The effect of variable amplitude loading on stress distribution within a cylindrical contact subjected to fretting fatigue

A finite element model of a cylindrical Hertzian contact on a test sample subjected to alternating shear loading has been developed. The model has been used to investigate shear stress distributions at the contact during variable amplitude fretting fatigue for a load configuration in which the sample cyclic stress is applied in phase with shear force on the cylindrical contact. It has been found that during constant amplitude cyclic loading, shear stress distributions and positions of the stick-slip boundary at load maxima and minima remain fixed. Application of overloads changes the stress distribution and the position of the stick-slip boundary attained by loading of subsequent cycles. The largest cycle maximum stress determines the position of the stick-slip boundary adopted by subsequent smaller amplitude cycles. In general variable amplitude fretting fatigue the position of the stick-slip boundary will be changing with each load cycle. Hence fatigue initiation processes will occur at locations dispersed over an extended region over the contact. The implications of this behaviour for models for fretting fatigue life calculation are explored.     

A photoelastic investigation of contact stresses in the backward extrusion process

Photoelasticity is used for investigating the normal and shear stress distribution at the billet-container interface in the process of backward extrusion in cylindrical and flat containers.Photoelastic gauges made from birefringent material were embedded in the side walls of special experimental dies. Cylindrical and flat lead specimens were extruded in experimental dies in a laboratory testing machine. As a result of the experiments it has been established that the contact stress distribution in backward extrusion has a complex character. The curves for the normal stresses at the container walls have a peak located ahead of the punch and this drops abruptly after the metal has penetrated into the clearance between the container wall and the punch. The shear stress changes its sign along the contact zone. The normal and shearing stresses at the cylindrical container walls are considerably higher than at the flat container walls at the same value of reduction ratio.     

Stress analysis of cushion form bearings for total hip replacements.

Cushion form bearings comprise a thin layer of low elastic modulus material on the articulating surface of the bearing, which can deform to help preserve a film of lubricant between the bearing surfaces and therefore reduce friction and wear. The long-term function of this type of bearing is dependent on the strength and durability of this compliant layer. Finite difference and finite element methods have been used to analyse the stress distribution in the compliant layer of cushion form bearing for artificial hip joints under physiological loading conditions. A good agreement between finite difference and finite element methods was found. Under normal loading, the highest value of the maximum shear stress was found to be at the interface between the compliant layer and the more rigid substrate close to the edge of the contact. The values of maximum shear stress in the centre of the contact close to the articulating surface were lower than in the equivalent Hertzian contact. A friction force acting at the surface had little effect on the stress distribution for coefficients of friction less than 0.05. However, for higher values of friction coefficient (larger than 0.2), corresponding to inadequate lubrication, the maximum shear stress increased by a factor of four and was found to be located at the surface. The analysis predicts that the mode of failure will be at the interface with the substrate under fluid film or mixed lubrication conditions and at the articulating surface when the bearing runs dry with higher levels of friction. Both failure modes have been observed experimentally under the conditions specified.     

Two-dimensional contact problem for a coating-graded layer-substrate structure under a rigid cylindrical punch

The two-dimensional frictionless contact problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated in this paper. The coating and substrate are homogeneous materials with distinct physical properties, while the intermediate layer is inhomogeneous with its shear modulus changing arbitrarily along the thickness direction. To approximate the through-thickness variation, a piecewise linear multi-layer model is used and the graded layer is divided into a number of sub-layers whose shear modulus is assumed to vary linearly. Poisson's ratio, however, is taken as a constant within the structure for simplicity. By using the transfer matrix method and Fourier integral transform technique, the governing equations are reduced to a Cauchy singular integral equation which is numerically solved to determine the normal contact pressure, contact region, the through-thickness stress fields and longitudinal stress distributions at interfaces. A parametric study is conducted, showing that both normal contact pressure and stress fields in the structure are significantly influenced by the shear modulus ratio and the thickness ratio of the exponentially graded layer but are less sensitive to the gradient index of the graded layer whose shear modulus follows a power law variation.     

