A friction contact stiffness model of fractal geometry in forced response analysis of a shrouded blade

To investigate the nonlinear vibration behavior of a shrouded blade with friction dynamic contact interface, a friction contact stiffness model is proposed to describe the friction force at different rough interfaces and different normal loads. In the proposed model, the friction contact interface is discretized to a series of friction contact pairs and each of them can experience stick, slip, or separate states. Fractal geometry is used to simulate the topography of contact surfaces. The contact stiffness is calculated using the Hertz contact theory and fractal geometry, which is related to contact interfaces parameters including normal load, roughness, Young??s modulus, and Poisson??s ratio. The trajectory tracking method is used to predict the friction force and it is not necessary to judge the transition condition among stick, slip, and separate states. It is suitable for complicated periodic motion of the contact interfaces. The forced response of a real shrouded blade is predicted using the proposed model and the multi-harmonic balance method. The effect of surface roughness, initial normal load, and contact area on the forced response of a shrouded blade is studied. It is shown that contact stiffness increases with normal load and fractal dimension. The resonant amplitude is sensitive to the initial normal load and contact surface roughness. The response can be influenced by the contact area, which is an important parameter for blade designers.     

包含几何误差的机械结合面法向刚度研究

对包含几何误差的机械结合面进行离散化,离散后的微表面的基准平面高度满足结合面几何误差分布.每个微表面内,微凸体的高度只受粗糙度的影响.基于接触理论建立了微表面的法向刚度模型,通过对微表面模型集成获得了结合面的法向刚度模型.通过对所建模型的数值仿真,揭示了结合面法向刚度与间隙的非线性关系,几何误差的幅值和波长对法向刚度的影响以及非线性刚度对结合面振动特性的影响.计算结果表明:法向刚度随着间隙的减少而迅速增加,几何误差会导致结合面宏观上的局部接触和应力集中;在相同干涉量下,法向刚度随着几何误差幅值的增加而增加,但与结合面的波长没有关系;非线性刚度会导致结合面固有频率的下降和振动位移的不对称.     

Ultrasonic assessment of rough surface contact between solids from elastoplastic loading-unloading hysteresis cycle

An ultrasonic method to characterize the elastoplastic contact between two rough surfaces is presented. Ultrasonic experiments are performed on three different interfaces formed by aluminum surfaces with different levels of roughness. The frequency-dependent ultrasonic reflection coefficient from the interface is measured during loading and unloading cycles as a function of pressure, from which the ultrasonic interfacial contact stiffness is reconstructed by the least-squares inversion procedure. It is shown that one should distinguish between the ultrasonic (dynamic) interfacial stiffness and static interfacial stiffness for rough surfaces in elastoplastic contact (they are identical for purely elastic contact). It is shown that ultrasonic stiffness is associated with local unloading stiffness. An elastoplastic micromechanical model is used to describe the plasticity-induced hysteresis in the ultrasonically measured interfacial stiffness during loading-unloading cycles. The topographic parameters of the interface contact are reconstructed by matching the model-predicted results with the experimentally determined ultrasonic stiffness. Using these parameters the real area of contact, which is not directly measurable, is predicted during loading-unloading cycles using the model.     

介观双粗糙弹塑性流体动力润滑界面法向接触刚度模型

弹性流体动力润滑状态通常出现在机械高副零部件的点/线接触部位,如齿轮、轴承和蜗轮蜗杆等.宏观上点/线接触在介观层面表现为两粗糙表面的接触,在微观层面上则又表现为微凸体间的接触.由于在中/重载荷作用下,粗糙表面上的微凸体发生接触后会产生弹塑性/塑性变形,从而使得两粗糙表面的弹流润滑接触转变为弹塑性流体动力润滑接触.此外,界面的接触刚度决定了机械装备的整机刚度.为了精确获得弹性流体动力润滑状态下界面法向接触刚度及其主要影响因素,基于界面的法向接触刚度由固体接触刚度和润滑油膜刚度两部分构成的思想,根据固体弹塑性理论和流体动力学理论,分别对界面间微凸体侧接触及部分膜流体动力润滑进行分析,从微观入手揭示双粗糙表面弹塑性流体动力润滑接触机理,进而建立考虑微凸体侧接触弹塑性变形的流体动力润滑界面法向接触刚度模型.通过仿真分析,揭示了法向载荷、卷吸速度、表面粗糙度及润滑介质特性等因素对润滑界面法向接触刚度的影响规律.研究表明：在相同速度、粗糙度及润滑油黏度的工况下,固体接触刚度和油膜接触刚度均随着法向接触载荷的增加呈非线性增大;在相同载荷、速度及润滑油黏度的工况下,接触表面粗糙度越大,表面形貌对于润滑...     

