An analysis of three-dimensional elasto-plastic sinusoidal contact

Researchers have developed many models to simulate the elasto-plastic contact of spheres. However, there does not appear to exist a closed-form analytical model for elasto-plastic three-dimensional sinusoidal contact. This work uses a finite element model (FEM) to characterize elasto-plastic sinusoidal contact. Although at initial contact the sphere and sinusoidal case are very similar and can both be described by the classic elastic Hertz contact case, once the contact is pressed past a certain range of deformation the two cases are very different. The model produces equations which can be used to approximately relate the area of contact to the contact pressure for elasto-plastic sinusoidal contact. The equations are fit to the FEM results and existing elastic solutions of sinusoidal contact. An empirical expression for the average pressure which causes complete contact between elasto-plastic sinusoidal contacts is also provided.     

Approaching Mixed Elastohydrodynamic Lubrication of Smooth Journal-Bearing Systems with Low Rotating Speed

When a conformal interface is under low velocity and heavy load conditions, solid contact (or dry contact) may occur even in a system with smooth surfaces. This paper presents two approaches for solving steady-state and transient mixed elastohydrodynamic lubrication problems of journal bearings with smooth surfaces under low rotating speed. The first approach uses the reduced Reynolds equation with a combined finite element–backward finite difference scheme and the second applies a zero film thickness equation to describe the mechanical behavior of mating surfaces at solid contact points. The major advantages of these two approaches are (1) no division of the solution domain into a lubricated area and a solid contact area is necessary and (2) the solid contact pressure, lubricant pressure, and eccentricity ratio can be solved simultaneously. Numerical examples are presented for the application of these approaches. For the steady-state cases under low velocity studied in this work, pressure distributions approach those found in a dry contact state. This comparison confirms that the contact treatments are proper. Moreover, a transient case under sinusoidal loading was analyzed with these two approaches, and the results showed good agreement. This comparison further supports the use of these approaches.     

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。     

Elastic Sinusoidal Wavy Surface Contact Under Full Stick Conditions

A purely normal contact problem of an elastic half-space with a three-dimensional periodic sinusoidal wavy surface and a rigid flat under the full stick condition is studied. The contacting points from mating surfaces have zero relative tangential displacement under the full stick condition. The scope of this study is restricted to a special case where the entire contact interface is in contact (referred to as complete contact) under the full stick condition. Complete contact is defined as when there are no gaps remaining between the surfaces. The corresponding state of stress of the half-space is derived analytically. According to the state of stress, we find (1) an analytical solution for the average pressure required to cause complete contact, (2) the location of the global maxima of the von Mises stress and (3) the critical magnitude of the waviness amplitude below which the plastic yielding of the half-space will never occur before the initiation of complete contact. The results are also compared with the solution under the perfect slip condition. We find that the location of the maximum von Mises stress may occur either on the contact interface or beneath it depending on the value of Poisson’s ratio.     

Numerical and finite element contact temperature analysis of real composite-steel surfaces in sliding contact

Numerical techniques have been developed and used to evaluate the contact temperature distribution between real composite-steel surfaces in sliding contact. To characterise the contact temperature problem of composite materials new definitions for composite Peclet numbers have been introduced. In case of `slow sliding' problems a stationary numerical technique was applied, whereas for `intermediate and fast sliding' problems transient finite element (FE) solutions were preferred. At first sliding contacts of a single steel asperity over polyetheretherketone (PEEK) or carbon fibre (CF)/PEEK composite surfaces were modelled in order to study the contact temperature development on a microscopic level. It was followed by contact temperature results for real composite-steel sliding surfaces; the latter helped to provide information about the actual stress conditions, which are necessary to model the wear process of this pair of materials in future works.     

Enhancement of a simplified model for maximum stress prediction

A simplified model for rapid estimation of maximum subsurface stress was previously reported by the authors. That model was found to predict the upper bound of the maximum von Mises stress in each layer below any surface with good accuracy. In this work, the model is enhanced by quantifying the difference between the predicted upper bound and the maximum stress for a specific rough surface. This is done by evaluating stress predictions for real rough surfaces, sinusoidal surfaces, ideal textured surfaces, and real rough surfaces with imposed computer generated texture. The difference between the predicted upper bound and the surface-specific maximum stress is found to be related to that surface’s roughness. The origin of this relationship is investigated in terms of apparent contact area. The enhanced simplified model provides an efficient means of estimating maximum stress in rough surface contact.     

