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Abstract

In contrast with dimple textures, surface roughness is a texture at the micro-scale, essentially which will influence the load-bearing capacity of lubricant film. The numerical simulation was carried out to investigate the influence of surface roughness on friction property of textured surface. The lubricant film pressure was obtained using the method of computational fluid dynamics according to geometric model of round dimple, and the renormalization-group k–ε turbulent model was adopted in the computation. The numerical simulation results suggest that there is an optimum dimensionless surface roughness, and near this value, the maximum load-bearing capacity can be achieved. The load-bearing capacity is determined by the surface texture, the surface roughness, and the interaction between them. To get information of friction coefficient, the experiments were conducted. This experiment was used to evaluate the simulation. The experimental results show that for the frequency of 4 and 6 Hz, friction coefficient decreases at first and then increases with decreasing surface roughness, which indicates that there exists the optimum region of surface roughness leading to the best friction reduction effect, and it becomes larger when area fractions increase from 2% to 10%. The experimental results agree well with the simulation results.

Keywords

Surface texture surface roughness load-bearing capacity

Introduction

The introduction of surface textures, some patterns such as dimples and grooves processed on friction surfaces,¹ is a well-known approach to improve the tribological properties of mechanical components in recent years.^2,3 The investigation shows that surface texture with proper patterns and dimensions could reduce friction force effectively^4–6; thus, it is widely used in bearings,⁷ internal combustion engines,^2,8–10 and mechanical seals.¹¹ Ramesh et al.¹² investigated the friction characteristics of micro textures on stainless steel surfaces. The numerical simulations solved by the Navier–Stokes equations were used to predict the texture-induced lift. It was found that the textured surfaces exhibit friction as much as 80% lower than the untextured surfaces during hydrodynamic lubricated sliding. Öqvist¹³ performed the numerical simulations of wear of a cylindrical steel roller oscillating against a steel plate with the special version of the finite element program NIKE2D. The simulation was done in steps, and the pressure and the sliding distance were recalculated as the surface geometry changed. The results show that allowing the time step to differ between the wear steps will speed up the wear simulation considerably. Wang et al.¹⁴ conducted the experiments and numerical simulations to investigate the effect of dimple size on friction coefficient and load-carrying capacity for the oil lubricated line contact. The numerical simulation results suggest that the radius of cylinder and the dimple size are the critical issues for the hydrodynamic effect in the case of line contact. Meng et al.¹⁵ investigated the influence of rectangle dimples with flat bottom on the friction of parallel surfaces at different sliding conditions based on lubrication equations. The influence on the friction coefficient and friction force was investigated with numerical simulations. The results show that this kind of dimples can reduce the friction coefficient with the small ratio of film thickness to roughness (h/Rq), small roughness, or large applied load. Yu et al.¹⁶ developed a numerical model of a single dimple based on the steady-state Reynolds equation to investigate the effect of different textural shapes and orientations on hydrodynamic lubrication. The results indicate that geometric shape and orientation have obvious influences on load-carrying capacity of contacting surfaces. In Yin et al.’s¹⁷ study, the comprehensive influence of surface texture and surface roughness on piston ring and cylinder liner was investigated. It was found that surface roughness plays an important role on tribological properties, and friction reduction effect varied under different surface roughness with the same texture. In most of previous researches, surface roughness is neglected and friction surfaces are considered absolutely smooth. Since surface roughness is an essential property of friction surfaces, surface textures play a role under certain conditions of surface roughness. Therefore, the study on the roughness of textured surface is meaningful.

