Physics-based modeling for fretting behavior of nominally flat rough surfaces

A physics-based modeling approach for fretting behavior of nominally flat rough contact is proposed. This approach employs physics-based models for partial slip of spherical contacts to formulate the contact forces at asperity tips. The individual asperity forces are added by a statistical method to obtain the fretting response of a flat rough contact. This approach suggests the plasticity index as an important parameter for studying the surface roughness effects on fretting. Fretting responses obtained by one of the models favorably compare with experimental results obtained from bolted steel lap joints. Tangential stiffness and energy loss per cycle obtained from the experiments and the model predictions deviate at higher preloads. This discrepancy is due to limitations of the modeling approach in accounting for plastic response to tangential loading.     

位移幅值对铜镁合金微动磨损行为的影响

在研制的多功能微动磨损试验机上,开展了不同位移幅值下铜镁合金微动磨损试验,以研究位移幅值对铜镁合金微动磨损行为的影响. 微动过程中记录摩擦系数曲线与F_t-D-N曲线,利用光学显微镜(OM)、扫描电镜(SEM)、能量色散X射线光谱仪(EDS)及三维形貌仪对损伤区域进行了微观分析. 结果显示:随着位移幅值的增加,铜镁合金微动运行状态由部分滑移进入完全滑移,未发现混合滑移状态;部分滑移区中呈现由弹性变形协调逐渐向塑性变形协调转变的趋势. 磨损体积随位移幅值的增加而增加,在完全滑移区中体积损失非常严重. 在弹性变形协调的部分滑移状态下,接触表面损伤轻微,而由塑性变形协调的部分滑移状态下,接触中心出现较大切应力,疲劳裂纹扩展至接触表面导致材料剥落,接触边缘有磨粒磨损和氧化磨损的痕迹. 在完全滑移状态下,接触表面损伤主要为疲劳剥层,磨粒磨损和氧化磨损.      

On the use of digital image correlation for slip measurement during coupon scale fretting fatigue experiments

Digital image correlation (DIC) is a full field three dimensional measurement technique that can quantify displacements and strains of a surface. In this paper, digital image correlation is used as a slip measurement technique during coupon scale fretting fatigue experiments. Slip measured with the novel DIC technique is compared to conventional slip measurement techniques as clip gauges and modified clip gauge measurements proposed by Wittkowsky et al. Slip measurements with the DIC system show lower slip values and higher tangential contact stiffness’s compared to (modified) clip gauge measurements. Slip measured with DIC is obtained closer to the contact compared to clip gauges, eliminating the influence of elastic deformations or fitting parameters. During the fretting fatigue experiments are two equal contacts simultaneously tested. However, the slip of both contacts is not identical with outliers of more than 10% difference in slip amplitude.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性，且表面电势和磁势是常数。微动接触依赖载荷的加载历史，所以首先求解单独的法向加载问题，然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区，其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换，磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组，然后数值离散为线性代数方程组，利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

Mechanics of advancing pin-loaded contacts with friction

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.     

钛合金与钴铬钼切向微动磨损行为研究

本文中以Ti6Al4V与CoCrMo合金为研究对象,在不同介质中开展了球/面切向微动磨损的试验研究,结合多种微观分析手段,揭示了不同条件下钛合金与钴铬钼间切向微动运行特性和损伤机理.结果表明：钛合金球与钴铬钼平面间的切向微动主要运行于部分滑移区和混合区.随着微动振幅的增加,F_t-D曲线从直线型向椭圆型转变,其中振幅较大时微动末期F_t-D曲线呈平行四边型.在部分滑移区,摩擦系数较小且保持不变,磨痕表面磨损轻微.在混合区,摩擦系数的变化因振幅的不同各存在两种情况.在振幅较小的混合区,磨斑边缘有磨屑堆积,中心以黏着为主.在振幅较大的混合区,磨痕表面以磨粒磨损为主.     

