Modelling of static friction in rubber–metal contact

A static friction model for contact between rough rubber and metal surfaces is developed. This model is based on the contact of a viscoelastic–rigid asperity couple. Single asperity contact is modelled in such a way that the asperities stick together in a central region and slip over an annulus at the edge of the contact. The slip area increases with increasing tangential load. Consequently, the static friction force is the force when the slip area is equal to the contact area. Using the model, the traction distributions, contact area, tangential and normal displacement of two contacting asperities are calculated. The single asperity model is then extended to multi-asperity contact, suitable for rough surfaces. This model allows calculation of the above-mentioned parameters for two rough surfaces (a rubber and a metal one) subjected to normal and tangential loads. A parametric study will be presented. The results are qualitatively in good agreement with those found in literature.     

Elastic–Plastic Spherical Contact Modeling Including Roughness Effects

The effect of material properties and surface roughness on the contribution of asperities and sphere bulk displacements to the total displacement of a rough spherical contact is investigated. A dimensionless transition load, above which the contribution of the bulk displacement exceeds the contribution of the asperities displacement, is found as a function of the plasticity index and dimensionless critical interference of the sphere bulk. A criterion is proposed for evaluating the importance of surface roughness in calculating the displacement of a rough spherical contact. Some experimental results with a spherical micro-contact are presented to verify the model.     

Surface separation and contact resistance considering sinusoidal elastic–plastic multi-scale rough surface contact

The current work considers the multi-scale nature of surface roughness in a new model that predicts the real area of contact and surface separation as functions of load. This work is based upon a previous rough surface multi-scale contact model which used stacked elastic–plastic spheres to model the multiple scales of roughness. Instead, this work uses stacked 3D sinusoids to represent the asperities in contact at each scale of the surface. By summing the distance between the two surfaces at all scales, a model of surface separation as a function of dimensionless load is obtained. Since the model makes predictions for the real area of contact, it is also able to make predictions for thermal and electrical contact resistance. In accordance with concerns in previous works that the iterative calculation of the real contact area in multi-scale methods does not converge, this work not only tests but also gives conditions required for convergence in these techniques. The results are also compared to other existing rough surface contact models.     

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。     

A numerical model of friction between rough surfaces

This paper describes a computational method to calculate the friction force between two rough surfaces. In the model used, friction results from forces developed during elastic deformation and shear resistance of adhesive junctions at the contact areas. Contacts occur between asperities and have arbitrary orientations with respect to the surfaces. The size and slope of each contact area depend on external loads, mechanical properties and topographies of surfaces. Contact force distribution is computed by iterating the relationship between contact parameters, external loads, and surface topographies until the sum of normal components of contact forces equals the normal load. The corresponding sum of tangential components of contact forces constitutes the friction force. To calculate elastic deformation in three dimensions, we use the method of influence coefficients and its adaptation to shear forces to account for sliding friction. Analysis presented in Appendix A gives approximate limits within which influence coefficients developed for flat elastic half-space can apply to rough surfaces. Use of the method of residual correction and a successive grid refinement helped rectify the periodicity error introduced by the FFT technique that was used to solve for asperity pressures. The proposed method, when applied to the classical problem of a sphere on a half-space as a benchmark, showed good agreement with previous results. Calculations show how friction changes with surface roughness and also demonstrate the method's efficiency.     

基于修正Iwan模型的螺栓结合面非线性建模研究

准确建立高保真的螺栓结合面非线性力学模型是分析高端装备的前提和基础。针对螺栓结合面的迟滞非线性力学问题,提出了一种修正Iwan模型的力学建模方法,使得传统唯象的Iwan模型各参数物理意义更加明确。首先,根据多尺度理论和数理统计方法,建立了具有连续光滑接触特性的结合面法向接触模型;然后,通过考虑动态和静态摩擦因数的差异并利用库仑摩擦定律,将修正后的Iwan唯象模型与具体的法向接触模型联系起来,提出了新的螺栓结合面切向响应模型;最后,基于Matlab仿真和已有的试验数据,验证了所建模型的正确性,并探究了加载条件、塑性指数和动静摩擦因数比对结合面接触特性的影响。研究表明：一个周期加、卸载的能量耗散是随着位移幅值的增加而递增;相比于塑性指数,动静摩擦因数比的改变对结合面切向载荷的影响更为显著,在后续研究中需重点考虑;微凸体临界滑移力分布受其他因素的影响主要体现在接触微凸体的数目、峰值点的位置以及曲线收敛速度的改变。     

Thermoelastohydrodynamic Analysis of Spur Gears with Consideration of Surface Roughness