In the experimental work by Ma et al.¹⁸ textured polydimethylsiloxane (PDMS) disks with different roughness were tested under a stationary GCr15 bearing steel ball using glycerol and deionized water lubricants. The results showed that there was an optimal roughness value range of the textured PDMS species under the mixed lubrication and the best frictional properties appear in this range. Ma et al.¹⁹ developed an analytical model for frictional performance of textured surfaces when surface roughness was considered. The results showed that the textured surfaces with the traverse surface roughness have the perfect frictional performance. The friction coefficient and the optimal depth of surface texture increase with the increase in the composite root-mean-square (RMS); when composite RMS < 0.5 µm, the friction coefficient and the optimal depth of surface texture do not change, and when composite RMS ≥ 0.5 µm, the larger the composite RMS, the larger the optimal diameter of surface texture. The optimal area ratio is not related to the composite RMS, and the optimal parameters are not related to the orientation parameter. Qiu and Khonsari²⁰ evaluated load-bearing capacity, friction force, and leakage by solving average Reynolds equation with multigrid method. It was found that load-bearing capacity could be enhanced by surface roughness, and surface roughness plays a less important role on load-bearing capacity than cavitation effect. Although some results have been achieved on the tribological properties of textured surface with surface roughness, further investigations are still needed.

This article aims to investigate the effects of surface roughness on the tribological properties of textured surface and attempt to find out the optimum surface roughness region, in which the best friction reduction properties can be obtained. In the study, the renormalization-group (RNG) k–ε turbulent model is solved and built with the method of computational fluid dynamics (CFD), and finally, experiments will be performed to verify the simulation results.

Physical model

The friction pairs can be simplified as two infinite parallel planes, which are also considered as rigid walls because the film pressure in hydrodynamic lubrication is relatively low. The upper wall keeps static and is considered absolutely smooth; the lower wall moves along x-direction with a relative velocity u, and it is uniformly distributed with periodic micro-dimples along both x- and y-directions. It is better to adopt the micro-dimple texture because it is featured with processing convenience^21,22 and perfect hydrodynamic lubrication effect.²³ The random directional surface roughness is introduced in the non-textured area, since the directionality of the roughness makes no difference to hydrodynamic lubrication performance.^19,24,25 In order to simplify the calculation, the composite roughness²⁶ of two surfaces is adopted in the calculation. The length along x- and y-directions is L. The depth of the dimple, the lubricating film thickness, and the radius of the dimple are d, d₀, and r, respectively. The geometric model of the textured surface with roughness is shown in Figure 1.

Figure 1.

Geometrical model of surface texture: (a) the micro-dimples which are uniformly distributed on the surface, where L is the length of the unit along x- and y-directions and r is the radius of the round dimple; (b) an enlarged drawing of a dimple, where d is the depth of dimple and d₀ is the lubricating oil film thickness. The roughness is presented as wavy line in the front view and particles in the top view.

Numerical study

Numerical simulation

The simulation was performed by CFD software (Fluent^®)^27,28 based on the physical model established. The fluid boundaries, which are perpendicular to x and y axes, are defined as periodic boundary and symmetric boundary, respectively. There are three turbulence models, namely, the standard k–ε model, the RNG k–ε model, and the realizable k–ε model. The choice of the turbulence models influences the resultant flow field and the computational resource and time required to achieve solutions. The RNG k–ε model is one of the turbulence models in the CFD simulation. This model was derived by using a rigorous statistical technique, which is called RNG theory. In contrast with other turbulence models, which are designed for high-Reynolds-number, the RNG theory is suitable for both high-Reynolds-number and low-Reynolds-number. The effective viscosity in other models is considered to be constant, while the RNG model provides an analytically derived differential formula to calculate it. Thus, the RNG k–ε model is widely used in numerical simulation. Benaissa et al.²⁹ used CFD simulation with the RNG k–ε modeling of turbulence and near-wall treatment to model water–clay mixtures flowing through a cylindrical pipe domain, since it is more accurate and reliable for a wider class of flows than the other models. Chen et al.³⁰ developed a new drift–flux model for particle distribution and deposition in indoor environment. The turbulent airflow field is modeled with the RNG k–ε turbulence model as it can achieve better agreements between simulated results and measured data when compared to other turbulence models. For the surface texture, Han et al.³¹ studied the hydrodynamic performance in terms of friction force, load-bearing capacity, and friction coefficient by using the CFD. The results show that the k–ε RNG model is more accurate to predict flow fields involving large flow separation. Ma et al.³² find that the turbulence occurs around the asperities, which leads to the declination of load-bearing capacity; this means that the physical parameters of lubricant change quickly and significantly with time and position. Therefore, the RNG k–ε turbulent model, proposed by Launder and Spalding,³³ is adopted in the simulation because it is applicable for calculation of turbulent flow especially when the streamlines are bent largely due to the surface texture. This model can be described as

