干气密封滑动摩擦界面切向接触刚度分形模型

为揭示干气密封滑动摩擦界面高频微幅自激摩擦振动规律,用分形参数表征摩擦界面形貌特性,根据重新建立的微凸体接触变形方式,以及对非协调弹性体在切向力作用下初始滑动问题的研究,建立了干气密封滑动摩擦界面切向接触刚度分形模型. 通过数值对切向接触刚度的影响因素进行了分析,研究结果表明:切向接触刚度随分形维数、真实接触面积和材料特性系数的增大而增大;切向接触刚度随特征尺度、摩擦系数的增大逐渐减小. 相比于分形维数、特征尺度和材料特性系数对切向接触刚度的影响,摩擦系数的影响相对较小. 这些研究结果为进一步研究干气密封高频微幅自激摩擦振动奠定了基础.      

Effect of phase on the frictional dissipation in systems subjected to harmonically varying loads

When contacting elastic systems are subjected to periodic loading, frictional slip occurs resulting in energy dissipation. Here we investigate the effect of the relative phase of harmonically varying tangential and normal loads on the frictional dissipation in a very simple uncoupled frictional system. We demonstrate that this effect is substantial when the system experiences periods of separation, but more modest when contact is continuous. The maximum dissipation occurs when the normal and tangential loads are approximately π/2 out of phase.     

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.     

Analysis of FRP composites under frictional contact conditions

This work studies numerically the tribological behavior of fiber-reinforced plastics (FRP) under different frictional contact conditions, using a boundary element methodology. The formulation uses the Boundary Element Method (BEM) with an explicit approach for fundamental solutions evaluation, for computing the elastic influence coefficients. To enforce the contact constraints on the potential contact zone: Signorini’s contact conditions and an orthotropic law of friction, contact operators over the augmented Lagrangian are considered in the formulation. The methodology and the proposed algorithm are applied to study two types of glass FRP and two types of carbon FRP, with the same fiber volume fraction, under frictional contact. In these studies, it can be observed how the fiber orientation and sliding orientation affect the normal and tangential contact compliance, as well as the contact traction distribution. Furthermore, the formulation considers a micromechanics model for FRP that allows also to study the influence of fiber volume fraction on normal and tangential contact compliances.     

Mathematic modeling and characteristic analysis for dynamic system with asymmetrical hysteresis in vibratory compaction

We investigate dynamic characteristics of vibratory compaction system with asymmetrical hysteresis. An asymmetrical model derived from Bouc-Wen differential equation is employed to describe hysteretic behavior of vibration engineering. A practical polynomial expression for hysteretic restoring force is deduced to be substituted into standard equation of the system, assuming that the non-linearity of the restoring force is weak. An asymptotic method, which combines Krylov-Bogolyubov-Mitropolsky (KBM) method with harmonic balance (HB) method, is applied to analyze steady-state responses of the asymmetrical hysteretic system subjected to harmonic excitation. Dynamic responses, such as the restoring force time histories and frequency responses of the system for the first order approximate, are obtained. Furthermore, numerical solution obtained using Runge-Kutta method as well as results of experiments (asphalt compaction on the Beijing-Fuzhou highway) are compared with the asymptotic solution. These results investigated that asymmetrical hysteretic model and the methods applied in this paper are quite appropriate for engineering applications.     

Frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane

The frictional contact problem for a layer resting on a homogeneous half plane is handled using linear elasticity theory in this study. The layer is in contact with a rigid cylindrical stamp that is on the layer and applies a concentrated force in the normal and tangential directions. Friction between the component couples of layer–stamp and layer–half plane is taken into account. The problem is reduced to a system of singular integral equations, in which the contact pressures and the contact areas are the unknowns, and it is treated using Fourier transforms and the boundary conditions for the problem. The system of singular integral equations is solved numerically using the Gauss–Jacobi integration formula with equilibrium and consistency conditions. Numerical results for the contact pressures and the contact areas are given as a solution for both the frictional and the frictionless cases. This work is the first study that investigates the effect of friction on the receding contact problem of a layer and a half plane with two contact areas.     

Relaxation and Recovery in Hydrogel Friction on Smooth Surfaces

Background

Hydrogels are crosslinked polymer networks that can absorb and retain a large fraction of liquid. Near a critical sliding velocity, hydrogels pressed against smooth surfaces exhibit time-dependent frictional behavior occurring over multiple timescales. The origin of these dynamics is unresolved

Objective

Here, we characterize this time-dependent regime and show that it is consistent with two distinct molecular processes: sliding-induced relaxation and quiescent recovery.

Methods

Our experiments use a custom pin-on-disk tribometer to examine poly(acrylic acid) hydrogels on smooth poly(methyl methacrylate) surfaces over a variety of sliding conditions, from minutes to hours.

Results

We show that at a fixed sliding velocity, the friction coefficient decays exponentially and reaches a steady-state value. The time constant associated with this decay varies exponentially with the sliding velocity, and is sensitive to any precedent frictional shearing of the interface. This process is reversible; upon cessation of sliding, the friction coefficient recovers to its original state. We also show that the initial direction of shear can be imprinted as an observable “memory”, and is visible after 24 hrs of repeated frictional shearing.

Conclusions

We attribute this behavior to nanoscale extension and relaxation dynamics of the near-surface polymer network, leading to a model of frictional relaxation and recovery with two parallel timescales.

     

Analysis of spatially extended excitable Izhikevich neuron model near instability

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincaré map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed.

     

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.     

