Prediction of subsurface stress in elastic perfectly plastic rough components

Understanding and anticipating the effects of surface roughness on subsurface stress in the design phase can help ensure that performance and life requirements are satisfied. One approach used to address this problem is to simulate contact between digitized real, machined surfaces, and then analyze the predicted subsurface stress field. Often, elastic-perfectly plastic contact models are used in these simulations because of their relative computational efficiency. Reported here is an analysis of the magnitude and location of maximum stress predicted using an elastic-perfectly plastic model. Trends are identified which then enable estimation of the upper bound of the simulation results based on surface discretization, operating conditions, and material properties. These estimations can be used as an effective and efficient tool for rapid prediction of maximum subsurface stress in real surface contact.     

Role of nanometer roughness on the adhesion and friction of a rough polymer surface and a molecularly smooth mica surface

Friction and adhesion measurements between surfaces of cross-linked, stiff polymers of varying roughness against smooth, bare mica surfaces were carried out in dry air as well as in the presence of lubricating oil. The nominal (macroscopic) contact area varies with the applied load according to the Johnson, Kendall and Roberts (JKR) theory, yet shows significant hysteresis due to the irreversibility arising from the loading/unloading curves of multiple asperities. Upon introducing the oil between the surfaces, the critical shear stress is reduced to zero due to the elimination of the adhesion force. However, the effect is less noticeable on the friction coefficient. Lastly, the effect of increasing the (RMS) roughness was greatest over the first few nanometers due to the diminution of the adhesion-controlled contribution to the friction, after which a further increase in roughness had less dramatic effects. A model is presented to account for the observed adhesion hysteresis during repeated loading/unloading cycles of purely elastically deforming rough surfaces. Bruno Zappone and Kenneth J. Rosenberg made equal contributions.     

Improved tooth trajectory model for prediction of milled surface geometry

The prediction on surface roughness and surface geometry in peripheral milling operation is a crucial but tedious task. The current researches concerned are almost based on circular tooth trajectory assumption to simplify analysis and modeling, and some models derived from true tooth trajectory are not concise enough or have certain limitation when put into practice. A novel idea on account of the principle of curvature circle approximation to true tooth path curve in cutting contact point nearby is presented, and the relevant mathematical theory is established. Then by means of specific curvature circles, mathematical models and analysis methods of surface roughness are discussed systematically, which cover two situations—cutting with and without runout effect. The validity and superiority of the models are demonstrated by experimental studies and numerical simulations. Finally, based on the suggested models and analytical methods, the effects of runout, feed rate, and cutter geometry on surface roughness and geometry are studied in depth, and several significant mathematical formulas and quantitative conclusions are reached, which would contribute to the theory of milled surface studies.     

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.     

考虑表面粗糙度的面齿轮齿面接触应力分析

根据齿轮啮合原理,得出了面齿轮的齿面方程,求得面齿轮齿面曲率。结合赫兹接触理论,推导了点接触面齿轮传动接触点的接触应力及应力沿齿面的分布规律,从齿根到齿顶,齿面接触应力先增大后减小,在靠近齿面中点处达到最大值。由粗糙表面接触理论,分析了面齿轮齿面微观弹塑性变形时的接触面积,并得到粗糙齿面接触时面齿轮齿面接触应力及其分布。对比分析了几种不同粗糙度条件下面齿轮齿面接触应力的变化规律,结果表明:齿面接触应力随表面粗糙度的增大而增大,与齿根处相比,齿顶接触应力受表面粗糙度影响更大。文中的分析可为面齿轮磨损及润滑机理的研究提供依据。     

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.     

