On the Repeatability of Friction and Wear Tests for Polyimides in a Hertzian Line Contact

Tribological properties for polymers are mainly experimentally determined, while few standards are available and variation in data is often large. Polyimide is slid against steel on a cylinder-on-plate tribotester at 50–200 N and 0.3 m/s. There is a statistical variation of ±7% on dynamic friction, ±10% on static friction, ±8% on wear rates from weight loss and ±12% from wear rates from dimensional measurements, or even higher at high normal loads. Different parameters influencing statistical repeatability are discussed. Friction for polymers shows higher variation and wear rates show lower variation than steel/steel pairs due to visco-elastic deformation that has a contribution to friction but reduces stress concentrations. It is experimentally verified that the visco-elastic deformation of polymers in line contact is higher than calculated from theoretical models. The role of recoverable and permanent deformation is verified and there is a difference in deformation at 50–100 N and 150–200 N revealed from static loading tests, creep tests and wear measurements. The limit between running-in and steady-state coincides with the stabilization in contact pressures after 250 μm diameter reduction. Besides test rig design, a variation in counterface roughness seems the second most important influence.     

A Molecular Dynamics Model for Single Adhesive Contact

The normal adhesive contact between a pair of asperities is performed using molecular dynamics. To simplify the problem, the equivalent contact problem of sphere–plane interaction is solved. Displacements in the contact zone are very small compared to the asperity size, therefore, the computational model is focused on the neighborhood of the contact area. The adhesion between the asperity and the plane is calculated as a sum of interactions between atoms of the asperity and the plane. A computational experiment of pull-on and pull-off is carried out to study the influence of the adhesion on the formation of the contact forces and deformations. The numerical results are compared with theoretical predictions.     

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first-and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theo-retical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is compli-cated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.     

盘-销摩擦系统摩擦接触力测试与特性分析

测量分析动态摩擦接触力是研究摩擦振动与噪声发生机理的关键.本文中建立了盘-销系统摩擦尖叫试验台架,成功再现了摩擦尖叫.采用三向力传感器对有无摩擦尖叫条件下的动态摩擦接触力进行了测量,并利用小波信号分解、概率密度函数、功率谱密度函数、时频分析等方法进行了分析和讨论.研究发现:在发生摩擦尖叫时,动态摩擦力和法向力发生高频波动,是系统噪声的激励源;无摩擦尖叫时的摩擦力和法向力的动态分量为典型的白噪声随机过程,呈非高斯分布;有摩擦尖叫时的摩擦力和法向力为窄带高频类谐波信号,摩擦力呈非高斯分布,而法向力近似为高斯分布;模态耦合是导致盘-销系统发生动态接触力高频波动以及摩擦尖叫的原因.     

A study of contact non-linearities in pin-loaded lugs: Separation,clearance and frictional slipping effects

Pin-loaded lugs with bush fitting are widely encountered in industrial applications to connect parts and transmit loads and motions. Due to their mechanical function, frictional contact inevitably takes place on the pin–bush and lug–pin interfaces, and can lead to non-linear behaviours occurrence under monotonic or periodic loading, such as bush–lug contact separation, pin–bush conforming contact effects in the presence of initial clearance, or bush–lug frictional slipping mechanisms. The aim of this paper is not to present new results of finite element simulations for lugs involving contact with friction but to provide a comprehensive study of those contact non-linearities through a dedicated analytical contact model.     

A Linearized Method to Measure Dynamic Friction of Microdevices

We propose and evaluate a linearized method to measure dynamic friction between micromachined surfaces. This linearized method reduces the number of data points needed to obtain dynamic friction data, minimizing the effect of wear on sliding surfaces during the measurement. We find that the coefficient of dynamic friction is lower than the coefficient of static friction, while the adhesive pressure is indistinguishable for the two measurements. Furthermore, after an initial detailed measurement is made on a device type, the number of trial runs required to take the data on subsequent devices can be reduced from 200 to approximately 20.     

轴承非线性油膜力的一种变分近似解

基于自由边值理论和凸集上的变分方法，提出一种求解当轴颈大扰动时实际轴承瞬态油膜力的近似公式。公式中引入一个参数来模拟油膜破裂自由边界（雷诺边界条件），则凸集上的泛函极值问题就转换为求此参数的代数极值问题。对椭圆轴承在轴颈作大范围扰动情况下的计算结果表明，这一方法达到了很高的精度，可用于转子－轴承系统的非线性动力分析，能大量降低数值计算瞬态油膜力所需的计算量。     

Contact with friction of a rigid cylinder with an elastic half-space

An exact solution to the problem of indentation with friction of a rigid cylinder into an elastic half-space is presented. The corresponding boundary-value problem is formulated in planar bipolar coordinates, and reduced to a singular integral equation with respect to the unknown normal stress in the slip zones. An exact analytical solution of this equation is constructed using the Wiener-Hopf technique, which allowed for a detailed analysis of the contact stresses, strain, displacement, and relative slip zone sizes. Also, a simple analytical solution is furnished in the limiting case of full stick between the cylinder and half-space.     

