Mathematical slip-line field solutions for ploughing a hard particle over a softer material

Wear mechanisms and friction in metals can be investigated by the analysis of the unit event represented by the interaction of a hard particle or asperity with a softer surface. Effective friction is the result of the interaction of many such asperities which constitute the roughness of the harder of the solid surfaces. Three types of plastic deformation at the metal surface can be identified: ploughing, edge formation and chip formation. Each mode of plastic deformation can be analysed using the slip-line field plasticity theory which requires as inputs the geometry of the hard particle and some information on the interface between the harder and the softer surfaces. The classical and the recent chord solution by Oxley assumes a sharp edge sliding against a metal surface but does not consider a curved roughness profile. However, the profiles of real asperities are more like waves with rounded summits. In the present work a new model for the asperities interaction is shown, using the slip-line field theory to calculate the friction forces, depth of sheared layer, average contact pressure and friction coefficient for a cylindrical hard particle sliding over a softer surface. The theoretical results are presented as friction graphs and maps in which the regions of elastic deformations are shown using the Hertz theory while the region of plastic strains is obtained from the present analysis. Present model results are in good agreement with experimental data obtained by Busquet et al. and are quite different from the Oxley chord model for sliding a circular particle.     

Contributions of adhesion and hysteresis to coefficient of friction between shoe and floor surfaces: effects of floor roughness and sliding speed

Abstract

Improving shoe–floor friction in order to reduce slip and fall accidents requires thorough understanding of the factors that contribute to friction. The friction between a sliding viscoelastic material (shoe) and a hard surface (floor) has two major components: adhesion and hysteresis. This study aimed to quantify the effects of floor roughness and sliding speed on adhesion and hysteresis to determine how each component contributes to the coefficient of friction. Experiments were conducted on a pin on disc tribometer using ceramic tiles with three levels of roughness, six sliding speeds, two common shoe materials and four liquid lubricants. Hysteresis was measured using a lubricant that minimised adhesion. Dry and lubricated adhesion was measured by subtracting hysteresis from the coefficient of friction. Analysis of variance regression models were used to determine the contributions of hysteresis, dry adhesion, sliding speed and fluid to lubricated coefficient of friction. Increased floor roughness led to increased hysteresis, while increased sliding speed reduced both adhesion and hysteresis. These findings are consistent with theory that states that larger asperities increase hysteretic deformation and that sliding speed affects deformation and real area of contact between a viscoelastic material and a hard surface. The model correctly predicted 83% of variation in coefficient of friction based on dry adhesion, hysteresis and fluid dependent constants. The sensitivity of hysteresis friction to shoe material and floor roughness indicates that optimising these parameters may be effective at reducing slip accidents on oily floor surfaces.     

Wear of boundary-lubricated metal surfaces

In the past, the friction and wear of boundary-lubricated metallic surfaces were attributed to adhesion and shearing of lubricants. However, examination of the friction and wear of pure metals lubricated with mineral oil indicates that while the friction coefficient was typical of the values obtained in boundary-lubricated sliding, the predominant wear mechanism was an abrasive-type mechanism. Scanning electron microscopy and surface profilometry revealed many ploughing grooves on the surfaces. These results indicate that the ploughing mechanism may be the predominant factor in controlling friction and wear of boundary-lubricated surfaces. On the basis of slip line field analysis and surface topography statistics an approximate expression for the wear coefficient was derived. It was found that the wear coefficient depends on the sharpness of the surface asperities (or the entrapped wear debris), the interfacial “friction” and the extent of the plastically deformed zone below the surface.     

Prediction of Archard's wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism

A recently developed model for sliding friction, in which the frictional force is assumed to result from the pushing of waves of plastically deformed material in the soft surface ahead of asperities on the hard surface, is used to calculate the magnitude of the resulting plastic strain increments which progressively deform the soft surface. On the assumption that a low cycle fatigue mechanism eventually results in detachment of wear particles from the soft surface as a result of this cyclic working of the surface, the calculated strain increments (the magnitudes of which vary with the roughness of the hard surface and the boundary lubrication conditions) are used to estimate wear rates. The results are expressed in terms of Archard's wear coefficient and, for very smooth surfaces and good lubrication, this is predicted to have extremely low values as observed in wear tests for such conditions. For rougher surfaces and less efficient lubrication it is shown that the wear coefficient can increase dramatically.     

