Fatigue crack propagation in rocker and roller-rocker bearings of railway steel bridges

In this work, a method is proposed for rolling contact fatigue crack propagation analysis using contact and fracture theories in conjunction with fatigue laws. The proposed method is used in the fatigue analysis of rocker and roller-rocker bearings of a railway open web girder bridge which is instrumented with strain gages. Using a contact algorithm based on the minimum energy principle for bodies in rolling contact with dry friction, the normal and tangential pressure distribution are computed. It is seen that the most critical location of a crack in bearings is at a point very close to the contact region, as expected.     

Rolling,sliding and torsion of micron-sized silica particles: experimental,numerical and theoretical analysis

The contact mechanics of individual, very small particles with other particles and walls is studied using a nanoindenter setup that allows normal and lateral displacement control and measurement of the respective forces. The sliding, rolling and torsional forces and torques are tested with borosilicate microspheres, featuring radii of about \(10\,\upmu \hbox {m}\) . The contacts are with flat silicon substrates of different roughness for pure sliding and rolling and with silicon based, ion-beam crafted rail systems for combined rolling and torsion. The experimental results are discussed and compared to various analytical predictions and contact models, allowing for two concurrent interpretations of the effects of surface roughness, plasticity and adhesion. This enables us to determine both rolling and torsion friction coefficients together with their associated length scales. Interestingly, even though normal contacts behave elastically (Hertzian), all other modes of motion display effects due to surface roughness and consequent plastic deformation. The influence of adhesion is interpreted in the framework of different models and is very different for different degrees of freedom, being largest for rolling.     

Experiments and simulations of direct shear tests: porosity, contact friction and bulk friction

The direct shear testers, in particular the Jenike cell, are widely used to measure the bulk material properties for the design of bulk handling equipment. This paper describes a study of the Jenike shear tester using both experiments and discrete element simulations. A total of 90 tests on spherical glass beads and paired glass beads were performed to study the influence of the particle shape, stress level and packing density on the bulk friction at limiting shear. The data are thus useful for validating particle scale simulations of densely packed granular systems. In an attempt to verify the predictive capability of discrete element method, closely matching 3-dimensional discrete element simulations of the shear tests were performed and compared with the experimental observations. The comparison for single spheres shows good quantitative agreement for the limiting bulk friction when there is a good match in the sample porosity. Further research is needed to produce a comprehensive validation of the discrete element method. Several salient observations from this study provide further insight into the roles of particle shape and contact friction on the resulting packing porosity and bulk friction.     

Microdynamic analysis of solid flow in a shear cell

Granular flow in a model shear cell under conditions relevant to those in an annular cell is investigated based on the results obtained by means of the discrete element method. The spatial and statistical distributions of microdynamic variables such as velocity, porosity, coordination number and contact force are established, and the dependence of these variables on some key physical and operational parameters of particles and the cell is studied. It is shown that the normal pressure, shear velocity of the cell, particle friction coefficient and rolling friction coefficient have noticeable influences on these microdynamic variables. However, the effects of wall friction coefficient and damping coefficient are negligible. There is a linear relationship between overall coordination number and packing density, when the coordination number ranges between 5 and 6.5. The deviation from the relation derives from the cases where the normal pressure is varied as a result of the significant change in the normal contact forces between particles.     

摆线针轮传动接触热弹流润滑特性

针对摆线针轮行星传动啮合过程中啮合齿面摩擦行为影响系统动态特性、传动效率及接触疲劳特性等问题,基于牛顿流体及指数率、Ree-Eyring模型建立摆线针轮线接触时变热弹流润滑数值分析模型,获得理想安装的摆线针轮副完整啮合周期内摩擦力、摩擦系数及摩擦损失功率变动。结果表明,基于牛顿流体及指数率流体模型所得摩擦系数与工程实际不符;基于Ree-Eyring模型纯滚动啮合产生的热效应在重载下对啮合过程中膜厚、摩擦损失功率影响较大,对压力、摩擦系数影响较小。研究非牛顿流体特征参数与摆线针轮传动设计参数对啮合中摩擦系数、摩擦损失功率影响规律表明,流体特征应力增加摩擦系数及损失功率均减小;短幅系数取较大值时大部分啮合区间摩擦系数增加、摩擦损失功率减小。     

Numerical investigation of the influence of frictional conditions in thread rolling operations with flat dies