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.     

Effect of thickness and boundary conditions on the behavior of viscoelastic layers in sliding contact with wavy profiles

In this work, the sliding contact of viscoelastic layers of finite thickness on rigid sinusoidal substrates is investigated within the framework of Green's functions approach. The periodic Green's functions are determined by means of a novel formalism, which can be applied, in general, to either 2D and 3D viscoelastic periodic contacts, regardless of the contact geometry and boundary conditions.Specifically, two different configurations are considered here: a free layer with a uniform pressure applied on the top, and a layer rigidly confined on the upper boundary. It is shown that the thickness affects the contact behavior differently, depending on the boundary conditions. In particular, the confined layer exhibits increasing contact stiffness when the thickness is reduced, leading to higher loads for complete contact to occur. The free layer, instead, becomes more and more compliant as thickness is reduced.We find that, in partial contact, the layer thickness and the boundary conditions significantly affect the frictional behavior. In fact, at low contact penetrations, the confined layer shows higher friction coefficients compared to the free layer case; whereas, the scenario is reversed at large contact penetrations. Furthermore, for confined layers, the sliding speed related to the friction coefficient peak is shifted as the contact penetration increases. However, once full contact is established, the friction coefficient shows a unique behavior regardless of the layer thickness and boundary conditions.     

Configurational Forces and the Dynamics of Planar Cracks in Three-Dimensional Bodies

This paper develops a three-dimensional framework for the evolution of planar cracks, concentrating on the derivation of balances and constitutive equations that describe the motion of the crack tip. The theory is based on the notion of configurational forces in conjunction with a mechanical version of the second law. This revised version was published online in August 2006 with corrections to the Cover Date.     

立式电机模态仿真与实验研究

振动是电机的重要性能指标。本文在MSC.NASTRAN仿真环境下,利用有限元方法对立式电机进行了电机整机的模态仿真,得到了整机的前五阶固有振动频率、振型等参数值。根据仿真结果,分析了整机的危险位置和振型。进行了电机模态试验,验证虚拟样机和数值模拟的有效性。结果表明,系统不会发生共振。最后,在力学分析的基础上对结构进行优化,为立式电机的改进和振动测试提供了参考。     

钢质网状可变球型机构三维力与变形测量

医学界为攻克脊柱压缩性骨质疏松难题,试图应用一种钢质网状可变球型(简称GWQ)机构,将其植入人体脊椎,通过有效变形达到支撑已经压缩的脊椎、恢复人体原高度之目的。针对该机构目前没有力与位移定量关系的现状,本文自行设计制作了GWQ测量传感器,将机构的空间受力问题转化为悬臂梁的弯曲变形问题,定量讨论了机构在三维空间不同位移约束条件下,各方向力与位移的关系,确定了机构三维空间中最优的工作方向,得出了驱动力与该方向上位移的关系曲线。结果表明在机构所置三维空间中,要使其工作效率最高,应选取y向为工作方向(沿脊柱方向),z向为施加外力方向。x、y向初始距离的比值n应大于0.8,驱动力一定时,工作力与n成正比。驱动力Fz与Z向位移Δlz成正比关系,但其变化率随Δlz的增大而减小。临床应用时可根据对该位移的监测实现对驱动力的控制。     

Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface

The paper deals with the estimation of the pressure distribution, the shape of contact and the friction force at the interface of a flat soft elastic solid moving on a rigid half-space with a slightly wavy surface. In this case an unsymmetrical contact is considered and justified with the adhesion hysteresis. For soft solids as rubber and polymers the friction originates mainly from two different contributions: the internal friction due to the viscoelastic properties of the bulk and the adhesive processes at the interface of the two solids. In the paper the authors focus on the latter contribution to friction. It is known, indeed, that for soft solids, as rubber, the adhesion hysteresis is, at least qualitatively, related to friction: the larger the adhesion hysteresis the larger the friction. Several mechanisms may govern the adhesion hysteresis, such as the interdigitation process between the polymer chains, the local small-scale viscoelasticity or the local elastic instabilities. In the paper the authors propose a model to link, from the continuum mechanics point of view, the friction to the adhesion hysteresis. A simple one-length scale roughness model is considered having a sinusoidal profile. For partial contact conditions the detached zone is taken to be a mode I propagating crack. Due to the adhesion hysteresis, the crack is affected by two different values of the strain energy release rate at the advancing and receding edges respectively. As a result, an unsymmetrical contact and a friction force arise. Additionally, the stability of the equilibrium configurations is discussed and the adherence force for jumping out of contact and the critical load for snapping into full contact are estimated.     

