单层涂层最佳厚度的有限元分析

采用有限元数值计算的方法对TiN、TiC、Si3 N4及SiC四种材料的硬涂层体系表面下的应力分布进行了模拟分析。结果表明 ,对于TiN材料 ,当涂层厚度与接触半宽之比t/a <0 .3时 ,表面下的最大剪应力分布对提高轴承疲劳寿命较为有利 ;t/a =0 .5时 ,涂层系统的摩擦力学性能最差。涂层厚度较薄时 ,位于赫兹接触中心附近的涂层表层上的最大剪应力要远大于基体内的最大静态剪应力 ;当t/a >0 .1时 ,涂层表面上的最大剪应力对提高轴承疲劳寿命较为有利 ;涂层材料与基体材料的弹性模量之比小于 2 .0时 ,有利于提高涂层系统的疲劳寿命     

Method and surface roughness aspects for the design of DLC coatings

The design of coatings for highly loaded component contacts, such as bearings, gears and valve train components involves several important factors, including load, friction, lubrication, surface characteristics and material parameters. This paper presents an investigation of the influence of the material, coating thickness and surface roughness on tensional stress levels for coatings that are more compliant than the substrate material. Specifically the effect of multiple asperity contact is studied in three dimensions. The simulation is based on a finite element model where the load is applied as several interacting Hertzian pressure distributions.The results show that the surface structure, in combination with the elastic properties of the coating, has a large influence on the tensional stress level in the coating. The highest tensional stress level in the coating occurs when contact spots almost overlap neighbouring cells and at the same time the size of the contact spots is in the same order of magnitude as the coating thickness.     

Improved Elastic Contact Model Accounting for Asperity and Bulk Substrate Deformation

An improved elastic contact model for a single asperity system is proposed accounting for both the effects of bulk substrate and asperity deformations. The asperity contact stiffness is based on the Hertzian solution for spherical contact, and the bulk substrate stiffness on the solution of Hertzian pressure on a circular region of the elastic half-space. Depending on the magnitude of the applied load, as well as the geometrical and physical properties of the asperity and bulk materials, the bulk substrate could have considerable contribution to the overall contact stiffness. The proposed single asperity model is generalized using two parameters based on physical and geometrical properties, and is also verified using finite element analysis. A parametric study for a practical range of geometric and physical parameters is performed using finite element analysis to determine the range of validity of the proposed model and also to compare it with the Hertz contact model. The single asperity model is extended to rough surfaces in contact and the contact stiffness from the proposed model and the simpler Greenwood–Williamson asperity model are compared to experimental measurements.     

Contact Analysis of Anisotropic Coatings with Application to Ball Bearings

Anisotropic coatings represent an important class of tribological materials that are used to reduce friction and wear in mating surfaces. In the present investigation, a three-dimensional finite element model was utilized to analyze the contact behavior of a spherical indentor normally loaded between two transversely isotropic coated surfaces. After initially being validated via comparison to theoretical results available in the literature, the numerical model was used to determine the stress and displacement fields for a diverse range of coating materials and thicknesses, indentor radii and materials, and loading conditions. By curve-fitting the numerical data, expressions were generated for predicting the contact behavior in the posed problem. The relevance of these expressions, as related to the optimization of engineering components, was subsequently ascertained and discussed.     

Flash temperature during impact of layered elastic solids

An analytical model to calculate the maximum flash temperature during oblique spherical impact of an elastic single layered solid is presented. The model is developed by combining the contact parameters obtained from a spherical impact model and flash temperature solution for the sliding contact interface of a layered solid. Dynamic thermomechanical finite element analysis is used to examine the validity of the analytical model with good success. The flash temperature, obtained when the coating is accounted for, is different from that when homogeneous material only is considered, and needs to be accounted for estimating flash temperatures during impact of layered media.     

