A finite element-based model of normal contact between rough surfaces

Engineering surfaces can be characterized as more or less randomly rough. Contact between engineering surfaces is thus discontinuous and the real area of contact is a small fraction of the nominal contact area. The stiffness of a rough surface layer thus influences the contact state as well as the behavior of the surrounding system. A contact model that takes the properties of engineering surfaces into account has been developed and implemented using finite element software. The results obtained with the model have been verified by comparison with results from an independent numerical method. The results show that the height distribution of the topography has a significant influence on the contact stiffness but that the curvature of the roughness is of minor importance. The contact model that was developed for determining the apparent contact area and the distribution of the mean contact pressure could thus be based on a limited set of height parameters that describe the surface topography. By operating on the calculated apparent pressure distribution with a transformation function that is based on both height and curvature parameters, the real contact area can be estimated when the apparent contact state is known. The model presented is also valid for cases with local plastic flow in the bulk material.     

Finite element fractal method for thermal comprehensive analysis of machine tools

Thermal contact resistance (TCR) has a great impact on the temperature distribution and thermal performances of machine tools, which changes constantly during the process of heat transfer under the influence of the mechanical and thermal load. In order to study the thermal behavior of machine tools comprehensively, the TCR has to be considered fully in the research. In this paper, a finite element fractal method is proposed by combining the advantages of the finite element method and the fractal theory. In the proposed method, the TCR is calculated by the fractal theory with consideration of the uneven pressure distribution and the pressure variation of contact surface. Based on the proposed method, the thermal comprehensive analysis is carried out on an ultra-precision machine tool considering the influence of the preload force, ambient air, and TCR. The pressure distributions and variations of contact surfaces in the machine tool are studied, which are used to calculate the TCR by the proposed method. Finally, the experiment is set up to validate the proposed method. The temperature variations of the motor, beam, and hydrostatic bearing obtained by the simulation agree well with the experimental values.     

Effect of roughness scale on contact stiffness between solids

In this work we have used the Hölder exponent to characterise the scale of roughness and to study the scale effect of high spatial frequencies on elastic contact between solids. The mathematical approach shows that the Hölder exponent of roughness is a sophisticated tool for modelling realistic surface roughness at different scales of observation. The incidence of Hölder exponent on the prediction of pressure, bearing area and stiffness is studied in elastic contact between a smooth plane and rough surface.     

The effect of surface roughness on contact and stress states of spur gears

The contact characteristics of spur gears are analysed, taking into consideration real surface micro-geometry, and using numerical algorithms. The contact pressure distribution, contact area, and rigid body rotation of the gears have been calculated for different types of gear surface according to machining: shaping, grinding, or milling. Finally, the sub-surface stress state is evaluated for different pressure distributions, by finite element method.     

A numeric investigation of friction behaviors along tool/chip interface in nanometric machining of a single crystal copper structure

The interaction between the tool rake face and the chip is critical to chip morphology, cutting forces, surface quality, and other phenomena in machining. A large body of existing literature on nanometric machining or nano-scratching only considers the overall friction behavior by simply regarding the total force along tool movement direction as the friction force, which is not suitable for describing the intriguing friction phenomena along the tool/chip interface. In this study, the molecular dynamic (MD) simulation is used to model the nanometric machining process of single crystal copper with diamond tools. The effects of three factors, namely, tool rake angle, depth of cut, and tool travel distance, are considered. The simulation results reveal that the normal force and friction force distributions along tool/chip interface for all cases investigated are similarly shaped. It is found that the normal force consistently increases along the entire tool/chip interface when a more negative rake angle tool is used. However, the friction force increases as the rake angle becomes more negative only in the contact area close to the tool tip, and it reverses the trend in the middle of tool/chip interface. Meanwhile, the increase of depth of cut overall increases the normal force along the tool/chip interface, but the friction force does not necessarily increase. Also, the progress of tool into the work material does not change the patterns of normal force, friction force, or friction coefficient distributions to a great extent. More importantly, it is discovered that the traditional sliding model with a constant friction coefficient can be used to approximate the later section of friction distributions. However, no friction model for traditional machining is appropriate to describe the first section of friction distributions obtained from the MD simulation.     

