Mathematical Description and Finite Element Equation of 3D Coupled Thermo-elastic Contact Problem

Through defining slide yield function and floating potential function of thermo-contact surface, the complementary equation of thermo-contact boundary has been reached, the fundamental equations to solve 3D thermo-contact coupled problem have been listed. On this foundation, the finite element equation and definite solution condition of contact heat transfer have been given out. Based on virtual work principle and contact element technology, the finite element equation of 3D elastic contact system has been deduced under the effect of thermal stress. The pseudo load brought by contact gap have been introduced into this equation in order to reflect the contact state change. During iteration, once contact rigidity matrix is formed, it won’t change, which will make calculation reduce greatly.

Winkler Support Model and Nonlinear Boundary Conditions Applied to 3D Elastic Contact Problem Using the Boundary Element Method

This work presents a numerical methodology for modeling the Winkler supports and nonlinear conditions by proposing new boundary conditions. For the boundary conditions of Winkler support model, the surface tractions and the displacements normal to the surface of the solid are unknown, but their relationship is known by means of the ballast coefficient, whereas for nonlinear boundary conditions, the displacements normal to the boundary of the solid are zero in the positive direction but are allowed in the negative direction. In those zones, detachments of nodes might appear, leading to a nonlinearity, because the number of nodes that remain fixed or of the detached ones (under tensile tractions) is unknown. The proposed methodology is applied to the 3D elastic receding contact problem using the boundary element method. The surface t r actions and the displacements of the common int erface bet ween the two solids in contac t under the influence of different supports are calculated as well as the boundary zone of the solid where the new boundary conditions are applied. The problem is solved by a double-iterative met hod, so in the final solut ion, t here are no t r act ions or pene trations between the two solids or at the boundary of the solid where the nonlinear boundary conditions are Simula ted. The effectiveness of the proposed method is verified by examples.

BOUNDARY ELEMENT METHOD FOR MOVING AND ROLLING CONTACT OF 2D ELASTIC BODIES WITH DEFECTS

A scheme of boundary element method for moving contact of two-dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.

Surrounding rock deformation analysis of underground caverns with multi-body finite element method

Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.

Numerical Simulation of Heat Transfer and Deformation of Initial Shell in Soft Contact Continuous Casting Mold Under High Frequency Electromagnetic Field

Heat transfer and deformation of initial solidification shell in soft contact continuous casting mold under high frequency electromagnetic field were analyzed using numerical simulation method; the relative electromagnetic parameters were obtained from the previous studies. Owing to the induction heating of a high frequency electromagnetic field （20 kHz）, the thickness of initial solidification shell decreases, and the temperature of strand surface and slit copper mold increases when compared with the case without the electromagnetic filed. The viscosity of flux de- creases because of the induction heating of the high frequency electromagnetic field, and the dimension of the flux channel increases with electromagnetic pressure; thus, the deformation behavior of initial solidification shell was different before and after the action of high frequency electromagnetic field. Furthermore, the abatement mechanism of oscillation marks under high frequency electromagnetic field was explained.

Discrete element method for adhesion properties evaluation of deep-sea sediment from macro and micro perspectives

The adhesion between the mining machine and the deep-sea sediments will significantly affect the driving performance of the mining machine in the deep-sea environment.When the mining machine and the deep-sea sediment interaction simulation was carried out,the accuracy of the particle interaction parameters will directly affect the simulation results.This study proposed a method to systematically calibrate the interaction parameters between deep-sea sediment and grouser through the combination of experiment and simulation.The uniaxial compression test and macro adhesion test and corresponding discrete element numerical simulation were carried out,modifying the contact parameters until the simulation results are close to the experimental results.Then the micro-parameters of the JKR adhesion contact model were back calibrated with the test results,and the contact parameters between soil particle-soil particle and soil particle-metal are calibrated.Besides,the adhesion test shows that the adhesion forces were ranked in the order of 5052<STi80<TA2<TC4 under the same surface roughness,which indicates the aluminum alloy 5052 has the best anti-adhesion performance.The relationship between surface adhesion force and microscopic contact parameters was studied by discrete element numerical simulation,and the result shows that the coefficient of static friction and the coefficient of rolling friction has little effect on adhesion force.While it is mainly affected by the coefficient of restitution and surface energy,the surface adhesion force tends to decrease with the increase of the coefficient of restitution and increase with the growth of surface energy.The obtained parameters of soil particle to soil particle and soil particle to metal affecting the adhesion can contribute to the design optimization for the grouser of mining machines to decrease surface adhesion and enhance its movability and mining efficiency.