基于真实粗糙齿面的齿轮传动接触应力分析

现行齿轮传动接触疲劳强度的设计基础是仅适用于一对光滑表面之间干接触的赫兹理论,这显然与齿轮传动实际状况有一定差异。为获得齿轮传动实际状况的齿面压力分布、油膜厚度及轮齿接触区次表面的应力分布,基于实测所得的表面粗糙度数据,采用有限元法对重载齿轮传动进行混合弹流润滑数值分析。结果表明:粗糙齿面接触时的齿面压力分布及轮齿接触区次表面应力分布均明显相异于赫兹分布或基于光滑齿面全膜弹流润滑计算所得的相应分布;齿面粗糙峰谷的存在会使齿面接触应力比赫兹接触应力增大25%左右,且齿面平均油膜厚度的最小值及接触应力的最大值均发生在啮入点而非节点。因此,现行的以赫兹应力为基础、以节点参数为依据进行齿轮传动接触强度设计的做法有失科学性和安全性。     

Computational approach to contact fatigue damage initiation analysis of gear teeth flanks

The paper describes a general computational model for the simulation of contact fatigue-damage initiation in the contact area of meshing gears. The model considers the continuum mechanics approach, where the use of homogenous and elastic material is assumed. The stress field in the contact area and the relationship between the cyclic contact loading conditions and observed contact points on the tooth flank are simulated with moving Hertzian contact pressure in the framework of the finite element method analysis. An equivalent model of Hertzian contact between two cylinders is used for evaluating contact conditions at the major point of contact of meshing gears. For the purpose of fatigue-damage analysis, the model, which is used for prediction of the number of loading cycles required for initial fatigue damage to appear, is based on the Coffin-Manson relationship between deformations and loading cycles. On the basis of computational results, and with consideration of some particular geometrical and material parameters, the initiation life of contacting spur gears in regard to contact fatigue damage can be estimated.     

材料非线性对混合陶瓷球轴承有限元分析的影响

重点研究了材料非线性行为在有限元法分析混合陶瓷球轴承接触问题中的影响。首先对混合陶瓷轴承中的轴承钢GCr15进行了材料单轴拉伸试验,以确定其材料性能参数,再通过对几种接触模型的材料线性和材料非线性有限元分析、试验研究和赫兹接触理论计算,将这些结果比较分析,得到材料非线性对有限元接触分析在不同情况下的影响,从而对材料非线性行为在有限元接触分析中的应用做出评估。     

基于向量式分析的轮轨接触模拟

介绍了一种新的区别于传统有限元方法的计算力学方法——向量式分析方法。在理论公式推导的基础上,通过自编程序,利用该方法对轮轨静态接触问题进行了模拟。计算结果表明,该方法得到的最大轮轨法向接触压力、接触斑大小、Von mises等效应力与Hertz接触理论和有限元软件ANSYS结果仅相差±5%,吻合很好。向量式分析方法具有有效处理连续体大转动的优点,可为进一步模拟高速轮轨滚动接触动态行为提供很好的借鉴。     

Effects of surface coating on elastohydrodynamic lubrication of line contacts

A numerical solution to the elastohydrodynamic lubrication (EHL) problem of two coated elastic bodies in line contact is introduced. The non‐Newtonian behavior of the lubricant is incorporated into EHL analysis using Eyring's nonlinear viscous model. The surface elastic deformations are computed from full elasticity analysis of layered elastic half‐space. The iterative Newton–Raphson technique is used in the numerical solution. Subsurface stresses are calculated using two different techniques, the numerical integral scheme based on Fourier transformation and the finite element method. The effects of surface coating (material and thickness) on the pressure profile and subsurface stresses are presented and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

用弹塑性有限元法对焊接接头裂尖场J积分的研究

采用平面应力弹塑性有限元法研究了中心裂纹板焊接接头裂尖场J积分参量及其应用的可行性，数值分析采用MARC软件的二维弹塑性分析模型，探讨了不同强度匹配（高，等，低匹配）的焊接接头试样在加载过程中裂尖场J积分的变化情况，计算结果表明，靠近焊接接头裂纹尖端的J积分回路明显的路径相关性，而远离裂尖的J积分回路表现出路径无关性，焊接接头强度匹配因子M对裂纹尖端的J积分值有很大的影响，对应于每一个载荷P／P0，J积分的值随M的增大而减小，特别是当P／P0＞1．0时这种情况更明显。     

Finite element modelling of brittle fracture of thick coatings under normal and tangential loading

This paper addresses coating fracture in hard brittle coatings subjected to combined normal and tangential loads through a finite element based methodology. The coating is modelled as an elastic layer perfectly bonded to an elastic substrate with a pre-microcrack, assumed to initiate at the contact trailing edge due to high tensile stress. The predicted results are consistent with previously published coating fracture results. The model predicts a significant effect of coating thickness on crack propagation for coatings with large elastic mismatch and the final propagated crack profile is predicted to depend on friction coefficient, coating fracture toughness and sliding displacement.     

