducted in a sliding condition. They found that the textured UHMWPE surface had a reduction of friction coefficient between 8% and 35% compared with the non-textured surface. Reciprocating wear tests were carried out and the results showed that the textured UHMWPE surface resulted in a lower wear depth and width in comparison to the non-textured surface. Zhang et al. [14,32] adopted the micro-imprint lithography technology to fabricate the UHMWPE surfaces. The tests were performed under a lubricated condition using distilled water at room temperature. The optimized area density of the textured UHMWPE surfaces was found range from 22.9% to 29.9%. The textured UHMWPE also presented a significant improve-ment to the total wear resistance. The average wear depth of the textured UHMWPE showed a 35.5% improvement than that of the non-textured system. All the results mentioned above demonstrate that texturing on the UHMWPE surface can significantly improve its tribological properties. However, similar to the current numerical simulations, the existing experimental studies have only investigated circle geometry dimples on the surface. There is a lack of data on effects of UHMWPE surfaces with other texture patterns. Therefore, numerical simulations have been introduced to further under-stand the overall improvement of tribological properties over a various range of contact geometries and texture patterns.
In this paper, a simulation model is presented to study the potential use of micro structures with different patterns to
improve the tribological properties of UHMWPE. The work was intended to investigate effects of UHMWPE surfaces with circle, square, rectangle and triangle patterns onfilm thickness and friction force. The effects of dimple parameters such as area density and depth are also investigated to obtain an optimal outcome in terms of a maximal film thickness and minimal friction force.
2. Analytical method
A two-dimensional lubrication model illustrated in Fig. 1 was developed to study the lubrication and friction perfor-mance of contact surfaces with consideration of effects of surface textures on the UHMWPE surfaces. The objective of the model is to predict the friction force obtained using different textured shapes of the UHMWPE surfaces to opti-mize their performances.
2.1. Textured shape and geometry
Fig. 1 shows a schematic of the model where the micro-textures were presented on the UHMWPE surface.
Four different shape including a circle, square, rectangle and triangle were chosen to study the optimum geometries for the maximum hydrodynamic effect and minimal friction force under the specific operation conditions. The geometrical parameters of the textured surfaces are presented in Fig. 2 and Table 1. The dimples were uniformly distributed with a base depth hd. Each dimple is located in the center of an
imaginary square area of ll. The dimple area density and dimple depth over diameter ratio are the two key parameters
CoCr UHMWPE Fa c(t) u
F
hFig. 1. Simple model of CoCr pin and UHMWPE slider.
Circle Square Rectangle Triangle
l d d l d l l 2d d x z c d l l l h hd x y
for the surface texturing. They are defined as sc¼π d2 4l2 ; ss¼ d2 l2; sr¼ 2d2 l2 ; st¼ ffiffiffi 3 p d2 4l2 ð1Þ δ¼hd l ð2Þ 2.2. Governing equations 2.2.1. Motion equation
The equations of motion for a slider–crank mechanism as seenFig. 3were adopted, which converts rotary to reciprocat-ing motion on a crank free to rotate 360 degrees. When the crank and connecting rod were extended in a straight line and the slider was at its maximum distance to the center of rotation of the crank, the crank angleθ is 0 degrees. When the crank rotated from 0 to 180 degrees, the connecting rod pulled the slider towards to the left. When the crank rotated from 180 to 360 degrees, the connecting rod pushed the slider towards to the right, causing the slider to reciprocate. The relationship between the sliding speed u and the crank angle θ can be described by Eq. (3) [33]. u¼rcωsinθ 1þ cos θ lr rc 2 sin2θ " #1 2 8 < : 9 = ; ð3Þ
where rc is the radius of the crank, lr is the length of the
connecting rod, andωis the rotating velocity of crank.
2.2.2. Reynolds equation
The hydrodynamic pressure distribution and thefilm thick-ness distribution (local clearance between contact surfaces) are governed by the two-dimensional incompressible Newtonian Reynolds equation[34], which is presented as
∂ ∂x h 3∂p ∂x þ ∂ ∂z h 3∂p ∂z ¼6μu∂h ∂xþ12μ ∂h ∂t ð4Þ
whereby, x and z are lateral and longitudinal direction in Cartesian coordinates, respectively, p is the hydrodynamic pressure, h is the film thickness, μ is the dynamic viscosity, andu is the sliding velocity.