Thermoelastohydrodynamic lubrication (TEHL) analysis for spur gears with consideration of surface roughness is presented. The model is based on Johnson’s load sharing concept where a portion of load is carried by fluid film and the rest by asperities. The solution algorithm consists of two parts. In the first part, the scaling factors and film thickness with consideration of thermal effect are determined. Then, simplified energy equation is solved to predict the surfaces and film temperature. Once the film temperature is known, the viscosity of the lubricant and therefore friction coefficient are calculated. The predicted results for the friction coefficient based on this algorithm are in agreement with published experimental data as well as those of EHL simulations for rough line contact. First point of contact is the point where the asperities carry a large portion of load and the lubricant has the highest temperature and the lowest thickness. Also, according to experimental investigations, the largest amount of wear in spur gears happens in the first point of contact. Effect of speed on film temperature and friction coefficient has been studied. As speed increases, more heat is generated and therefore film temperature will rise. Film temperature rise will result in reduction of lubricant viscosity and consequently decrease in friction coefficient. Surface roughness effect on friction coefficient is also studied. An increase in surface roughness will increase the asperities interaction and therefore friction coefficient will rise.     

基于JKR模型的粗糙圆柱表面线黏着接触分析*

利用粗糙平面接触模型,假定表面单个微凸体的接触采用JKR黏着接触模型,同时考虑圆柱体表面的整体变形,建立了粗糙圆柱表面线黏着接触模型,推导出表面等效压力分布方程。把压力方程量纲一化,采用修正Newton-Raphson法对方程进行迭代求解,计算出粗糙圆柱表面存在表面力作用下的等效压力分布曲线。结果表明外载荷不小于零时,接触中心压力为正,微凸体被压缩;而接触边缘处压力为负,微凸体被拉伸,表明黏着区域主要分布在接触边缘。同时计算出接触半宽随外载荷的变化曲线,当外载荷为拉伸力并大于某一临界值时,表面分开。并且与经典的接触模型进行了对比,发现低载时模型之间的差别较大,而载荷比较大时趋于一致。     

An experimental study on roughness noise of dry rough flat surfaces

This paper presents an experimental study of the friction noise, between two rough and dry flat surfaces. The domain of interest is the dry contact under light pressure where the roughness is the dominant cause of noise. The results show that, for sliding rough surfaces under light load, the fundamental mechanism of radiated noise is the presence of shocks occurring between antagonist asperities of sliding surfaces. The radiated roughness noise is controlled simultaneously by the detailed topography of the surfaces in contact, the sliding speed and the dynamics of the surfaces. In terms of topography and sliding speed, it was shown that the roughness noise is simultaneously an increasing linear function of the logarithm of the surface roughness and the sliding speed. In terms of dynamics, the roughness noise is generated for light dynamical coupling. Hence, the natural modes of samples are stiffer than the contact and therefore the resulting vibrations are not affected by the additional rigidity. The deformation of surfaces during contact is very light and its magnitude is negligible compared to the surface roughness.     

Effects of Interfacial Strength and Roughness on the Static Friction Coefficient

A finite element model is used to simulate sliding inception of a rigid flat on a deformable sphere under combined normal and tangential loading. Sliding inception is treated as the loss of tangential contact stiffness under combined effects of plasticity, crack propagation and interfacial slip. Energy dissipation distribution is used to quantify the relative contribution of these mechanisms on the increased compliance during tangential loading. Materials with different strength and toughness properties, and varying local interface conditions ranging from fully adhered to finite friction, are studied to relate variations in plastic deformations, crack and slip to the sliding inception. For fully adhered contact condition, crack and fracture toughness have no effect on sliding inception, with plasticity, the dominant failure mechanism. A measure of recoverable strain (yield strength to Young’s modulus ratio) is found to be the most influential parameter in sliding inception. Interfacial slip is expectedly the dominant mechanism for sliding inception for lower coefficient of friction, modeling lubricated contacts. Interplay of plasticity and interfacial slip is found to govern the onset of sliding for higher local friction coefficients. Furthermore, the single asperity results are incorporated in a statistical model for nominally flat contacting rough surfaces under combined normal and tangential loading to investigate the stochastic effects due to surface roughness and material property uncertainties. The results show that the static coefficient of friction strongly depends on the normal load, material properties, local interfacial strength and roughness parameters.     

A partial elastohydrodynamic theory for the running-in process of hobbed gears

The running-in process of hobbed gears has been studied experimentally. The initial wear was found to be small although it increased with running speed and load. To explain the results, a simulation procedure was developed that was based on a random surface model and a proposed relation between film thickness, surface roughness and running conditions. A new oil model was used for the analysis of conditions between meshing rough flanks. The wear and deformation of asperities during the running-in period is due to direct contact between the asperities. The parameters determining wear and deformation are the adhesion and temperature between the asperities in contact.     