Effects of wafer curvature caused by film stress on the chemical mechanical polishing process

A theoretical model based on two-body contact theory is established to simulate the contact pressure distribution arising from wafer curvature which is caused by film stress during CMP process. Both wafer and pad deformations during the contact process are considered. The profiles of the contact pressure distribution for wafers with different curvature radius are simulated. The influences of wafer curvature on mean removal rate and within wafer removal rate nonuniformity (WIWNU) are simulated and compared with the experimental data. According to the two-body contact model, when the pad is in contact completely with the wafer, the profile of the contact pressure has almost the same trend whether the wafer has an upward or a downward curvature. The mean value of the contact pressure will increase with increasing of radius of downward curvature. WIWNU will decrease with increasing pre-polish wafer bow from concave (upward curvature) to convex (downward curvature). The results from the simulation correlated with the experimental data and demonstrated the validity of the model. The results are helpful for controlling and reducing the wafer to wafer removal rate nonuniformity and within wafer removal rate nonuniformity in CMP.     

Probability Model for the intermolecular force with surface roughness considered

This paper studies the intermolecular force considering both the roughness of the air-bearing surface and the disk surface by simulation. A model is developed to deal with the intermolecular force, the contact force and the air-bearing force based on the probability distributions of the roughness of the surfaces. The intermolecular force is linked with the contact force when its repulsive term is stronger than its attractive term. In such a case, all the intermolecular force, the contact force and the air-bearing force can be extended to the various flying height regions. Some interesting results are observed and discussed. It is found that both the Hamaker constant and the surface roughness have significant influences on the intermolecular pressure. Compared with the intermolecular pressure with smooth surfaces, that with the surface roughness considered shows greater attractive pressure at the flying height higher than 0.7 nm approximately, but much smaller values between 0.26 and 0.7 nm approximately. A negative stiffness region exists when the minimum flying height is between −0.2 and 1.2 nm for the case studied in this paper. It shows that the Probability Model is suitable for the intermolecular force calculation with the surface roughness considered.     

微观随机粗糙表面接触有限元模型的构建与接触分析

基于相关文献提出粗糙表面模拟方法,通过软件工具在ANSYS中建立微观粗糙表面接触有限元模型,利用该模型分析载荷对弹塑性变形和接触面积的影响。结果表明:随着正压力的增大,粗糙表面上不断地有微凸峰与平面发生弹性接触变形,接触斑点(或接触斑点群)的数目逐渐增加,斑点中心区域的弹性变形很快达到最大,微凸峰负荷变形的同时也使斑点四周区域受到挤压;初始接触时,轮廓高度较大的微凸峰率先发生弹性变形,随着压力的增大,金属材料所受应力达到屈服极限同时粗糙表面的弹性变形和塑性变形的集中区域不断增加,真实接触面积不断增大;接触区数目的增多和接触区面积的增加都可以导致接触面上真实接触面积增加;随着压力的增大,真实接触面积的增大并不是由于接触区数目的增多,而是微观接触区面积的增大。     

依据各向异性分形几何理论的固定结合部法向接触力学模型

基于各向异性分形几何理论,考虑微凸体变形特点、表面微凸体承受法向载荷的连续性和光滑性原理,以及区分微凸体分别处于弹性、塑性变形时的一个微凸体实际微接触面积,建立固定结合部法向接触力学模型。采用二变量Weierstrass-Mandelbrot函数模拟各向异性三维分形轮廓表面。推导出划分弹塑性区域的临界弹性变形微接触截面积、结合部量纲一法向载荷、结合部量纲一法向接触刚度的数学表达式。数值仿真结果表明：当表面形貌的分形维数、分形粗糙度一定时,真实接触面积随着结合部法向载荷的增大而增大;结合部法向接触刚度随着真实接触面积、结合部法向载荷、相关因子或材料特性参数的增大而变大;当分形维数由1变大时,结合部法向接触刚度随着分形维数的变大而增大;当分形维数增加到趋近于2时,结合部法向接触刚度有时却会随着分形维数的增加而降低。结合部法向接触力学模型的构建,有助于分析固定接触表面间的真实接触情况。     

The frictional pattern of tactile sensations in anthropomorphic fingertip

In this report, to consider the technology of frictional tactile sensations (FTS) for a prosthetic fingertip, the anthropomorphic fingertip (silicone) was compared with the human fingertip in terms of sliding friction (reciprocating sliding on an acrylic plate under a load force of ∼2.5 N max.) and the prototype of a FTS was demonstrated. In the results, the friction coefficient of the human fingertip changed according to the contact location more than the anthropomorphic fingertip. In the demonstration, the prototype FTS that faked the human fingertip could generate a high friction coefficient and the peculiar signal pattern at each contact location. Moreover, the prototype FTS recognized a slight difference in the surface roughness of the copier paper. In conclusion, the friction coefficient in the human fingertip increases when increasing the contact area under the same load force. Increasing the contact area induces stiction and stick-slip phenomena, generating a high friction coefficient and vibrations. Moreover, the high friction coefficient amplifies slight contact signals and supports FTS in a prosthetic fingertip.     