Contact of rough surfaces: A simple model for elasticity, conductivity and cross-property connections

Two rough plates with multiple contacts of diverse microgeometries are pressed against one another. Two types of contacts can be distinguished: Hertzian ones and “welded” areas. We find that for circular contacts (1) the two types produce the same effect on the incremental stiffness of the interface and on the effective conductivity across it if their contact areas are the same; (2) for both contact types, the compliance and the conductivity are controlled by the same microstructural parameter, where S_k is the kth contact area; (3) the explicit cross-property connection is established that gives the (incremental) stiffness in terms of the conductivity; it holds for an arbitrary mixture of Hertzian and welded contacts and does not require any knowledge of their microgeometries. Whereas the two types of contacts produce the same effect on the incremental stiffness, the Hertzian contacts cause non-linearities (the incremental stiffness increases with loading). The non-linearity is controlled by the microstructural parameter that is sensitive to contrasts of curvatures of the contacting parts. Model predictions are generally in good agreement with experimental data on conductivities of rough metal surfaces and stiffnesses of rough rock surfaces.     

The Tribological Effect of Mechanically Produced Micro-dents by a Micro Diamond Pyramid on Medium Carbon Steel Surfaces in Rolling-sliding Contact

In order to evaluate the effects of micro-pockets on the lubrication and the pitting durability of medium carbon steel surfaces, in the present paper, using the roller with a small number of micro-dents marked by a diamond pyramid whose total area was, to minimize the effect of work-hardening, set negligibly small compared to the contact area as the follower in a two-roller testing machine, the pitting durability was tested under poor lubrication conditions and/or severe loading levels. The results successfully demonstrate the effect of such micro-pockets on the pitting durability and scuffing resistance of surfaces in rolling-sliding contact.     

A Unifying Explanation for the Damping of Turbulence by Additives or External Forces

Recent calculations for the turbulent flow of a suspension of solid spheres in a gas were carried out by solving a Navier Stokes equation for the fluid that recognizes the presence of particles as external point forces. These show that a strong damping of the fluid turbulence can be realized at remarkably small volume fractions. The suggestion is made that the presence of point forces, pseudo-point forces, or added point shear stresses could provide a general explanation for turbulence suppression caused by additives or by the acceleration of a turbulent boundary-layer.     

无刷直流力矩电动机系统传函的精确描述

本文介绍无刷直流力矩电动机系统结构与运行原理；采用Ｐａｒｋ变换建立了无刷直流力矩电动机系统的动态数学模型；通过频域分析，推出精确描述无刷直流力矩电动机系统特性的传递函数；讨论了无刷直流力矩电动机系统参数对整个控制系统的影响。     

Slip-shakedown analysis of a system of circular beams in frictional contact

In automotive components, the cumulative microslip phenomenon is often observed for engine assemblies. This phenomenon results in an accumulation of the relative slips in a preferred tangential direction on the contact interface of two solids under cyclic loadings. A significant relative displacement may occur and leads to the assembly failure. In particular, a global rotation of the bearing shell may result from this mechanism of cumulated slips in conrod big end systems. To discuss this rotation problem, a model of two circular beams in frictional contact and submitted to a periodical rotating load is considered here. The aim is to give some simplified estimates of the critical rotation load based on a slip-shakedown analysis. The discussion holds for Tresca friction and can be extended to Coulomb friction under the assumption of small coupling. The static and kinematic slip-shakedown approaches are discussed. The obtained analytical results are shown to be in agreement with the finite element computations.     

结合部切向接触刚度分形模型研究

根据球体与平面接触的切向接触刚度和粗糙表面的接触分形理论，从理论上首次建立了结合部切向接触刚度分形模型，该模型具有尺度独立性。通过对所建模型的数字仿真，直观地给出了结合部切向接触刚度与其影响因素之间的非线性关系，并与实验研究结果具有较好的一致性，从而说明了该模型是合理的。