In order to facilitate the analysis, the following non-dimensional expressions are introduced:
X¼ x lr; Z¼ z lr; P¼ p p0; H¼ h lr; U¼ u rcω; T¼ t T0; FaðtÞ ¼ FaðtÞ p0A ; FfðtÞ ¼ FfðtÞ p0A ð5Þ In which X andY denote the non-dimensional coordinates.
P, H, U and T denote the non-dimensional pressure, film thickness, viscosity and time, respectively. Further, the nor-malizing pressurep0is the atmospheric pressure andA is the
contact area. Fa is external force acting on the stationary specimen. Ff is the instantaneous friction force. Substituting Eq.(5)into Eq.(4), the formulation of the Reynolds equation in its non-dimensional form is obtained as:
∂ ∂X H 3∂P ∂X þ∂∂ Z H 3∂P ∂Z ¼ε1∂ H ∂X þε2 ∂H ∂T ð6Þ
where the non-dimensional parameterε1 and ε2 are given as:
ε1¼ 6up0 lr ð7Þ ε2¼ 12p0 T0 ð 8Þ The mating surfaces were assumed to be nominally parallel about x axis. The end effects in the z direction were also neglected here. The pressure distribution over each long-itudinal pores column is the same, repeating itself in the z
direction. Therefore, it is sufficient to consider only one pores column.
2.2.3. Boundary conditions
The Reynolds boundary conditions were used to solve the loading capacity of the lubricating film. The following boundary conditions (Fig. 4and Eq. (9)) were applied to the Reynolds equation[35]. pðz;x¼0Þ ¼pb; pðz;x¼LrÞ ¼pt ∂p ∂zðz¼ r1;xÞ ¼∂p ∂zðz¼r1;xÞ ¼0 ð9Þ Table 1
Parameters on the textured UHMWPE surface.
Symbol Definition Symbol Definition
hd Dimple depth d Diameter or side length
l Dimple pitch δ Depth over diameter
sc Area density of circular shape ss Area density of squared shape
sr Area density of rectangular shape
st Area density of triangular shape
θ
Slider Crank
Connecting rod
Fig. 3. Slider-crank mechanism.
z x pb x=0 x=l p(x, r1) p(x, -r1) pt
Fig. 4. Geometrical model of the textured UHMWPE surface with boundary conditions.
2.2.4. Load balance equation
Numerical solutions are obtained under given load condi-tions, so thefinal pressure distribution should comply with the
load balance condition listed as Eq.(10):
Fa∬pdxdz¼0 ð10Þ
whereby, Fa is external force acting on the stationary specimen.
Using Eq.(5), the friction force in its non-dimensional form becomes:
Fa∬PdXdZ¼0 ð11Þ
2.2.5. Friction force equation
The instantaneous friction force due to shear stresses in the fluidfilm during the reciprocation was calculated from Eq.(12) below [35]: FfðtÞ ¼∬τdxdz¼∬ 1 2 ∂p ∂xhþη u h dxdz ð12Þ Using Eq.(5), the friction force in its non-dimensional form becomes: FfðtÞ ¼∬ l2r 2AH ∂P ∂Xþ ηulr p0AH dXdZ ð13Þ 2.3. Solving equations
Thefinite difference method was applied to obtain simulta-neous treatment of the Reynolds equation. A non-uniform and refined grid structure was applied in the region of the pores. A successive over-relaxation iteration method was used to achieve this whereas the convergence criterion is limited to an error of 0.0001 as deduced in Eq. (14). A step by step analysis of the solution scheme is presented in Fig. 5.
Error¼PiPjHi;jH 0 i;j P i P jHi;jo0:0001 ð 14Þ Fig. 5. Flowchart demonstrating the numerical procedure.
Fig. 6. Pressure distribution of squared texture whenθis 2701,δis 0.12,ssis 20%, anddis 80mm.
