A novel dynamic friction experiment using a modified kolsky bar apparatus

A novel dynamic friction experiment using the Kolsky bar concept was developed. The technique is complementary to the plate impact and other macroscopic friction experiments in the sense that sliding velocities and pressures not attainable otherwise can be investigated. The experimental results reported in this article show that the technique provides accurate and repeatable measurement of time-resolved friction. The apparatus is simpler and easier to operate than the plate impact facility. However, it cannot achieve the same level of contact pressure. Several material pairs have been investigated. In particular, the kinetic friction coefficient of Ti-6Al-4V sliding against WC/Co (cermet) and 4340 steel sliding against WC/Co were measured and compared with the values reported by Prakash and Clifton in 1993. Atomic force microscopy is used to characterize the surface topography before and after the friction tests.     

滚动问题中摩擦力的判断

刚体滚动时摩擦力的判断是工程力学中极易引起学生困惑的问题. 在对摩擦力产生原因进行分析的基础上, 确定了刚体纯滚动时静摩擦力的计算公式和判定方法. 刚体作纯滚动时静摩擦力所作总功为零, 仅实现刚体平动动能和转动动能之间的相互转化, 其方向总是阻碍主动力引起的物体运动趋势并使其向另一种运动转化; 刚体作有滑滚动时滑动摩擦力所作总功为负, 其方向与刚体滑动方向相反, 并实现刚体平动动能和转动动能之间的相互转化.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

与冲蚀有关的粘着与犁沟摩擦系数

提出一种与冲击磨损有关的有效摩擦系数，它被定义为冲击过程中，每一瞬间的切向有效摩擦力与法向载荷之比．有效摩擦力被表示为剪切项与犁沟项之组合．剪切项依赖于剪切金屑接合点的状态——滑移或滚动．犁沟项依赖于冲击物在冲击途中使靶材料发生移动的状态．此有效摩擦系数被应用于研究刚性球自由斜冲击延性靶问题．在忽略剪切项仅计及犁沟项的情况下，研究表明，Hutchings实验中的有效冲击摩擦系数是冲击过程与初始冲击角的函数，就时间平均而言，大于Hutchins为拟合计算与实验结果所取的摩擦系数常值0.05．有迹象表明，对于与固粒延性冲蚀有关的刚性球自由斜冲击延性靶问题，在一定条件下，有效摩擦系数主要由犁沟效应确定．     

Oblique Bounce of a Rubber Ball

Measurements are presented on the oblique impact of a hollow rubber ball incident on a polished granite surface, and the results are compared with those for a solid rubber superball. The hollow ball had a much higher coefficient of sliding friction than the superball, resulting in significant differences in all bounce parameters, at all angles of incidence. The hollow ball gripped the surface at all observed angles of incidence, resulting in one or two reversals in the direction of the friction force during the impact. The friction force was measured directly, as was the rotation speed of the ball during the impact. The results show that the tangential coefficient of restitution of a ball depends on both the coefficient of sliding friction and the ratio of the tangential to the normal vibration frequency of the ball.     

深部煤岩界面超低摩擦时变模型及能量转化研究

深部煤岩超低摩擦型冲击地压实质是巨量煤岩体沿煤岩界面发生失稳滑动的时变过程,期间煤岩界面摩擦力和摩擦系数随时间变化,同时伴随煤岩界面摩擦力做功向煤岩冲击动能释放能量转化特征.为定量描述煤岩界面能量转化规律,引入量纲分析法,实验测定了煤岩弹性系数、阻尼系数和待定系数,给出了深部煤岩界面摩擦系数表达式.以沈阳红阳三矿为研究对象,通过实验研究和工程实际相结合,定义了冲击动能转化率新指标,验证了所建模型可靠性,定量描述了煤岩界面摩擦力做功向煤岩冲击动能转化规律.研究结果表明:深部煤岩界面摩擦系数随冲击载荷幅值增大而线性降低,随冲击载荷频率增大而线性增加.深部煤岩界面摩擦力的降幅和降低速率变化急剧,当冲击载荷幅值为5000 N、冲击载荷频率为500 Hz时,深部煤岩界面摩擦力降幅为97%、降低速率为38.9 kN/ms～41.38 kN/ms时发生超低摩擦效应.首次从摩擦力降低幅值和降低速率定量表征超低摩擦效应.结合实验和工程实际分析发现,能耗比实验结果均值为0.441,红阳三矿“11.11”冲击地压计算结果为0.488,两者较为接近,进一步证明所建模型合理性.     