Investigation into Channel Angular Extrusion and the UREAD energy absorption technique

Channel Angular Extrusion (CAE) processes are characterised by imposing high level of strain into deformable materials using simple tools where the material is deformed through a specific path. Because of the high strains tool stresses could be critical. The process is capable of reducing the thickness of flat sheets or slabs, and using equal channels, it could be used for material refinement where internal grain size changes to nano-scale structure by intense shearing. In this paper, the applications of CAE have been extended to include the construction of Universal Re-usable Energy Absorption Devices (UREAD) using equal channels. An investigation is carried out into the distribution of contact stresses at the tool/material interface. The model employs the slab method of analysis and splits the material inside the channels, which intersects at 90°, into two zones; one causes the deformation while the other remains rigid. Normal stresses that may develop at the contact surface between the deformable material and the tools are analysed for various cases of CAE and are compared with those obtained by the Finite Element Analysis. Experimental investigation on UREAD devices using lead are also presented where the energy absorbed reached a maximum of 160 J for 100 mm cross-sectional area and 30 mm stroke. An experimental set up for measuring contact pressure in CAE/ECAE is introduced and measurements at different depth of the CAE entry channel are presented. The sensing mechanism is based upon the sensitive pressure pin technique.     

Validation of a simplified numerical contact model

Surface roughness tends to have a significant effect on how loads are transmitted at the contact interface between solid bodies. Most numerical contact models for analyzing rough surface contacts are computational demanding and more computationally efficient contact models are required. Depending on the purpose of the simulation, simplified and less accurate models can be preferable to more accurate, but also more complex, models. This paper discusses a simplified contact model called the elastic foundation model and its applicability to rough surfaces. The advantage of the model is that it is fast to evaluate, but its disadvantage is that it only gives an approximate solution to the contact problem. It is studied how surface roughness influences the errors in the elastic foundation solution in terms of predicted pressure distribution, real contact area, and normal and tangential contact stiffness. The results can be used to estimate the extent of error in the elastic foundation model, depending on the degree of surface roughness. The conclusion is that the elastic foundation model is not accurate enough to give a correct prediction of the actual contact stresses and contact areas, but it might be good enough for simulations where contact stiffness are of interest.     

用于改善手持工具人机效果的有压反求实验

为减小手持工具使用者承受的压强峰值并提高总体舒适度,设计了有压反求的实验方法,根据人体曲面在压力下的形状得到工具手柄表面曲面.在舒适度问卷中给出舒适度描述词、分析描述词权重并进行统计分析,得到手柄表面曲面贴合程度与舒适度间的定量关系.对问卷评价的结果分析表明,该曲面可改善体表压力分布状况,减小人体表面承受的压强峰值.     

环形刀宽行加工圆弧过渡区域算法的研究

基于广域曲率吻合原则,研究了利用环形刀侧铣加工组合曲面圆弧过渡区域的新方法。首先建立环形刀的几何模型,通过调整刀具姿态角,使刀具表面和工件表面在不发生干涉的条件下实现密切接触。通过迭代判断使下行刀轨的驱动线和当前刀轨在精度范围内搭接,实现刀轨的合理编排。最后,以某航空发动机叶片为例计算了刀轨。结果表明,该算法能够精确地加工出圆弧过渡曲面,刀轨之间的没有明显的残高,加工效率较球头刀提高了5倍。     

The effect of a thin coating of insulating material on the performance of cutting tools

The thermal properties of cutting tools have a dominant effect on metal cutting because of their influence on the length of the contact between the tool and the chip and on chip curvature. Low thermal conductivity of the tool is generally considered desirable.Experiments show that tools made from materials of high thermal conductivity but coated with layers of material of low conductivity have a cutting performance similar to that obtained when the whole tool is made from the material of low thermal conductivity even when the thickness of the coating is of the order of 5–10μm.A theoretical explanation of this behavior based on a discrete (i.e. non-continuum) model of the tool surface and on transient heat conduction considerations is presented.     