3. Results and discussion
The film thickness and friction force are suitable measures of the effectiveness of the surface texture [36]. An extensive parametric investigation was performed to find the optimum values that maximize the film thickness and minimize the friction force. As a result the parametric analysis was able to determine the optimum textured geometry, area density and dimple depth of the UHMWPE surfaces.
3.1. Pressure distributions
Generally, the pressure distribution between two nominally parallel smooth surfaces is zero when the input pressure equals the output pressure. However, different surface textures have proven to affect the overall pressure distribution. Consider a typical case consisting of crank angle θ¼2701, depth over diameter δ¼0.12, area density ss¼20% and d¼80mm. The
pressure distributions on the surface with square shaped textures as shown inFig. 6demonstrates that the pressure distributions were affected significantly by the new surface texture geometry. Take thefirst dimple inFig. 6as an example, along the moving direction the pressure decreased in thefirst part of half-dimple to a minimum value and then increased abruptly to a maximum value. It was shown that the pressure was lower at the entrance of the dimple and higher towards the exit. Hence, it was deduced that the pressure decreased when the lubricant flowed from a small region to a large region. As a result of the lubricant
flowing from a larger area to a smaller area, a wedge effect was observed that led to an increase in the pressure near the output, which increases the load capacity of the lubricants. However, it is impossible for hydrodynamic lubricatingfilm to exist between smooth surfaces without textures.
3.2. Area density
The variations of the dimensionless average film thickness and friction with the area densities are shown inFig. 7. It can be seen that the dimensionless averagefilm thickness initially increased and friction decreased with increasing of area densities. However, as the area density ratio continued to increase a reversal was observed whereby the dimensionless averagefilm thickness decreased and friction increased for all the textures evaluated. As a result, the optimal area density was found to be in the range of 12% to 36%. More particularly, the tribological properties were superior when the area densities were 26%, 17%, 20% and 21% for the circular, rectangular, squared and triangular shaped textures respectively. Addition-ally, as show in Table 2, the dimensionless average friction also reduced by 10.1%, 18.1%, 18.6% and 15.4%, respec-tively. A possible explanation may be that increasing area density can increase the average film thickness with the reduction of the fluid friction force. For the squared texture shown in Fig. 7, when the area densities were between 20% and 40%, the dimensionless averagefilm thickness and friction had no obvious change. The results revealed that the tribolo-gical property was superior when the area density was closest to 20% making the squared texture the optimum geometry.
3.3. Pore radius
The variations of the dimensionless average film thickness and friction with the pore radii are shown in Fig. 8. The optimal area densities previously calculated were now chosen to obtain the optimal radius for each shape as shown inTable Table 2
The results of optimal area densities.
Type Radius (μm) Depth (μm) Optimal area density (%)
Circle 40 9.6 26
Rectangle 40 9.6 17
Square 40 9.6 20
Triangle 40 9.6 21
3. When the radius was between 65μm and 90μm, the dimensionlessfilm thickness and friction force had no obvious change for the circular texture. The results revealed that the tribological property was superior when the radius was closest to 65μm. Similarly for the other shapes, the tribological property was superior when the radius was closest to 40μm, 50μm and 65μm for the rectangular, squared and triangular textures, respectively.
Additionally, the dimensionless average friction reduced by 13.1%, 12.5%, 17.0% and 17.4%, respectively, when the radius changed from 20μm to 100μm. This is attributed to the fact that when the area density and depth arefixed, there is difficulty in generating hydrodynamic loading capacity with small radii. The radii cannot be too large as this increases the surface roughness increasing friction.
3.4. Pore depth
The influence of the pore depth on average film thickness and friction was also investigated. The optimal area densities and radius previously calculated were now chosen to obtain the optimal depth for each shape as shown inTable 4. As shown in Fig. 9, for the circular and triangular textures, the averagefilm thickness increased and friction decreased with the increasing of hd when the pore depth was below 9.6μm. On the other
hand, the average film thickness increased and friction
decreased as hd increased beyond 9.6μm. Similarly, the
average film thickness increased and friction decreased with the increasing ofhdwhen the pore depth was below 7.2μm for the squared and rectangular textures. Whereas, the averagefilm thickness increased and friction decreased with the increasing of hdbeyond 7.2μm.