The Influence of DLC Coating on EHL Friction Coefficient

High hardness, high elastic modulus, low friction characteristics, high wear and corrosion resistance, chemical inertness, and thermal stability are factors that make diamond-like carbon (DLC) coatings the subject of many studies. For the same reasons they also seem suitable for use in, amongst others, machine components and cutting tools. While most studies in the literature focus on the influence of coatings on wear and friction in boundary lubrication and pure sliding contacts, few studies can be found concerning rolling and sliding elastohydrodynamic lubrication (EHL) friction, especially in the mixed and full film regime. In this article tests are carried out in a Wedeven Associates Machine tribotester where an uncoated ball and disc pair is compared to the case of coated ball against uncoated disc, coated disc against uncoated ball, and coated disc against coated ball. The tests are conducted at two different temperatures and over a broad range of slide-to-roll ratios and entrainment speeds. The results are presented as friction maps as introduced in previous work (Bj?rling et al. in J Eng Tribol 225(7):671, 2011). Furthermore a numerical simulation model is developed to investigate if there is a possibility that the hard, thin DLC coating is affecting the friction coefficient in an EHL contact due to thermal effects caused by the different thermal properties of the coating compared to the substrate. The experimental results show a reduction in friction coefficient in the full film regime when DLC-coated surfaces are used. The biggest reduction is found when both surfaces are coated, followed by the case when either ball or disc is coated. The thermal simulation model shows a substantial increase of the lubricant film temperature compared to uncoated surfaces when both surfaces are coated with DLC. The reduction in friction coefficient when coating either only the ball or the disc are almost the same, lower than when coating both the surfaces but still higher than the uncoated case. The findings above indicate that it is reasonable to conclude that thermal effects are a likely cause for the decrease in coefficient of friction when operating under full film conditions, and in the mixed lubrication regime when DLC-coated surfaces are used.     

Studies on friction and transfer layer: role of surface texture

Friction influences the nature of transfer layer formed at the interface between tool and metal during sliding. In the present investigation, experiments were conducted using “Inclined Scratch Tester” to understand the effect of surface texture of hard surfaces on coefficient of friction and transfer layer formation. EN8 steel flats were ground to attain surfaces of different textures with different roughness. Then super purity aluminium pins were scratched against the prepared steel flats. Scanning electron micrographs of the contact surfaces of pins and flats were used to reveal the morphology of transfer layer. It was observed that the coefficient of friction and the formation of transfer layer depend primarily on the texture of hard surfaces, but independent of surface roughness of hard surfaces. It was observed that on surfaces that promote plane strain conditions near the surface, the transfer of material takes place due to the plowing action of the asperities. But, on a surface that promotes plane stress conditions the transfer layer was more due to the adhesion component of friction. It was observed that the adhesion component increases for surfaces that have random texture but was constant for the other surfaces.     

Effect of Impregnation of Iodine Complex on Friction of Anodic Oxide of Aluminum

Polyvinyl pyrrolidone-Iodine complex (PVP-I) molecules were impregnated into the anodic oxide of an aluminum disk specimen. It was rubbed against a silicon nitride ball specimen using a ball-on-disk type friction test rig. Over the limited range of parameters studied (load: 0.2-1.0 N, sliding velocity: 0.6 mm/s, and sliding distance: 1-7 m), the coefficient of friction decreased to a value as low as 0.01 from values of 0.3 to 0.7 for the anodic oxide surface. Single-crystal iodine rubbed against silicon nitride showed a coefficient of friction of 0.1. The low coefficient of friction is attributed to the thin PVP-I film on the relatively hard anodic oxide. The mechanism of coefficient of friction reduction is the same as that of a thin soft film on a hard substrate.     