关于复合式微动的研究

在新型径向微动试验装置上 ,改变试样的倾斜角度 ,实现了径向微动和切向微动的复合 .考察了 GCr15钢球 /2 0 91铝锂合金在倾斜 30°和 45°以及不同外加载荷条件下的复合微动损伤行为 ,并分析了其磨痕特征     

二硫化钼粘结固体润滑涂层的径向和切向微动损伤的比较研究

通过径向和切向微动试验考察了二硫化钼粘结固体润滑涂层的微动摩擦学特性 ,并利用扫描电子显微镜、能量色散谱和X射线光电子能谱等分析了两类微动损伤区的微观特征 .结果表明 :二硫化钼粘结固体润滑涂层具有良好的抗径向微动损伤性能 ;切向微动条件下无混合区存在 ,涂层损伤强烈依赖于位移幅值 ,并伴随MoS2 的氧化 ;径向微动损伤呈现切向微动部分滑移区的特征     

微动频率对钢丝拉扭复合微动腐蚀疲劳行为影响研究

拉扭复合微动腐蚀疲劳是深井提升钢丝绳主要失效形式之一,深井提升钢丝绳振动频率决定钢丝间微动频率,直接影响钢丝拉扭复合微动腐蚀疲劳机理和损伤程度,进而制约深井提升钢丝绳服役安全性. 本文作者通过自制钢丝拉扭复合微动腐蚀疲劳试验机开展了酸性电解质溶液中钢丝拉扭复合微动腐蚀疲劳试验,通过钢丝切向力-位移幅值和扭矩-扭转角滞后回线分析了拉扭复合微动腐蚀疲劳过程中钢丝间接触状态及轴向和扭转方向钢丝耗散能,运用扫描电子显微镜和三维白光干涉表面形貌仪考察了拉扭复合微动腐蚀疲劳过程中钢丝磨痕形貌和磨损深度轮廓特性,采用X射线三维成像系统揭示了钢丝拉扭复合微动腐蚀疲劳裂纹扩展演化规律,通过电化学分析仪分析试验后钢丝Tafel极化曲线和阻抗谱以探究钢丝电化学腐蚀倾向和耐腐蚀性,揭示了微动频率对拉扭复合微动腐蚀疲劳过程中钢丝间接触状态、钢丝耗散能、微动磨损机理、疲劳裂纹扩展演化和疲劳寿命、电化学腐蚀倾向和耐腐蚀性的影响规律. 结果表明:在拉扭复合微动腐蚀疲劳过程中,随着微动频率的增加,钢丝间由完全滑移和部分滑移混合状态变为完全滑移状态,钢丝扭矩-扭转角滞后现象削弱,钢丝切向力-位移幅值和扭矩-扭转角滞后回线对应的耗散能均总体降低,钢丝间摩擦系数和钢丝磨损深度均降低,钢丝磨损机理均为磨粒磨损、黏着磨损、疲劳磨损和腐蚀磨损,钢丝最大裂纹深度和裂纹扩展速率均降低,疲劳寿命增加,钢丝电化学腐蚀倾向下降和耐腐蚀性增强.      

位移幅值对690合金管/405不锈钢块切向微动磨损特性的影响

采用自制的微动磨损试验机，开展了690合金管/405不锈钢的切向微动磨损试验，研究了位移幅值(15、30、80和200 μm)对其微动磨损特性的影响. 试验结果表明:当位移幅值改变时，微动运行状态会发生改变. 当位移幅值为15 μm时，微动状态为部分滑移区，此时摩擦系数最小，磨损率最低，微动损伤最轻微；当位移幅值为30 μm时，微动运行于混合区，摩擦系数明显高于部分滑移区；而当位移幅值为80和200 μm时，微动运行于完全滑移区，稳定阶段的摩擦系数与混合区的接近. 总体而言，随着位移幅值的增大，磨痕宽度增大，磨损加剧，磨损体积增加. 部分滑移区的磨损机制主要为黏着磨损和剥层，混合区主要的磨损机制为剥层，而完全滑移区的磨损机制主要为剥层磨损和磨粒磨损.      