固-液结合面法向动态接触刚度及阻尼的理论模型与实验分析

固-液接触状态广泛存在于机床核心单元关键零部件的接触运动副中,精确获得固-液结合面法向接触刚度及阻尼参数是高档数控机床产品在研发阶段就存在的一个关键理论与技术问题,并且仍然尚未根本解决.固-液结合面在介观层面上表现为两个粗糙表面的接触,在微观层面上表现为微凸体之间的接触,并在中/重载荷作用下微凸体可能会发生弹性/弹塑性...     

Experimental investigation on surface deformation of soft half plane indented by rigid wedge

In this work, the mechanical behavior of a block of soft material subject to large deformation from a series of wedge-shaped indenters is evaluated. Data fields acquired from digital image correlation (DIC) are compared with the existing theoretical models. The slope angles of the wedges vary from 5° to 73.5°, and the minimum measurement uncertainties of the DIC system are established in advance to define the accuracy. It is concluded that the assumptions underpinning the analytical theory make it difficult to characterize large deformation of soft materials during contact. The strain fields are also obtained from the measured displacement field and verify the previously postulated existence of two deformation sectors, namely, a so-called shrinkage sector symmetric to the loading axis and an expansion sector, which become smaller with the increasing load and decreasing wedge angle.     

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

On the experimental investigation of the stiffness of clamped machined surfaces

Experiments were conducted to determine the effects of surface texture and normal load on the stiffness of joints formed by two machined surfaces. The experiments involved deformation measurements and examination of the contact surfaces of joints subjected to normal loads. It was shown that surface-displacement results can be affected by assuming that the compressive strain in the joint specimen is the same as in an equivalent solid piece. The elastic stiffness of joints were found to increase with an increase in the maximum nominal surface pressure. Results were also shown to illustrate that the elastic stiffness of a joint is affected by the loading history. Surface-profile measurements indicated that the topography of a joint surface changed with normal load, and that the deformation of a surface profile was related to the permanent change measured by extensometers placed across the joint interface.

     

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.     

考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析

为建立更完善和精确的结合面接触刚度模型,本文根据分形理论和摩擦学原理,从微观角度建立了考虑摩擦因素的结合面切向接触刚度分形预估模型.通过数值仿真分析研究了接触载荷、分形维数、摩擦系数和接触面积等因素对结合面切向接触刚度的影响.分析结果表明:结合面切向接触刚度随法向载荷和分形维数的增加而增大,而随分形尺度参数的增大而减小;摩擦系数对结合面切向接触刚度的影响较大,不同实际接触面积下的切向刚度相差较大;当分形维数较小时,摩擦系数对结合面切向刚度的影响将降低.这些研究对于进一步开展结合面的动力学特性研究具有重要意义.     

固定接触界面法向静弹性刚度

基于Hertz接触理论推导了两个微凸体之间互相作用的法向接触静弹性刚度.根据修正后的一个微接触点的平截面积尺寸分布,给出了界面的总法向接触静弹性条件刚度、总条件载荷的解析解.将法向静弹性刚度的解析解嵌入到有限元软件中,获得整机的理论模态.通过实验对解析解进行了定量验证.以机床结合部为研究对象,在理论振型与实验振型一致的...     

考虑弹塑性变形阶段的干气密封接触模型

为探究干气密封摩擦界面在变形全阶段的接触特性,基于分形接触理论及微观接触力学理论,充分考虑微凸体变形的3个阶段,通过余弦函数构建干气密封全阶段接触模型,并分别与GW模型、KE模型和ZMC模型三种经典接触模型及相关文献的试验数据作对比,验证本文中接触模型的合理性与正确性.最后对干气密封摩擦界面接触特性的主要影响因素进行探究.模型研究结果表明：干气密封摩擦界面的接触特性与分形维数、特征尺度及两表面的真实接触面积有关.接触特性与分形维数和两表面真实接触面积呈正相关,与特征尺度呈负相关.分形维数越大,接触载荷与接触刚度的数量级就越大,且接触载荷变化范围相对较大.当特征尺度每次以1个数量级递增时,接触载荷与接触刚度的变化范围较小,都在1个数量级内.     

表面织构对界面接触参数影响的实验研究

机械接触表面的接触刚度和接触阻尼是直接影响界面振动水平的两个重要动力学参数。本文介绍了一种测试机械连接界面接触刚度和接触阻尼的实验装置和方法,并针对用两种不同加工方法(激光加工及线切割)加工出的具有不同尺寸织构的试样与光滑平面相接触的界面进行了测量,初步探索了平面接触刚度和接触阻尼的表面织构效应,并得出结论：织构及润滑对接触刚度会产生一定影响,而实验中均未观察到这两者对接触阻尼有明显影响。     

双材料单伸臂叠合梁的界面滑移与自振特性分析

将叠合梁划分为接触区和分离区,接触区界面间的摩擦作用会对叠合梁的滑移、刚度和自振频率产生影响.本文给出了单伸臂叠合梁在均布荷载和集中力作用下,考虑叠合界面摩擦作用的滑移应变和滑移分布的表达式;推导了考虑叠合界面间摩擦力及摩擦力产生的抵抗弯矩共同作用下的截面刚度.假设梁按等波长和等刚度两种形式自由振动,运用传递矩阵法推导...     