A Study on the Physical Properties of Banana Straw Based on the Discrete Element Method

To improve the application of discrete element models(DEM)to the design of agricultural crushers,in this study a new highly accurate model is elaborated.The model takes into account the fiber structure,porous nature of the material and the leaf sheath coating structure.Dedicated experimental tests are conducted to determine the required“intrinsic”and basic contact parameters of the considered banana straw materials.A large number of bonding parameters are examined in relation to the particle aggregation model in order to characterize different actual banana straws.Using the particle surface energy contact model,the viscosity characteristics of the crushed material are determined together with the related stacking angle(considered as the main response factor).Through single factor experiment analysis,it is found that when the surface energy is 0.9 J·m-2,the relative error between simulations and physical experiments is 5.288%.

Geometrically Exact Theory of Contact Interactions–Further Developments and Achievements

The focus of the current contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The construction of the corresponding computational contact algorithms are considered in accordance with the geometry of contact bodies in a covariant form. These forms can be easily discredited within finite element methods independently of order of approximation and, therefore, the result is straightforwardly applied within iso-geometric finite element methods. This approach is recently became known as geometrically exact theory of contact interaction [10]. Application for contact between bodies with iso- and anisotropic surface, for contact between cables and curvilinear beams as well as recent development for contact between cables and bodies is straightforward. Recent developments include the improvement of the curve-to-surface (deformable) contact algorithm.

Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics

In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.

高面板坝挤压墙-垫层料接触面的大型单剪试验及力学特性研究

21世纪以来高面板堆石坝多采用挤压墙施工技术,研究挤压墙-垫层料接触面力学特性以真实预测面板应力变形对于确保大坝安全相当重要。目前锯齿状挤压墙-垫层料接触面的单剪试验和离散元仿真成果均未见到。为此以某200m级高坝为参照,开展挤压墙-垫层料接触面大型单剪试验,比较了锯齿状和平面状两种不同型式挤压墙-垫层料接触界面力学特性的差异。首次采用离散元数值单剪试验分析了接触区垫层料的位移特征及其影响因素,发现与平面状挤压墙相比,锯齿状挤压墙导致垫层料颗粒发生更剧烈的转动并导致靠近接触面的垫层料变形加大。基于锯齿状挤压墙-垫层料接触面的单剪试验成果确定了接触面本构模型及其参数,有助于提高面板堆石坝的面板应力变形计算准确性。

Influence of Surface Properties Modified with Fine Shot Peening on Scuffing

Recently, gears of high strength, reliability, and surface-damage-resistant under severe service conditions are required to achieve the weight saving and downsizing of a product. For the high-speed condition in particular, it is important to understand the influence of the surface properties on the scuffing resistance. If the effective surface profile to improve the lubrication property was found, the metal surfaces could be obtained with both surface strength and surface lubricity. Herein, the influence of surface properties modified with fine shot peening, which can form the arbitrary surface profile, on the scuffing resistance in the rolling-sliding contact machine element, was investigated. The scuffing test was performed using a two-cylinder rolling contact test machine. In a specific sliding, a faster roller of 60% and a sliding velocity of 1.75 m/s were utilized. The scuffing test results with shot-peened test rollers and those with non-shot-peened test roller were compared. The influence of the surface roughness of the shot-peened test roller was also discussed. We found that the shot-peened roller had a better scuffing resistance compared with the roller without the shot-peening process.