$\frac{\partial}{\partial t} (ρ k) + \frac{\partial}{\partial x_{i}} (ρ k u_{i}) = \frac{\partial}{\partial x_{j}} [α_{k} μ_{e f f} \frac{\partial k}{\partial x_{j}}] + G_{k} + ρ ε$ (1)

$\frac{\partial}{\partial t} (ρ ε) + \frac{\partial}{\partial x_{i}} (ρ ε μ_{i}) = \frac{\partial}{\partial x_{j}} [α_{ε} μ_{e f f} \frac{\partial ε}{\partial x_{j}}] + C_{1 ε}^{*} \frac{ε}{k} G_{k} - C_{2 ε} ρ \frac{ε^{2}}{k}$ (2)

where

$μ_{eff} = μ + μ_{t}$

$μ_{t} = ρ C_{μ} \frac{k^{2}}{ε}$

$C_{1 ε}^{*} = C_{1 ε} - \frac{η (1 - \frac{η}{η 0})}{1 + β η^{3}}$

where k is turbulent kinetic energy and ε is turbulent dissipation rate; other parameters are listed in Appendix 1. The simulation based on Reynolds equation will be performed as well, and the comparison will be made between the results obtained from Reynolds equation and RNG k–ε turbulent model.

The dimensionless parameters can be defined as r⁺ = (2r)/L, $R_{a}^{+} = R_{a} / d_{0}$ , and Re = ρuL/η, where R_a, ρ, u, and η are surface roughness, density of lubricant, velocity, and dynamic viscosity, respectively. r⁺, R_a⁺, and Re are dimensionless dimple radius, dimensionless surface roughness, and Reynolds number, respectively. The area fraction is defined as Sp = πr²/L², which also can be calculated by Sp = πr⁺²/4. In the simulation, various parameters are set up to study the effects of Re and R_a⁺ on load-bearing capacity; the data settings are shown in Table 1.

Table 1.

Value of simulation variables.

Variables	Values
r⁺	0.2	0.4	0.6	0.8
R _a ⁺	0.1	0.3	0.6	–
Re	20	40	60	80

Simulation results and discussion

Figure 2 gives the relationship of hydrodynamic pressure P and dimensionless surface roughness under different Reynolds number Re. Hydrodynamic effect of textured surface with R_a⁺ = 0.4 is enhanced significantly; however, it gradually diminishes with continuous increase in R_a⁺, under the condition of r⁺ = 0.2, as shown in Figure 2(a). It shows the same variation tendency of P under the condition of r⁺ = 0.4 and r⁺ = 0.6, as shown in Figure 2(b) and (c), respectively. It can be seen that there is an optimum R_a⁺, and near this value, the maximum load-bearing capacity is achieved, whereas the load-bearing capacity of textured surface is declined when the surface roughness is out of the optimum region. For the textured surface with roughness, surface roughness can be considered as textures in less scale than dimples. The load-bearing capacity is determined by the integrated effect of dimples and surface roughness. The lower surface roughness has less influence on hydrodynamic lubrication, and it arouses turbulence which reduces load-bearing capacity; the integrated effect of textured surface with lower roughness is weakened. When the increasing roughness falls in optimum region, the roughness generates significant hydrodynamic effect because of the dominant hydrodynamic effect rather than turbulence. However, hydrodynamic effect is declined when surface roughness is greater, which implies that the surface roughness–induced turbulence effect is dominant in this case.

Figure 2.

Load-bearing capacity related to dimensionless surface roughness for (a) r⁺ = 0.2, (b) r⁺ = 0.4, and (c) r⁺ = 0.6, based on RNG k–ε turbulent model.