ANALYSIS OF THERMAL-ELASTIC STRESS OF WHEEL-RAIL IN ROLLING-SLIDING CONTACT

A coupling thermo-mechanical model of wheel/rail in rolling-sliding contact is put forward using finite element method. The normal contact pressure is idealized as the Hertzian distribution, and the tangential force presented by Carter is used. In order to obtain thermal-elastic stress, the ther-mal-elastic plane stress problem is transformed to an elastic plane stress problem with equivalent fictitious thermal body force and fictitious boundary distributed force. The temperature rise and ther-mal-elastic stress of wheel and rail in rolling-sliding are analyzed. The non-steady state heat transfer between the contact surfaces of wheel and rail, heat-convection and radiation between the wheel/rail and the ambient are taken into consideration. The influences of the wheel rolling speed and wear rate on friction temperature and thermal-elastic stress are investigated. The results show the following: ① For rolling-sliding case, the thermal stress in the thin layer near the contact patch due to the friction temperature rise is severe. The higher rolling speed leads to the lower friction temperature rise and thermal stress in the wheel; ② For sliding case, the friction temperature and thermal stress of the wheel rise quickly in the initial sliding stage, and then get into a steady state gradually. The expansion of the contact patch, due to material wear, can affect the friction temperature rise and the thermal stress during wear process. The higher wear rate generates lower stress. The results can help under-stand the influence of friction temperature and thermal-elastic stress on wheel and rail damage.     

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.     

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.     

A new roughness parameter to evaluate the near-surface deformation in dry rolling/sliding contact

Within this work, a two-dimensional finite element model for rolling contact of a wheel on a rail is presented that accounts for the roughness of the contact surfaces. The rail material is modeled with elastic–plastic behavior. The maximum of the plastic shear strain is concentrated close to the surface of the rail and is mainly influenced by the surface roughness. A concept is proposed that demonstrates one crucial parameter of the roughness determines surface deformation (based on results of a sinusoidal roughness model). This roughness parameter depicts the ratio between asperity height and width. Numerical validation is achieved for predicting plastic shear strains in rough surfaces. The plastic shear strain is associated with surface damage, such as cracks and wear.     

三维板料成形过程的有限元分析

基于有限变形理论建立了三维金属板料成形过程的弹塑性有限元数学模型。数学模型采用物质坐标系中的Total Lagrange描述、J 2型本构方程和等向强化假设,考虑了板料的厚向异性,对于金属板料与模具的摩擦定律。为简化计算采用薄膜单元。为了改善节点接触状态变化时计算的收敛性,提出了“弹性边界层”方法。采用根据此模型编制的程序模拟了机油收集器基本件的成形过程,并与试验结果进行了比较。     

A New Contact Model for Multilayered Solids with Rough Surfaces

A new numerical model is proposed to investigate the normal contact of multilayered solids with rough surfaces. The Hankel transform and the transfer matrix technique are used to solve the problem of the deformation of a multilayered solid. Then, the normal contact of an asperity is solved with Abel transform. Using this solution, an asperity-based contact model of rough surfaces is developed considering interactions between asperities. Numerical results are presented and compared to finite element calculations. The present model provides good results. The effects of interactions and the solid layers properties are discussed.     

基于真应力-应变关系的粗糙表面法向接触模型

提出一种粗糙表面的法向弹塑性接触分析的建模方法。基于微凸体的弹塑性有限元接触模型,分别研究了40Cr、45和Q235三种钢材料的微凸体与刚性平面的法向接触特性。有限元模型中采用三种材料的真应力-应变关系,考察了不同强化特性对微凸体接触性质的影响。建立了微凸体在弹性、弹塑性、塑性变形阶段统一的接触变量变化规律的表达式。在此基础上应用概率统计理论建立粗糙表面法向弹塑性接触模型。所建立的接触模型中微凸体接触变量的变化规律完全基于弹塑性有限元模型的计算结果,无需将微凸体的变形过程区分为不同的变形阶段,避免了接触变量在各阶段采用不同函数表达式带来的连续性和光滑性问题,以及在弹塑性阶段采用插值函数的随意性问题。通过与其他接触模型的计算结果相比较,证明了所提出接触模型的合理性。     

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。