Considerations for the incorporation of measured surfaces in finite element models

This work discusses some of the benefits, techniques, challenges, and considerations associated with the incorporation of measured surfaces in finite element (FE) models including how much surface data to measure and import into the model, the shape of the surface geometry to create, the presence and effect of surface layers and impurities, the required mesh density for rough surfaces, the nature of the element formulations and material properties at small length scales, the differences between measurement and FE coordinate systems, the limitations and idealizations of the FE method, issues associated with boundary conditions and their ability to impose or prevent conformal contact, and issues associated with the size of the pinball region and the contact stiffness relative to the nature of the surface. It also describes some current and future research directions that can be used to validate and expand existing techniques and to improve our understanding of surface phenomena.     

On the Modeling of Elastic Contact between Rough Surfaces

The contact force and the real contact area between rough surfaces are important in the prediction of friction, wear, adhesion, and electrical and thermal contact resistance. Over the last four decades various mathematical models have been developed. Built on very different assumptions and underlying mathematical frameworks, model agreement or effectiveness has never been thoroughly investigated. This work uses several measured profiles of real surfaces having vastly different roughness characteristics to predict contact areas and forces from various elastic contact models and contrast them to a deterministic fast Fourier transform (FFT)-based contact model. The latter is considered “exact” because surfaces are analyzed as they are measured, accounting for all peaks and valleys without compromise. Though measurement uncertainties and resolution issues prevail, the same surfaces are kept constant (i.e., are identical) for all models considered. Nonetheless, the effect of the data resolution of measured surface profiles will be investigated as well. An exact closed-form solution is offered for the widely used Greenwood and Williamson (GW) model (Greenwood and Williamson, Proceedings of the Royal Society of London A, vol. 295, pp. 300–319), along with an alternative definition of the plasticity index that is based on a multiscale approach. The results reveal that several of the theoretical models show good quantitative and qualitative agreement among themselves, but though most models produce a nominally linear relationship between the real contact area and load, the deterministic model suggests otherwise in some cases. Regardless, all of the said models reduce the complicated surface profiles to only a few key parameters and it is therefore unrealistic to expect them to make precise predictions for all cases.     

An Elastic-plastic Adhesion Model for Contacting Fractal Rough Surface and Perfectly Wetted Plane with Meniscus

The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a micro-sized interface.Today, more and more research works are devoted to understand the adhesion mechanism. This paper concerns the elastic-plastic adhesion of a fractal rough surface contacting with a perfectly wetted rigid plane. The topography of rough surface is modeled with a two-variable Weierstrass-Mandelbrot fractal function. The Laplace pressure is dealt with the Dugdale approximation. Then the adhesion model of the plastically deformed asperities with meniscus can be established with the fractal microcontact model. According to the plastic flow criterion, the elastic-plastic adhesion model of the contacting rough surfaces with meniscus can be solved by combining the Maugis-Dugdale (MD) model and its extension with the Morrow method. The necessity for considering the asperities' plastic deformation has been validated by comparing the simulation result of the presented model with that of the elastic adhesion model. The stiction mechanism of rough surfaces with meniscus is also discussed.     

板料成形有限元模拟中的拉格朗日分析方法

数值模拟中的模拟方法对于建立一个可信赖的有限元模型非常重要。板料成形中包含大变形、大位移和摩 擦行为,模拟结果对不同的有限元模型有很大的不确定性。采用有限元软件MARC基于不同拉格朗日法建立了一 个有限元模型来分析深冲压成形过程。模拟中板料作为变形体,模具看作刚体,接触面间的摩擦约束采用修正的库 仑摩擦模型。板料应变、厚度的模拟和实验结果比较表明完全拉格朗日法(T.L.)和更新拉格朗日法(U.L.)的主 要区别在大变形和大位移上,小变形和小位移两者吻合较好。     

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

A statistical model of elasto-plastic asperity contact between rough surfaces

This work models statistically elasto-plastic contact between two rough surfaces using the results of a previous finite element analysis of an elasto-plastic sphere in contact with a rigid flat. The individual asperity contact model used accounts for a varying geometrical hardness effect that has recently been documented in previous works (where geometrical hardness is defined as the uniform pressure found during fully plastic contact). The contact between real surfaces with known material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. The asperity is modeled as an elastic-perfectly plastic material. The model produces predictions for contact area, contact force, and surface separation. The results of this model are compared to other existing models of asperity contact. Agreement exists in some cases and in other cases it corrects flaws, especially at large deformations. The model developed by Chang, Etsion and Bogy is also shown to have serious flaws when compared to the others. This work also identifies significant limitations of the statistical models (including that of Greenwood and Williamson).     

机油盘冲压过程截面的有限元模拟与实验验证

板料冲压过程的模具设计是一个费时费力的过程。采用有限元可以降低设计费用 ,缩短设计周期。本文采用有限元软件 MARC基于拉格朗日的弹塑性本构方程建立了一个有限元模型来分析机油盘的成形过程。模拟中考虑板料的厚向异性 ,接触面间的摩擦约束采用库仑摩擦模型。模具看作刚体 ,板料作为变形体。模拟和实验结果的比较表明模拟的壁厚变薄分布与测量结果吻合得很好 ,因而理论模拟的结果可用于真实情况的预测     

Computer simulation of the contact of rough surfaces

A program for the computer simulation of the contact of two rough surfaces has been developed, which makes it possible to determine the real area of contact and the penetration of microasperities at specified parameters of microgeometry under specified loads for friction pairs with fairly soft coatings or without coatings. The model has been tested using a comparison of the results of numerical simulation with the experimental data, which has shown their good agreement. The results can be used to simulate the contact of the rough surfaces, including the case when one of these surfaces is covered with a solid-lubricating or other functional coating.     

