Residual stresses and retained austenite evolution in SAE 52100 steel under non-ideal rolling contact loading

Residual stresses are introduced and modified during manufacturing as well as by normal use under rolling contact loading. Operations such as heat treatments, shot peening, grinding, etc., are known to alter the magnitude and distribution of residual stresses. Our work revolves around the changes in magnitude and distribution of residual stresses, as they relate to deformation and the strain induced transformation of retained austenite. The residual stresses and retained austenite measurements were carried out using X-ray diffraction techniques. The rolling contact fatigue lives of different variants of SAE 52100 bearing steel were evaluated in a 5-ball-rod rolling contact fatigue machine under testing conditions leading to surface nucleated failure, i.e. non-ideal rolling contact. The tests were accelerated by applying well controlled micro-indentations on the wear track. The contribution of the residual stresses and amount of retained austenite to the rolling contact fatigue life were analyzed.     

Influence of reverse yielding on residual stresses induced by autofrettage

The paper investigates the influence of reverse yielding on residual stresses induced by autofrettage. On the basis of reverse loading tests, a material model is developed and implemented into analytical procedures capable of treating the elasto-plastic deformation behaviour of thick-walled tubes during both loading and unloading phases. The results show that residual hoop stresses are drastically reduced near the tube bore as compared with residual stresses obtained from conventional isotropic hardening analysis. Pure kinematic hardening analysis is also shown to overestimate residual hoop stress induced by autofrettage.     

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.     

大型复杂结构安定性数值分析的新方法及其应用

大型复杂结构承载后普遍存在局部高应力区,特别是某些巨型结构,由于受几何尺寸和制造能力的限制,其局部高应力往往会接近甚至超过材料的屈服极限,因而成为弹性范围内的设计难题。应用安定性分析设计准则,则可通过利用材料的塑性承载能力很好地解决这类问题。为此,在大型复杂结构的强度分析中引入安定性理论,应用Melan安定下限定理,通过将峰值载荷下的弹塑性应力场与弹性参考应力场相减,构造定理要求的自平衡应力场,并推导了相应的安定性判定条件。在此基础上,结合弹塑性增量有限元技术,通过不同载荷水平下的加载-卸载计算,计算相应载荷水平下的残余应力场。根据加载-卸载得到的残余应力场与构造的自平衡场的关系,按照安定性判定条件确定安定极限载荷,从而建立了一种适合于大型复杂结构安定性数值分析的新方法,并应用该方法对某125MN锻造液压机的主液压缸缸体结构进行了安定性分析。     

A Coupled Euler-Lagrange Model for More Realistic Simulation of Debris Denting in Rolling Element Bearings

Abstract

The objective of this study is to investigate the effects of the contamination of lubricants on denting in rolling element bearings. A dynamic, explicit finite element model (FEM) is developed to reproduce and analyse the elastic–plastic response of the surfaces when a spherical particle passes through a heavily loaded contact area. To cope with mesh distortion issues due to the high deformation of the debris along the process, a novel Eulerian approach is used to model the particle. A parametric study is conducted with the coupled Euler-Lagrange (CEL) model to determine the influence of the debris size, bearing loading, friction coefficient, material properties, and relative sliding between the surfaces on the indentation features. The FEM results emphasize the major role of the material properties of the three bodies on the dent geometry, pointing out that the softer surface undergoes more severe damage. In the same way, the protection of one of the surfaces by a specific heat treatment such as nitriding leads to more severe damage on the other one. The results exhibit a direct link between the particle and dent sizes. For large particles, a change in the dent geometry is observed when the deformed particle size overcomes the contact width because the particle is no longer enclosed in the contact and is therefore spread more easily. The model reproduces two important aspects of the indentation in rolling element bearings, which are the asymmetry of the dent and the residual stresses distribution, providing interesting prospects for future work on the fatigue failure caused by these defects.     

深沟球轴承的载荷分布与刚度特征研究

采用有限元法计算了"奇压"与"偶压"两种受载形式下深沟球轴承的静力学响应。对比讨论了轴承内接触应力分布、轴承变形及刚度的变化特征。结果表明当外载荷达到某一值时,关键滚动体与外圈滚道接触中心的接触应力明显大于与内圈滚道接触中心的接触应力,并随着载荷的增加,这个趋势越发明显;两种受载形式下,轴承的位移与刚度表现出明显的差异,奇压形式下,轴承的径向位移小于偶压形式下的径向位移,而奇压形式下的轴承刚度则大于偶压形式下的刚度;相同载荷作用下,静力学方法计算的轴承径向位移小于有限元法计算结果。     

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.     

