Three-dimensional modeling of elasto-plastic sinusoidal contact under time dependent deformation due to stress relaxation

In the current work, the effect of stress relaxation in contact between sinusoidal surfaces is studied using FE simulations. There are a few works on the elastic and elasto-plastic contact between sinusoidal surfaces, but the transient effects such as creep and stress relaxation are not considered in these works. Stress relaxation causes significant change in the contact area and pressure between the contacting surfaces. The Garofalo formula is used to model the transient behavior of stress relaxation. The results for the contact area and contact pressure are presented and discussed. Empirical equations are developed to predict contact area and pressure by fitting to the FEM results. The equations are dependent on the initial surface separation, aspect ratio, and the Garofalo constants.     

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.     

六辊CVC轧机辊系变形的有限元分析

建立了运用有限元软件ANSYS求解具有特殊辊廓曲线和辊间接触状态的六辊CVC轧机辊系三维弹性变形的有限元模型，合理解决了对辊间接触压扁变形的建模问题，实现了对较复杂变形的求解。以国内某1420冷轧机组为研究对象，结合现场实际数据，运用有限元软件ANSYS求解六辊CVC轧机的辊系三维弹性变形，计算结果与实测数据吻合较好。     

ANALYSIS ON THERMAL ELASTO-PLASTIC ASPERITY CONTACTS OF LAYERED MEDIA

A thermal elasto-plastic asperity contact model is investigated, which takes into account the steady-state heat transfer and the asperity distortion due to thermal elasto-plastic deformations. A hard coating and a soft coating are applied to study the correlations between contact area and contact pressure, average gap and contact pressure, coating thickness and contours of the contact stress distribution, etc. The effects of material properties, coating thickness, frictional coefficient, and the heat input combinations on the stress distribution are investigated and discussed. The frictional heat input increases the maximum value of yon Mises stress. Finally, the appropriate thickness of the hard coating is also discussed. To protect the substrate, one can choose hard coating and the thickness of that is suggested that can be hc=70 Rm.     

Analysis and Convenient Formulas for Elasto-Plastic Contacts of Nominally Flat Surfaces: Average Gap,Contact Area Ratio,and Plastically Deformed Volume

Interaction of nominally flat engineering surfaces that leads to a large contact area exists in many mechanical systems. Considering periodic similarity of surface geometry, a numerical three-dimensional elasto-plastic contact model can be used to simulate the contact behaviors of two nominally flat surfaces with the assistance of the continuous convolution and Fourier transform (CC-FT) algorithm. This model utilizes the analytical frequency response functions (FRF) of elastic/plastic responses of materials and provides contact performance results, including the average surface gap, the contact area ratio, and the volume of plastically deformed material, which may be defined as performance variables. Following the digital filtration technology, rough surfaces can be numerically generated with specified autocorrelation length and the first four orders of statistical moments. A group of contact simulations are conducted with various working conditions. The effects of topographic and material properties on the contact behaviors are discussed. With a multi-variables regression method, empirical formulas are developed for the performance variables as functions of surface statistical characteristics, material properties, a hardening parameter, and the applied load in terms of pressure.     

材料属性温度相关热弹塑性接触问题研究

应用有限元方法建立了可考虑屈服应力温度相关效应的粗糙表面热弹塑性接触模型。研究了摩擦力和不同热输入情况下圆柱体与弹塑性平面的接触力学特性。求解了考虑屈服应力温度相关效应的粗糙表面热弹塑性接触问题,探讨了摩擦热效应对表面温升、接触压力、平均间隙及接触体应力分布的影响。提出了考虑热膨胀系数温度相关效应的热弹塑性接触模型。通过刚性圆柱体与半无限大平面的热弹塑性接触研究了热膨胀系数温度相关效应对接触体应力分布的影响。
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Elasto-Plastic Contact of Rough Surfaces

An isothermal elasto-plastic asperity contact model is developed and presented in this paper, which deals with micro plastic flows of materials and the influence of the elasto-plastic deformation of materials on the behavior of contacting surfaces. The model is solved with the incremental form of a simplex-type algorithm. The von Mises yield criterion is used to determine the onset of the plastic deformation. The effectiveness and validity of the model are studied through analyzing a Hertzian contact problem. Substrate stresses are calculated and differences are observed. Furthermore, the contact pressure, real area of contact, and average gap of real rough surfaces under the elastic, elastic-perfectly-plastic, and the elasto-plastic contact conditions are numerically investigated and the results are compared.     