三方程线性弹性-阻尼DEM模型及碰撞参数确定

建立了一种考虑法向接触力、切向接触力(含静滑动摩擦力及动滑动摩擦力)和力矩(含由切向力产生的力矩及静滚动摩擦力矩和动滚动摩擦力矩)的三方程线性弹性-阻尼离散单元模型,并将该模型应用到颗粒物料的三维数值模拟中,讨论了模型中几个重要碰撞参数--刚性系数、阻尼系数及摩擦系数的选择及其对计算结果的影响,同时也探讨了时间步长等计算参数对模拟结果的影响.为了验证算法和参数选择的正确性,本文对几个有代表性的颗粒系统进行了数值试验研究,并对计算结果进行了细致的分析,验证了新模型和参数选择的正确性.     

A finite element study of the deformations, forces, stress formations, and energy losses in sliding cylindrical contacts

This work presents the results of a finite element analysis (FEA) used to simulate two-dimensional (2D) sliding between two interfering elasto-plastic cylinders. The material for the cylinders is modeled as elastic-perfectly plastic and follows the von Mises yield criterion. The FEA provides trends in the deformations, reaction forces, stresses, and net energy losses as a function of the interference and sliding distance between the cylinders. Results are presented for both frictionless and frictional sliding and comparisons are drawn. The effects of plasticity and friction on energy loss during sliding are isolated. This work also presents empirical equations thatt relate the net energy loss due to sliding under an elasto-plastic deformation as a function of the sliding distance. Contour plots of the von Mises stresses are presented to show the formation and distribution of stresses with increasing plastic deformation as sliding progresses. This work shows that for the plastic loading cases the ratio of the horizontal force to the vertical reaction force is non-zero at the point where the cylinders are perfectly aligned about the vertical axis. In addition, a “load ratio” of the horizontal tugging force to the vertical reaction force is defined. Although this is analogous to the common definition of the coefficient of friction between sliding surfaces, it just contains the effect of energy loss in plasticity. The values of the contact half-width are obtained for different vertical interferences as sliding progresses.     

A comprehensive study on the behavior of a rigid block on an oscillating ground with friction,elastic and viscous forces

This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal.     

Flow-induced vibration of curved cylinder arrays subject to loose support

In this paper, an improved model is developed aimed at analyzing the fluidelastic vibration of a single flexible curved tube which is surrounded by rigid cylinders and subjected to cross-flow and loose support. Based on the previous model, the axial extension of the curved tube described by von Karman nonlinearity has been accounted for in the current research. Simulations are performed to explore the effect of quasi-steady fluid force model and velocity-limited friction model on the post-instability behavior. Numerical results show that the out-of-plane response is confined to a limit cycle by the von Karman nonlinearity and the in-plane vibration is induced by the out-of-plane vibration through the nonlinear coupling. When the loose support comes into play, the nonlinear impact forces become dominate. The results are presented; comparisons are made to analyze the parameters influencing the fretting-wear damage, such as normal work rate, contact ratio and impact force level.     