One possible explanation is that when the pore depth is too shallow i.e. less than 4.8μm, there is insufficient lubricant to form the requiredfluidfilm for a hydrodynamic lubrication and the wedge effect is not obvious. A vortex sheet may exist at the bottom of the oilfilm when the pore depth is too large (greater than 14.4μm), which affects the load-bearing capacity of oil film.
3.5. Rotating speeds
The variations of the dimensionless average film thickness and friction with alterations of speed were also studied. As can be seen in Fig. 10, the dimensionless average film thickness increased and friction decreased with the increasing of speed using the optimal area density, radius and depth for all the four shapes. This is because the hydrodynamic effects are enhanced in high speed. Therefore, it may be concluded that particular surface textures can improve the tribological performance of the interface at a relatively high speeds. Squared textures
Table 3
The results of optimal radius.
Type Optimal area density (%) Depth (μm) Optimal radius (μm)
Circle 26 9.6 55
Rectangle 17 9.6 40
Square 20 9.6 50
Triangle 21 9.6 55
Fig. 9. Effects of the pore depth on (a) the dimensionless averagefilm thickness and (b) friction force. Table 4
The results of optimal depth. Type Optimal area density
(%) Optimal radius (μm) Optimal depth (μm) Circle 26 55 9.6 Rectangle 17 40 7.2 Square 20 50 7.2 Triangle 21 55 9.6
presented significantly lower friction compared with the other three textures.
According to the results provided in Fig. 10, it was found that optimized circular shaped texture with area density 26%, pore depth 9.6μm and pore radius 55μm achieved significant friction reduction. Similar results are found for the circular shaped texture have been validated by Etsion [37], where optimized circular dimples at area density 25%, depth 8μm and radius 50μm were also obtained. Similarly, optimized rectangular shaped texture parameters consisted of an area density of 17%, pore depth of 7.2μm and pore radius of 40μm. Optimal parameters for the triangular shaped texture consisted of an area density of 21%, pore depth of 9.6μm and pore radius of 55μm. Lastly, optimal parameters for the squared shaped texture consisted of an area density of 20%, pore depth of 7.2μm and pore radius of 50μm, which has also shown to have a superior tribogical performance over all the above mentioned textures.
4. Conclusions
In this paper, the lubrication and friction behavior of contact between CoCr pins and surface textured UHMWPE disks was analyzed. Four texture patterns were investigated using the above mentioned model to study which texture pattern gave superior tribological properties in terms of the film thickness and friction force. The geometries of different dimple shapes which included the circle, rectangle, square and triangle were optimized in terms of load-carrying capacity and friction reduction. The range of hd, d and area density used in the
simulations are shown inTable 5. From the present investiga-tion, the following conclusions have been drawn:
1. The area density, dimple radius and depth have an obvious influence on the load-carrying capacity. For each of the dimple shapes considered, the optimum geometries were found to be in the range of 40odo90μm, 4.8ohdo14.4
μm and 12%oarea densityo36%.
2. Under the condition of having optimum area density, radius and depth for each individual geometry, the rectangular texture was found to provide the maximum load-carrying capacity of all shapes considered in this study. The optimum geometries identified in this study were found to be Ss¼20%, d¼50μm and hd ¼7.2μm.
3. When the speed increased from 100 rpm to 300 rpm, the dimensionless average film thickness for the circular, rectangular, squared and triangular shapes increased 8.3%, 9.0%, 8.5% and 7.7% respectively, and the dimen-sionless average friction decreased 8.1%, 8.5%, 7.9% and 7.3%, respectively. The results indicated that it is bene-ficial to increase the load-carrying capacity under high speed.
The theoretical model developed in this study analyzed a homogenous surface texture consisting of a single geome-trical pattern without cavitation conditions. Further studies will aim to consider surfaces incorporating complex textures consisting of several shapes working in unison. For the convenience of comparison with existing numerical and experimental results, the current model is assumed under reciprocating motion. The real loading conditions will be considered in future models.