螺栓联接结合面三维分形刚度模型与实验研究

为更准确地分析螺栓联接体的静动态特性,根据三维分形理论,考虑微凸体弹塑性接触在内的4种变形阶段,分别得到螺栓联接结合面的法向载荷与切向载荷,进而建立了螺栓联接结合面法向刚度与切向刚度模型,并分析了各参数对螺栓联接结合面刚度模型的影响关系。开展了有限元分析与实验研究,应用所建立的法向刚度与切向刚度模型,将考虑结合面影响的螺栓联接体有限元分析结果分别与忽略结合面影响的螺栓联接体有限元分析结果以及实验结果对比。研究结果显示,增大预紧力、工作载荷、分形维数、材料特性参数,或是减小分形尺度参数,可增大螺栓联接结合面的刚度;应用所建立结合面刚度模型的螺栓联接体有限元分析结果与实验结果误差在8%以内,远小于忽略结合面影响的有限元分析误差。

基于形函数的非一致网格接触修形新方法

针对接触压力分布不均导致机械零部件过早失效的问题,提出了一种非一致网格接触修形新方法。基于单元形函数和“虚拟节点”建立了非一致网格接触节点之间的力学关系,推导得到了节点修形量与接触压力之间的数学方程,提出了一种通过最小化最大接触压力求解修形量的极小极大模型,并根据其数学特点将该模型转换为线性规划模型,提高了修形量计算的效率和全局收敛性。通过三个弹性接触修形实例,验证了该方法对一般弹性接触修形问题的适用性和有效性。

表面织构对滑动电接触界面摩擦学行为的影响

目的利用表面织构减摩抗磨的优良特性,将其应用于电接触摩擦表面,探讨它对滑动电接触界面摩擦磨损及电接触可靠性的影响。方法利用激光系统制备2种织构,即方坑型表面织构(SPT)和沟槽型表面织构(GT),并与光滑表面的载流摩擦学信号进行对比分析。利用ABAQUS模拟试验,分析界面接触应力、电压和位移的变化特性。结果随着试验的进行,GT表面的摩擦因数逐渐增大,并与光滑表面达到同一水平(0.7),SPT表面的摩擦因数在整个试验过程中始终较低(0.4)。光滑表面在电接触过程中发生了多频振动现象,2种织构表面的振动信号非常微弱,尤其是SPT表面,仅出现了100 Hz的振动频率。光滑表面和GT表面出现较严重的磨损现象,而SPT表面磨损轻微。有限元分析结果表明,表面织构的存在能够避免应力集中现象,GT表面的应力较大(90MPa),且始终分布在沟槽棱边。结论在电接触状态下,2种织构表面均能不同程度地降低界面的摩擦因数和摩擦力,其中SPT表面的减摩降磨效果最显著。GT表面沟槽棱边的损伤和磨屑堆积是导致其逐渐失去减摩效果的主要原因。模拟分析结果证实,SPT表面织构的存在能避免应力集中,有利于改善磨损和降低振动强度。虽然GT表面的最大应力分布也具有时变特征,但是其值较大,且分布在沟槽棱边,导致沟槽织构的减摩效果逐渐减弱。

基于共轭修形的大模数摆线齿锥齿轮齿面建模及承载性能分析

针对大模数摆线齿锥齿轮在专用铣齿机上难以加工的问题,提出一种面向加工中心的摆线齿锥齿轮齿面模型构建方法。基于摆线齿锥齿轮加工原理,根据刀具与大轮之间的几何位置关系,建立大轮切齿参数计算方法;根据大轮切齿加工数学模型,推导大轮理论齿面,并通过齿面离散方法获得大轮数值齿面;基于齿轮啮合数学模型推导出与大轮完全共轭的小轮齿面,通过在完全共轭小轮齿面法线方向上构建二阶修形差曲面并进行叠加,获得与大轮齿面呈局部共轭的小轮数值齿面。最后,建立有限元齿面加载接触分析流程,以一对矿用减速器大模数摆线齿锥齿轮副为例,利用ABAQUS软件进行齿轮三维建模和有限元加载接触仿真。结果表明:在实际加载工况下,通过共轭修形构建的小轮齿面与大轮齿面呈局部内对角接触,并且加载接触区受啮合错位影响在大轮齿面内部移动,未脱离齿面产生边缘接触,齿面接触区满足工程需要。仿真结果验证了共轭齿面修形建模方法的可行性。

Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface

Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.