Influence of Initial Residual Stress on Material Properties of Bearing Steel During Rolling Contact Fatigue

Rolling contact fatigue (RCF) experiments were performed on AISI M50 bearing balls using a single ball test rig to investigate the evolution of the material properties within the RCF-affected subsurface region. Using a combination of micro-indentation and miniature compression testing methods, the influence of contact stress, initial residual stresses, and the number of contact cycles on the resulting evolution of material properties was investigated. It was found that the balls with initial residual compressive stresses show less change in material properties after RCF loading than the balls without such initial residual stresses. The formation of a light etching region (LER) is shown to not correlate with a decrease in material strength and hardness, but it does serve as a predictor for failure due to spall.     

轴承套圈冷辗加工过程有限元模拟分析

运用大型通用有限元程序 ,建立轴承套圈冷辗加工的力学模型 ,采用非线性Lagrange大变形有限元方法 ,对工件金属的弹塑性变形过程进行模拟分析。通过工件工作区的应力分布云图考察金属材料的塑性流动情况 ,分析冷辗成形的机理。观察模型加载后不同时间应力分布云图的变化 ,并对比不同尺寸的辗辊、以及大小不同的载荷对工件加工变形过程的影响。分析冷辗加工中经常出现的轴承套圈失圆等异常情况形成的原因     

Influence of Residual Stresses Introduced by Manufacturing Processes on Bearing Endurance Time

By enhancing surface properties and by reducing weight and size of machine elements, future trends in resource efficiency for machines can be fulfilled. Rolling element bearings are widely used machine elements. By improving their boundary zone properties, there is a potential to extend maintenance-free operating periods, postpone replacements or increase the lifespan of the complete system. The aim is to set favorable boundary zone properties by enhancing the residual stress state within the manufacturing process. For this, the processes hard turning and deep rolling were investigated. The influence of the initial residual stress state on fatigue life was calculated using a model based on the approach of Ioannides and Harris. The resulting residual stresses after the manufacturing process and their changes during operation in a bearing test rig are discussed and compared to those of standard bearings. The tests prove that pre-induced residual stresses increase is able to significantly delay rolling contact fatigue-related bearing failures.     

Macroscopic and microscopic changes in the surface layers of annealed and case-hardened steel rollers due to rolling contact

Measurements of the residual stress and observations of the microstructure at the surface and in the subsurface of rollers were performed during rolling contact fatigue tests of annealed 0.45% carbon steel and case-hardened nickel-chromium steel rollers. Compressive residual stresses in annealed rollers were induced by the rolling contact. With case-hardened rollers they were induced by heat treatment prior to the rolling contact fatigue tests. After the rolling contact fatigue tests the compressive residual stresses on the surface of the annealed rollers and in the subsurface of the case-hardened rollers relaxed; a characteristic substructure was formed by the stress cycles, which caused surface failure. It was confirmed that the microcracks leading to surface failure initiate on the surfaces of annealed rollers and in the subsurface of case-hardened rollers.     

Elastic-plastic finite-element modelling of cold rolling of strip

The rolling of copper strip has been simulated using an elastic-plastic finite-element method (EPFEM) for plane-strain deformation. The use of this program, which includes both material and geometric non-linearities, permits the identification of elastic and plastic deformation in rolling, and also the effects of unloading. The rolling model is based on the physically realistic concept that the strip is drawn into the roll gap by the action of interface friction.The results clearly show the maximum pressure associated with the neutral point and are in good quantitative agreement with earlier work. In addition, the stresses and deformation outside the nominal contact are presented.     

Service Loading of Rolling Bearings in Wind Turbine Gearboxes: X-ray Diffraction Material Response Analysis of White Etching Crack Premature Failures

Rolling bearings in wind turbine gearboxes occasionally fail prematurely due to white etching cracks. The appearance of preparatively opened fracture faces indicates damage initiation from the surface in most cases due to brittle spontaneous tensile stress–induced cracking. Under the influence of decomposition products of the penetrating lubricant, branching crack growth is subsequently driven by corrosion fatigue. The material response analysis of rolling bearings from all gearbox locations, based on X-ray diffraction residual stress measurements, reveals vibrations in service as the root cause of surface crack initiation. The occurrence of high local friction coefficients in the rolling contact is described by a tribological model. Depth profiles of the equivalent shear and normal stresses are respectively compared with the measured residual stress patterns and a relevant fracture strength. White etching crack failures are experimentally reproduced on a rolling contact fatigue test rig under increased mixed friction. Causative vibration loading is evident from material response analysis. The generation of compressive residual stresses by cold-working the surface is proven to be an effective countermeasure.     