Simulation of the interaction between driver and seat

Test is one of methods to acquire human-seat pressure distribution in driving, with the deficiency of being uneasy to obtain the stress information of soft tissue inside human body and the sheer force of interface between human and seat, which can be obtained by simulation. But current simulation method focuses mainly on calculation itself other than combining it with posture prediction and cab packaging parameters, which cause it difficult to acquire accurate pressure calculation results without accurate posture of human body, and make it almost meaningless to design optimization. Therefore, a human body geometric model with posture change capability is built and linked up with Cascade Prediction Model（CPM）, which takes cab packaging parameters as inputs. A detailed finite element model of driver human body is constructed and used to conduct the driver-seat interaction simulation between human body and seat. Good accordance of pressure distribution is observed between simulation and test, which validates the simulation. In addition to the distribution pattern, curves on key sections are used to analyze the pressure and shear stress on the seat surface, as well as soft tissue stress inside human body. The simulation shows that the maximum stress of buttocks locates under the ischial tuberosity, and the maximum stress of trunk occurs near the scapula posterior and the lower waist. These are the places where fatigue usually occurs. The maximum pressure of seat appears at the driver-seat contact area corresponding to the driver＇s maximum skin tissue stress. In order to guide the seat design and cab packaging and study the influence of posture to pressure distribution, finite element models for different levels of cab packaging parameters are created by using CPM. The pressure distributions are calculated and their tendencies varying with cab packaging parameters are obtained. The method presented provides a new way to accurately simulate the interaction between driver human body and seat, and to guide the seat design and cab packaging so as to improve seating comfort.     

一种结构解耦型变刚度驱动软体手抓握能力分析

为了实现变刚度驱动软体手的精确抓取,设计了一款结构解耦型的变刚度驱动(变刚度与变形驱动)软体手指。建立了软体手指的指尖力模型,并计算了手指指尖力,将实验测试的手指指尖力数据与计算结果进行比较,证明了手指指尖力模型在一定精度范围内能够预测手指的抓握行为。基于软体手指的指尖力模型对软体手的结构尺寸进行设计,并根据设计的软体手进一步研究指腹的抓握能力,通过仿真与实验的相互印证得到了软体手指腹抓取的抓握力模型。仿真和实验结果表明,软体手的抓握能力与手指的刚度、变形驱动能力以及软体手的抓握形态有关。     

A study of deformation of the machined workpiece and tool under different low cutting velocities with an elastic cutting tool

To understand the effects of cutting velocity, tool elastic deformation generated by high normal stresses during metal cutting processing and artificial tool flank wear on the cutting process, an iterative mathematical model for calculating the tool–workpiece contact problem was developed in this paper under the assumption of elastic cutting tools. In this model, the finite element method is used to simulate cutting of mild steel by the P20 cutting tool with constant artifical tool flank wear under the condition of three different cutting velocities. The results obtained in the simulation were found to match the experimental data reported by related studies. The simulation results also indicate that the thrust and the cutting forces are functions of cutting velocity. Besides, both the normal stress on the tool rake face and the residual stress of machined workpiece generally decrease with increase in cutting velocity. According to the findings in this study, though the residual stress of the machined workpiece decreases as the cutting velocity increases, its value is still higher than that in ordinary conditions due both to the influence of tool flank wear and tool elastic deformation. Also, the phenomenon of curvature at the workpiece end easily occurs.     

Spindle with built-in acoustic emission sensor to realize contact detection

Recently, the demand for realizing micromachining through small-diameter tools has increased. When performing microfabrication using a numerically controlled machine tool, a machining error may be introduced if the relative position of the tool tip and workpiece surface deviates during tool change. Therefore, it is critical to determine this relative position in an actual machining condition at a specific spindle speed. We are currently developing an air bearing turbine spindle with a built-in acoustic emission sensor that can detect the contact of the tool tip with the workpiece surface in real time. The acoustic emission (AE) signal generated at the tool tip can be accurately detected by placing the AE sensor in direct contact with the tool end surface inside the main shaft floated by air. In this study, we investigated the possibility of contact detection between the tool tip and the workpiece surface at the submicrometer level through the proposed spindle. The results of the performed evaluation experiments indicated that by using the spindle with a built-in acoustic emission sensor, the contact of the small-diameter tool tip with the workpiece surface could be detected with damage to the workpiece at the submicrometer level on average.     

Measurements of pressure and area dependent tangential contact stiffness between rough surfaces using digital image correlation

The present paper describes an experimental technique to accurately measure the tangential contact stiffness between two rough contacting surfaces manufactured from the titanium alloy Ti-6Al-4V. The digital image correlation method is employed to measure the local displacement field. The effect of normal contact pressure, nominal contact area and fretting wear on tangential contact stiffness is investigated. The experiments indicate that the tangential contact stiffness is approximately proportional to the nominal contact area and the normal pressure raised to the power of 0.64. Multiple experiments with the same parameters show good repeatability given the number of variables involved.