The effect of tangential elasticity of the contact layer between stator and rotor in travelling wave ultrasonic motors

In travelling wave ultrasonic motors the elliptical motion of material points of the stator drives the rotor due to frictional mechanisms. The motor characteristic strongly depends on the mechanical properties of the components stator, rotor and contact layer. In order to predict the motor behaviour, a model for the contact between stator and rotor has been developed. The goal of the present paper is to point out the importance of the tangential elasticity of the contact layer which is responsible for the formation of stick zones and also for the amount of friction losses and overall efficiency. Therefore a comparison with a model with a contact layer rigid in tangential direction is given. Based on a visco-elastic foundation model for the contact layer, torque-speed curves as well as torque-efficiency curves are computed. Experimental investigations for identification of parameters, check of assumptions and model validation are carried out. Finally, the model is used to show the results of parameter variations for normal force, vibration amplitude and modulus of elasticity of the contact layer.     

Interaction of thermal contact resistance and frictional heating in thermoelastic instability

Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is frictional heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has never been investigated. In this paper, we consider an idealized problem in which a thermoelastic rod slides against a rigid plane with both frictional heating and a contact resistance. For sufficiently low sliding speeds, the results are qualitatively similar to those with no sliding. In particular, there is always an odd number of steady-state solutions; if the steady-state is unique it is stable and if it is non-unique, stable and unstable solutions alternate, with the outlying solutions being stable. However, we identify a sliding speed V₀ above which the number of steady states is always even (including zero, implying possible non-existence of a steady-state) and again stable and unstable states alternate. A parallel numerical study shows that for V>V₀ there are some initial conditions from which the contact pressure grows without limit in time, whereas for V<V₀ the system will always tend to one of the stable steady states.     

A power-form method for dynamic systems: investigating the steady-state response of strongly nonlinear oscillators by their equivalent Duffing-type equation

This paper aims to apply a transformation method that replaces the elastic forces of the original equation of motion with a power-form elastic term. The accuracy obtained from the derived equivalent equations of motion is evaluated by studying the finite-amplitude damped, forced vibration of a vertically suspended load body supported by incompressible, homogeneous, and isotropic viscohyperelastic elastomer materials. Numerical integrations of the original equations of two oscillators described by neo-Hookean and Mooney–Rivlin viscohyperelastic elastomer material models, and their equivalent equations of motion, are compared to the frequency–amplitude steady-state solutions obtained from the harmonic balance and the averaging methods. It is shown from numerical integrations and approximate steady-state solutions that the equivalent equations predict well the original system dynamic response despite having higher system nonlinearities.

     

Influence of frictional anisotropy on contacting surfaces during loading/unloading cycles

This paper presents numerical investigations on the loading and unloading of a three-dimensional body in frictional contact with a rigid foundation. The evolution of the sliding process during loading/unloading cycles is analyzed. The important case of anisotropy is examined along with the effect of the sliding rule. The solution algorithm is based on a variational inequality which combine the contact problem and the frictional problem. The numerical results of the punch problem show the hysteretic and irreversible behavior occurring when friction is anisotropic.     

含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

ROCK INITIATION AND PROPAGATION SIMULATION UNDER COMPRESSION-SHEAR LOADING USING CONTINUOUS-DISCONTINUOUS CELLULAR AUTOMATON METHOD

A continuous-discontinuous cellular automaton method is developed for rock initiation and propagation simulations, in which the level set method, discontinuous enrichment shape functions and discontinuous cellular automaton are combined. No remeshing is needed for crack growth analysis, and all calculations are restricted to cells without an assembled global stiffness matrix. The frictional contact theory is employed to construct the contact model of normal pressure and tangential shear on crack surfaces. A discontinuous cellular automaton updating rule suitable for frictional contact of rock is proposed simultaneously with Newton's iteration method for nonlinear iteration. Besides, a comprehensive fracturing criterion for brittle rock under compression-shear loading is developed. The accuracy and effectivenesss of the proposed method is proved by numerical simulation.     

水工圆形隧洞围岩衬砌摩擦滑动接触的新解法

在实际工程中,围岩和衬砌接触时,它们之间并非完全光滑,也并非可以承受任意大的摩擦力.如果围岩与衬砌之间的剪应力大于所能承受的最大静摩擦力,接触面间将发生切向滑动,定义接触面上产生最小滑动量的状态为衬砌的真实工作状态,这种接触即为摩擦滑动接触.以库仑摩擦模型模拟围岩和衬砌之间的摩擦滑动接触,在考虑支护滞后效应的前提下,利用平面弹性复变函数方法列出了应力边界条件、应力连续条件以及位移连续条件的方程, 再结合最优化理论,建立了具有一般性的摩擦滑动接触解法.在利用混合罚函数法求解最优化问题的过程中,减少了设计变量的个数,极大地简化了优化模型,提升了优化过程的迭代速度以及优化结果的精度.以此为基础,获得了围岩和衬砌相互作用下圆形水工隧洞的应力解析解.该方法可以求解光滑接触和完全接触两种极限情况,具有一般性.同时,利用一种精确的计算方法得到了不同情况下满足完全接触条件摩擦系数的阈值,还分析了衬砌和围岩边界上切向应力的变化规律.      

柔性梁斜碰撞问题的非线性动力学建模和实验研究

本文研究柔性梁点面斜碰撞问题。用Hertz接触模型处理法向撞击力,分别用Hertz切向接触模型和Coulomb摩擦力模型处理粘滞状态和滑动状态的摩擦力。从精确的应变与位移的关系出发,用绝对节点坐标法建立了柔性梁的动力学方程。为了准确地处理斜碰撞切向运动的复杂状态,提出滑动-粘滞切换的准则,在此基础上,设计了斜碰撞实验,数值对比了法向撞击力和法向速度的时间历程的仿真计算结果与实验结果,验证了Hertz理论在斜碰撞情况下的正确性。另一方面切向速度的实验与理论的结果对照表明滑动-粘滞切换准则的有效性。