Modeling of geometry effects in fretting fatigue

The stress field that results from two bodies in contact is an important aspect that governs the fretting fatigue behavior of materials. Applied loads as well as contact geometries influence the contact stresses. The profile of an indenter and the boundary conditions provide sufficient information from which the surface tractions and the corresponding subsurface stresses have been calculated in a semi-infinite halfspace using singular integral equations. In this investigation, a numerical subroutine was developed to calculate the surface tractions and the corresponding surface and subsurface stresses of an arbitrary finite thickness infinite plate subjected to loading through a random indenter. The results from the detailed stress analysis of the contact region are required by both an initiation and fracture mechanics approach. While initiation criteria involving stress gradient fields, such as sharp notches and edges of contact in fretting fatigue, are not well established or agreed upon, stress intensity factor calculations using tools such as weight functions are more reliable. The stress intensity analysis, which is used to determine whether an initiated crack will continue to grow if it is above the threshold, depends on many variables in the stress analysis such as pad and specimen geometry, loading configuration and friction coefficient. The contact stress analysis has been used to determine equivalent stress parameters that are related to the initiation of a crack. Similarly the numerical subroutine for the contact stresses is used in conjunction with the stress intensity analysis to determine the influence of the geometry, loading configuration and friction coefficient on the stress intensity factor. Results from high-cycle fretting fatigue experiments are used to determine the threshold stress intensity factor for a given configuration. The combination of the numerical and experimental analysis is then used to develop a tool for high-cycle fretting fatigue based on a threshold approach involving a go–no go criterion.     

Analysis of the elastic punch-substrate contact under fretting: Monotonic and cyclic loading of the punch

The object of this paper is to analyze the elastic behaviour of a 2-D contact problem between a right-angled flat punch and a semi-infinite substrate, subjected to a constant normal compressive load and a cyclic shear load using a finite element code. The knowledge of the stress and strain fields produced close to the corners of the punch under different loading conditions as a function of the friction coefficient will allow insight to be gained into the fretting fatigue problem associated to this cyclic loading. In order to better understand the behaviour and analyze the possibility of using fracture mechanics approaches to study the stress field close to the punch corners, two different models have been compared to each other: one without continuity solution between the punch and the substrate and the other with a couple of contact surfaces between them. Using the continuous model, a particularization of the general analytic solutions of Williams has been proposed. The complete stress field around the corners of the punch for this model has been obtained for any values of the punch size, normal and shear loads. Some general guides for understanding and systematizing the punch-substrate behaviour have been extracted from the above solution and that of a sliding wedge, provided by the literature, which enable a systematic numerical analysis of the problem. Further on, a more detailed study of the slip between punch and substrate, as well as of the stress field, has been accomplished using finite element analysis guided by the previous semi-analytical results. The study has been completed for the whole load process: compressive normal load, monotonic shear load, and cyclic shear load.     

The subsurface stress field caused by both normal loading and tangential loading

The subsurface stress field caused by both normal loads and tangential loads has been evaluated using the rectangular patch solution. The effect of tangential loading on the subsurface stress field has been investigated in detail for both the cylinder-on-cylinder contact and a spur gear teeth contact. For the cylinder-on-cylinder contact, the subsurface stress fields are moved more to the direction of tangential loads and the positions where the maximum stress occur are getting closer to the surface with the increasing tangential loads. The subsurface stress fields of the gear teeth contact are expanded more widely to the direction of tangential loads with the increasing tangential loads. The friction coefficient of a gear teeth contact is low because they are operated in a lubricated condition, and therefore surface tractions in the EHL condition hardly affect on the subsurface stress field.     

FEM Comparison of Ball and Roller Bullgears

A structural finite element model has been developed for calculating the forces transmitted through the rolling elements (load distribution) in a bullgear assembly. The elastic structural model consists of 3-D beam elements used to approximate the global race deflection and non-linear springs that approximate the combined rolling element/raceway contact deflections. For rollers, an upperbound on the contact stress (assuming linear variation of force along the length of the roller) is estimated by modeling the rollers as pairs of nonlinear springs. The finite element approach iteratively solves the contact forces at each, rolling element. Contact stresses are then calculated from the contact, forces using Hertz contact theory. This approach is applied to analyze two proposed designs of ball and crossed roller bearing, bullgear assemblies used for rotating the radar antenna on top of a ship's mast. The loads analyzed include those arising from wind loading and from out-of-flatness of the inner race of the bearings due to deflection of the mast. The distribution of the load and the maximum contact stresses for the proposed bullgear assemblies are estimated and compared. It is found that the maximum contact stress in the crossed roller bearing is less than that in the ball bearing for both types of loads. Furthermore, the analysis shows that the out-of-flatness loading produces significantly higher stresses than wind loading.     