GCr15钢-CVDCr_7C_3镀层摩擦副摩擦振动的研究

本文系统地研究了GCr15钢球-CVDCr_7C_3镀层钢盘摩擦副滑动干摩擦引起的摩擦力(切向力)振动特性及其对材料摩擦磨损性能的影响。试件系统在垂直和水平方向上均处于低刚度、小阻尼状态。试验信号由微机采集、处理并进行频谱分析。结果表明,摩擦力振动的类型与正压力有关,而与拖动速度无关;摩擦力呈周期性自持振动时具有与相对滑动速度典型的非线性关系,振动频率接近(略低)于系统在切向的固有频率,而与拖动速度无关;摩擦力呈非平稳随机振动时,振动频率与系统在法向的振动频率有关,而与系统在切向的固有频率及拖动速度都无关;摩擦偶件运动的平稳性与摩擦力振动的类型有关,而与平均摩擦系数无关;摩擦力所耗费的能量与正压力呈比例关系。     

Development of a New Method to Investigate the Dynamic Friction Behavior of Interfaces Using a Kolsky Tension Bar

To understand interfacial interaction of a bi-material during an impact loading event, the dynamic friction coefficient is one of the key parameters that must be characterized and quantified. In this study, a new experimental method to determine the dynamic friction coefficient between two metals was developed by using a Kolsky tension bar and a custom-designed friction fixture. Polyvinylidene fluoride (PVDF) force sensors were used to measure the normal force applied to the friction tribo pairs and the friction force was measured with conventional Kolsky tension bar method. To evaluate the technique, the dynamic friction coefficient between 4340 steel and 7075-T6 aluminum was investigated at an impact speed of approximately 8 m/s. In addition, the dynamic friction coefficient of the tribo pairs with varied surface roughness was also investigated. The data suggest that higher surface roughness leads to higher friction coefficients at the same speed of 8 m/s.     

Wave induced sliding at the interface between a layered elastic medium and a half-space

The sliding interface between an unrestrained elastic half-space and a grounded layered half-space excited by an incident harmonic wave is investigated. The problem is formulated considering various possible boundary conditions and boundary inequalities at the sliding interface. The Coulomb friction model without distinction between the static and kinetic coefficients of friction is considered to govern the sliding condition. Three possible bands at the interface, namely slip, stick, and separation, are considered. The interface is assumed to be preloaded under normal and shear stresses. The solution is developed by modifying the problem of welded interface, which then is reduced to a set of algebraic equations. The effects of the incident angle, layer thickness, friction coefficient and externally applied stresses on the drift velocity of the unrestrained half-space are studied numerically for a pair of materials. It is shown that the sliding interface, and hence the drift velocity of unrestrained half-space is noticeably influenced by the layered medium. These results are expected to be useful for the development of a new kind of ultrasonic drive in future.     

爆炸地冲击作用下浮放设备滑移抛离分析

从基础和设备间的接触力特点出发,采用Matlab/SIMULINK仿真软件建立了爆炸地冲击作用下浮放设备的滑移抛离模型,并验证了该模型的正确性。通过输入实测爆炸地冲击加速度波得出在真实爆炸环境中浮放设备的运动历程可分为相对静止、滑移、抛离、滑移减速等四个阶段。并根据其特点,提出了合理简化加速度波,采用该加速度波形,分析得到了浮放设备运动响应与动摩擦系数、爆炸地运动参数的关系。     

An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems

This paper presents a method for the analytical prediction of sliding motions along discontinuous boundaries in non-smooth dynamical systems. The methodology is demonstrated through investigation of a periodically forced linear oscillator with dry friction. The switching conditions for sliding motions in non-smooth dynamical systems are given. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction. This analytical prediction provides an accurate prediction of sliding motions in non-smooth dynamical systems. The switching conditions developed in this paper are expressed by the total force of the oscillator, and the nonlinearity and linearity of the spring and viscous damping forces in the oscillator cannot change such switching conditions. Therefore, the achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces processing a C ⁰-discontinuity.     