Acknowledgments
This work was supported by China Postdoctoral Science Foundation funded project (Grant no. 201003672).
Fig. 10. Effects of the speed on (a) the dimensionless averagefilm thickness and (b) friction force.
Table 5
Geometrical parameters of the patterns.
Dimples depthhd(μm) 2.4, 4.8, 9.6, 12.0, 14.4, 16.8, 19.2, 21.6, 24.0 Dimples diameterd (μm) 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200 Area density (%) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
References
[1]D. Dowson, et al., Influence of counter face topography on the wear of ultra high molecular weight polyethylene under wet or dry conditions, J. Am. Chem. Soc. 12 (1985) 171–187.
[2]N. Mohamad Raffi, V. Srinivasan, A study on wear behavior of γ -UHMWPE sliding against 316L stainless steel counter face, Wear 306 (1–2) (2013) 22–26.
[3]V. Saikko, V. Vuorinen, H. Revitzer, Analysis of UHMWPE wear particles produced in the simulation of hip and knee wear mechanisms with the RandomPOD system, Biotribology (2015) 30–34.
[4]D. Choudhury, et al., Tribological investigation of ultra-high molecular weight polyethylene against advanced ceramic surfaces in total hip joint replacement, Proc. Inst. Mech. Eng. J: J. Eng. Tribol. 229 (4) (2015) 410–419.
[5]H.S. Jaggi, et al., Morphological correlations to mechanical performance of hydroxyapatite‐filled HDPE/UHMWPE composites, J. Appl. Polym. Sci. 132 (1) (2015).
[6]S.A. Mirsalehi, et al., Nanomechanical and tribological behavior of hydroxyapatite reinforced ultrahigh molecular weight polyethylene nano-composites for biomedical applications, J. Appl. Polym. Sci. 132 (23) (2015).
[7]J.D. DesJardins, B. Burnikel, M. LaBerge, UHMWPE wear against roughened oxidized zirconium and CoCr femoral knee components during force-controlled simulation, Wear 264 (3–4) (2008) 245–256. [8]K. Plumlee, C.J. Schwartz, Improved wear resistance of orthopaedic
UHMWPE by reinforcement with zirconium particles, Wear 267 (5) (2009) 710–717.
[9]C.-x He, W.-m Ding, L.-p Shi, Friction and wear properties of carbon blackfilled ultrahigh molecular weight polyethylene composite, Tribiol-ogy 24 (5) (2004) 453–456.
[10]A.S. Alghamdi, I.A. Ashcroft, M. Song, Creep resistance of novel polyethylene/carbon black nanocomposites, Int. J. Mater. Sci. Eng. 15 (2014) 16.
[11]L.-R. Tan, et al., Factors influencing the resistivity–temperature behavior of carbon blackfilled isotactic polypropylene/high density polyethylene composites, Polym. Bull. 71 (6) (2014) 1403–1419.
[12]E. Oral, et al., Effects of simulated oxidation on the in vitro wear and mechanical properties of irradiated and melted highly crosslinked UHMWPE, J. Biomed. Mater. Res. B: Appl. Biomater. (2015) 215–223. [13]Y. Takahashi, et al., Mechanisms of plastic deformation in highly cross-linked UHMWPE for total hip components—the molecular physics viewpoint, J. Mech. Behav. Biomed. Mater. 42 (2015) 43–53. [14]B. Zhang, W. Huang, X. Wang, Biomimetic surface design for ultrahigh
molecular weight polyethylene to improve the tribological properties, Proc. Inst. Mech. Eng. J: J. Eng. Tribol. 226 (8) (2012) 705–713. [15]B. Zhang, et al., Comparison of the effects of surface texture on the
surfaces of steel and UHMWPE, Tribol. Int. 65 (0) (2013) 138–145. [16]B. Sagbas, M.N. Durakbasa, Effect of surface patterning on frictional
heating of vitamin E blended UHMWPE, Wear 303 (1–2) (2013) 313–320.
