Preliminary investigation of the effect of roughness in Dynarat simulation

Surface roughness has a significant effect on how loads are transmitted at the contact interface between solid bodies. It causes high local pressures in the contacting roughness peaks, i.e., asperities. Even for a low friction coefficient the surface roughness will still play an important role in the early surface wear. A dynamic ratcheting model (Dynarat) for studying the wear rate of ductile materials in rolling/sliding contact is presented. The material is divided into equal-sized rectangular elements (or ‘bricks’). Each material brick accumulates plastic shear strain when the orthogonal shear stress exceeds the brick's shear yield stress. When the accumulated plastic strain exceeds a critical value, the ductility is exhausted and the material is deemed to have failed. Inclusion of surface roughness and refinement of the near-surface brick size cause earlier failure of bricks very close to the surface. In order to model surface roughness, brick size needs to be reduced to, at most, a few microns. The purpose of this investigation is to study the effect of surface roughness in the Dynarat model by comparing the model prediction with the results from two different rolling sliding wear testing machines. Further development of the model is needed, such as more inclusive representations of microstructural behaviour. In addition to that, the ratcheting equation, which drives the Dynarat model, needs to be improved to cover other rail materials and more loading configurations.     

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.     

考虑摩擦因数与滑动速度相关时的轮轨滚动接触有限元分析

使用与滑动速度相关的摩擦因数替代库伦摩擦定律中的常系数,结合mixed Lagrangian/Eulerian方法建立轮轨滚动接触有限元模型,分析牵引力主导的蠕滑工况下的干燥状态的轮轨滚动接触特性。通过与摩擦因数取值为常数的轮轨滚动接触分析结果对比发现:与滑动速度相关的摩擦因数对轮轨滚动接触最大接触应力和接触斑面积影响不大,均在1%以内;但是对轮轨接触斑内最大Mises应力、最大纵向切应力、最大横向切应力和最大等效塑性应变影响较大,特别是对最大纵向切应力影响幅度近20%;更需要引起注意的是对轮轨滚动接触摩擦力矢量分布和切向塑性应变分布影响明显,这对轮轨滚动接触疲劳损伤分析非常重要。     

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。     

Multiscale Finite Element Modeling of Wheel–Rail Rough Normal Contact Measurements Using Pressure Measurement Film

ABSTRACT

This article presents a multiscale modeling approach for reproducing the measurement of the wheel–rail contact area using pressure measurement film when the roughness of the mating surfaces cannot be neglected. The microscopic contact behavior between the film and test bodies was investigated with the aid of the finite element method based on scanned surface data and was later implemented in a macroscopic model that reproduced the contact area measurement procedure. The validity of the modeling technique was confirmed by the consistency between simulated results and experimental measurements. It was also demonstrated that the response of the pressure measurement film to roughness variations is consistent with the governing contact mechanics.     

Deformation due to contact between a rough surface and a smooth ball

Theoretical and experimental results are presented to evaluate the deformation behavior of the contact between a real rough flat surface and a smooth ball. There are three deformation responses: plastic deformation of the asperities only, plastic deformation of the bulk only and combined plastic deformation of both the asperities and the bulk. The effects of the surface roughness and the Hertzian contact parameters on the effective contact pressure are presented. The experimental results confirmed the theoretical prediction very well. For a given Hertzian contact situation the surface roughness plays an important role in controlling the deformation behavior of the contacting surfaces. A criterion is presented to predict the deformation behavior of contacting engineering surfaces.     

粗糙表面弹性微动接触数值研究

由于实际工程表面多为粗糙表面,这里研究了粗糙表面对微动接触中压力和切向应力的影响。研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷。首先,建立接触算法和模型,其算法核心是利用共轭梯度法(CGM)计算微动接触中的表面压力及切向应力并使用快速傅里叶变换(FFT)加快计算速度。然后,在验证算法正确的基础上,分析正弦和非高斯粗糙表面接触的压力和切向应力的分布,通过对光滑与粗糙表面的研究对比,表明:(1)在正弦表面接触切向应力分布呈现尺寸效应;(2)在非高斯表面接触中,切向应力分布跟光滑表面形状类似;同时由于粗糙峰存在,粗糙表面下的切向应力比光滑表面下的要大,研究粗糙表面微动接触对实际工程具有重要意义。     

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.     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

A statistical model of elasto-plastic asperity contact between rough surfaces

This work models statistically elasto-plastic contact between two rough surfaces using the results of a previous finite element analysis of an elasto-plastic sphere in contact with a rigid flat. The individual asperity contact model used accounts for a varying geometrical hardness effect that has recently been documented in previous works (where geometrical hardness is defined as the uniform pressure found during fully plastic contact). The contact between real surfaces with known material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. The asperity is modeled as an elastic-perfectly plastic material. The model produces predictions for contact area, contact force, and surface separation. The results of this model are compared to other existing models of asperity contact. Agreement exists in some cases and in other cases it corrects flaws, especially at large deformations. The model developed by Chang, Etsion and Bogy is also shown to have serious flaws when compared to the others. This work also identifies significant limitations of the statistical models (including that of Greenwood and Williamson).     