Rolling Element Bearing Contact Geometry Analysis

Rolling element bearings are subjected to a variety of loads during the operation of machinery. Raceway contact geometries should be designed and analyzed in a manner which accurately models internal contact stress distributions for these different load cycle conditions. To properly determine contact stresses, analyses should determine the orientation of rolling elements relative to the raceways through consideration of load, bearing alignment and bearing internal geometry. Since design loads are not always well defined and machinery upgrades may increase loads, contact geometry designs should have sufficient flexibility to handle conditions differing from the initial design loads. An analytical procedure with examples is discussed.     

The effects of contact configuration and coating morphology on the tribological behaviour of tetrahedral amorphous diamond-like carbon (ta-C DLC) coatings under boundary lubrication

ABSTRACT

Tribological studies were carried out with tetrahedral amorphous diamond-like carbon (ta-C DLC) coatings, varying in thickness and roughness, using two different contact configurations lubricated with seven types of hydraulic oils. Tribopair of cast iron and ta-C coated steel were tested in both non-conformal and conformal, unidirectional sliding contacts. The friction and wear results were mainly affected by the thickness of the coating in the non-conformal contact and the surface roughness of the coating in the conformal contact. Tests done with mineral base oil containing rust inhibitor in the non-conformal contact and with Polyalphaolefins and synthetic ester base oils in the conformal contact resulted in the lowest friction while that with mineral base oil containing zinc resulted in high friction and counterface wear. The results highlight the interdependence of contact configuration, lubricant chemistry, coating’s surface morphology and coating’s thickness in determining the tribological behaviour of ta-C coatings under boundary lubrication.     

Relative fatigue life estimation of cylindrical hollow rollers in general pure rolling contact

Solid and hollow cylindrical rollers in pure rolling contact have been modelled. The two rollers are subjected to a combined normal and tangential loading. The tangential loading is one‐third of the normal loading value. The finite element package, ABAQUS, is used to study the stress distribution and the resulting deformations in the bodies of the rollers. Then the Ioannides–Harris fatigue life model for rolling bearings is applied on the ABAQUS numerical results to investigate the fatigue life of the solid and hollow rollers. Using the fatigue life of the solid rollers as the reference fatigue life, the relative fatigue lives of hollow rollers are determined. Four main different hollowness percentages are been studied: 20, 40, 60 and 80%. The hollowness percentage is the ratio of the diameter of the hole to the outer diameter of the cylinder. For each of those hollowness percentages, two cases are studied – when the two rollers in contact are hollow and when one hollow roller is in contact with a solid roller. This study includes two main models: Model 1, where the two cylindrical rollers in contact are of the same size, and Model 2, where the two rollers in contact are not of the same size. The estimated relative fatigue lives of hollow rollers showed a great improvement of the fatigue life compared with solid rollers under the same loading conditions. This was a result of the redistribution of stresses in the contact zone in the case of hollow rollers. Redistribution of stresses over a larger volume of the roller body decreased the peak stress and reduced the volume under risk. Increasing the hollowness percentage from 20 to 60% increased the flexibility of the roller, and better stress distribution was achieved, which resulted in improving the fatigue life. Although 80% of hollowness rollers have more flexibility than 60% of hollowness rollers, the bending stresses (σ_b) on the inner surface of the rollers tend to decrease the fatigue life. Copyright © 2007 John Wiley & Sons, Ltd.     

Determination of Static Load Distributions from Elastic Contacts in Rolling Element Bearings

A method has been developed for recording the elastic roll body contacts in the load zone for both radial and thrust rolling element bearings subjected to various static loading conditions. Employed in this investigation were a ball bearing and four types of roller bearings which included cylindrical, needle, tapered and spherical. Inspection of the contact areas, or footprints, yields a qualitative measure of the extent of loading arc, load sharing among rolling elements, contact characteristics such as end loading and effects of misalignment. Quantitative data on individual contacts permits the determination of load and stress distributions. Summation of the vertical components of individual roll body loads agrees with the total load applied to the whole bearing, thereby demonstrating the practicability and accuracy of this technique. Correlation of roll body loads with theoretical values varied, depending on angular position from the radial load plane. Finally, this paper indicates how static stress levels on the most heavily loaded element may be obtained and used as a basis for bearing life prediction.     