Pressure Distribution of a Multidisc Clutch Suffering Frictionally Induced Thermal Load

The transient thermal and thermoelastic analysis of an automotive multidisc clutch is performed to investigate the thermal deformation and the contact pressure distribution of the friction surfaces. An alternating finite volume method (FVM) and finite element method (FEM) for temperature distribution and contact pressure distribution, including the coupling between temperature, displacement, and contact pressure, is employed in MATLAB. A penalty function method is used to impose the constraints on the contact boundary. The computational results indicate that the contact pressure distributions on the surfaces near the pressure plate are more uniform than those near the opposite plate, and the nonuniformity is enlarged with the temperature rise. The contact pressure and temperature distributions on the two friction surfaces of the separate plate are dissimilar and asymmetric, which is in good agreement with the test results. The results further show that the contact pressure peaks diminish and the noncontact regions reduce due to the heat conduction and convection when the engagement ends.     

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。     

应力松弛条件下O形圈的密封性能研究

为了研究O形圈的应力松弛规律及其在应力松弛条件下的密封性能,通过O形圈应力松弛试验,得到其轴向载荷衰减规律,将这些载荷值导入ANSYS中计算出O形圈的接触压力,并利用逾渗理论计算出O形圈密封面的泄漏率。研究结果表明:应力松弛条件下,O形圈上的轴向载荷随时间缓慢下降,初始压力越大轴向载荷衰减得越快,总体来看O形圈上的轴向载荷随时间遵循F_z=Aexp(-t/B)+C的衰减规律;施加的载荷越大O形圈与其接触面各点的接触压力越大,且不同载荷下O形圈与其接触面各点的接触压力均大于介质压力;应力松弛条件下O形圈密封面的泄漏率极小。试验、仿真计算及理论分析均表明,O形圈在应力松弛条件下具有良好的密封性能,证明了O形圈作为静密封的可靠性。     

Elastic and elastic-perfectly plastic analysis of an axisymmetric sinusoidal surface asperity contact

ABSTRACT

Closed-form finite-element empirical models are available for elastic and elastic–plastic spherical and sinusoidal contact. However, some of these models do not consider the effect of interaction with adjacent asperities or require extensive numerical resources because they employ a full 3-D model. Therefore this work has analysed and quantified the behaviour of an elastic and elastic- perfectly plastic axisymmetric sinusoidal surface in contact with a rigid flat for a wide range of material properties and different values of the amplitude to wavelength ratio from initial to complete contact (high load). The numerical results agreed well with the Hertz model and the Jackson–Green elastic–plastic spherical contact model at low loads. Empirical equations for elastic and also elastic-perfectly plastic cases are formulated for the contact pressure, contact area and surface separation. From the current analysis, it is found that it is not any single parameter, but different combinations of material properties and surface roughness that govern the whole contact behaviour. The critical value of the amplitude of the sinusoidal asperity below which it will deform completely elastically from initial to complete contact is established. At low values of amplitude normalized by the critical amplitude, it was found that the contact behaved similar to a spherical contact, with the average pressure (hardness) always remaining lower than three times the yield strength. However, at higher values the average pressure increased toward a value as high as six times the yield strength at complete contact. All of these equations should be useful in rough surface contact modelling, lubrication analysis, electrical contact modelling and in many other applications.     

Deterministic mixed lubrication modelling using roughness measurements in gear applications

The presence of surface roughness on the teeth of hardened and ground power transmission gears is an unavoidable consequence of their manufacture. The paper discusses the effect of surface roughness when the elastohydrodynamic lubricant film thickness developed between the gear tooth surfaces is small compared to the heights of the roughness features. The ratio of these quantities, called the Λ value, may be well below unity in typical applications. For such thin film conditions the moving roughness features cause the elastohydrodynamic contact between the gears to be highly transient in nature. Surface roughness features on the working surfaces of the gears move past each other during meshing and these asperity encounters are associated with extreme pressure perturbations, or with film breakdown and isolated asperity boundary lubrication events. The paper reviews approaches used to study this problem and describes a coupled approach to solving the elastic and hydrodynamic equations. This allows numerical solutions to be obtained for these extreme conditions so that transient contact events associated with mixed lubrication can be predicted in a unified numerical solution scheme. Typical results obtained from such an analysis are presented including surface fatigue modelling and contact strain energy calculations.     

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).     