Numerical simulation technology has become an important part of the process design stage in bulk metal forming operations. With increasing computing performance, three dimensional simulations within the product design process are thus becoming increasingly feasible. However, the modeling of friction within numerical simulations is still posing a challenge, especially in very friction sensitive processes, such as rolling of axisymmetric parts. Within the presented work, the process of rolling with flat dies with consideration of friction (according to Amontons-Coulomb) is simulated and analyzed. With the developed model, tribological loads as well as the influence of friction is investigated. These numerical findings are contrasted with experimental results obtained with an industrial forming machine. It is shown that the numerically obtained results are highly sensitive regarding numerical and physical contact modeling parameters. This is due in part to the highly varying frictional conditions (relative sliding velocity, contact normal stress) within the contact zone. Additionally, it is shown that the contact zone exhibits properties that favor static friction rather than sliding friction. This observation is especially important for an adequate empirical characterization of friction for thread and profile rolling processes.     

水工钢闸门滚轮的滚动摩擦力臂计算方法

为了解决水工钢闸门滚轮在受载荷作用时产生的滚动摩擦力臂的计算方法问题,将滚轮与钢轨的接触问题简化为圆柱与圆柱座之间的接触问题,并以接触线为底作半圆,假设接触线上各点的压力与此半圆在该点的高度成正比。同时根据无限半平面Boussinesq问题的解法推导出滚动摩擦力臂的解析解。最后采用ANSYS建立滚轮全模型与钢轨进行接触分析来验证滚动摩擦力臂解析解的正确性。结果表明该滚动摩擦力臂计算公式简化合理,计算精度能够满足实际要求。     

The role of rolling friction in granular packing

In order to study the effects of the rolling friction of the particles on granular packing, we present a detailed analysis of circular disk assemblies with the rolling friction under macroscopic one-dimensional compression. The rolling friction of the particles produces a resisting moment to the rolling at each contact. A series of 2-D DEM simulations are performed with various values for the rolling friction parameter. We focus on several macroscopic and microstructural properties of granular media and analyze them as a functions of the rolling friction. From these results, we show that the rolling resistance, which results from the rolling friction of the particles, contributes to the inhibition of the rearrangement of the particles and increases the magnitude of the fabric anisotropy under packing. In addition, from both microscopic and macroscopic points of view, we describe that the stress state in a granular packing can vary considerably depending on the rolling resistance.     

Rolling–sliding contact fatigue of surfaces with sinusoidal roughness

Surfaces of mechanical components under combined rolling and sliding motions may be subjected to accelerated contact fatigue failure due to increased number of microscopic stress cycles and pressure peak heights caused by rough-surface asperity contacts. Available rolling contact fatigue (RCF) theories were developed mainly for rolling element bearings, for which the effect of sliding is usually insignificant. In various types of gears, however, considerable sliding exist in the critical tooth contact area below the pitch line, where excessive wear and severe pitting failures originate. Ignorance of sliding is most likely the reason why the conventional RCF models often overestimate gear fatigue life. This paper studies the effect of sliding motion on the contact fatigue life of surfaces with sinusoidal roughness that mimicks the topography from certain manufacturing processes. A set of simple equations for stress cycle counting is derived. Mixed elastohydrodynamic lubrication simulations are executed with the considerations of normal loading and frictional shear. Relative fatigue life evaluations based on a subsurface stress analysis is conducted, taking into account the two sliding-induced mechanisms, which are the greatly increased number of stress cycles and the pressure peak heights due to surface interactions. Obtained results indicate that sliding leads to a significant reduction of contact fatigue life, and rough surface asperity contacts result in accelerated pitting failure that needs to be considered in life predictions for various mechanical components.     

Copper based superhydrophobic microchannels: fabrication and its effect on friction reduction

Copper based superhydrophobic surfaces are fabricated using a laser electrodeposited composite method, which is able to form a dual rough microstructure. It is found that the static contact angles on these special microstructure surfaces are bigger than 150° and rolling angles are smaller than 5° when there is no low energy material coating on surfaces. It is also found that the pressure drops on microchannel surfaces composed with these microstructures show an increasing trend with the widening of channel. Under the condition of laminar flow, they are obviously smaller on superhydrophobic microchannels than on a smooth channel. Owing to the superhydrophobic structures, the friction factor reduces compared with a smooth surface. The biggest reduction value is 48·8%, and the smallest is 46·9%.     

