Finite Element Analysis of Precursors to Macroscopic Stick–Slip Motion in Elastic Materials: Analysis of Friction Test as a Boundary Value Problem

In this study, we apply the finite element method to investigate precursor to frictional sliding phenomena arising immediately prior to macroscopic stick–slip transitions in elastic bodies within the framework of a continuum theory. Using a numerical model that mimics an actual experimental system, we study the behavior of contact surface nodes to assess the influence of stiffness, driving velocity, initial conditions, and discretization conditions on the propagation characteristics of microscopic slips. In particular, we show that the initial distribution of frictional stress arising due to the Poisson effect has a significant effect on the propagation characteristics in slip regions. Next, based on the results of a finite element analysis of precursor phenomena that accounts for the influence of bulk compliance, we consider the determination of parameters in rate-dependent friction models. With regard to the behavior of sliding friction, we show that the relationship between friction tests and friction models is fundamentally different from the relationship between material tests and constitutive models for material deformation. We conclude that a proper understanding and classification of friction tests, friction models, and the relationship between these tests and boundary value problems are crucial ingredients in the application of computer-aided engineering techniques to sliding-friction phenomena; indeed, friction tests must ultimately be treated as boundary value problems.     

蹄-鼓式制动器热弹性耦合有限元分析

首先探讨蹄—鼓式汽车制动器的摩擦接触热弹性耦合非线性动力学问题及其分析方法,包括摩擦生热模型、多物理场中的弹性体有限元模型、接触问题模型的建立方法以及相应的数值分析方法。然后,利用有限元分析软件ADI-NA建立一种新型蹄—鼓式制动器热弹性耦合动力学分析的三维有限元模型,确定对模型求解的位移边界条件和热边界条件,设定材料物性参数、加载过程及模拟工况,探讨进行制动器热弹性耦合有限元分析的过程,通过仿真计算得到制动器工作过程中摩擦副间接触力分布、制动鼓瞬态温度场、应力场、变形场等重要信息。     

Kinetic friction characterizations of the tubular rubber seals

In this paper, both the kinetic friction characterizations and the stick–slip motion phenomena for the tubular rubber seals are studied. First, the kinetic friction model of the rubber seal is established to explain the kinetic friction mechanism of the tubular rubber seals. Second, both the measurement principle and the test instrument for the kinetic friction properties of the tubular rubber seals are developed, and then both the normal force curve and the friction force curve are obtained. Finally, the influences of the sliding velocity and the compressive displacement on the kinetic friction properties and the stick–slip motion of the tubular rubber seals are analyzed. The results will play an important role for designing and evaluating advanced rubber seal components.     

Novel frictional algorithm implementing angular increment for two-dimensional frictional systems

This study proposes a new frictional algorithm that implements angular increment. The proposed algorithm is used to solve the numerical solutions of dynamic problems in two-dimensional frictional systems. It can accurately obtain the motion responses of a lumped mass under time-varying external forces, and it can compensate for the shortcomings of the numerical frictional algorithm that implements a time step. Specifically, the proposed algorithm 1) overcomes the difficulties encountered when the angles between resultant tangential forces and slip motion are infinitely close, 2) provides accurate solutions for two-dimensional systems under fierce planar motions, and 3) calculates the responses of the mass within a reasonable period. We compare the computation accuracy, efficiency, and robustness of the proposed frictional algorithm and the previous frictional algorithm [1] through several representative scenarios. We reveal that the proposed algorithm has superior computation accuracy, efficiency, and robustness for two-dimensional frictional problems involving slip/stick transitions and sharp bending.