基于热力耦合模型的切削加工残余应力的模拟及试验研究

航空精密薄壁零件具有复杂的型腔结构,切削加工残余应力是薄壁零件精度稳定性的重要影响因素,因此必须对切削加工残余应力进行研究。根据热—弹塑性有限元理论,建立切削加工三维有限元模型,对航空铝合金材料Al2A12进行切削加工非线性弹塑性有限元模拟分析,对切削加工表面残余应力进行预测和计算。通过有限元分析,得到不同切削参数、刀具参数条件下的已加工表面残余应力的模拟结果,并对结果进行比较分析,得到各个因素对工件已加工表面残余应力的基本影响规律;进行不同加工工序条件下的切削加工残余应力的有限元模拟,在加工表面已有一次切削加工残余应力分布的情况下,进行二次切削加工有限元模拟,得到二次切削加工对工件已加工表面残余应力的影响规律;并且进行不同切削参数对残余应力影响的试验研究,验证有限元模型的正确性。     

焊接残余应力对弹塑性接触应力场的影响

对接触应力场的力学分析,以前发表的文章都是在弹性或理想弹塑性的假设下作出的。由于实际材料在屈服后的加工硬化,以上假设显然有较大的近似性。运用弹塑性力学的原理和数值计算方法,考虑了材料的加工硬化,讨论了焊接残余应力对弹塑性接触应力场的影响,并给出了亚表面塑性区随循环周次的变化。还用实验证明了焊接残余应力对工件的接触疲劳寿命的危害性。     

齿轮接触安定分析

以Hertz理论为基础,建立齿轮的接触模型.针对齿轮接触表面层变曲率的特点,构造出局部坐标下残余应力应变场的分布状态,分析在此残余应力场分布状态下,齿轮接触的静力安定和机动安定的条件.采用应力应变释放的算法和不同啮合点局部坐标之间的转换法则,模拟齿轮在重复啮合过程中残余应力应变的累积过程,求解安定状态下残余应力的分布状况,确定齿轮接触的安定极限与摩擦因数和齿轮啮合位置之间的变化情况.     

Simulation of the cold rolling of strip using an elastic-plastic finite element technique

Strip rolling is simulated using an elastic-plastic finite element technique which includes the extent of both elastic and plastic deformation outside the nominal contact deformation zone. Solutions for non-steady and steady-state rolling are obtained. The stress and strain distributions within the workpiece, the velocity fields (absolute and relative to the roll surface), and the normal pressure and shear stress distributions along the arc of contact are calculated. Analyses are conducted with different levels of friction, material properties, workpiece dimensions and reductions. The results are compared with previous theoretical and experimental work, with which good agreement is found. The usefulness of numerical analyses for the investigation of parameters relevant to industrial rolling practice is demonstrated.     

A Theoretical Study of Residual Stress Effects on Fatigue Life Prediction

Recently, the trend has been toward the use of the full subsurface stress field in rolling element bearing fatigue life prediction (stress field-based life models). By using the stress field-based bearing life models, more accurate assessments of such things as fitting practice and thermal treatments on the bearing performance are achieved. However, one aspect missing in most models has been the consideration of the changing residual stress during operation of the bearing. This study was conducted to investigate the time dependent residual stress on contact fatigue life predictions.

This study concluded that the changes in residual stress during operation were most likely a fatigue reaction of the material to the pre-fatigue residual stress and cyclic contact stress fields. The materials fatigue response changes the instantaneous values of the material constants in most stress field-based life equations, thus making them in-calculable. As such, the pre-fatigue residual stress field should be used in the stress field-based models.     

Simulation and experiment of secondary contact stiffness of rough surface

Machined surfaces usually need to be loaded several times during assembly. The surface morphology after the simulation loading may be quite different from the physical loading, which subsequently causes differences between the contact stiffness after secondary simulation loading and secondary physical loading results. The fractal theory was used to reconstruct the measured surface morphology, followed by contact stiffness simulation and test. The results show that contact stiffness of new morphology obtained by the first simulated loading using the elastic-plastic deformation theory are smaller than the first loading test results, with an average error of −9.71 %. Contact stiffness of used morphology obtained by the first simulated loading using the pure elastic deformation theory are in good agreements with the second loading test results, with an average error of 4.71 %. However, the average contact stiffness of new morphology obtained by the second simulated loading using the elastic-plastic deformation theory, which is traditionally used for contact analysis, are 2.15 times larger than the second loading test result. These research results demonstrate a feasible finite element method (FEM) for solving the contact problem of rough surfaces that need to be assembled multiple times.

     

A First Order Solution for the Stress Concentration Present at the End of Roller Contact

An approximate solution of the “critical” maximum compressive stress present in rolling contact fatigue is given. Geometries normally used in rolling contact rig tests having contact areas varying from rectangular to full elliptical contact are considered. For cylinders in contact it is shown that the first order solution for end of contact stress is considerably above the nominal line contact Hertz stress usually calculated. Confirmation of the approximate stresses calculated is provided by deformation studies just into the plastic regime, and rolling contact fatigue tests on both cylindrical and 100-inch radius toroidal specimen rollers.