Elastic–plastic adhesive contact of rough surfaces based on plastic asperity concept

The paper describes an analysis of adhesive contact between rough surfaces with small-scale surface asperities using an elastic–plastic model of contact deformation based on fictitious plastic asperity concept developed by Abdo and Farhang [Int. J. Non-Linear Mech. 40 (2005) 495]. The model considers simultaneous occurrence of elastic and plastic behaviours for an asperity. The well-established elastic adhesion index and plasticity index are used to consider the different contact conditions that arise as a result of varying load and material parameters. The load-separation behaviour for different combinations of these parameters is obtained. Comparison with previous elastic–plastic model that was based on elastic-then-plastic assumption is made showing significant differences.     

Modeling the effect of skewness and kurtosis on the static friction coefficient of rough surfaces

Engineering surfaces possess roughnesses that exhibit asymmetrical height distributions. However, the Gaussian distribution is most often used to characterize the topography of surfaces, and is also used in models to predict contact and friction parameters. In this paper, the effects of kurtosis and skewness on different levels of surface roughness are investigated independently. This is accomplished by adopting the Pearson system of frequency curves and used in conjunction with a static friction model for rough surfaces to calculate the friction force and friction coefficient. This study is the first attempt to independently model the effect of kurtosis and skewness on the static friction and friction coefficient. It is predicted that surfaces with high kurtosis and positive skewness exhibit lower static friction coefficient compared to the Gaussian case. More importantly, it is predicted that, for high kurtosis values, the static friction coefficient decreases with decreasing external force rather than increasing as seen with increasing skewness. This is a very promising result for applications involving smooth lightly loaded contacts such as magnetic storage devices and microelectromechanical systems. The practical significance of the present model is specifically demonstrated on static friction predictions in magnetic storage head–disk interfaces. Such predictions can be used to determine the optimal characteristics of such devices prior to fabrication to achieve lower friction in terms of surface roughness, mechanical properties, apparent contact area, and operational environment.     

Contact Analysis of Non-Gaussian Surfaces for Minimum Static and Kinetic Friction and Wear

Most statistical contact analyses assume that surface heights and peak (summit) height distributions follow a Gaussian distribution. However, engineering surfaces are frequently non-Gaussian with a degree of non-Gaussian character dependent upon materials and surface finishing processes used. For example, magnetic rigid disk surfaces used in magnetic storage industry are highly non Gaussian. The use of a Gaussian analysis in such cases can lead to erroneous results. This study for the first time presents a method to carry out a statistical analysis of non-Gaussian surfaces. Real area of contact, number of contacts, contact pressure and meniscus force (in wet interfaces) are calculated for probability density functions having different skewness and kurtosis. From these curves, the optimum value of skewness and kurtosis can be predicted for minimum static/kinetic friction. It is found that a range of positive skewness (between 0.3–0.7) and a high kurtosis (greater than five) significantly lower the real area of contact and meniscus contribution implying low friction and wear. Also, sensitivity of film thickness to static friction goes down for a surface with a positive skewness and a high kurtosis.     

The contact behavior of elastic/plastic non-Gaussian rough surfaces

A three-dimensional contact analysis was conducted to investigate the contact behavior of elastic--perfectly plastic solids with non-Gaussian rough surfaces. The effect of skewness, kurtosis and hardness on contact statistics and the effect of skewness and kurtosis on subsurface stress are studied. Non-Gaussian rough surfaces are generated by the computer with skewness, Sk, of −0.3, 0.0 and 0.3, and kurtosis, K, of 2.0, 3.0 and 4.0. Contact pressures and subsurface stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and patch solutions. Variation of fractional elastic/plastic contact area, maximum contact pressure and interplanar separation as a function of applied load were studied at different values of skewness and kurtosis. Contact pressure profiles, von Mises stresses, tensile and shear stress contours as a function of friction coefficient were also calculated for surfaces with different skewness and kurtosis. In this study, it is observed that surfaces with Sk = 0.3 and K = 4 in the six surfaces considered have a minimum contact area and maximum interplanar separation, which may provide low friction and stiction. The critical material hardness is defined as the hardness at which severe level of plastic asperity deformation corresponding to the Greenwood and Williamson’s cut-off A _plastic/A _real = 0.02 occurs for a given surface and load condition. The critical material hardness of surfaces with Sk = 0.3 and K = 4 is higher than that of other surfaces considered.     