Surface topography and integrity effects on sliding wear

The effect of surface roughness and integrity on the sliding wear of metals was investigated experimentally. The results are consistent with the delamination theory of wear. The initial wear rate was influenced by the surface roughness and the applied load but the steady state wear rate was independent of the initial roughness. Under low applied loads delamination of smooth surfaces commences soon after sliding is initiated, whereas the delamination of rough surfaces is delayed until the original asperities are worn. Consequently, under low loads the initial wear rate of a smooth surface is higher than that of a rougher surface. The opposite is found under high loads since original asperities are removed immediately. It is also shown that machining damage to the surface or the subsurface (in the form of deformation, voids and cracks) accelerates the initial wear rate of the machined surface.     

Elastic conformity in Hertzian contacts

The study of elastic conformity within rough surface contacts is presented in terms of a conformity parameter derived as a function of normal load, elastic-modulus and the geometry of asperities within the interface. The parameter can be used in conjunction with the profile structure function to determine the wavelength of features which will elastically conform, and those remaining, which will appear to the contact as roughness. Experimental confirmation of the parameter's ability to define the minimum wavelength of surface asperity conformity is shown through optical studies of the contact interface created when laser-milled steel balls are pressed against a chromium plated glass disc under various loads. Practical applications demonstrated include the parameter's ability to identify surface features responsible for generating vibration in rolling bearings by an elastic percussion mechanism, and to explain interactions between surface roughness structure and the apparent ehd film-thickness generated during rolling contact. The parameter is also shown to reduce to the well known plasticity index when conditions are allowed to approach the elastic limit.     

Micro–Macro-Shear-Displacement Behavior of Contacting Rough Solids

Interlocking asperities are shown to have a fundamental effect on the friction behavior of contacting solids through theoretically derived shear force–displacement relationship. The key aspect of this relationship is the asperity contact orientation probability distribution obtained using the random process theory in terms of measurable surface roughness parameters. Thus, the obliquity of surface asperity contact is included in the contact shear analysis in a fundamental manner. The interlocking asperities are found to result in a normal load-dependent friction coefficient for a contact. The interlocking also affects contact partial slip and the shear displacements that precede sliding. The derived relationship can be used to evaluate factors, such as asperity adhesion, plasticity, damage, normal-shear coupling and scale dependency, which are difficult to separate in experiments and atomistic simulations.     

Validation of a simplified numerical contact model

Surface roughness tends to have a significant effect on how loads are transmitted at the contact interface between solid bodies. Most numerical contact models for analyzing rough surface contacts are computational demanding and more computationally efficient contact models are required. Depending on the purpose of the simulation, simplified and less accurate models can be preferable to more accurate, but also more complex, models. This paper discusses a simplified contact model called the elastic foundation model and its applicability to rough surfaces. The advantage of the model is that it is fast to evaluate, but its disadvantage is that it only gives an approximate solution to the contact problem. It is studied how surface roughness influences the errors in the elastic foundation solution in terms of predicted pressure distribution, real contact area, and normal and tangential contact stiffness. The results can be used to estimate the extent of error in the elastic foundation model, depending on the degree of surface roughness. The conclusion is that the elastic foundation model is not accurate enough to give a correct prediction of the actual contact stresses and contact areas, but it might be good enough for simulations where contact stiffness are of interest.     

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.     

Metal transfer in the frictional contact of a rough hard surface

The frictional behaviour between a hard rough surface and a soft smooth surface was examined under lubricated and unlubricated conditions. Transfer of soft metal to hard asperities in contact with it caused significant changes in the shape, size and height distributions of the asperities. Thus metal transfer reduced the effect of the initial surface roughness of the hard metal on friction.     

Calculation of friction for indenter with fractal roughness that slides against a viscoelastic foundation: Improved model

Additional results on calculating the deformation force of friction for a rough indenter sliding on a viscoelastic foundation are presented. The results consider the influence of the roughness on the normal contact load. As in earlier studies, the deformation properties of a foundation are described by the Kelvin model and the roughness of an indenter is represented by the Cantor–Borodich fractal, which consists of a set of rectangular asperities.     

Analysis of rough line contacts operating under mixed elastohydrodynamic lubrication conditions

Heavily loaded machine elements, such as gears, usually operate in the mixed lubrication regime. Surface roughness has a significant effect on the pressure distribution, the subsurface stress field, and the friction coefficient. Based on the superposition of a dry rough and a fully flooded smooth contact, a mixed lubrication model has been developed. The roughness profile is assumed to be known. Surface deformation is calculated by taking into account the pressure distribution that is built up by asperity contacts, asperity interactions, and lubricant flow. Thermal and sliding effects are incorporated into the analysis. Non‐Newtonian lubricant behaviour is considered by using a power‐law rheological model. The pressure distribution, subsurface stress field, and friction coefficient were calculated from the model at several points along the contact path for an FZG type C gear pair. It was shown that a significant part of the load is carried by the contacting asperities. The position of the maximum shear stress is very close to the surface.