Shear deformation of voids with contact modelled by internal pressure

The behaviour of voids in a ductile material subject to simple shear or to a shear-dominated stress state is analyzed numerically. Here the stress triaxiality is so low that instead of void volume growth to coalescence there is void closure leading to micro-cracks that rotate in the shear field. At some stage of the deformation, the void surfaces will come in contact so that sliding with or without friction will start to occur. To avoid problems with strong mesh distortion in the large strain field around the deforming void and with mesh resolution at the tip of the crack, an internal pressure is applied as an approximate representation of void surfaces pressed together in frictionless sliding, and also remeshing is applied. This micromechanical model for a strain hardening elastic–plastic material shows that a maximum overall shear stress is reached, at which localization of plastic flow occurs, leading to final failure in the material.     

依据各向异性分形几何理论的固定结合部法向接触力学模型

基于各向异性分形几何理论,考虑微凸体变形特点、表面微凸体承受法向载荷的连续性和光滑性原理,以及区分微凸体分别处于弹性、塑性变形时的一个微凸体实际微接触面积,建立固定结合部法向接触力学模型。采用二变量Weierstrass-Mandelbrot函数模拟各向异性三维分形轮廓表面。推导出划分弹塑性区域的临界弹性变形微接触截面积、结合部量纲一法向载荷、结合部量纲一法向接触刚度的数学表达式。数值仿真结果表明：当表面形貌的分形维数、分形粗糙度一定时,真实接触面积随着结合部法向载荷的增大而增大;结合部法向接触刚度随着真实接触面积、结合部法向载荷、相关因子或材料特性参数的增大而变大;当分形维数由1变大时,结合部法向接触刚度随着分形维数的变大而增大;当分形维数增加到趋近于2时,结合部法向接触刚度有时却会随着分形维数的增加而降低。结合部法向接触力学模型的构建,有助于分析固定接触表面间的真实接触情况。     

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。     

热力耦合下微接触点塑性应变沿深度变化分析

在考虑粗糙实体弹塑性变形、热力耦合、微凸体间相互作用和摩擦热流耦合等影响下,运用有限元法数值模拟具有三维分形特性的粗糙面与刚性平面间滑动摩擦过程,分析了粗糙实体接触凸点塑性变形随深度变化情况。发现：在速度的突变和闪点温度形成时,摩擦接触表层等效塑性应变增大明显;在这一摩擦表层,过不同接触点的纵向剖面塑性应变沿深度分布不同：有的是接触表面塑性变形最大,有的是在接触微凸体表面下某一深度塑性变形最严重,而接触凸点表面的塑性应变稍小些。这与相关文献用SEM研究干摩擦后金属摩擦表层变形照片后发现的结果一致。滑动摩擦过程中,金属粗糙摩擦接触表层塑性变形的不断累积,将会导致材料表层中的夹杂或微观缺陷周围萌生微孔和裂纹源。     

A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

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.     

Real area of contact and boundary friction in metal forming

Upper-bound models for asperity flattening on a workpiece surface undergoing bulk plastic deformation are developed. It is found that the effective hardness of the surface can be greatly reduced by the presence of underlying plastic flow. Theoretical predictions of the variation of real area of contact with strain show excellent agreement with experiments using model asperities in rolling. Friction models which allow for the reduction in effective hardness are developed for cases in which roughness is concentrated on either the workpiece or tooling.     

A surface roughness parameter in Hertz contact

The influence of surface roughness on the accuracy with which the Hertz theory of elastic contact predicts the contact pressure and contact area between a sphere and a plane is examined theoretically and experimentally. Statistical theories of surface contact suggest that the influence of surface roughness is governed primarily by a single non-dimensional parameter α defined by $\text{α }\text{σR}\text{a}{}_0{}^2$ where σ is the combined roughness of the two surfaces, R is the radius of the sphere and a₀ is the contact radius for smooth surfaces given by the Hertz theory. Experimental measurements of contact area correlate well with this parameter. Provided that the value of α is less than about 0.05, errors in the application of the Hertz theory due to roughness of the surfaces are not likely to exceed about 7%.     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

Wheel–rail contact: Roughness, heat generation and conforming contact influence

The reliability of the dynamic railway simulations is completely conditional upon the precision with which the wheel–rail contact problem is solved. This is because most of the external forces the rail vehicle is subjected to during circulation are transmitted through this contact. To solve this problem, normally a series of assumptions are made (non-influence of the surface roughness, non-influence of the heat generated on the contact, etc.) in order to obtain an efficient solution to the problem. However, it must be pointed out that the possible influence of some of these simplifications has not been analysed whereby a detailed investigation is required permitting an evaluation of the order of magnitude of the errors related to these simplifications. In this work, the influence of the following assumptions in the resolution of the wheel–rail contact problem shall be thoroughly analysed: assumption of smooth surfaces, assumption of non-influence of thermal effects and assumption that the dimensions of the contact are much lower with respect to those of the curvature radii of the surfaces.