     

Modeling of Frictional Resistance of a Capsule Robot Moving in the Intestine at a Constant Velocity

Capsule robot is the direction for future development of capsule endoscopy. The imperfection of friction model between the capsule robot and the intestine has been one of the biggest obstacles of its development. Uniform motion is the main mode of the capsule robot in the intestine. However, the frictional resistance variation of the capsule robot in this period has not been understood completely until now. This is the research content in the paper. First, some experiments are conducted to measure actual frictional resistance with a homemade experiment platform. Next, the model of the frictional resistance at a constant velocity is established based on the hyperelasticity of the intestinal material and the interactive features between the capsule robot and the intestine. At last, the theoretical result of the model is proved to be reasonable by simulation analysis. The model is efficient to describe the frictional resistance variation at a constant velocity and can be seen as another kind of stick–slip motion. The work is hoped to perfect the friction model between the capsule robot and the intestine and contribute to the development of the capsule robot.     

基于热力耦合的钢轨接触疲劳裂纹扩展特性分析

采用热弹塑性有限元法和裂纹尖端位移法,对轮轨全滑接触状态下的钢轨表面斜裂纹的扩展特性进行分析.热力耦合有限元模型中,考虑轮轨自由表面与环境热对流、裂纹表面间热传导和温度对材料参数的影响,通过移动边界条件模拟轮轨接触区的移动,计算轮轨摩擦因数、裂纹表面间的摩擦因数和裂纹角度对钢轨表面裂纹扩展特性的影响.计算结果表明:在热...     

A static friction model for tube bulge forming using a solid bulging medium

In a metal working process, the friction between the material and the tools influences the process by modifying the strain distribution of the workpiece. From a numerical point of view, a constant coefficient of friction (Coulomb’s friction) is commonly used in finite element simulations to model the frictional behaviour of contacting solids. However, friction coefficient varies in time and space with many parameters. We presented here a theoretical model of static friction in rubber/metal contact which allows the determination of the static coefficient of friction as a function of local contact conditions. Simulations using finite element software ABAQUS/Explicit were carried out for an axisymmetric tube bulging operation using the defined friction model. We compared the computed tube thickness related to the constant coefficient of static friction with the defined friction model. The results clearly showed that the new friction model provides better agreement between experiments (Girard, Grenier, Mac Donald, J Mater Process Technol 172:346–355, 2006) and results of numerical simulations.     

Computational investigation of slip rate dependent friction as a potential contribution to displacement bursts in nanoindentation of nickel

When nanoindentation is used for material characterization in small indentation depths, surface roughness and frictional effects can play an important role. In the present computational study the implications of a slip rate dependent frictional behavior in the tip-flat/rough sample contact are investigated. A potential contribution of stick–slip phenomenon generated/enhanced by the adopted velocity-weakening friction approximation to pop-in like displacement bursts is observed. Undoubtedly discrete plastic events are the dominant source of pop-ins in a general setting, however the investigated frictional effect is shown to give a potential contribution to experimentally observed nanoindentation displacement bursts in the studied setup.     

Numerical algorithms for two-dimensional dynamic frictional problems

Conventional integration schemes for the equations of motion encounter numerical problems near transitions between stick and slip in two-dimensional frictional contact problems. Here we explore the dynamical behaviour close to these transitions and develop analytical patches that can be used to develop a state-variable algorithm, where the system toggles between states of stick and slip.     

Effects of different restraints on the weld-induced residual deformations and stresses in a steel plate

Effects of three different plate boundary constraints on the residual stress field and deformation are investigated numerically during butt-joint welding. For the numerical solution of the heat transfer equations, the finite element method is used to predict the temperature profile as well as residual stress field due to three different plate boundary conditions. The distortion of the welded plate is modeled as a nonlinear problem in geometry and material, adopting a finite element solution based upon the thermo–elastic–plastic large deflection theory. High-strength shipbuilding steel AH36 with temperature-depending material properties and nonlinear stress–strain material properties (bilinear isotropic hardening option uses the von Mises yield criteria) are assumed for the numerical analysis. For verifying the results, the temperature profile is compared with the result obtained in a previous research. In the mechanical analysis, three different boundary conditions are applied. Effects of plate thickness, plate width, and mesh model on the residual stress with boundary constraint are studied.     