Werkstoffanstrengung bei Wälzbeanspruchung – Einfluß von Reibung und Eigenspannungen

Material Stressing under Rolling Contact – Influence of Friction and Residual Stresses Material stressing of parts in rolling contact is in the main made up by the normal load to be transmitted, by surface friction due to slippage of the body in rolling contact and by residual stresses. The effects of varying slippage rates are described as well as the additional influence of residual stresses on magnitude, position and direction of load. By the aid of mere mechanical reflections the formation of flat and steep White Bands can be interpreted which are observed in long-lived ball bearings subjected to high stresses. The report shows that residual stresses and friction must not be neglected when describing the material stressing by rolling contact. This especially applies to residual stresses originating from rolling contact.     

Analysis of Critical Stress for Subsurface Rolling Contact Fatigue Damage Assessment Under Roll/Slide Contact

As one of the main failure modes of component operated under rolling contact loading, the rolling contact fatigue is classified into two types: subsurface initiated and surface initiated. Different stresses such as orthogonal shear stress, maximum principle shear stress, and octahedral shear stress have been applied as the critical stresses for the assessment of the subsurface cracks’ initiation due to rolling contact fatigue. The influences of friction on distributions of the ranges of orthogonal shear stress, maximum principle shear stress, and octahedral shear stress in subsurface were analyzed with reference to the results of the reference articles. The results show that friction does influence the subsurface distributions of these stresses to a certain extent. However, the upper limits of both the maximum principle shear stress and octahedral shear stress are smaller than that of range of orthogonal shear stresses under the rolling contact conditions of usual steel components. Hence, it is more appropriate that the orthogonal shear stress be selected as the critical stress for the assessment of subsurface rolling contact fatigue.     

Effect of friction on deformation during rolling as revealed by embedded pin technique

Abstract

The paper investigates the effects of friction on the heterogeneity of deformation during rolling through studies using plane strain (2D) and three-dimensional (3D) finite element models designed to simulate the deformation of the embedded pin inserts during rolling. Redundant work due to friction is defined as a path function along the arc of contact. Since deformation during rolling is profoundly influenced by the amount of redundant work, which depends on friction as a path function along the arc of contact, the study has focused especially on methods of representing these frictional effects. The friction studied has been in one of two classes: the coefficient of friction being constant or varying parabolically along the arc of contact. The results show that the values of shear stress and normal pressure along the arc of contact depend upon the friction profile. The magnitude of these frictional effects is revealed by the through thickness variation of the relative pin insert displacement. This displacement changes in the 3D model because transverse spread reduces the amount of displacement along the axial direction. Comparison of the simulations with experimental pin insert shapes shows close agreement between the predicted and experimental results, while revealing the direction of further work needed to provide suitable mechanics models to interpret experimental pin insert data.     

Frictional contact of flexible and rigid bodies

 This paper is about planar frictional contact problems of both flexible and rigid bodies. For the flexible case a nonlinear finite element formulation is presented, which is based on a modified Coulomb friction law. Stick-slip motion is incorporated into the formulation through a radial return mapping scheme. Linearly interpolating four node elements and three node contact elements are utilized for the finite element discretization. The corresponding tangent stiffness matrices and residual vectors of the equations of motion are presented. In the rigid body case the contact problem is divided into impact and continual contact, which are mathematically described by linear complementarity problems. The impact in normal direction is modeled by a modified Poisson hypothesis, which is adapted to allow multiple impacts. The formulation of the tangential impact is grounded on Coulombs law of friction. The normal contact forces of the continual contact are such that colliding bodies are prevented from penetration and the corresponding tangential forces are expressed by Coulombs law of friction. Examples and comparisions between the different methods are presented. Received: 10 January 2001     

Role of Friction in Cold Ring Rolling

1. Introduction Cold ring rolling is a main technology used to manu- facture various precise seamless ring shape parts. It has been increasingly used in many industrial fields such as bearing, machine, automobile, petrochemicals, aeronau- tics, astronautics and atomic energy because of its many technical superiorities such as considerable saving in en- ergy and material cost, high quality, high efficiency, and low noise, etc. To research and develop advanced precise cold ring rolling technolog…     

