- Original article
- Open Access
Effect of Micro-Dimples on Hydrodynamic Lubrication of Textured Sinusoidal Roughness Surfaces
© The Author(s) 2018
- Received: 20 February 2017
- Accepted: 9 August 2018
- Published: 20 August 2018
Surface texturing has been applied to improving the tribological performance of mechanical components for many years. Currently, the researches simulate the film pressure distribution of textured rough surfaces on the basis of the average flow model, and however the influence of roughness on the film pressure distribution could not be precisely expressed. Therefore, in order to study the hydrodynamic lubrication of the rough textured surfaces, sinusoidal waves are employed to characterize untextured surfaces. A deterministic model for hydrodynamic lubrication of micro-dimple textured rough surfaces is developed to predict the distribution of hydrodynamic pressure. By supplementing with the JFO cavitation boundary, the load carrying capacity of the film produced by micro-dimples and roughness is obtained. And the geometric parameters of textured rough surface are optimized to obtain the maximum hydrodynamic lubrication by specifying an optimization goal of the load carrying capacity. The effect of roughness on the hydrodynamic pressure of surface texture is significant and the load carrying capacity decreases with the increase of the roughness ratio because the roughness greatly suppresses the hydrodynamic effect of dimples. It shows that the roughness ratio of surface may be as small as possible to suppress the effect of hydrodynamic lubrication. Additionally, there are the optimum values of the micro-dimple depth and area density to maximize the load carrying capacity for any given value of the roughness ratio. The proposed approach is capable of accurately reflects the influence of roughness on the hydrodynamic pressure, and developed a deterministic model to investigate the hydrodynamic lubrication of textured surfaces.
- Hydrodynamic lubrication
- Surface texturing
- Roughness surface
- Sinusoidal wave
Surface texturing has become an efficient process of generating various texture patterns to improve tribological properties of mechanical components in the last decades. In the development of surface texturing technology there have been great efforts to reveal the role of geometrical parameters of surface texture in tribology . Specially, the research on hydrodynamic lubrication of surface texture has attracted much attention and long been a great challenge to scholars and engineers .
The development of mechanical engineering has created a greater demand for understanding and utilizing the lubrication and anti-friction mechanisms of surface micro-geometry [3, 4]. Optimization design of surface textures is one of the key factors for improving the tribological performance of mechanical components . Compared with the experimental investigation, the lubrication performance of textures can be precisely quantified by numerical analysis .
Based on the operating conditions and the contact geometry of mechanical components, the proper analytical model can be established to simulate the distribution of lubricant film thickness and pressure of the textured surfaces [7, 8], with the geometrical parameters of surface textures analyzed systematically by the numerical simulation. For example, a simplified model of “piston/cylinder” with micro-dimples was developed to predict the tribological performance of reciprocating automotive components by Ronen et al. . The three- dimensional instantaneous pressure distribution over the textured surface was simulated to analyze the effect of micro-dimples on the hydrodynamic lubrication. It is shown that the geometric parameters of micro-dimples, such as area density and dimple depth, have a critical influence on the distribution of film pressure, especially of the dimple depth.
Furthermore, the effect of different shapes of textures on the hydrodynamic pressure could also be analyzed by the numerical studies [10, 11]. Therefore, other than an analysis of a single type of texture , the numerical simulation may be a good way to evaluate the pros and cons of various types of textures under some typical operating conditions . Besides, the effect of textured area on the hydrodynamic lubrication could also be analyzed by numerical analysis [14, 15]. The physical mechanisms of two types of surface texturing concepts to generate hydrodynamic pressure, full periodic texturing and partial texturing, could be revealed by numerical analysis. There are the micro-dimple “individual effect” and “collective effect” corresponding to the full periodic texturing and partial texturing, respectively.