[17]A. Ramesh, et al., Friction characteristics of microtextured surfaces under mixed and hydrodynamic lubrication, Tribol. Int. 57 (2013) 170–176. [18]Z.W. Guo, et al., Study on influence of cylinder liner surface texture on
lubrication performance for cylinder liner – piston ring components, Tribol. Lett. 51 (1) (2013) 9–23.
[19] E. de la Guerra Ochoa, et al., Optimising lubricated friction coefficient by surface texturing, Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 227 (11) (2013) 2610–2619.
[20] M. Tauviqirrahman, et al., Numerical study of the load-carrying capacity of lubricated parallel sliding textured surfaces including wall slip, Tribol. Trans. 57 (1) (2014) 134–145.
[21] M. Tauviqirrahman, et al., A study of surface texturing and boundary slip on improving the load support of lubricated parallel sliding contacts, Acta Mech. 224 (2) (2013) 365–381.
[22] M. Qiu, A. Delic, B. Raeymaekers, The effect of texture shape on the load-carrying capacity of gas-lubricated parallel slider bearings, Tribol. Lett. 48 (3) (2012) 315–327.
[23] K. Li, et al., Friction and wear performance of laser peen textured surface under starved lubrication, Tribol. Int. 77 (2014) 97–105.
[24] M. Cho, H.-J. Choi, Optimization of surface texturing for contact between steel and ultrahigh molecular weight polyethylene under boundary lubrication, Tribol. Lett. 56 (3) (2014) 409–422.
[25] Y.K. Zhou, et al., Development of the theoretical model for the optimal design of surface texturing on cylinder liner, Tribol. Int. 52 (2012) 1–6. [26] B.F. Yin, et al., Effect of laser textured dimples on the lubrication performance of cylinder liner in diesel engine, Lubr. Sci. 24 (7) (2012) 293–312.
[27] A. Chyr, et al., A patterned microtexture to reduce friction and increase longevity of prosthetic hip joints, Wear 315 (1–2) (2014) 51–57. [28] D. Choudhury, et al., Tribological investigation of ultra-high molecular
weight polyethylene against advanced ceramic surfaces in total hip joint replacement, Proc. Inst. Mech. Eng. J: J. Eng. Tribol. (2014) 410–419. [29] A. Ronen, I. Etsion, Y. Kligerman, Friction-reducing surface-texturing in
reciprocating automotive components, Tribol. Trans. 44 (3) (2001) 359–366.
[30] E. Tomanik, Modelling the hydrodynamic support of cylinder bore and piston rings with laser textured surfaces, Tribol. Int.59 (2013) 90–96. [31] T.S. Kustandi, et al., Texturing of UHMWPE surface via NIL for low
friction and wear properties, J. Phys. D: Appl. Phys. 43 (1) (2010) 015301.
[32] B. Zhang, X.L. Wang, The design and fabrication of dimples pattern on the surface of UHMWPE, In: Rupeng Zhu, Ning He, Yucan Fu, Changyong Yang (eds). Materials Science Forum, Trans Tech Publica-tion, 2012, pp. 421–426.
[33] N. Morris, et al., The influence of piston ring geometry and topography on friction, Proc. Inst. Mech. Eng. J: J. Eng. Tribol. (2012) 141–153. [34] A. Abdelgaied, et al., Quantification of the effect of cross-shear and
applied nominal contact pressure on the wear of moderately cross-linked polyethylene, Proc. Inst. Mech. Eng. H: J. Eng. Med. 227 (1) (2013) 18–26.
[35] S. Wen, P. Huang, Principles of Tribology, Wiley, 2012.
[36] A. Kovalchenko, O. Ajayi, A. Erdemir, G. Fenske, I. Etsion, The effect of laser texturing of steel surfaces and speed-load parameters on the transition of lubrication regime from boundary to hydrodynamic, Tribol. Trans. 47 (2) (2004) 299–307.
[37] I. Etsion, Y. Kligerman, G. Halperin, Analytical and experimental investigation of laser-textured mechanical seal faces, Tribol. Trans. 42 (3) (1999) 511–516.