Inverse analysis for evaluation of the shear modulus of inhomogeneous media by torsion experiments

The present paper addresses the problem on torsion of a circular indentor with a flat base on a half-space covered by an inhomogeneous coating with shear modulus arbitrarily varying in-depth. Approximate analytical solution of this problem is developed. The obtained formulas allow one to determine the distribution of contact stresses under indentor, as well as the dependence of the torsion moment applied to the indentor from the twisting. It is shown that the approximate formulas are asymptotically exact both at large and small values of characteristic dimensionless geometrical parameter of the problem.Based on the analysis of the derived solution, we suggest evaluation technique for the shear modulus of a functionally-graded coating in the case when it depends on one parameter only. The technique uses the data received in the course of torsion experiments by a series of indentors of various radii.     

复合材料管接头与钢管间摩擦力及其对管接头强度的影响——数值分析

通过定义接触单元, 建立了复合材料套管接头与钢管连接的有限元分析模型。分析了在钢管端部受到弯曲、压缩和扭转载荷条件下, 复合材料管接头的应力状态, 并采用Tsai-Wu 强度准则对复合材料管接头进行了强度分析。重点研究了随着摩擦系数的变化复合材料管接头与钢管间摩擦力的变化规律及其对复合材料接头强度的影响。结果表明, 随着摩擦系数的增大, 复合材料管接头与钢管间最大正应力减小, 最大摩擦力增大; 在以弯曲载荷为主的组合载荷作用下, 复合材料管接头的安全裕度增大。      

Effect of crack face contact and friction on Brazilian disk specimens—A finite difference solution

A full curvilinear transformation is employed to study the effect of contact and friction on Brazilian disk specimens containing a crack and subjected to concentrated loads at angles 0° <  < 90°. Homogeneous and bimaterial disks made of glass and epoxy are considered. The effect of loading angle and friction coefficient on the stress intensity factors, as well as the contact length is studied. The results are compared to available semi-analytical and finite elements results. It is found that when the crack faces are in contact without stick zones, an increase in friction causes a decrease of the normal gap, tangential shift and stress intensity factors. When stick conditions appear in the contact zone, an increase in the coefficient of friction also results in increasing the stick zone within the contact zone.     

Crack Growth in Rolling Bodies under the Conditions of Dry Friction and Wetting

Within the framework of a two-dimensional mathematical model, we study the development of a surface macrocrack in the course of unidirectional rolling under the conditions of dry friction and wetting. The damaged body in a rolling couple is modeled by an elastic half plane with an edge cut (crack) and the action of the counterbody is simulated by the translational motion of Hertzian contact forces along the boundary of the half plane with taking into account the friction forces. We compute the crack-growth paths depending on the coefficient of contact friction between the bodies and the orientation and length of the crack. The numerical calculations are performed by the step-by-step method based on the use of the singular integral equations of the theory of elasticity for bodies with curvilinear cracks and the criterion of generalized opening. It is shown that, for high coefficients of friction between the bodies of the rolling couple (f = 0.20–40; dry friction), a branch propagates from the original fatigue shear macrocrack into the bulk of the material of the driven body. In the case of low friction coefficients (f < 0.20; wetting), a branch mainly propagates along the boundary of the body in the direction of motion of the counterbody. We propose an explanation of the mechanism of development of burrow-type defects often encountered in railroad rails.     

Prediction of the Service Life of Rolling Bodies According to the Development of a Subsurface Crack

Within the framework of the fracture mechanics of solid bodies under the conditions of rolling-contact fatigue, we study the paths of propagation of a subsurface crack and determine the residual service life of the rolling surfaces (in terms of their crack resistance) under the conditions of dry friction. The stress intensity factors and growth paths of an initially rectilinear crack are analyzed depending on its orientation, location, and length and on the friction coefficient f (f = 0.2–0.4) for the rolling bodies in contact under the assumption that the crack propagates according to the mode-I mechanism. We establish the ranges of the indicated parameters in which the crack is completely open (its lips are not in contact). Some features of propagation of horizontal cracks and formation of spalling in the rolling bodies are discovered. It is shown that it is difficult for a horizontal crack to appear on the surface according to the (mode-I) mechanism of normal tension. The residual service life of the subsurface layers of rolling bodies made of 75KhGST rail and 9KhF roll steels and weakened by subsurface cracks is evaluated.