A deterministic FE contact analysis of 3D rough surfaces with textures and comparison with classic statistical contact models

Accurate contact calculations of real rough surfaces are fundamental but complicated. The model-based methods are convenient and straightforward. But these methods ignore some factors and may lead to less accurate results. This is especially true when considering multi-scale topographic features of engineering rough surfaces. Based on artificially generated rough surfaces, the deterministic contact analysis of two 3D rough surfaces is conducted by the finite element method(FEM). The calculations show that when the separation between surfaces reduces, results of classic model-based methods are quite different from those of this study, especially when the roughness distribution and textures are considered. As friction pairs are working under increasing harsh conditions, the accurate contact calculation in this paper will be of great significance.

Analysis of asphalt mix surface-tread rubber interaction by using finite element method

The surface texture of the pavement plays a very important role in driving the frictional properties at the tire rubber-pavement interface. Particularly, the hysteretic friction due to viscoelastic deformations of rubber depends mainly on the pavement surface texture. In the present paper, the effect of micromechanical pavement surface morphology on rubber block friction was brought in by comparing the friction results for three different asphalt mix morphological surfaces, named stone mastic asphalt （SMA）, ultra-thin surfacing （UTS） and porous asphalt （PA）. The asphalt surface morphologies of these mixes were captured by using an X-ray tornographer, from which the resulting images micromechanical finite element （FE） meshes for SMA, UTS and PA pavements were developed by means of the SimpleWare software. In the FE model, the rubber and asphalt binder were modeled as viscoelastic （V-E） materials and the formulation was given in the large deformation frame- work. FE simulations were then carried out by using contact algorithm between rubber and the road surface. It was observed that the rubber friction inversely varies with the sliding speed and positively varies with the pressure for all the pavement morphological and stiffness conditions. Furthermore, it was observed that the highly porous pavement surface results in large dissipation of energy, hence, large rubber friction which shows that the mix characteristics of pavements have a simaificant effect on rubber friction.

柔性结构系统振动状态有限元仿真分析

以VMC850立式加工中心为研究对象,用ANSYS Workbench建立VMC850立式加工中心弹簧-阻尼单元模拟结合面的接触特性,基于此结合面等效方法建立整机有限元模型,并进行静、动态分析,用瞬态结构动力分析进行动态特性分析。

一种结合部法向刚度的预估方法

提出一种结合部法向刚度的预估方法。通过表面形貌测量仪获取粗糙表面的轮廓数据,拟合生成粗糙表面轮廓曲线,在此基础上建立考虑摩擦的二维粗糙表面的有限元弹塑性接触模型,用罚函数法计算压力在0～0.8 MPa的加载过程中接触层的应力、位移和接触面积。计算结果表明,粗糙表面真实的接触面积在低载荷下快速增大,高载荷下的增大速度很缓慢,在载荷为0.8 MPa时的接触面积与名义面积的比为0.3%,真实的接触面积远低于宏观的接触面积;载荷为0.8 MPa时两个表面最高的法向接触应力为924 MPa,最高的Mises应力为434 MPa,接触点附近的材料处于塑性状态,接触点上的应力远高于基体内部应力;分析模型的法向接触刚度取决于少数接触点的接触刚度,接触点的接触刚度则取决于接触点的形貌。采用不同几何尺寸的试样试验,获得的结合部法向刚度数据与计算结果能比较好地吻合,表明该方法是可行的。