Thermal ratchetting of a tube with non-uniform thickness

Two-dimensional (plane stress) finite-element analyses have been carried out to investigate the thermal ratchetting behaviour of a thin tube with an eccentric bore (eccentricity/mean wall thickness = 0.2). The tubes were subjected to steady internal pressure and cyclic, linear through-thickness temperature gradients. If the mechanical loading is characterized by the nominal mean stress (σ_m) at the thinnest section, the ratchetting boundary is accurately predicted by a simple, analytical, beam model. For high thermal loads ( ) the maximum mid-thickness ratchet strains are conservatively predicted. However, for lower thermal stresses the mid-thickness ratchet strains are underpredicted. The value of the creep stress exponent has no effect on the ratchet strains obtained under complete redistribution conditions. The first cycle ratchet strains under no-creep conditions are practically identical to the complete redistribution values.     

Tribological Performance of PTFE–Metal Binary Coatings in Rolling/Sliding Contact

Tribological performance of surface coatings with embedded PTFE reservoirs in rolling/sliding contact is reported. Using two different coating materials and two shapes and patterns of PTFE reservoirs test samples in the form of discs were prepared and tested in a four-ball contact configuration under loads corresponding to nominal contact pressure of 0.5 and 1.0 GPa. It was found that one coating, namely aluminium–bronze with embedded PTFE reservoirs is suitable for applications where rolling is also associated with a degree of sliding and there is no external lubrication.     

Notes on contributors

Various metallic pairs were tested under conditions of unlubricated solid contact. Experiments were conducted for repetitive impulsive and continuous sliding contact. Wide ranges of materials and conditions (nominal contact stress and relative transverse sliding velocity) and a variety of loading modes (pure normal impact at various frequencies, compound impact at various sliding velocities, and pure sliding under various stress levels) were explored.Particular attention was focused on the establishment of subsurface material zones developed in the tests, in situ. These zones exhibit dependences on velocity, stress, material, test duration and loading mode. The experimental findings, based on several analysis techniques, serve to characterize subsurface zone composition and morphology. Both surface and subsurface features were examined by optical and electron microscopy and analyzed by energy-dispersive X-ray techniques to allow interpretations concerning the role of external parameters, material transport and debris formation, as well as insight into operative mechanisms which act on specific materials under prescribed conditions to cause wear.     

Effect of surface texturing on elastohydrodynamically lubricated contact under transient speed conditions

Effect of surface topography modifications on lubrication film thickness within non-conformal lubricated contact operated under transient speed conditions is observed. Optical test rig is used to observe the lubricant film behaviour between the flat surface of a chromium coated glass disc and a steel ball under simplified operational conditions modelling the cam and tappet contact. Numerical simulation was used to be able to choose the operating conditions suitable for experiments. An array of micro-dents was produced on the ball surface to be able to demonstrate the effect of surface topography on lubrication film formation. Experiments were carried out under elastohydrodynamic lubrication conditions. Obtained results have shown that surface texturing could represent the way how to increase lubrication efficiency of rolling/sliding non-conformal contacts under transient operational conditions through the lubricant emitted from micro-dents. It was found that the lubricant emitted from the micro-dents helps to separate rubbing surfaces especially under thin film lubrication conditions where the rubbing surfaces moves in the opposite direction.     

Fatigue life investigation of solid and hollow rollers under pure normal loading

Two solid and hollow cylindrical rollers in pure rolling contact subjected to pure normal loading have been modelled. Using a finite element package called ABAQUS, the stress and strain distributions in the two rollers in contact have been determined. The relative fatigue life of the hollow rollers compared to solid rollers has been investigated using the fatigue life model for rolling bearings developed by Ioannides and Harris. Different hollowness percentages have been studied: 20, 40, 60 and 80%. The hollowness percentage is the ratio of the diameter of the hole to the outer diameter of the cylinder. Both cases were studied – when the two rollers in contact are hollow and when only one of them is hollow while the other one is solid. Making the rollers hollow will result in redistribution of stresses over a larger volume in the contact zone due to the flexibility of the hollow rollers. That decreases the peak stress in the contact zone of the hollow cylinder when compared to the solid cylinder. Hollow cylinders have more flexibility when subjected to normal loading. And so, the stresses are redistributed so that the fatigue life is improved. The best stress redistribution and so fatigue life improvements have been found when both cylinders have around 60% hollowness. Copyright © 2007 John Wiley & Sons, Ltd.     

Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads

In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin's approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented.     