Influence of Non-Gaussian-Distributed Surface Roughness on the Static Performance of Slider Bearings

An investigation on full fluid film lubrication assuming non-Gaussian-distributed surface roughness has been conducted. A typical slider bearing is chosen as the research object. Edgeworth expansion containing skewness and kurtosis is introduced to approximate the roughness density function. Using Christensen's stochastic roughness model, effects of roughness direction and non-Gaussian distribution properties on the working performance of slider bearings have been quantitatively analyzed. The results show that the variation range of working performance caused by skewness and kurtosis is up to 9.82%. Effects of skewness and kurtosis on the performance are nontrivial and should not be neglected. Compared to the Gaussian distribution, Edgeworth series can represent physical rough surfaces more accurately. Though the effects of skewness and kurtosis on the working performance are complicated, some laws can still be found. For example, large skewness decreases the load capacity, whereas large kurtosis reduces friction force. According to the results, we can choose certain machining processes that can produce the desired surface roughness.     

On the Modeling of Elastic Contact between Rough Surfaces

The contact force and the real contact area between rough surfaces are important in the prediction of friction, wear, adhesion, and electrical and thermal contact resistance. Over the last four decades various mathematical models have been developed. Built on very different assumptions and underlying mathematical frameworks, model agreement or effectiveness has never been thoroughly investigated. This work uses several measured profiles of real surfaces having vastly different roughness characteristics to predict contact areas and forces from various elastic contact models and contrast them to a deterministic fast Fourier transform (FFT)-based contact model. The latter is considered “exact” because surfaces are analyzed as they are measured, accounting for all peaks and valleys without compromise. Though measurement uncertainties and resolution issues prevail, the same surfaces are kept constant (i.e., are identical) for all models considered. Nonetheless, the effect of the data resolution of measured surface profiles will be investigated as well. An exact closed-form solution is offered for the widely used Greenwood and Williamson (GW) model (Greenwood and Williamson, Proceedings of the Royal Society of London A, vol. 295, pp. 300–319), along with an alternative definition of the plasticity index that is based on a multiscale approach. The results reveal that several of the theoretical models show good quantitative and qualitative agreement among themselves, but though most models produce a nominally linear relationship between the real contact area and load, the deterministic model suggests otherwise in some cases. Regardless, all of the said models reduce the complicated surface profiles to only a few key parameters and it is therefore unrealistic to expect them to make precise predictions for all cases.     

Effect of surface roughness parameters on mixed lubrication characteristics

In this paper, a computer program was developed to generate non-Gaussian surfaces with specified standard deviation, autocorrelation function, skewness and kurtosis, based on digital FIR technique. A thermal model of mixed lubrication in point contacts is proposed, and used to study the roughness effect. The area ratio, load ratio, maximum pressure, maximum surface temperature and average film thickness as a function of skewness and kurtosis are studied at different value of rms. Numerical examples show that skewness and kurtosis have a great effect on the contact parameters of mixed lubrication.     

两弹塑性接触粗糙表面的静密封流量

当峰高的概率密度为指数分布时,利用泰勒公式推导了弹性载荷的近似解析解,给出了塑性载荷的严格解析解,导出了静密封流量的经验表达式。通过密封表面的泄漏量与表高标准差的3次方成正比。在塑性接触状态,存在一个临界塑性指数,当塑性指数大于临界塑性指数时,总载荷与塑性指数、粗糙度参数皆无关,量纲一的塑性泄漏量与较软材料的硬度有关,与两接触粗糙表面的复合弹性模量无关。     

基于不同微观固体接触模型的轮轨表面变形特性分析

针对轮轨表面接触变形问题,采用不同的统计型微观固体接触模型,即Greenwood-Williamson （GW）模型,Chang-Etsion-Bogy （CEB）模型和Zhao-Maietta-Chang （ZMC）模型,研究轮轨接触表面变形特性。利用Newton-Raphson方法对微观固体接触模型公式进行求解,并同时求解间隙方程和载荷平衡方程。考虑不同粗糙度和不同塑性指数下各微观固体接触模型的压力分布情况,以及接触半径随载荷的变化情况。并将不同微观固体接触模型的结果和Hertz模型结果对比,结果表明弹塑性微观接触模型（CEB,ZMC）比弹性模型（GW）有着更小的接触压力以及更宽的接触半径,最大压力均小于最大Hertz接触压力,接触半径均大于Hertz接触半径。     

rms skew and kurtosis of surface profile height distributions: some aspects of sample variation