The genesis of friction

The genesis of friction is explained in terms of a new theory. Contrary to the postulates of the adhesion theory of friction, this theory postulates that the frictional force (and thus the friction coefficient μ) is affected by the sliding distance and the environment because of the changing contributions of three components of friction, i.e. that due to the deformation of surface asperities (denoted μ_d), that due to plowing by wear particles and hard asperities (denoted μ_p) and that due to the adhesion of the flat portions of the sliding surface (denoted μ_a). Therefore the coefficient of friction is not a simple material property. There are four or six stages of the friction regime depending on the sliding conditions. The initial friction coefficient μ_i can range from 0.1 to 0.2 for most machined surfaces. μ_i is largely independent of environmental conditions (including lubricants), materials and surface topography. μ_p varies from 0 to 1.0 and μ_a from 0 to 0.4. Only μ_a depends on the quality of surface adhesion. The history-dependent frictional behavior of materials is represented in the “friction space” diagram. According to this theory, the compatibility of sliding surfaces is dictated more by the mechanical properties of materials such as hardness than by their relative solubility at low temperatures.     

不同微细造型几何形貌对润滑性能影响的数值模拟

建立了圆柱形、球冠形、锥形、六角形截面、三角形截面、正方形截面等表面微细造型几何形貌的数学模型,结合微细形貌润滑理论模型,采用多重网格法,分析了这些不同几何形貌对两滑动表面摩擦润滑性能的影响。分析结果表明:球冠造型形成油压的区域要明显大于圆柱和圆锥造型形成的油压区域;在相同表面占有率和微细造型深度下,正三角形造型有效油膜压力的区域较大,在相对滑动的表面中形成的间隙大,摩擦因数小。     

Sliding velocity dependency of the friction coefficient of Si-containing diamond-like carbon film under oil lubricated condition

In this study we investigated the sliding velocity dependency of the coefficient of friction for a Si-containing diamond-like carbon (DLC-Si) film in an automatic transmission fluid (ATF) under a wide range of contact pressures. The DLC-Si film and a nitrided steel with a surface roughness, Rz_JIS, of around 3.0 μm were used as disk specimens. A high-carbon chromium steel (JIS-SUJ2) bearing ball was used as a ball specimen. Friction tests were conducted using a ball-on-disk friction apparatus under a wide range of sliding velocites (0.1-2.0 m/s) and contact pressures (P_max: 0.42-3.61 GPa) in ATF. The friction coefficients for the nitrided steel had a tendency to decrease with an increase in sliding veloicity under all the contact pressure conditions; however, the friction coefficients for the DLC-Si film were stable with respect to sliding velocities under all the contatct pressures. These results indicate that the DLC-Si film suppresses the stick-slip motion during sliding againt steel in ATF, which is a desired frictional characteristic for the electromagnetic clutch disks used under lubrication. Furthermore, the DLC-Si film showed a higher wear resistance and lower aggression on the steel ball specimen than the nitrided steel. There were less hydrodynamic effects on the friction coefficient for the DLC-Si film possibly due to maintenance of the initial surface roughness and its poorer wettability with the fluid. X-ray photoelectron spectroscopy (XPS) analysis of the sliding surfaces revealed that the adsorption film derived from the succinimide on the sliding surfaces of the DLC-Si film and the mating steel ball also contributed to the sufficient and less sliding-velocity-dependant friction coefficients.     

Friction characteristics of nanoscale sliding contacts between multi-asperity tips and textured surfaces

Nanoscale sliding contacts of smooth surfaces or between a single asperity and a smooth surface have been widely investigated by molecular dynamics simulations, while there are few studies on the sliding contacts between two rough surfaces. Actually, the friction of two rough surfaces considering interactions between more asperities should be more realistic. By using multiscale method, friction characteristics of two dimensional nanoscale sliding contacts between rigid multi-asperity tips and elastic textured surfaces are investigated. Four nanoscale textured surfaces with different texture shapes are designed, and six multi-asperity tips composed of cylindrical asperities with different radii are used to slide on the textured surfaces. Friction forces are compared for different tips, and effects of the asperity radii on the friction characteristics are investigated. Average friction forces for all the cases are listed and compared, and effects of texture shapes of the textured surfaces are discussed. The results show that textured surface II has a better structure to reduce friction forces. The multi-asperity tips composed of asperities with R=20r0 （r0=0.227 7 nm） or R=30r0 get higher friction forces compared with other cases, and more atoms of the textured surfaces are taken away by these two tips, which are harmful to reduce friction or wear. For the case of R=10ro, friction forces are also high due to large contact areas, but the sliding processes are stable and few atoms are taken away by the tip. The proposed research considers interactions between more asperities to make the model approach to the real sliding contact problems. The results will help to vary or even control friction characteristics by textured surfaces, or provide references to the design of textured surfaces.     