Pre-sliding Behaviour of Single Asperity Contact

The pre-sliding and static friction force behaviour at asperity level between a smooth ball and a smooth flat surface at different normal loads, as well as friction behaviour during full slip has been studied. The normal load dependence of the friction force and the preliminary displacement is discussed when the mean contact pressure is kept under 100 MPa. The theoretical model to calculate the shear stress and the preliminary displacement in the contact is discussed and the experimental data were used to verify the model. The results show that for low applied normal loads the adhesion force has an influence on the friction force measurements. Furthermore, the results for the friction force and preliminary displacement show good agreement with the theoretical trends. The experiments along with the model can be used to analyse the tangential traction in the contact and the behaviour of the stick–slip area. The measurement results along with the model were used to calculate the maximum shear stress at the point of sliding for different applied normal loads. It is also shown that at low applied normal loads the shear stress is not constant as compared to relatively high applied normal loads due to the presence of adhesion force.     

Characterization of the contact between a punch and a half-infinite substrate in a fretting situation

This paper analyzes the behavior of a mechanical system formed by a flat punch with square edges at 90 over a half-infinite substrate made of the same material under normal reversible constant and tangential loads, typical of a fretting situation. Based on previous studies of the behavior of such a system, both static and cyclic behavior are analyzed. The analysis is carried out using both analytical and numerical solutions, the latter being obtained with finite and/or boundary element codes. The kinematic behavior of the contact zone is studied (slipping, separation, or adherence), as well as the stress state of the substrate in the area surrounding the edges of the punch. The very same analyses have been made of a system equal to the latter but replacing the contact by continuity. The comparison of the solutions of the two systems gives the validity range of different continuous models, easier to use in representing the behavior of the punch–substrate system.     

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。     

FE-simulation of the effects of machining-induced residual stress profile on rolling contact of hard machined components

Compared with grinding, hard turning may induce a relatively deep compressive residual stress. However, the interactions between the residual stress profile and applied load and their effects on rolling contact stresses and strains are poorly understood, and are difficult to measure using the current experimental techniques due to the small-scale of the phenomena. A new 2-D finite element simulation model of bearing rolling contact has been developed, for the first time, to incorporate the machining-induced residual stress profile instead of only surface residual stresses. Three cases using the simulation model were assessed: (a) measured residual stress by hard turning, (b) measured residual stress by grinding, and (c) free of residual stress. It was found that distinct residual stress patterns hardly affect neither the magnitudes nor the locations of peak stresses and strains below the surface. However, they have a significant influence on surface deformations. The slope and depth of a compressive residual stress profile are key factors for rolling contact fatigue damage, which was substantiated by the available experimental data. Equivalent plastic strain could be a parameter to characterize the relative fatigue damage. The magnitudes of machining-induced residual stress are reduced in rolling contact. The predicted residual stress pattern and magnitude agree with the test data in general. In addition, rolling contact is more sensitive to normal load and residual stress pattern than tangential load.     

New results for the fretting-induced stress concentration on Hertzian and flat rounded contacts

Recent work on fretting fatigue has emphasized the role of stress concentration on fretting damage, while previous work had concentrated on empirical parameters to assess influence of fretting on fatigue life. In particular, analogies with fatigue in the presence of a crack or a notch have been noticed, suggesting that the stress field induced by frictional contact per se may explain the reduction of fatigue life due to fretting.In the paper, new analytical and numerical solutions are produced for the stress concentration induced in typical fretting contacts involving the Hertzian geometry or the flat punch with rounded corners in view of application to the dovetail joints. Normal and tangential load (in the Cattaneo–Mindlin sense) is considered with “moderate” or “large” bulk stresses.     

滑动接触中摩擦发热的数值分析

在滑动接触中，存在摩擦起热问题，运动机理对接触行为参数特性的影响不同于纯滚动接触，采用有限元方法，利用ANSYS软件，对2维滚滑模型进行分析，通过研究接触区的温度，接触应力和变形在运动学状态下的变化特性，可以看到接触状态的非稳定性必定会造成实际摩擦状态的不同，这也是形成接触表面不均匀磨损的原因之一。     

Analysis of rough line contacts operating under mixed elastohydrodynamic lubrication conditions

Heavily loaded machine elements, such as gears, usually operate in the mixed lubrication regime. Surface roughness has a significant effect on the pressure distribution, the subsurface stress field, and the friction coefficient. Based on the superposition of a dry rough and a fully flooded smooth contact, a mixed lubrication model has been developed. The roughness profile is assumed to be known. Surface deformation is calculated by taking into account the pressure distribution that is built up by asperity contacts, asperity interactions, and lubricant flow. Thermal and sliding effects are incorporated into the analysis. Non‐Newtonian lubricant behaviour is considered by using a power‐law rheological model. The pressure distribution, subsurface stress field, and friction coefficient were calculated from the model at several points along the contact path for an FZG type C gear pair. It was shown that a significant part of the load is carried by the contacting asperities. The position of the maximum shear stress is very close to the surface.     