The unit of scale of a surface profile height distribution may be described by its rms value. To describe the shape of that distribution the use of its moment coefficients of skewness and kurtosis has been proposed. This paper discusses the sample variation of these parameters. The effects of sampling from highly non-normal populations, such as those found with worn surfaces, and the influence of correlation between profile ordinates are considered with a view to establishing suitable sample sizes for required parameter confidence limits     

Interfacial potential barrier theory of friction and wear

An interfacial potential barrier theory to calculate friction and wear is proposed by considering the micro interaction of frictional surfaces. The theory suggests that the performance of friction and wear depends on the magnitude and distribution of the interfacial potential barrier on contact surfaces. The calculation methods of the interfacial potential barrier and standard interfacial potential barrier are then studied and the formulas to calculate the friction force, friction coefficient, and quantity of adhesion wear are derived based on the theory. With its independence and stability, the standard interfacial potential barrier can be used as an index to describe the frictional performance of materials. The calculation results of the friction force with some existing experimental data are consistent with the experimental results performed with an ultra high vacuum atomic-force microscope, which proves that the theory and method are feasible.     

Analysis of wheel and rail adhesion under wet condition by using elastic–plastic microcontact model

This paper presents a numerical model to investigate the adhesion characteristics of the wheel/rail contact with consideration of surface roughness under wet conditions. The elastohydrodynamic lubrication theory is used to obtain the load carried by water, and the statistical elastic–plastic microcontact model presented by Zhao–Maietta–Chang is applied to calculate the load carried by asperities contact. Meanwhile, the thermal influencing reduction factor is used to consider the inlet heating effects on the film thickness, and the change of water viscosity is also taken into consideration due to the flash temperature generated by the moving rough surfaces. Furthermore, the present work investigates the dependence of the wheel/rail adhesion coefficient on train speed, surface roughness amplitude, the initial temperature, the plasticity index and the maximum contact pressure under wet condition. Copyright © 2014 John Wiley & Sons, Ltd.     

数字滤波法模拟粗糙表面的误差分析

计算机模拟加工表面是数值模拟研究表面形貌特征对摩擦和润滑性能影响的前提。基于低通数字滤波技术,通过比较计算机模拟表面和实测磨削表面的粗糙度、峰度、偏度、面积支承率和自相关函数,研究了低通数字滤波法模拟加工表面高度分布特征和自相关函数的精确度,并对加工表面模拟过程中产生的高度分布误差进行了具体分析和讨论。分析结果表明:低通数字滤波法在模拟非高斯粗糙表面时模拟精确度主要受目标表面高度分布特征的影响较大,而且该方法生成非高斯表面存在一定的局限性无法生成特定高度分布的粗糙表面。     

Modelling of fluid continuum considering 3D surface parameters in hydraulic assemblies

Friction in servo hydraulic assemblies reduces the response characteristics of the system. The friction is influenced by various factors including the geometry (form and surface errors) of the sliding surfaces. In this work, functionally significant 3D surface parameters from the Birmingham parameters are investigated for reduced friction. A 3D surface modelling approach is presented using random process modelling as the basis. An exponential decay areal autocorrelation function is used to model the grinding and honing processes which are commonly employed for the manufacture of the hydraulic assemblies. Honed surface is modelled with the crosshatches of appropriate angle. Method of surface modelling is validated using the data obtained through measurements on a practical surface. Different surface maps with varying surface parameters of the ground and honed surfaces are generated. The fluid continuum gap geometries of the hydraulic assemblies are modelled using these surface maps as envelopes. Pressure distribution, velocity and viscous friction force are used as measurands of the frictional characteristics. Using computational fluid dynamics (CFD) approach, these measurands are evaluated for different functionally significant Birmingham parameters. Based on further analysis, negative skewness, lower kurtosis values, higher valley fluid retention index were found to have lower frictional characteristics.     

A Mixed Lubrication Model for Journal Bearings with a Thin Soft Coating—Part II: Flash Temperature Analysis and its Application to Tin Coated Al-Si Bearings

Flash temperature has a profound influence on the tribological behavior of contact surfaces. An asperity flash temperature model is developed for journal bearings with a thin soft coating. The asperity flash temperature of tin coated 339 Al-Si alloy bearings in contact with case hardened steel journals is analyzed. Factors influencing the flash temperature are discussed. Correlations of the flash temperature with asperity roughness parameters, such as the RMS roughness and skewness values, are explored. It was found that the maximum rise in temperature increased as the roughness and skewness increased.     