石墨烯在金刚石基体表面的纳米摩擦学行为研究

采用热化学气相沉积法(Thermal Chemical Vapor Deposition，TCVD)和机械剥离法分别制备了单层和少层石墨烯并转移至MPCVD制备的多晶金刚石基体表面，利用原子力显微镜研究了大气环境下石墨烯在金刚石基体上的纳米摩擦和磨损性能. 研究结果表明:单层和少层石墨烯在金刚石基体上具有良好的减摩作用，摩擦系数分别为0.03和0.014. 然而，由于石墨烯和金刚石表面之间的物理吸附作用较弱，其摩擦力会略高于SiO₂/Si基体表面石墨烯的摩擦力. 随扫描速度升高，金刚石表面的单层与少层石墨烯的摩擦力的变化可以分为自然对数正比上升，基本保持不变以及黏性阻尼增加三个阶段. 在磨损试验中，TCVD法制备和转移石墨烯的过程中产生的缺陷和污染物降低了单层石墨烯的耐磨性能，而机械剥离的少层石墨烯因为无缺陷的石墨烯晶体结构在金刚石基体上展现了优异的耐磨特性. 本研究可为以金刚石为基体的石墨烯固体润滑剂使用提供理论基础.      

Mechanics and mechanism of cut resistance of protective materials

A sliding sharp edge penetrating material is one of the most dangerous cases of cutting because it requires the smallest applied load. A better understanding of the cutting mechanism is a fundamental step to develop new and more performing protective materials. This study aims at analyzing cutting mechanics and mechanism in the presence of friction. The International Standard ISO 13997 cut test method consists in measuring the distance that a straight blade slides horizontally to cut through a material under a constant applied normal force and was used to investigate cutting phenomena.In practice, cut resistance of a material is contributed by the intrinsic strength of material and the frictional distribution. Two types of friction distributions are involved in cutting: a macroscopic friction induced by the gripping of the material and by the applied normal load on the two sides of the blade; and the other the sliding friction associated with cut through of the material that occurs along the face of the blade tip. For most materials, frictional forces due to lateral gripping could be several times greater than the friction due to the applied normal force. Thus, the cutting energy required for breaking molecular chains is much smaller than the energy dissipated for friction. The elastic modulus, the structure of the material as well as the sliding velocity have significant influence on the friction. Therefore all these properties can affect the cutting resistance results.     

Illustrative examples of anisotropic friction with sliding path curvature effects

A constitutive equation of anisotropic friction with sliding path curvature effects defined in the preceding companion paper is completed with illustrative examples. Friction coefficients, inclination angles and coefficients of tangent and normal components of the friction force with respect to the sliding direction are given in the case of non-homogeneous friction properties which form concentric circles in a contact surface. Motion of a material point in the surface with non-homogeneous friction is investigated for radial, concentric circular and arbitrary trajectories. Essential changes of sliding trajectories of the material point are observed for various values of coefficients of parametric tensors in the constitutive equation.     

On the sliding instabilities at rough surfaces

In this paper, the onset of sliding between two elastic half-spaces in contact, subjected to a tangential force, is studied within the framework of critical phenomena. First, it is shown that the contact domain between two rough surfaces is a lacunar set and that the distribution of contact stresses is multifractal. By applying an increasing tangential force, under constant normal load, the so-called regime of partial-slip comes into play. However, the continuous and smooth transition to full sliding, predicted by the classical Cattaneo-Mindlin theory, is not confirmed by the experiments, which show marked frictional instabilities. A numerical multi-scale procedure is proposed, taking into account the redistribution of stress, consequent to partial-slip, among the contact areas at all scales. It is shown that the lacunarity of the contact domain delays the onset of instability, when compared to compact Euclidean domains. Independently of the assumptions made for the frictional behaviour at the scale of the asperities (Coulomb friction for meso-scale asperities, adhesion for micro-scales), renormalization permits the critical value of the tangential force which provides the instability to be found. Moreover, the multifractal analysis of the domains where the shear resistance is activated captures the size-scale effects on the friction coefficient, currently evidenced by the experiments.