多轴随机应变加载下铝合金缺口件有限元分析及寿命预测

在应变控制下对7075-T7451铝合金实心棒带U型环状缺口试件进行拉—扭比例、非比例恒幅和随机加载疲劳试验。查明名义剪切应力最大值与轴向应力最大值的下降规律,并用两者最先开始下降时的循环数比值来评估裂纹萌生寿命。利用弹塑性有限元法分析不同加载条件下试件缺口根部的循环应力、应变响应。基于有限元计算得到的应力、应变结果,采用拉伸型多轴疲劳损伤模型预测随机加载条件下缺口试件的疲劳裂纹萌生寿命,计算结果与试验得到的寿命比较吻合。     

Effects of variable loading conditions on the dynamic behaviour of planetary gear with power recirculation

Variable loads to which gearboxes are subjected are considered as one of the main sources of non-stationarity in these transmissions. In order to characterise their dynamic behaviour in such conditions, a torsional lumped parameter model of a planetary gear with power recirculation was developed. The model included time varying loading conditions and took into account the non-linearity of contact between teeth. The meshing stiffness functions were modelled using Finite Element Method and Hertzian contact theory in these conditions. Series of numerical simulations was conducted in stationary conditions, with different loading conditions. Equation of motion was solved using Newmark algorithm. Numerical results agreed with experimental results obtained from a planetary gear test bench. This test bench is composed of two similar planetary gears called test planetary gear set and reaction planetary gear set which are mounted back-to-back so that the power recirculates through the transmission. The external load was applied through an arm attached to the free reaction ring. Data Acquisition System acquired signals from accelerometers mounted on the rings and tachometer which measured instantaneous angular velocity of the carrier’s shaft. The signal processing was achieved using LMS Test.Lab software. Modulation sidebands were obtained from the ring acceleration measurements as well as a non-linear behaviour in case of variable loading resulted by a transfer of the spectral density from the fundamental mesh stiffness to its second harmonic.     

精梳机墙板动应力集中问题的分析与优化设计

精梳机的墙板具有尺寸大、结构复杂的特点,存在严重的动应力集中问题,而直接对其进行最优化设计又存在很大的困难。因此针对墙板的结构特点和受载条件,建立了相应的简化分析模型。模型分单矩形孔模型和双矩形孔模型。单矩形孔模型用于分析孔洞的几何形状与孔边最大动应力的变化规律,包括边长比、孔角半径;双矩形孔模型用于分析孔之间的相对位置与孔边最大动应力的变化关系。根据得出的规律对精梳机墙板的结构进行了改进,结果显示墙板的应力峰值减小为原来的三分之一。由此验证了该简化模型是合理的,由该模型得出的结论可以帮助我们进一步认识矩形孔夹杂对结构应力分布的影响规律,从而为矩形孔结构的设计与优化提供了参考。     

基于有限元分析的裂纹比拟法估算微动疲劳寿命

采用Ansys有限元软件对方足微动桥/平面试样接触状态进行分析,确定试样微动接触面上应力场分布和接触面三区(黏着区、滑移区、张开区)分布特征,分析接触面上接触状态随外加交变载荷的变化规律,在此基础上改进微动疲劳(fretting fatigue,FF)寿命估算的裂纹比拟法(crack analogue method,CAM)。选取不同水平的循环载荷及不同名义接触压力对Ti811钛合金试样在350℃下进行微动疲劳试验,验证改进裂纹比拟法(modified crack analogue method,MCAM)的准确性。结果表明,微动疲劳中接触面压应力与剪应力在黏/滑交界区存在突变,张应力幅在滑移/张开分界处达到最大值,裂纹易在此萌生并扩展。改进的裂纹比拟法估算值与实验结果取得良好的一致性。     

纯水密封径向间隙优化设计及仿真计算

纯水密封摩擦力大、泄漏量大、寿命短,无法为矿井液压系统稳定工作提供可靠有效的保障,从而导致开采过程中出现安全隐患。针对上述问题,利用有限元分析软件ANSYS建立复合密封件二维轴对称模型,在其他条件相同的情况下,分析不同径向间隙、不同压力载荷对密封静态和动态性能的影响,得到密封接触应力变化时对密封性能的影响规律,通过对不同径向间隙进行参数化设计,找到满足工作条件的最优径向间隙。仿真分析表明:径向间隙为0.25 mm时,复合密封件在1.5倍公称压力下的接触应力为49.854 MPa,密封效果最好;径向密封间隙为0.375 mm时,接触应力过小会导致泄漏现象产生;径向间隙为0.125 mm时,虽然密封性能进一步提升,但是接触应力的增大导致密封件磨损加速。实验表明:0.25 mm径向间隙液压缸密封寿命可达到20000次,较0.125 mm径向间隙液压缸密封寿命长约1/3。     

Load capacity of components with initial point contact

Formulas have been derived for the critical loads corresponding to the onset of plastic deformation in different loading stages. Likewise, a formula has been obtained for the limiting load corresponding to sharp deviation of the size of the surface impression from the values predicted by the Hertz equations, which describes elastic behavior. A means of increasing the load capacity with initial localized contact is considered.