An example of stick–slip and stick–slip–separation waves

The dynamical problem of a brake-like mechanical system composed of an elastic cylindrical tube with Coulomb's friction in contact with a rigid and rotating cylinder is considered. This model problem enables us to give an example of non-trivial periodic solutions in the form of stick–slip or stick–slip–separation waves propagating on the contact surface. A semi-analytical analysis of stick–slip waves is obtained when the system of governing equations is reduced by condensation to a simpler system involving only the contact displacements. This reduced system, of only one space variable in addition to time, can be solved almost analytically and gives some interesting informations on the existence and the characteristics of stick–slip waves such as the wave numbers on the circumference, stick and slip proportions, wave celerities, tangential and normal forces. It is shown in particular that the stick–slip–separation solutions would occur for small normal pressures or high rotational speeds. Since the analytical discussion becomes cumbersome in this case, a second approach based on numerical analysis by the finite element method is performed. The existence and the characteristics of stick–slip and stick–slip–separation waves are discussed numerically.     

考虑粗糙结合面弹塑性接触的黏滑摩擦建模

提出一种同时考虑粗糙面上微凸体弹性变形和塑性接触的切向黏滑摩擦建模方法。采用Hertz弹性理论和Mindlin解描述弹性接触微凸体的切向载荷和相对变形的关系;采用AF(Abbott-Firstone)塑性理论和Fujimoto模型描述塑性接触微凸体切向载荷和相对变形的关系。再利用GW(Greenwood-Williamson)模型统计分析方法建立粗糙表面切向载荷和相对变形之间的关系。将模型与仅考虑微凸体弹性接触情况的模型进行对比,并研究了不同塑性指数对切向载荷和相对变形关系的影响。结果表明：与完全弹性接触模型相比,本文模型引入了塑性接触理论,能够更好地描述粗糙表面切向载荷和相对变形关系,并且考虑不同接触条件下弹性变形微凸体和塑性变形微凸体对切向接触载荷的贡献,在微滑移阶段,主要由弹性接触变形影响,而在进入宏观滑移阶段之后,切向行为主要由塑性变形影响。界面切向载荷由黏着和滑移接触作用共同决定,随着切向变形的增加,滑移接触力逐渐增加,而黏着接触力先增加后减少,反映了界面由微滑移逐渐向宏滑移演化的过程。随着塑性指数的增加,粗糙面上发生塑性接触的微凸体数目逐渐增加,切向黏滑行为主要受到塑性接触特征的控制。     

A note on the crack analogue model for fretting fatigue

The contact of a flat punch over a half-plane under constant normal loads, and oscillating tangential and bulk loads is studied, with the aim to improve the crack analogue (CA) model for fretting fatigue (FF) (Acta Mater. 46(9) (1998) 2955). New analytical results are found for a range of conditions, finding the effect of bulk loads and of partial slip which were not considered in the original CA model. Implications for the FF life assessment methodology are found to be significant.     

润滑油脂对钢丝微动磨损特性的影响

在自制的微动摩擦磨损试验机上,以矿用钢丝为研究对象,探讨润滑油脂对钢丝微动磨损特性的影响规律.结果表明:润滑油脂使钢丝微动运行区域中部分滑移区和混合区显著缩小,滑移区增大;摩擦系数和磨损量显著降低,跑合期延长;润滑油脂条件下,部分滑移区损伤轻微,环状区域较光滑,混合区和滑移区摩擦氧化减少,损伤以表面疲劳及磨粒磨损为主,磨痕表面较平滑,损伤程度明显小于干摩擦条件.     