粗糙表面塑性变形对弹流润滑性能的影响

利用弹塑性动压润滑理论来分析线接触条件下粗糙表面的塑性变形对润滑性能的影响。首先计算总变形量,然后根据弹塑性理论对总变形量进行修正获得弹塑性变形量。计算中采用直接迭代法对雷诺方程进行数值求解,用多重网格法得到弹塑性变形量。为定量分析塑性变形的影响,采用余弦粗糙度来代替实际的粗糙表面,通过改变余弦粗糙度的峰高、波长和相位来表征粗糙度的变化,以此来分析粗糙度对弹塑性流体润滑的影响。计算结果表明:考虑塑性因素后,在接触的高压区膜厚变小,油膜分布曲线变得平坦,同时接触区域的油膜压力也明显变小;此外塑性变形因素的存在使得接触区的压力和油膜分布宽度增加,第二压力峰和最小膜厚点后移。     

A Finite Element Study of an Elasto-Plastic Disk or Cylindrical Contact Against a Rigid Flat in Plane Stress with Bilinear Hardening

This work presents a finite element study of elasto-plastic cylindrical contact. The geometry could also be described as a vertically aligned disk whose axis of symmetry is parallel to the contact surface. The cylinder is considered to be in the plane stress state. The material of the cylinder is modeled as elasto-plastic with bilinear hardening (also known as linear hardening). Simulations for a range of material properties and deflections typical to engineering applications are carried out. A mesh convergence study has also been performed. By employing symmetry, the cylinder has been modeled as a quarter circle and a straight line is used to model the opposing rigid flat surface. The finite element results for the elastic and fully plastic cylindrical contact cases are compared to other existing models such as Hertz contact and spherical elasto-plastic models. Since the case considered is plane stress, the stress distribution is significantly different from elasto-plastic spherical contacts, which would be closer to a plane strain case. An empirical relationship is fit to the results to allow for prediction of the contact width as a function of displacement and force.     

金属基/陶瓷复合双涂层的正接触应力分析

以球形压头为模型，采用I—deasCAD／CAE软件对Hertz弹性接触状态下金属基／陶瓷双涂层系统的应力分布情况进行了理论建模，并基于模型计算了在不同的涂层厚度／接触半宽度比和外涂层／过渡层／基体弹性模量比情况下的应力分布情况。双层系统具有相同的厚度和不同的弹性模量。论述了无涂层弹性半空间体的有限元分析结果与经典的Hertz接触力学解析解结果的一致性，计算结果有助于工程中陶瓷涂层的设计与应用。     

考虑界面端应力奇异性的螺栓连接支承面接触压力计算模型

将螺栓连接支承面接触问题简化为集中载荷和力矩耦合作用的有限刚度平头压模接触问题,利用BOGY特征值方程,分析双材料界面端应力奇异性发生的几何条件;依据GLADWELL接触力学理论,构建集中载荷和力矩耦合作用下平头压模接触压力计算模型,利用此模型分析螺栓预紧力、装配间隙和被连接件材料对螺栓连接支承面接触压力分布的影响规律。结果表明：在规定预紧力范围、装配等级和常用被连接件材料下,螺栓连接支承面不会发生退让接触,而界面端部出现明显的应力奇异性,其中预紧力变化对界面端应力奇异性强度影响不明显,但装配间隙和被连接件材料的变化对界面端应力奇异性强度影响显著;当被连接件材料弹性模量大于螺栓材料时,支承面内侧应力奇异性强度大于外侧,反之内侧应力奇异性强度明显小于外侧。此外,以平头压模为算例,采用有限元法验证了构建模型的准确性。     

点接触弹流动压性能的多网格法分析

点接触问题主要研究在一定载荷作用下,运动球体间的接触力学性能,涉及物体的弹性变形和流体动压的相互作用。本文应用多网格重积分方法,在给定的物体几何结构、载荷、速度、流体性质条件下,对运动球体的弹性变形、流体膜的厚度分布、流体膜的压力分布等参数的性能及其关系做了研究。分析结果反映出这类问题的基本特征和参数之间相互作用的规律。这一分析技术为相关结构和参数的设计及进一步分析提供了一个强有力的手段。     

含涂层真实粗糙表面的弹塑性接触特性研究

运用有限元法、线性规划法和塑性增量理论对含涂层真实粗糙表面的弹塑性接触问题进行了分析。通过改变涂层材料的弹性模量、屈服极限及涂层厚度，研究了不同条件下接触面积与接触压力、平均间隙与接触压力的关系及变化规律，给出了3种数值方法的解与弹性解的比较，分析了各主要因素对接触压力、接触面积及平均间隙的影响。     

环面型无级变速传动的速比建模与应力分析

利用非定轴空间点啮合理论分析了环面型牵引式无级变速传动的速比变化过程,并由此建立了调速油缸的行程与速比之间的对应关系模型,该模型为速比的精确控制奠定了基础。在考虑切向牵引力对接触区域的影响条件下,采用三维弹性接触有限元法分析了接触区内的接触应力和子表面切应力的分布状况,该分析结果可用于动力传动单元的接触疲劳寿命设计。     