An Investigation into the Effect of Normal Load Frequency on Fretting Fatigue Behavior of Al7075-T6

Most previous studies on fretting fatigue have been accomplished under constant normal loading and less attention has been paid to cyclic normal loading. An innovative test apparatus was specially designed and manufactured for fretting fatigue tests under cyclic loading in this work and the fretting fatigue behavior of Al7075-T6 was investigated at different normal load frequencies. A finite element model was developed to study the effect of normal load frequency on the contact stress distribution. It was found that the cyclic normal load has a more damaging effect on fretting fatigue life compared to constant normal load, particularly at lower frequencies. The results showed that at the normal load frequency of f = 1 Hz, fatigue life decreased by 52% in the high cycle fatigue regime and 28% in the low cycle fatigue regime. The experimental results also indicated that at the normal load frequency of 80 Hz, the fretting fatigue life converged to its corresponding life under constant normal load condition. The fracture surface and the fretting area of the specimens were examined using both optical and scanning electron microscopy (SEM). The experimental observations showed that the dominant partial slip condition with a wider slip region compared to constant normal loading, severe delamination, and higher oxidation rate due to the normal load release at each cycle, are the most important reasons for significant reductions in fretting fatigue life, under cyclic normal loading, especially for low normal load frequencies.     

Friction and wear of highly-elastic solids

It is shown that the normal forces set up by large shear deformations make sliding impossible when a critical compressive deformation, of the order of 10%, is imposed on a sliding block of highly-elastic material. When the compressive load is maintained constant, rather than the deformation, the way in which the compressive stress is distributed leads to sliding only by means of slip bands which originate at the leading edge of the block and then pass through the contact zone from front to back, as found by Schallamach¹. Thus, a discontinuity is predicted in frictional sliding as the compressive stress is increased from zero, and this occurs at a critical value which depends upon the coefficient of friction, the shear modulus of the material, and the detailed shape of the contact zone. Corresponding changes in wear behavior are inferred.     

H13热作模具钢冲头的早期断裂原因

某H13热作模具钢冲头在锻打钻杆管端后,抽出时发生早期断裂。通过断口形貌观察、化学成分分析、显微组织观察、微区成分分析等方法探讨了冲头断裂的原因。结果表明:该冲头断裂的性质为疲劳断裂;冲头工作部位外壁区域存在的大尺寸Al2O3、MnS、VC等夹杂物以及气孔、疏松等缺陷处易产生应力集中而成为疲劳裂纹源,在热应力、拉应力、压应力和弯曲载荷的反复作用下,横向微裂纹萌生并以发散形式快速失稳扩展,导致冲头断裂;该冲头中钼、钒的含量远低于标准值下限,导致冲头的高温力学性能降低,从而造成了冲头的疲劳断裂。     

Cyclic tangential loading of dissimilar elastic bodies

A two-dimensional fretting fatigue problem involving normal and tangential loading of dissimilar elastic bodies in contact is analyzed. The bodies are brought into contact by a monotonic normal load and then a cyclic tangential load is superimposed with the normal load held constant. The Hertz half plane assumption is retained for each body and the region of contact is divided into a central zone of stick and two external regions of micro-slip in each of which the Amontons-Coulomb law of sliding friction is assumed to apply. The effect of the interaction between the normal and shear stresses due to the mismatch in elastic constants is quantified by comparing the present rigid-elastic numerical solution (extreme case) to the Cattaneo-Mindlin closed form solution for elastically identical materials.     

Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM

The problem of an elastic cylinder in normal contact between transversely isotropic layered substrate surfaces is investigated using the finite element method (FEM). A two-dimensional finite element model is developed which accurately determines the normal stress, contact length, and approach distance of layered surfaces. Numerical results, which are initially verified using Hertzian theory, are obtained at 756 distinct conditions by varying coating material, coating thickness, normal load, cylinder radius, and cylinder material. The numerical results are normalized with respect to Hertzian contact theory and a dimensionless anisotropic coating material parameter, ζ, is introduced. Numerical expressions for the normalized maximum normal stress, contact length, and approach distance are subsequently determined by curve-fitting the results of the 756 simulations performed. The relevance of such expressions are ascertained and discussed by comparing predicted results to isotropic layer theory presented by Gupta and Walowit [P.K. Gupta, J.A. Walowit. Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lubrication Technol., Vol. 94 (1974) pp. 250–274.]     