Microscopic asperity contact and deformation of ultrahigh molecular weight polyethylene bearing surfaces

The effect of the roughness and topography of ultrahigh molecular weight polyethylene (UHMWPE) bearing surfaces on the microscopic contact mechanics with a metallic counterface was investigated in the present study. Both simple sinusoidal roughness forms, with a wide range of amplitudes and wavelengths, and real surface topographies, measured before and after wear testing in a simple pin-on-plate machine, were considered in the theoretical analysis. The finite difference method was used to solve the microscopic contact between the rough UHMWPE bearing surface and a smooth hard counterface. The fast Fourier transform (FFT) was used to cope with the large number of mesh points required to represent the surface topography of the UHMWPE bearing surface. It was found that only isolated asperity contacts occurred under physiological loading, and the real contact area was only a small fraction of the nominal contact area. Consequently, the average contact pressure experienced at the articulating surfaces was significantly higher than the nominal contact pressure. Furthermore, it was shown that the majority of asperities on the worn UHMWPE pin were deformed in the elastic region, and consideration of the plastic deformation only resulted in a negligible increase in the predicted asperity contact area. Microscopic asperity contact and deformation mechanisms may play an important role in the understanding of the wear mechanisms of UHMWPE bearing surfaces.     

A numerical analysis of the elastohydrodynamic line contact film formation at motion start-up

A mathematical model is proposed of the process of formation of the elastohydrodynamic (EHD) lubricant layer between resilient cylinders that begin to rotate in the lubricating material medium from the resting state. The model assumes division of the whole contact region into three zones: the zone within which dry motion is described by the equations of the elastohydrodynamic theory of lubrication, the transient zone, and the dry contact zone. The method of the numerical solution of this system of equations is presented. The calculations are performed for the lubricating material that was used in the published experimental study of the process of formation of the EHD lubricating layer between the resilient ball and the flat resilient base. It is shown that the calculation results well agree with the experimental data both qualitatively and quantitatively providing that the transient region dimensions are adequately selected. The function of the pressure distribution, the lubricating layer thickness, the lubricating material flow, the rate of approach of the surfaces over the contact region at different moments of time, the time dependencies of the lubricating layer thickness at different points of the contact region, and the coordinates of the boundary points of the dry contact region is also presented.     

基于ABAQUS的橡胶密封圈应力松弛分析

橡胶O形密封圈在高温工况下会发生应力松弛并导致密封失效。基于橡胶黏-超弹本构模型,利用有限元软件ABAQUS建立橡胶O形密封圈与沟槽接触的非线性有限元模型,分析O形密封圈在不同压缩率、不同油压、不同温度下的应力松弛情况及应力分布。结果表明:接触界面上的接触应力分布近似呈抛物线;O形密封圈应力在初期先急剧衰减,而后逐渐缓慢降低;压缩率和油压对应力松弛影响不大,但油压太大会降低密封可靠性;温度升高使应力松弛速率明显增大,并使最终应力降低,降低密封的可靠性。     

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.     

Implementation of Hertz theory and validation of a finite element model for stress analysis of gear drives with localized bearing contact

An analytical approach for stress analysis of gear drives with localized bearing contact based on the Hertz theory is proposed. The proposed approach provides a complete and effective solution of the contact problem but satisfaction of the hypotheses for application of the Hertz theory is its main drawback. On the other hand, a finite element model has been developed and validated in terms of the contact area, maximum contact pressure, pressure distribution, maximum Tresca stress, and Tresca stress distribution underneath the contacting surfaces. Validation of the finite element model is provided for those cases wherein the Hertz theory can be applied. The obtained results confirm the applicability of the proposed approach for gear drives with localized bearing contact wherein edge contact is avoided by surface modifications and whole crowning of tooth surfaces is provided.     

Measurement of Pressure Distribution in EHL—Development of Method and Application to Dry Static Contacts

The development and application of a new technique to measure the pressure distribution in an elastohydrodynamic contact is described. The method uses optical interferometry to measure the local compression of a thin elastic layer sandwiched between the loaded surfaces. The elastic-layer thickness is mapped as a line profile across the contact and the measured compression is calibrated to give a pressure distribution. The data are acquired through a single triggered image rather than a scanning system so that transient pressures can be measured. The current study is limited to static contacts, and pressure profiles are presented for a number of contact conditions. These include smooth and textured surfaces and entrained debris. The results are compared to theoretical predictions for smooth surfaces.     

渗氮钢粗糙表面的弹塑性接触研究

利用弹塑性有限元和单纯形法求解弹塑性接触模型，分别模拟了屈服强度呈梯度变化的渗氮钢、未经处理的匀质材料和硬涂层材料粗糙表面的弹塑性接触行为。与未经处理的匀质材料相比，渗氮钢可承受更大接触载荷。在相同载荷作用下，渗氮钢表面粗糙峰接触面积较小，平均间距较大，接触体内材料不易发生屈服，从而显著提高接触性能。和硬涂层材料相比，渗氮钢接触体内等效von Mises应力分布平缓，没有应力突变。最后讨论了渗氮层和硬涂层的厚度对粗糙表面接触特性的影响。