Effects of Fiber Diameter and Tribotest Conditions on Nonlubricated Frictional Behavior of a Microsized Metal Fiber

Experimental determination of the frictional properties of a microsized fiber wrapped around a cylinder has been of long-standing interest to the academic community. The purpose of the current experiments was to explore the diameter dependence of such microsized fibers in nonlubricated friction using a highly accurate tribometer. For this work, NbTi superconducting material was used for the fibers and polyvinyl chloride (PVC) was used as the cylinder material. Significant effects were observed in the kinetic friction coefficient for different fiber diameters, normal forces, and sliding speeds. Moreover, the effects of fiber diameter on the frictional stability were measured. Smaller fiber diameters and low sliding speeds both produced poor frictional stability. The most likely explanation for the observed stick–slip phenomena is hypothesized to be a combination of creep mechanics and plastic deformation of the junctions on the contacting surfaces.     

机械密封的黏滑分析

机械密封副磨损与黏滑引起的振动有关。以密封副动静环为摩擦副进行摩擦磨损试验,通过分析摩擦因数曲线的变化趋势以及机械密封副的磨损形貌,提出在动环与静环相对运动的过程中发生了黏滑振动。考虑动环刚度,构建密封副黏滑模型,通过仿真分析黏滑对密封副表面形貌的影响以及密封副的黏滑磨损机制。结果表明:动环在摩擦扭矩的作用下扭转导致黏滑;动环的最大转速在黏滑过程中达到转轴转速的2倍;黏滑在快速启动阶段并没有发生,仅在速度波动阶段出现,而当速度恢复稳定上升阶段,黏滑现象消失;黏滑最终造成密封副表面严重的黏着磨损。     

Elasto-plastic contact problem of laying wire rope using FE analysis

The three-dimensional elasto-plastic contact model, formulated with variational equalities, has been described for laying wire rope in this paper. The augmented Lagrangian multiplier method has been applied to calculate both the normal contact force and friction contact force, and the radial return mapping algorithm has been employed to handle stick/slip phases of friction. With a graphical user interface (GUI), a program for calculating boundary conditions of a three-dimensional finite element modelling is developed to create external files, which are in the format of the ANSYS parametric design language (APDL) and the external files can be accessed by ANSYS for nonlinear analysis. FE simulation of a simple wire strand has been given and the effects of friction coefficient and self-rotating ratio on the contact stress have been analysed. Also the effects of them on the forming stress and strain have been discussed.     

On the motion of the structure varying multibody systems with two-dimensional dry friction

In the present paper the dynamics of the structure varying multibody systems caused by stick-slip motion with two-dimensional dry friction are analyzed. The methods to determine friction force both in stick and slip states are described. The direct method of considering the wagon bogie system as a structure varying system was used to consider two dimensional friction at the wheelset-side frame connection. The concept of friction direction angle used to determine the friction force components of two-dimensional dry friction both in the stick and slip motion states was used. A speed depended friction coefficient was used and described approximately by hyperbolic secant function. All switch conditions were derived and friction forces both for stick and slip states. Some simulation results are provided.     

二维库伦摩擦力系统的精确解及新数值算法研究*

在路径坐标系下,引入了恒定外部激励力二维库伦摩擦力系统滑移轨迹的精确解。当量纲一的外部激励力F>1时,系统会最终进入黏滞状态,给出了对应的黏滞的位置和黏滞发生的时刻;当F<1时,系统会保持滑移状态。当初始时刻外部激励力的方向与初始速度方向之间的夹角值较大时(接近于反向),则在轨迹中存在一个滑移方向发生剧烈变化的拐点,特别的,当F>1时,拐点接近于黏滞位置。传统积分算法不易求解含有转换及捌点的二维库伦摩擦力系统。假设在足够小的时间步长内,时变外载荷激励可以近似认为保持恒定不变,则利用上述解析解能够建立一种新的库伦摩擦力系统数值求解算法,进而分析粗糙接触表面多结点模型的微滑移以及微滑移诱发的磨损与能量损耗等。     

Dissipated energy and boundary condition effects associated to dry friction on the dynamics of vibrating structures