三维表面粗糙度测量方法综述

表面粗糙度测量是评估零件表面特性的重要手段。经过二十多年的发展,三维表面粗糙度逐渐成为反映工件表面特性的重要指标。本文总结并比较了多种三维表面粗糙度的测量方法及特点,根据测量过程是否接触被测表面,将三维表面粗糙度测量方法分为接触式测量法与非接触式测量法。接触式测量法主要包括触针扫描法;非接触式测量法主要包括光学法(相移干涉显微法、相干扫描干涉法、数字全息法、共聚焦显微法、共聚焦色差显微法、点自动对焦法、变焦法、激光三角法和光切法)和电镜法(扫描电子显微法、扫描隧道显微法、扫描近场光学显微法和原子力显微法)。针对每种测量方法的发展现状,本文讨论了其适用范围及局限性,并指出未来的发展方向。     

Basic principles of rough surface contact analysis using numerical methods

A detailed account of the principles involved in using numerical elastic contact techniques on digitized measurements from rough surfaces is presented in relation to two- and three-dimensional topography data. The main results of such analyses are shown to include the detailed interface geometry and the subsequent contact pressure distribution involved. Methods of defining the resulting sub-surface stresses created by this contact pressure distribution are also presented for static normal loading, and for the case of a normal load in the presence of a frictional surface shear. The problems posed in dealing with plastic asperity contacts are also discussed, together with an outline of how the numerical methods described have been modified further to allow analysis of rough layered bodies of dissimilar materials, thus offering a very useful design tool for surface coatings.     

铣削加工粗糙度的智能预测方法

提出了一种基于最小二乘支持向量机的铣削加工表面粗糙度智能预测方法.首先进行了铣削工艺参数对工件表面粗糙度影响的正交实验,再通过对主轴转速、进给速率和切削深度三因素,以及各因素之间交互三水平实验的数据分析,找出了铣削工艺参数对工件表面粗糙度影响的一些规律.利用最小二乘支持向量机算法建立了铣削预测模型,通过该模型能在有限实验基础上利用工艺参数方便地得到粗糙度预测值.实际预测表明,在相同情况下,该模型构造速度比反向传播神经网络建模预测方法高2个～3个数量级,预测精度高10倍左右.     

Role of Rubber Stiffness and Surface Roughness in the Tribological Performance on Ice

The aim of this work is to investigate the effect of slider surface roughness and stiffness on the friction between rubber compounds and ice surfaces in order to provide insight into rubber–ice friction generation mechanisms. For this purpose, rubber compounds were designed to have different levels of macroscopic roughness and cured stiffness by modifying the filler system and plasticizer loading. In order to accurately evaluate the effects of surface and bulk rubber property on ice friction, linear friction tests were performed on laboratory ice with varied frictional heat buildup by modifying the friction test protocol. The results showed that the friction force was in general increased through the ploughing effect of a rough rubber block sliding on smooth ice. The increase in friction by ploughing was more pronounced when the contacting rubber block had sufficiently low stiffness and when the accumulation of frictional heat on ice was sufficiently high. It was also evidenced that a sufficiently hard rubber with test conditions leading to low heat buildup on ice could nevertheless lead to an opposite influence of roughness on rubber–ice friction; that is, lower friction force with a slider with a higher roughness.     

A model for the liquid-mediated collapse of 2-D rough surfaces

Small-scale devices are particularly vulnerable to adverse effects of adhesion because of large surface area to volume ratios. Additionally, small gaps can be easily bridged at high humidity or when there are other contaminant liquids present. The bridging of a portion of an interface by a liquid droplet of given volume tends to pull surfaces in closer proximity due to the sub-ambient pressures that arise. In turn, the area spanned by the bridge will increase and lead to a greater adhesive force. A previous study considering a liquid bridge between two elastic half-spaces initially separated by a uniform gap demonstrated that, under certain conditions, an instability will arise whereby the surfaces come into full contact. Owing to the regularity of the geometry considered, the problem was amenable to a semi-analytical treatment and the stability condition was expressible analytically in terms of a single dimensionless group. In the present work, we develop a model to include the effects of surface roughness. The influence of asperities on the surface is treated by means of a recently developed multi-scale model that considers the full range of wavelengths comprising the surface profile. In the simulations, two nominally flat rough surfaces are brought together under a prescribed load and a liquid bridge of given volume is introduced in the contact, the initial areal coverage being determined by the initial mean surface separation. The interface configuration is then iterated until a configuration is found that satisfies the equations of elasticity and capillarity for the given liquid volume. As a result of the simulation, critical values are found for combinations of parameters that delineate stable and unstable conditions.     