新的粗糙表面弹塑性接触模型

提出一种新型的粗糙表面弹塑性微观接触模型.该模型的建立基于接触力学理论和接触微凸体由弹性变形向弹塑性变形及最终向完全塑性变形的转化皆是连续和光滑的假设.研究单个微凸体在载荷逐渐增加时的变形规律,并重点推出弹塑性变形区间的接触方程.在此基础上应用概率统计理论导出了粗糙表面的接触载荷、平均分离和实际接触面积之间的数学关系式.在不同的塑性指数和载荷条件下,该模型与GW弹性模型和CEB弹塑性模型就实际接触面积和法向距离的预测结果进行了对比.结果表明,在同样塑性指数和载荷条件下比GW模型预测的实际接触面积大但法向距离小,且两者的差距随塑性指数和载荷的增加而增大.因此该模型的预测结果更加符合人们的试验观察和直觉,能够更加科学和合理地描述两个粗糙表面的微观和宏观接触状态.     

Effect of stiffness of multi-level hierarchical attachment system on adhesion enhancement

Geckos are known for their remarkable ability to cling on and detach from ceilings and walls using a unique attachment system. Their foot pads are covered by a large number of small hair (setae) that contain many branches per seta with a lower level of spatulae. This hierarchical structure gives the gecko adaptability to create a large real area of contact with rough surfaces. In this study, using the three-level hierarchical model recently developed to simulate a gecko seta contacting with random rough surface, the effects of spring stiffness and number of springs on the adhesion enhancement of multi-level hierarchical model are investigated. One- and three-level hierarchically structured spring models with different spring stiffnesses and number of springs on each level in contact with various rough surfaces are considered. The efficiency of attachment-the adhesion coefficient, the adhesion force, the number of contacts and the adhesion energy-for the three-level models with different stiffness is investigated in contact with different rough surfaces.     

Generation of reference data of 3D surface texture using the non-causal 2D AR model

In this paper, the non-causal 2D AR model was proposed as a new method for generation of reference data of the 3D surface texture. Specification parameters to engender various topographical properties were the correlation distances in the x and y directions, the power index which determined the decaying pattern of the auto-correlation function, the root mean deviation, the skewness and the kurtosis. Isotropic surfaces were generated and compared with results by the causal 2D AR model which has been proposed in the past researches. It was found that the error of generation by the non-causal 2D AR model was smaller than that by the causal 2D AR model. Anisotropic surfaces and non-Gaussian distributed surfaces were also generated successfully.     

Interfacial potential barrier theory of friction and wear

An interfacial potential barrier theory to calculate friction and wear is proposed by considering the micro interaction of frictional surfaces. The theory suggests that the performance of friction and wear depends on the magnitude and distribution of the interfacial potential barrier on contact surfaces. The calculation methods of the interfacial potential barrier and standard interfacial potential barrier are then studied and the formulas to calculate the friction force, friction coefficient, and quantity of adhesion wear are derived based on the theory. With its independence and stability, the standard interfacial potential barrier can be used as an index to describe the frictional performance of materials. The calculation results of the friction force with some existing experimental data are consistent with the experimental results performed with an ultra high vacuum atomic-force microscope, which proves that the theory and method are feasible. __________ Translated from Tribology, 2007, 27(1): 54–59 [译自: 摩擦学学报]     

Microscopic measurement of the degree of mixing for nanoparticles in polymer nanocomposites by TEM images

For polymer nanocomposites, the small size of the fillers makes it difficult to analyze the degree of mixing quantitatively and often requires direct assessment via transmission electron microscopy (TEM). To date, qualitative comparisons and indirect measurements of the degree of mixing by measurement of certain properties are the most common methods. Better methods to quantitatively characterize the degree of mixing in nanocomposites would aid in studies investigating the effect of process conditions on the mixing behavior. Alumina/PET nanocomposites of identical composition, but with different degrees of mixing were prepared using a batch mixer. For evaluation of the degree of mixing with respect to both dispersion and distribution, three different techniques were applied and compared. TEM particle density was useful for dispersion, but did not adequately characterize distribution, while the Morisita's index gave poor results due to a wide range of effective particle sizes. Both methods ranked the samples differently compared to direct visual observation. In contrast, the skewness calculated by the quadrat method produced results consistent with visual rankings, and was found to be most effective in comparing and quantifying the degree of mixing. Although the quadrat method requires proper selection of quadrat size for a particular particle concentration, the skewness from the quadrat method was found to be most suitable as a standard index for the degree of mixing in nanocomposites. The usefulness of the quadrat method was verified using a second set of nanocomposites prepared by a twin screw extruder showing the potential for application of this technique for process development and quality control in commercial nanomanufacturing processes.