In turbomachines, dry friction devices (under platform dampers, shrouds, and tie-wire) are usually introduced to reduce resonant responses of bladed disks. Dry friction between rubbing elements induces a highly nonlinear dynamic behaviour which flattens the frequency response functions. It is clear that such behaviour requires an optimisation process to find the optimum parameters that lead to the minimum forced response amplitudes. However, different interpretations still remain concerning the explanation of the physical origin of this type of flattening. The most common one is based on dissipated energy. In this case, heat resulting from the relative frictional motion between contacting surfaces is supposed to bring sufficient dissipation to flatten response functions. On the other hand, a different approach considers that a decrease in vibrational amplitudes is explained by changes in boundary conditions induced by a stick/slip behaviour. In this study, a single degree-of-freedom system is used and analysed both in time and in frequency domains (Harmonic Balance Method) in order to show the contribution of respectively energy dissipation and change of contact state on peak levels.     

Parametric studies on drill-string motions

Experimental and numerical investigations are conducted into drill-string motions. The numerical efforts are carried out by using a reduced-order model with attention to stick–slip interactions between a drill string and an outer shell. These efforts are complemented by experimental studies conducted with a unique, laboratory scale model. Qualitative and quantitative changes in the system behavior are studied with respect to the rotation speed and mass imbalance. Comparisons are made between the numerical findings and the corresponding experimental results. In addition, the influence of contact conditions between the drill string and the outer shell on the drill-string dynamics is also examined. The findings of the work suggest that small changes in the system rotation speed can have a significant influence on the nature of drill-string motions and they also provide guidelines for steering the system out of regions of undesirable dynamics and maintaining drill-string motions close to the center of a borehole.     

Structural damping caused by micro-slip along frictional interfaces

Damping in built-up structures is often caused by energy dissipation due to micro-slip along frictional interfaces (e.g., at bolted joints), which provides a beneficial damping mechanism and plays an important role in the vibration behavior of such structures. A careful study of the micro-slip phenomenon has been carried out using the finite element method. Two classical joint configurations, the press-fit joint and the lap-shear joint, have been used as the model problems. The focus of this paper is to evaluate the effect of dry friction on the damping response of frictional joint interfaces, to understand the evolution of the slip and stick regions along a joint interface during loading, and to quantify the amount of energy dissipation during cyclic loading and its dependence on structural and loading parameters. Finite element predictions are found to compare well with experimental measurements and are used to examine the validity and limitations of early analytical treatments in the literature.     

Macroscopic versus microscopic description of friction: from Tomlinson model to shearons

In this Letter we investigate the response of an embedded system that is subject to an external drive, which is chosen to be either a constant velocity or a harmonic shear. Two approaches are introduced that cover macroscopic and microscopic aspects of the problem and mimic recent measurements on friction using the surface forces apparatus. The first approach is based on the Tomlinson model and its generalization, and allows for the investigation of the coupled lateral–normal response to a lateral drive. We propose a method for analyzing both linear and nonlinear response of confined systems driven harmonically. The method provides a way to deduce the microscopic parameters responsible for dissipation. The second approach focuses on the microscopic level. The shear is shown to excite “shearons”, which are collective modes of the embedded system with well-defined spatial and temporal patterns that dominate the frictional properties of the driven system. We demonstrate that the slip relaxation in stick–slip motion and memory effects are well described in terms of the creation and/or annihilation of shearons.     

Modeling of abrasive wear by the meshless smoothed particle hydrodynamics method

Numerical modeling of surface wear proves to be a very challenging mathematical and numerical problem. Basically nonlinear processes of wear and creation of plastic zones are only the beginning of a large list of factors that have to be incorporated into a numerical model to adequately describe the frictional interaction of solid bodies. This article presents a new approach to numerical modeling of abrasive wear of friction composites under nonstationary friction. It utilizes the meshless smoothed particle hydrodynamics method together with the standard finite element method. The presented numerical examples illustrate both verification of the new approach, as well as results of abrasive wear modeling.