The effect of substrate properties on tribological behaviour of composite DLC coatings

The unique features of DLC coatings in providing low friction and low wear and, at the same time, causing low wear to the counterface make them very attractive in industrial applications, in improving tribological performance of mechanical components on various substrates. In this study, composite DLC coatings have been deposited on sintered ferrous alloy, M42 tool steel, 2618 aluminium alloy, and 6063 aluminium extrusion substrates using the combined CFUBMS–PACVD technique. The effect of mechanical properties of substrate materials on tribological behaviour of the composite DLC coatings has been investigated at various loads on a ball-on-disk wear machine in dry air. A transition load was usually observed for coatings on the various substrates except for the aluminium extrusion; above the transition load the coating was completely destroyed via some spallation/fragmentation process after 2 h sliding, and the wear rate increased dramatically with further increase in load. The coating system on sintered ferrous alloy substrate exhibited the highest transition load among the four types of substrates studied. This is considered to have resulted from the combined effects of the lower elastic modulus of the porous sintered ferrous alloy substrate, which decreases the stress concentrations in the contact region, and the surface roughness and porosity, which enhance the bonding strength between the coating and the substrate under multi-contact conditions. The high elastic modulus of the tool steel substrate leads to tensile stress conditions in the sliding contact region and therefore makes coatings deposited on such a substrate more prone to breakdown/fragmentation, resulting in a transition load close to that for coatings on the soft 2618 aluminium alloy substrate. For coatings on the 6063 aluminium extrusion substrate, significant plastic deformation occurred in the substrate at loads above 1.5 N. However, despite the heavy deformation in the substrate, coatings on this substrate were not scraped off, as were coatings on the 2618 aluminium alloy substrate, even at a load as high as 20 N. The specific wear rate increased continuously with load, no apparent transition load being explicitly identifiable. This study shows that hard DLC coatings can be applied on both hard and soft substrates for improvement of the tribological behaviour of mechanical components.     

重载RV减速器的摆线针轮疲劳寿命预测

以某型重载RV减速器中的摆线针轮为研究对象,利用有限元分析软件建立轮齿接触等效模型,得到了摆线轮齿面的接触应力分布并分析了其最大接触应力区,基于刚柔耦合动力学建模,得到了最大接触应力区的应力-时间历程。采用疲劳累计损伤理论,基于疲劳寿命专用仿真软件,以有限元结果和载荷谱为输入,分析了摆线针轮在相应外部循环载荷作用下的最终寿命,研究结果表明：摆线轮最大应力部位和危险部位在分度圆附近且靠近端面,最大应力为817 MPa,疲劳寿命为106.673次,等效寿命为5 233 h,为摆线轮的抗疲劳优化设计提供了参考价值。     

On the shear stress of elastohydrodynamic lubrication in elliptical contacts

Results of mathematical modelling of elastohydrodynamic lubrication of rolling contacts are presented. Effects of dimensionless parameters such as speed, normal load, elliptical parameters and coefficient of limiting shear stress on shear stress distributions have been studied. Moreover, profiles on hydrodynamic pressure and film thickness in EHD contacts have been studied. It has been found that shear stress profiles on two contact surfaces in entraining direction are similar with each other in some way. Shear stresses of fluid film on contact surfaces vary with many factors, which reveals the mechanism of traction in elastohydrodynamically lubricated contacts.     

The contact and friction between flat belts and pulleys

Rubber coated nylon flat belts running over pulleys in practice display friction coefficients between 0·3 and 0·8. This paper studies the causes of the friction variations. Adhesive friction theory considers the friction force to be the product of the real areas of contact between the sliding surfaces and the shear stress at the contacts: these two quantities have been separately measured by running belts over transparent perspex pulleys and directly observing the contacts. It has been found that variations in contact from one belt to another due to their method of manufacture are as significant in explaining differences in their friction behaviour as are variations in shear stress caused by their different rubber formulations. Real areas of contact were less than one third of the apparent area and varied with load, elastic modulus and roughness of the belt surface in a way broadly understandable in terms of elastic contact mechanics. Shear stress were about 0·5 Nmm⁻², perhaps determined by hydrocarbon films. Some belts showed real areas of contact not directly proportional to load. This led to their friction coefficients being load dependent.