Based on the above review, the key geometrical parameters exerting considerable effects on the lubrication could be clarified by the distribution of film pressure . Consequently, a series of studies have been done to investigate the hydrodynamic lubrication of surface textures [17–20]. However, in order to make it easier for the analytical model to be developed and solved, the influences of surface roughness have almost been ignored. And yet, the effect of surface roughness on hydrodynamic lubrication should not be ignored as the surface roughness and the average thickness of lubrication film are in the same magnitude [21, 22].
The average flow model has been introduced to study the influence of surface roughness on the hydrodynamic lubrication of textured surfaces by Qiu et al. . However, the average flow model was proposed by means of statistical theory, and the film pressure distribution could not reflect precisely the micro-surface structure’s influence on the film pressure . Thus, those kinds of studies have always been controversial in the tribological community . By computing the film pressure through rough surfaces which were simulated with sinusoidal waves, the tribological mechanisms of the surfaces could be known more.
In this paper, the hydrodynamic lubrication of the relative movement of two parallel sliders are investigated with provision for surface roughness. Sinusoidal waves [21, 24] are employed to characterize the micro-structure of rough surfaces, with an analytical model of textured rough surfaces with micro-dimples developed to predict the hydrodynamic pressure.
By using the multigrid method, the Reynolds equation, Eq. (10), is solved coupling with appropriate boundary conditions and the film thickness equations. For details, please refer to Venner et al. , Fesanghary et al.  and Ji et al. .
Number of dimples, Np;
Roughness ratio, σ (A0/hc);
Dimensionless wavelengths, Wx or Wy;
Dimple aspect ratio, δ (Hp/H0);
Area density of dimples, Sp.
Input parameters for case study
Minimum film thickness h0 (μm)
Reference value of film thickness hc (μm)
Reference value of dimple radius rc (μm)
Amplitude of the sinusoidal wave A0 (μm)
Wavelengths of the sinusoidal wave wx or wy (μm)
Dimple radius rp (μm)
Dimple depth hp (μm)
Area density Sp
Dynamic viscosity η (mPa·s)
Sliding speed U (m/s)
Ambient pressure pa (Pa)
1 × 105
Cavitation pressure pc (Pa)
1 × 105
Bulk modulus β (Pa)
1 × 108
3.1 Effect of Number of Dimples on Dimensionless Average Pressure
3.2 Effect of Surface Roughness on Dimensionless Average Pressure
3.3 Effect of Micro-dimple Dimple on Dimensionless Average Pressure
The influence of the interaction between adjacent micro-dimples of the hydrodynamic pressure is of significance, whether along or perpendicular to the direction of the motion. As a result the interactions between neighboring dimples cannot be simply omitted in either direction.
The influence of roughness on the hydrodynamic pressure of textured surface is significant. The hydrodynamic pressure decreases with the increment of the roughness ratio because the roughness greatly suppresses the hydrodynamic effect of dimples.
There are the optimum values of the dimple depth ratio and area density to maximize the hydrodynamic pressure at any roughness ratio, respectively. The roughness ratio has no obvious effect on the optimum value of dimple depth ratio and the area density.
J-HJ carried out the numerical simulation and manuscript writing. C-WG carried out the analysis of the numerical results. Y-HF revised the manuscript. All authors read and approved the final manuscript.
Jing-Hu Ji, born in 1982, is currently an associate professor at School of Mechanical Engineering, Jiangsu University, China. He received his PhD degree from Jiangsu University, China, in 2012. His research interests include surface engineering, tribology, laser surface texturing.
Cai-Wei Guan, born in 1991, is currently a master candidate at School of Mechanical Engineering, Jiangsu University, China. Her research interests include tribology, laser surface texturing.
Yong-Hong Fu, born in 1965, is currently a professor at School of Mechanical Engineering, Jiangsu University, China. He received his PhD degree from Jiangsu University, China, in 2008. His research interests include tribology, surface engineering, laser surface texturing, internal combustion engine, mechanical seal and die technology.
The authors declare that they have no competing interests.
Supported by National Natural Science Foundation of China (Grant Nos. 51305168, 51375211, 51375213), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK20130524), and Research Foundation for Advanced Talents of Jiangsu University, China (Grant No. 13JDG090).
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