Surface roughness effects on curved pivoted slider bearings with couple stress fluid

In this paper the effect of surface roughness on the performance of curved pivoted slider bearings is studied. A more general type of surface roughness is mathematically modelled by a stochastic random variable with nonzero mean, variance and skewness. The averaged modified Reynolds type equation is derived on the basis of Stokes microcontinuum theory for couple stress fluids. The closed‐form expressions for the mean pressure, load‐carrying capacity, frictional force and the centre of pressure are obtained. Numerical computations show that the performance of the slider bearing is improved by the use of lubricants with additives (couple stress fluid) as compared to Newtonian lubricants. Further, it is observed that the negatively skewed surface roughness increases the load‐carrying capacity and frictional force and reduces the coefficient of friction, whereas the positively skewed surface roughness on the bearing surface adversely affects the performance of the pivoted slider bearings. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Analysis and experimental investigation of a simplified burnishing process

A slipline field model of a simplified burnishing process is used to derive equations for estimating the burnishing force, the depth of the burnished layer and the plastic strains in this layer. A detailed comparison is made between predicted and experimental results. An observation of considerable practical interest is the high quality surface finish (low surface roughness) which can be obtained by the burnishing process described.     

Hardness of a surface containing uniformly spaced pyramidal asperities

Pyramidal asperities of different apical angle were machined on a flat copper surface. Hardness was estimated from the load–displacement graphs obtained by pressing a spherical rigid indenter onto the asperities. The variation of hardness with apical angle and pitch was recorded with a view to contributing to the development of a general framework for relating measured hardness to the surface roughness. This revised version was published online in July 2006 with corrections to the Cover Date.     

A metrological model for maximum expiration

A metrological model for maximum expiration formulated by means of complex model reduction and selection of a parameter set for estimation was the purpose of this investigation. Reduction of the model was based on the forward-inverse method. Carrying out regression analysis showed that the properties of the airways were well approximated by exponential functions. The cross-sectional areas, airway lengths and compliances were replaced by these exponential relationships. Some other dependencies between mechanical quantities were also included. This reduced the number of parameters from 132 to 12. The complex and reduced models for maximal expiration were implemented on a PC and compared. The sensitivity index expressing the effect of parameter reduction was 3.2%. The selection of parameters for estimation was based on sensitivity analysis. This analysis showed that the reduced model was insensitive or weakly sensitive to eight parameters. This allowed for the selection of four parameters that influence the shape of the maximal expiration curve more than the others.     

Improved analytical model for residual stress prediction in orthogonal cutting

The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann’s model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volume-constancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann’s model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann’s model.     

工程表面粗糙度两用测量系统

介绍了一种新型工程表面粗糙度两用测量系统的设计原理、仪器结构及测试结果。该系统可采用接触法和非接触法两种测量方式,接触法测量范围达±１００μｍ,最小分辨率为０．００５μｍ;非接触法测量范围达±２５０μｍ,最小分辨率为０．０１μｍ。     

Fractal prediction model of thermal contact conductance of rough surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces,which has been widely studied since last few decades,and for predicting which many theoretical models have been established.However,the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity.In this paper,a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes:elastic,elastoplastic and fully plastic.Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model.The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area.The larger the fractal dimension,or the smaller the fractal roughness,the larger the thermal contact conductance is.The thermal contact conductance increases with decreasing the ratio of Young’s elastic modulus to the microhardness.The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface,which provide certain reference to the further study on the issue of heat transfer between contact surfaces.     

变形抗力预测模型及其应用研究

为提高变形抗力的预测精度,提出了一种基于混合最小二乘支持向量机和数学模型的组合方法.在该方法中,最小二乘支持向量机的参数通过基于退火策略的自适应粒子群优化算法自动获得.仿真实验结果表明,该组合方法不仅能够重现样本数据的变形抗力,还能非常精确地预测非样本数据.通过与其它文献中常用方法的比较发现,该方法在变形抗力预测的有效性和精确性方面都有很大提高.