The evolution of the process zone when a complete contact is subject to cyclically varying loads

A rigid punch pressed against an incompressible half-plane by a constant normal load is subject to both a cyclically varying shearing force, and a synchronously varying underlying bulk tension. The evolution of the slip/stick distribution along the contact interface is found during a loading cycle. An asymptotic approach is subsequently used to determine the order of singularity, and hence spatial distribution of the local stress state. A generalised stress intensity factor is then defined to scale the corresponding asymptotic solution, and hence map out the evolution of the process zone. The analysis shows that there is a smooth transition in the form of the asymptotic solution in moving from an ‘adhered’ contact edge to a ‘slipping’ contact edge, and vice versa. The implications of the results to fretting fatigue are discussed.     

基于DIC方法的残余应力快速测量系统

结合数字图像相关(Digital Image Correlation,DIC)方法与钻孔法,开发了残余应力快速测量系统。该系统可分为两部分:适用于现场测量的便携式机械系统与针对残余应力测量而改进的基于DIC算法的程序。在四点弯曲加载平台上对工件进行载荷释放前后的残余应力测量试验,通过与应变片测量结果进行对比,该残余应力测量系统的精度达到了应变片测量的同等精度。同时,该测量系统解决了传统应变片测量系统对心误差大、操作繁琐、效率低和测量结果稳定性差等问题,具有较高的工程应用价值。     

Fracture Properties of Concrete–Concrete Interfaces Using Digital Image Correlation

The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete–concrete jointed interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement, crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis matches well with those measured experimentally.     

Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads

If the nominal contact tractions at an interface are everywhere below the Coulomb friction limit throughout a cycle of oscillatory loading, the introduction of surface roughness will generally cause local microslip between the contacting asperities and hence some frictional dissipation. This dissipation is important both as a source of structural damping and as an indicator of potential fretting damage. Here we use a strategy based on the Ciavarella-Jäger superposition and a recent solution of the general problem of the contact of two half spaces under oscillatory loading to derive expressions for the dissipation per cycle which depend only on the normal incremental stiffness of the contact, the external forces and the local coefficient of friction. The results show that the dissipation depends significantly on the relative phase between the oscillations in normal and tangential load—a factor which has been largely ignored in previous investigations. In particular, for given load amplitudes, the dissipation is significantly larger when the loads are out of phase. We also establish that for small amplitudes the dissipation varies with the cube of the load amplitude and is linearly proportional to the second derivative of the elastic compliance function for all contact geometries, including those involving surface roughness. It follows that experimental observations of less than cubic dependence on load amplitude cannot be explained by reference to roughness alone, or by any other geometric effect in the contact of half spaces.     

Interfacial slip and creep in rolling contact incorporating a cylinder with an elastic layer

A systematic approach for investigating the interfacial behaviour of tyred systems is proposed. A two-dimensional contact model of an elastic strip, shrink-fitted onto a wheel, and subjected to different rolling contact conditions, has been adopted to illustrate the method. The model combines existing techniques to explore individual elastic contact problems and it enables us to characterise the behaviour at the strip/substrate interface caused by loads induced by a quasi-static application of stationary and moving loads on the surface of the layer. The solution is compared to the stationary load case and regimes of local slip, full stick, separation and frictional creep are identified and collated for a variety of loading conditions, materials and geometries. Further, this article presents an investigation of frictional shakedown for layered systems subjected to periodic contact loading. The term shakedown is here referred to as the possibility of developing interfacial residual stresses at the layer/substrate interface such that frictional slip, originally activated by the applied external contact load, ceases after a few loading cycles. The possible applicability of the Melan’s theorem for elastic frictional system is investigated and preliminary results presented.     

A coupled damage-plasticity model for the cyclic behavior of shear-loaded interfaces

The present work proposes a novel thermodynamically consistent model for the behavior of interfaces under shear (i.e. mode-II) cyclic loading conditions. The interface behavior is defined coupling damage and plasticity. The admissible states’ domain is formulated restricting the tangential interface stress to non-negative values, which makes the model suitable e.g. for interfaces with thin adherends. Linear softening is assumed so as to reproduce, under monotonic conditions, a bilinear mode-II interface law. Two damage variables govern respectively the loss of strength and of stiffness of the interface. The proposed model needs the evaluation of only four independent parameters, i.e. three defining the monotonic mode-II interface law, and one ruling the fatigue behavior. This limited number of parameters and their clear physical meaning facilitate experimental calibration. Model predictions are compared with experimental results on fiber reinforced polymer sheets externally bonded to concrete involving different load histories, and an excellent agreement is obtained.