When r⁺ is increased to 0.6, the optimal dimensionless roughness increases to R_a⁺ = 0.6, which suggests that the optimal surface roughness increases with the increase in area fraction, since increasing dimensionless dimple radius implies increasing area fractions. Thus, it is unnecessary to polish the material surface to rather low surface roughness before surface texturing, which has instructive function for surface texture.

Figure 2 also shows the relationship between load-bearing capacity and Reynolds number. It can be seen that Re has a very significant effect on the load-bearing capacity, and the load-bearing capacity is increased with increase in Re, which agrees well with Han et al.’s³¹ study.

Experimental details and discussion

Experimental details

The frictional tests were conducted on UMT-3 multifunctional test system (CETR Instruments, USA), which is shown in Figure 3. This apparatus was equipped with the loading range from 10 N to 1 kN, linear reciprocating velocity from 0.1 mm/s to 50 m/s, and spindle speed from 0.001 to 10,000 r/min. A flat upper specimen slides against a flat lower specimen under reciprocating motion, which is shown schematically in Figure 4. The reciprocating motion was achieved by slider-crank mechanism in this tester, thus the average velocity can be calculated from reciprocating frequency and stroke length. A constant load of 50 N was applied normally to the upper specimen during all of the tests, and the friction generated in the direction of movement was measured by an x-force sensor. The upper specimen was made of P20 (HRC 34), and it had dimensions of 6 mm in length, 3 mm in width, and 10 mm in height. The lower specimen was made of 1045 (HRC 15), and it had dimensions of 43 mm in length, 32 mm in width, and 6 mm in thickness.

Figure 3.

Photograph of UMT-3 tribometer.

Figure 4.

Schematic of relative motion of specimens. The upper specimen keeps still and the lower specimen moves back and forth.

The dimples were machined on the lower specimen by the circuit board engraver, the variation of diameter of dimple was achieved by changing different diameters of drills, the interval and depth of the dimples were controlled by the computer, and the process of the dimples is shown in Figure 5. The diameters of dimples are 160, 260, and 360 µm, and the corresponding area fractions are 2%, 5%, and 10%, respectively. All the dimples were drilled to the same depth of 40 µm. After drilling, the lower specimens were grinded against sandpapers of 150, 360, 800, and 3000 grits and marked as 1, 2, 3, and 4, respectively. The surface roughness was measured using the T1000A portable stylus-type profilometer (Harbin Measuring and Cutting Tool Group Co. Ltd., China). The profilometer was set to a cut-off length of 0.8 mm. Roughness measurements, on the non-textured region of specimens, were repeated four times, and surface roughness values were recorded. It can be seen that the larger the grits of sandpapers, the smaller the surface roughness of specimens; the correspondence of grits and surface roughness is shown in Table 2. The burrs around the dimple rim, resulting from drilling, could be removed as well during the grinding.

Figure 5.

Processing schema of the surface texture.

Table 2.

Surface roughness and mark number of specimens.

Items	Values
Grits of sandpapers	150	360	800	3000
Surface roughness of specimens (µm)	0.40–0.50	0.19–0.24	0.09–0.13	0.02–0.04
Mark number	1	2	3	4

To ensure the face-to-face contact of the frictional pairs, the sandpapers with 150, 360, 800, and 3000 grits were prepared to fix on the lower specimen before the tests. Then, the upper specimen and lower specimen with sandpapers whose grits varied from low to high were installed on the tester, running for 2 min at the reciprocating frequency of 2 Hz and a normal load of 2 N for each sandpaper. Finally, the obtained surface roughness of upper specimen was 0.02–0.04 µm, and the face-to-face contact of the frictional pairs was obtained as well. Experiments were carried out in ambient environment (25°C, 50 RH) over a stroke length of 20 mm at reciprocating frequencies of 2, 4, and 6 Hz, and the corresponding average velocities are 0.08, 0.16, and 0.24 m/s. The sliding contact zone was fully soaked in lubricant, oil of SAE 30, whose density and viscosity are 850 kg/m³ and 0.04678 Pa·s, respectively, at the temperature of 25°C. The friction test conditions are summarized in Table 3. The experimental data were collected while the tests were repeated four times and each friction test was carried out with a duration of 30 min.