Friction of Undulated Surfaces Coated with MoS2 by Pulsed Laser Deposition

Solid lubricants such as molybdenum disulfide can provide very low friction, but their effectiveness especially in the geometrically constrained sliding pairs is limited by plowing of coated surfaces by wear particles. Even in the presence of solid lubricants wear particles cause higher friction by plowing the interface. To minimize plowing, undulated surfaces with microgrooves perpendicular to the sliding direction can be used to trap wear particles. Smooth and undulated stainless steel surfaces were coated with molybdenum disulfide by pulsed laser deposition (PLD) and friction tested. Under identical test conditions, the friction coefficient of coated undulated surfaces is between 20–40 percent lower than that of coated smooth surfaces. The friction coefficient of undulated uncoated surfaces is about 100–350 percent less than that of smooth uncoated surfaces. Moreover, the entrapment of wear particles at the interfaces of geometrically constrained bearings may lead to seizure even when bearing surfaces are coated with solid lubricants. The use of undulated surf aces on these sliding systems has shown improved operating time and a reduced maintenance cycle.     

Finite element calculations on the influence of surface roughness on friction

Two-dimensional finite element calculations are used to describe the interaction between a hard rigid asperity and an asperity with an elastic-plastic material behaviour. In the calculations the hard asperity is moved through the soft asperity while the separation of the surfaces is kept constant. The normal and shear forces and the friction coefficient are determined for different separations. The influence of adhesive friction in the contact zone and the influence of the radii of the asperities are also investigated. The finite element model is compared with an analytical model.     

An elastic–plastic asperity interaction model for sliding friction

A finite-element model of the interaction of an elastic–plastic asperity junction based on cylindrical or spherical asperities is used to predict sliding friction coefficients. The modelling differs from previous work by permitting greater asperity overlaps, enforcing an interface adhesional shear strength, and allowing material failure. The results of the modelling were also used to predict friction coefficients for a stochastic rough surface. The asperities were based on the titanium alloy Ti-6Al-4V, and the magnitudes of the predicted friction coefficients were generally representative of experimental measurements of sliding friction. The results suggest that friction arises from both plasticity and tangential interface adhesion.     

Surface topography and tribology of cast iron in boundary lubrication

This work aims to study and understand the influence of the surface topography on wear of grey cast iron used for heavy duty diesel engine cylinder liners. A micro-alloyed grey cast iron was tested with different surface topographies. These were polished surfaces, honed surfaces (with two different honing parameters) and three model surfaces with well defined grooves on a polished specimen.Reciprocating friction tests using a steel ball rubbing against a flat or a cylindrical sample (extracted from a cylinder liner) were carried out on a Cameron Plint test rig. A commercial synthetic oil for diesel engine was used as the lubricant. The friction coefficient and the electrical contact resistance were measured during the tests. The wear volume of the cylinder liner part was also measured at the end of the test.The influence of the surface topography on the tribochemical film formation and on the wear behaviour of cast iron was established. Surfaces exhibiting lots of surface asperities had the highest wear, mainly due to delayed formation of protective tribochemical film. In our test conditions, the spacing between the grooves on model specimens had no influence on the wear behaviour of the cast iron specimens.     