Frictional contact of two rotating elastic disks

We study the problem of constrained uniform rotation of two precompressed elastic disks made of different materials with friction forces in the contact region taken into account. The exact solution of the problem is obtained by the Wiener-Hopf method.An important stage in the study of rolling of elastic bodies is the Hertz theory [1] of contact interaction of elastic bodies with smoothly varying curvature in the contact region under normal compression. Friction in the contact region is assumed to be negligible. If there are tangential forces and the friction in the contact region is taken into account, then the picture of contact interaction of elastic bodies changes significantly. Although the normal contact stress distribution strictly follows the Hertz theory for bodies with identical elastic properties and apparently slightly differs from the Hertz diagram for bodies made of different materials, the presence of tangential stresses results in the splitting of the contact region into the adhesion region and the slip region. This phenomenon was first established by Reynolds [2], who experimentally discovered slip regions near points of material entry in and exit from the contact region under constrained rolling of an aluminum cylinder on a rubber base. The theoretical justification of the partial slip phenomenon in the contact region, discovered by Reynolds [2], can be found in Carter [3] and Fromm [4]. Moreover, Fromm presents a complete solution of the problem of constrained uniform rotation of two identical disks. Apparently, Fromm was the first to consider the so-called “clamped” strain and postulated that slip is absent at the point at which the disk materials enter the contact region.Ishlinskii [5, 6] gave an engineering solution of the problem on slip in the contact region under rolling friction. Considering the problem on a rigid disk rolling on an elastic half-plane, we model this problem by an infinite set of elastic vertical rods using Winkler-Zimmermann type hypotheses. Numerous papers of other authors are surveyed in Johnson’s monograph [7].The exact solution of the problem on the constrained uniform rotation of precompressed rigid and elastic disks under the assumptions of Fromm’s theory is contained in the papers [8, 9]. In the present paper, we generalize the solution obtained in [8, 9] to the case of two elastic disks made of different materials.     

A numerical analysis of partial slip problems under Hertzian contacts

In this study the tangential partial slip problems in Hertzian contact regions are treated by a numerical technique. The tangential loading may include tangential forces in the contact plane and a twisting moment normal to the contact plane. The Coulomb’s law of friction and the property that the direction of friction must oppose the relative motion lead to nonlinear equations. The Newton-Raphson method is utilized to solve these nonlinear equations. Numerical results for tangential tractions and sizes of stick and slip zones may be determined, and they agree with existing analytical results for circular contacts.     

Micromechanical analysis of friction anisotropy in rough elastic contacts

Computational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a micro-to-macro scale transition scheme yields a macroscopic friction model with orientation- and pressure-dependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak non-associativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials.     

脂润滑对100C6钢微动磨损特性的影响

探讨了在不同振幅及载荷作用下脂润滑对１００Ｃ６钢微动磨损特性的影响,研究表明,脂润滑可缓解微动接触表面的损伤,滑移区域中润滑脂减摩效果优于部分滑移区和混合区,润滑脂在接触界面之间很难保持有效润滑;在稳定的脂润滑上微动区域的划分变化不大。     

基于共轭梯度法和快速傅立叶变换的粗糙表面微动接触数值研究

实际工程表面多为粗糙表面,研究粗糙表面的表面形貌对微动接触中压力和应力的影响具有重要意义。本文研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷。首先,建立接触算法和模型,算法核心是利用共轭梯度法CGM(Conjugate gradient method)计算微动接触中的表面压力及切向应力并利用快速傅里叶变换FFT(Fast Fourier transform)加快计算速度。然后,对单峰表面、正弦表面和随机粗糙表面的接触进行数值研究。结果表明,表面幅值对切向载荷-位移曲线以及接触过程中的能量耗散有影响,表面幅值越大,相同切向载荷作用下产生的切向位移越大,能量耗散也越大。     

Fretting contact of two elastic solids with graded coatings under torsion

In this paper, the fretting contact problem for two elastic solids with graded coatings is investigated. We assume a conventional axisymmetric Hertzian contact takes place between two elastic solids under the action of the normal pressure. The application of the torque produces an annulus of slip. It is assumed that the surface shear traction within the contact area is limited by Coulomb’s friction law and the torsion angel was produced within the central adhesion zone as a rigid body. The linear multi-layer model is used to model the functionally graded coating with arbitrarily varying shear modulus. This model divides the coating into a series of sub-layers with the elastic modulus varying linearly in each sub-layer and continuous on the sub-interfaces. By using the transfer matrix method and Hankel integral transform technique, this problem is formulated as the solution of the Cauchy singular integral equations. The contact tractions are calculated by solving the equations numerically. The results show that the appropriate gradual variation of the shear modulus can significantly alter the contact tractions. Therefore, graded coatings may have potential applications in improving the resistance to fretting contact damage at the contact surfaces.