面向对象的接触问题的有限元分析

工程实际中接触问题是十分普遍的，本文基于接触单元法，采用面向对象的程序设计技术，实现了物体弹性接触的有限元分析，并提出了一种求解刚度方程的改进方法，可对零件接触表面接触载荷的分配与分布，因接触引起的应力分布变化及变形情况进行有效地研究。     

Residual stress in some elasto-plastic problems of rolling contact with friction

The problem or rolling contact is of a great interest from the practical and cognitive points of view. It concerns for example a wheel passage on a rail, as well as many other processes where rolling or rolling with sliding is involved. Particularly, residual stresses distributions in the subsurface area due to plastic deformations are of significant importance: these stresses strongly influence fatigue limit and cracking tendencies of the material. A motion of the wheel on the rail (or of a roller on a strip) often has a very complex character: it consists of rolling, sliding in the longitudinal direction due to brakings and accelerations, sliding in the transversal direction, etc. Investigations conducted on this field by many authors have not yet delivered a unique solution. The aim of this paper is to determine the influence of some of these components of the wheel motion (separately and in common action) on residual stresses distributions. The problem has been investigated numerically by the FEM method, using the program SEGLA developed by the authors. The program can be applied to solving linear and nonlinear 2D, axisymmetric and 3D problems with elasto-plastic effects in the nonlinear contact and fracture mechanics. It uses three, four, six, eight and nine-node elements and also the special “spring” elements to model contact. The applied algorithm allows automatic analysis of these fragments of boundary, which enter and leave the contact; in the area where the “new” contact is created the program introduces additional elements.     

风力发电机偏航轴承载荷分布及接触角数值解法研究

基于赫兹弹性接触理论,推导了滚子与轴承内外圈接触变形时的接触刚度,建立了偏航轴承受复杂载荷时受力平衡的非线性方程组,井运用带有松弛因子的牛顿-拉夫逊法求解非线性方程组,得到了承载时偏航轴承各滚子的接触应力和接触角.最后,用经典理论公式和有限元方法对此方法计算结果进行了验证,证明了文中计算方法的正确性,为兆瓦级风力发电机轴承的设计计算提供了参考依据,具有一定的工程应用价值.     

Surface contact stress-based nonlinear virtual material method for dynamic analysis of bolted joint of machine tool

The components of machine tools are mainly fixed and connected by bolts. The performance of the assembly can be affected by the dynamic characteristics of the bolted joints. This paper presents a nonlinear virtual material method based on surface contact stress to describe the bolted joint for accurate dynamic performance analysis of the bolted assembly. Fractal geometry theory is used to describe the surface topography. The elastic modulus and shear modulus of one micro-contact are derived based on fractal contact theory. The equivalent elastic modulus, Poisson ratio, and density of the bolted joint can be obtained through the weighted mean method. In order to obtain the stress distribution, the contact surface is assumed flat in the macro-scale, and the uneven distribution of contact stress can be obtained by the finite element method (FEM). The contact surface can be divided into several sections, and the parameters of a virtual material layer can be determined based on the mean contact stress. Both theoretical and experimental results for a bolted joint are obtained for a box-shaped specimen under equal pre-tightening force and bending moment effect. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 4.41%, which indicates that the present nonlinear virtual material method is appropriate for the bolted joint in modeling CNC machine tools.     

传热界面真实接触面积计算与分析

在热流通过两相互接触材料尤其是金属材料的界面时，真实接触面积是界面传热的一个主要影响因素。当承受大应力的两接触体之间具有相对滑动或相对滑动趋势时，粗糙表面在压力和粘着力及剪切力的作用下接触粗糙峰发生弹性、弹一塑性或完全塑性变形，真实接触面积与压力之间的关系随变形机制而发生变化，在力的作用下材料的变形机制由表面微观几何形貌和力学性质决定。计算表明，单个粗糙峰接触面积与载荷的关系受变形机制的影响，粘着力对接触面积的影响可以忽略，表面相对滑动将增加真实接触面积。     

Note on the complete contact between a flat rigid punch and an elastic layer attached to a dissimilar substrate

The contact pressure distribution is found for a square ended rigid punch, pressing normally onto an elastic layer, itself attached to an elastically dissimilar half-plane, under plane deformation. Each interface may be either frictionless or adhesive, and it is shown that the shear traction assumption has only a very small influence on the contact pressure, which is found as a perturbation on the classical Flamant half-plane solution. For thin layers the contact pressure distribution is only weakly dependent on the pad aspect ratio.