粗糙表面微凸体对液黏传动的影响

为研究液黏传动过程中粗糙表面的承载特性,将分形理论引入到两粗糙表面摩擦过程之中,分析传动过程中混合摩擦和边界摩擦两阶段的微凸体承载过程,考虑微凸体弹塑性变形,对M-B模型进行修正,建立修正的微凸体承载模型。建立基于修正M-B模型的微凸体承载模型。通过数值仿真得到有效面积系数、分形参数对液黏调速离合器传动过程的影响规律;对修正的微凸体承载模型的计算结果与M-B模型的计算结果进行对比分析。结果表明:微凸体接触载荷和传递转矩随着面积比的增大而增大,当有效面积系数与尺度系数增大时,接触载荷与传递转矩均有所增大;分形维数为1.5时,微凸体接触载荷与传递转矩最小且随面积比的变化最为缓慢;在整个接触区域内,弹性变形区域的面积、接触载荷以及传递转矩最大,其次是弹塑性变形区域,塑性变形区域最小;考虑弹塑性变形时,微凸体接触载荷与传递转矩均有所下降;修正M-B模型和M-B模型间的修正系数范围在25%以内,修正系数随着有效面积系数、尺度系数的增大而增大,随着分形维数的增大而减小。     

Deformation and wear behaviour of the junction in quasi-scratch friction

The initial scratching of soft metals by relatively hard metallic asperities involves considerable plastic deformation and wear of the harder metal. Thus the penetration effect on friction is reduced successively as sliding proceeds, leading to the shearing type of friction. Such a transition state of sliding can be defined as a quasi-scratch friction process because ploughing precedes the steady sliding condition.The deformation and wear behaviour at a friction junction was investigated using model experiments between a mild steel conical rider and a flat copper surface. Changes in geometry of the rider and pile-up of the flat metal were examined metallographically and with a microscope. It was found that a stable value of the friction force is determined from the geometric shape of the junction attained after the completion of transient sliding and the effect of initial asperity shape on the friction force becomes insignificant.     

Analyzing Elastic-Plastic Real Rough Surface Contact in Running-in

A numerical method is presented for evaluating the elastic-elastic contact of real rough surface contacts during running-in. For the surface contact, an elastic-plastic model based on the variational method is applied to analyze the pressure distribution and contact area of worn surfaces during running-in. In conjunction with the classical statistic model of Greenwood and Williamson, the numerical result showed that the plasticity index Ψ was decreased to one in the elastic range as running-in proceeded. In comparison with the Hertzian solution, the influence of the asperities is very significant on the pressure distribution, thereafter causing a higher peak value of contact pressure. For the subsurface, the interior stress from the von Mises criterion was calculated to evaluate the subsurface stress field subject to both normal and tangential forces. In the calculated of the interior stress, the total stress is decomposed into a fluctuating component and a smooth component. The fluctuating part is solved by using FFT from the concept of the convolution theorem while the smooth part is obtained directly by analytical solution. Calculations of contact area and subsurface stress on experimentally produced surfaces whose topography has been determined using an atomic force microscope and friction coefficient front sliding have been carried out. The results showed that asperities and friction coefficient gave rise to stress increase in the near-surface stress field and produced a high stress zone towards the surface. As a result, transverse asperity cracking was produced. The calculations and supporting experimental evidence clearly confirmed that the reduction of peak pressure during running-in decreased the plastic deformation of contact.     

Friction characteristics of a ferritic-austenitic stainless steel during lubricated reciprocating motion

This report describes friction measurements of stainless steel against stainless steel during lubricated, small-amplitude reciprocating motion. The experimental investigation was divided into two parts. First, four different lubricants were evaluated using a response surface design, during which the average contact pressure and the sliding velocity were varied. Secondly, a 2⁴ factorial design with three replicate runs was performed. Here, the coefficient of friction in the initial stage and the duration of that stage were studied. The independent variables were the average contact pressure, sliding velocity, surface roughness and type of lubricant. In the early state (stage I), the value of the frictional force is controlled by plowing of the surfaces by asperities. In many lubricated contacts, this is the practically useful stage. The experimental results from the response surface design show that the duration of stage I depends on the type of lubricant. Adhesive wear can take place before 100 cycles. The factorial design indicates that the coefficient of friction in the initial stage is affected by the type of lubricant, surface roughness and the simultaneous change of the surface roughness and type of lubricant. The duration of the initial stage is affected by a change in the surface roughness, average contact pressure and a simultaneous change in average contact pressure and surface roughness. A two-parameter Weibull analysis was performed on the data from the factorial design. For the tests where lubricant no. 3 was used, a mixed distribution was indicated for the duration of stage I. This mixed distribution indicates that a weakest-link process as well as a healing process were involved.