Table 3.

Friction test conditions.

Upper specimen	AISI P20
Lower specimen	AISI 1045
Load (N)	50
Reciprocating frequency (Hz)	2	4	6
Average sliding velocity (m/s)	0.08	0.16	0.24
Reciprocating stroke (mm)	20
Lubricant	SAE 30
Temperature (°C)	25

Experimental results and discussion

The friction coefficient of samples under different reciprocating frequencies (2, 4, and 6 Hz) is shown in Figure 6. Note that the surface roughness decreases with the marked numbers, that is, the larger the marked number, the smaller the surface roughness. When area fraction is 2%, as shown in Figure 6(a), friction coefficient decreases with decreasing surface roughness for the frequency of 2 Hz. For the frequency of 4 and 6 Hz, friction coefficient decreases at first and then increases with decreasing surface roughness, which indicates that there exists the optimum region of surface roughness leading to the best friction reduction effect. When area fraction is 5% and 10%, the experimental results show the same tendency, as shown in Figure 6(b) and (c), respectively. Besides, for the area fraction of 2% and 5%, it can be found that the specimens marked 3 with surface roughness of 0.09–0.13 µm have the lowest friction coefficient under the frequency of 4 and 6 Hz. When the area fraction increases to 10%, the specimens marked 2 with surface roughness of 0.19–0.24 µm have the lowest friction coefficient for the frequency of 4 and 6 Hz, which suggests that the optimal surface roughness increases with the increase in area fractions. As a result, for the frequency of 4 and 6 Hz, there exist the optimum regions of surface roughness, which become larger under higher area fractions. The best friction reduction effect can be obtained with optimum roughness under high frequency of 4 and 6 Hz because the hydrodynamic effect can be enhanced by surface texture with their corresponding optimum roughness and increasing reciprocating frequency, as analyzed in the previous section. The experimental results agree well with Menezes’^24,34 study.

Figure 6.

Friction coefficient of samples with different surface roughness under reciprocating frequency of 2, 4, and 6 Hz for (a) Sp = 2%, (b) Sp = 5%, and (c) Sp = 10%.

From the numerical study in section “Numerical study,” it is shown that there exists optimum region of surface roughness in low frequency, although the load-bearing capacity of film is weak. However, in experimental study, the optimum region of surface roughness is not found for the low frequency of 2 Hz. The main reason is that the hydrodynamic effect is not pronounced under the low frequency of 2 Hz. Therefore, for the low frequency, the hydrodynamic effect may be influenced by other parameters, and attention should be paid on this point in further studies.

Conclusion

Experiments and numerical simulation were carried out to investigate the influence of surface roughness on the friction coefficient and load-carrying capacity of textured surface. According to the geometric model of dimple texture, the simulation was conducted to study the variation of film pressure with different roughness. Then, the experimental research was performed to get the information of friction coefficient through reciprocating motion. Some conclusions with referential value have been obtained as follows:

In contrast with dimple textures, surface roughness is a texture at the micro-level, essentially which will influence the load-bearing capacity of lubricant film. The numerical simulation results suggest that there is an optimum R_a⁺, and near this value, the maximum load-bearing capacity can be achieved. The load-bearing capacity is determined by the surface texture, the surface roughness, and the interaction between them.

The experimental results show that the friction coefficient decreases with decreasing surface roughness for the frequency of 2 Hz. For the frequency of 4 and 6 Hz, friction coefficient decreases at first and then increases with decreasing surface roughness, which indicates that there exists the optimum region of surface roughness leading to the best friction reduction effect, and it becomes larger when area fractions increase from 2% to 10%. The results from the experiments show good agreement with the simulation results.

Footnotes

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

The project is supported by the National Natural Science Foundation of China (Grant Nos. 51375480,51305441) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Influence of surface roughness on the friction property of textured surface

Abstract

Keywords

Introduction

Physical model

Numerical study

Numerical simulation

Simulation results and discussion

Experimental details and discussion

Experimental details

Experimental results and discussion

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References