Optimization of the rough cutting factors of impeller with five-axis machine using response surface methodology

Turbo-machinery gradually has expanded its business into the automotive and aircraft industries. A core part of turbo-machinery is the impeller which can lead to manufacturing problems because it has twisted surfaces. Therefore, impeller machining requires five-axis machining technology and expert knowledge. Five-axis machining has the advantages of being able to select a variety of tool axis in the machining and remove uncut region which are impossible in the three-axis machining, which could obtain high productivity and good surface quality. Rough cutting is one very important operation as it affects productivity in the impeller machining and it is necessary to determine cutting strategies and select optimal cutting condition. This paper proposes a statistical method to optimize the rough cutting parameters in impeller machining by response surface methodology and efficient strategy to divide cutting region. Firstly, the rough operation was divided into three steps to remove volume from inducer to exducer and two steps were also added to remove the fillets between blade surfaces and hub surfaces. These machining strategies are selected as the qualitative factors when the response surface method is used. Secondly, cutting time was set as the response factor for productivity, and step-down, step over, and feed rate were determined as independent factors. Finally, the response surface model was estimated by a single surface in order to predict rough cutting time and the optimum cutting conditions were searched by the estimated model.     

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.     

The Effect of Scale-Dependent Hardness on Elasto-Plastic Asperity Contact between Rough Surfaces

Statistical methods are used to model elasto-plastic contact between two rough surfaces using a recent finite element model of elasto-plastic hemispherical contact and also recent advances in strain gradient modeling. The elasto-plastic hemispherical contact model used to model individual asperities accounts for a varying hardness effect due to deformation of the contact geometry that has been documented by other works. The strain gradient model accounts for changes in hardness due to scaling effects. The contact between surfaces with hypothetical material and surface properties, such as the elastic modulus, yield strength, and roughness are modeled. A model is also constructed to consider a variable asperity contact radius to evaluate if the strain gradient model will affect it differently. The models produce predictions for contact area, contact force, and surface separation. The strain gradient effects decrease the real area of contact and increase the average contact load in comparison to the model without these effects. The strain gradient model seems to have a larger influence on the predictions of contact load and area than does considering a variable asperity contact radius for the cases considered in this work.     

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.     

Model selection in finite element model updating using the Bayesian evidence statistic

This paper considers the problem of finite element model (FEM) updating in the context of model selection. The FEM updating problem arises from the need to update the initial FE model that does not match the measured real system outputs. This inverse system identification-problem is made even more complex by the uncertainties in modeling some of the structural parameters. Such uncertainty often results in a number of competing forms of FE models being proposed which leads to lack of consensus in the field. A model can be formulated in a number of ways; by the number, the location and the form of the updating parameters. We propose the use of a Bayesian evidence statistic to help decide on the best model from any given set of models. This statistic uses the recently developed stochastic nested sampling algorithm whose by-product is the posterior samples of the updated model parameters. Two examples of real structures are each modeled by a number of competing finite element models. The individual model evidences are compared using the Bayes factor, which is the ratio of evidences. Jeffrey's scale is then used to determine the significance of the model differences obtained through the Bayes factor.     

Multi-objective optimization of oblique turning operations using finite element model and genetic algorithm

Multi-objective optimization of oblique turning operations while machining AISI H13 tool steel has been carried out using developed finite element (FE) model and multi-objective genetic algorithm (MOGA-II). The turning operation is optimized in terms of cutting force and temperature with constraints on required material removal rate and cutting power. The developed FE model is capable to simulate cutting forces, temperature and stress distributions, and chip morphology. The tool is modeled as a rigid body, whereas the workpiece is considered as elastic–thermoplastic with strain rate sensitivity and thermal softening effect. The effects of cutting speed, feed rate, rake angle, and inclination angle are modeled and compared with experimental findings. FE model is run with different parameters with central composite design used to develop a response surface model (RSM). The developed RSM is used as a solver for the MOGA-II. The optimal processing parameters are validated using FE model and experiments.     

Limits of applicability of elastic contact models of rough surfaces

Recent stochastic models for analyzing the contact of rough surfaces assume that the asperities are microhertzian, i.e. that they can be approximated as second-order surfaces in the vicinity of contact points, and that the asperities deform elastically. Using a plane strain solution from the literature for a sinusoidally corrugated half-space, the range of validity of these assumptions is shown to be related to the mean square surface slope and the macrocontact pressure. By extension to random surfaces characterized by a one-dimensional spectral density function an interval on the surface spatial frequency is found over which the asperities deform elastically but without completely flattening. A numerical example is given.     

含非规则粗糙间隙表面铰链关节的平面柔性多连杆传动系统动态误差与运动副磨损周期行为分析

传统旋转间隙关节接触模型假定销轴和衬套接触面形状是规则的并忽略了磨损效应的影响,降低了机构动力学模型预测精度。提出了一种含非规则粗糙间隙表面铰链关节的平面柔性多连杆机构多体动力学建模、磨损预测和动态误差分析方法。为准确描述运动副元素间碰撞行为,考虑滑动轴承间隙关节的磨损效应,提出了一种非规则粗糙间隙表面铰链关节的改进接触模型。在此基础上,考虑柔性杆的影响,基于绝对节点坐标法建立了含非规则粗糙间隙表面铰链关节的平面柔性多连杆传动系统多体动力学模型。与基于传统光滑间隙模型的结果相比,基于非规则粗糙间隙改进模型的多连杆机构动态响应更接近于试验值,验证了所提出计算方法的有效性。仿真结果表明,选用CuSn10P和CuPb30作为铰链衬套材料能够有效降低多连杆机构滑块动态响应偏差和提高机构的运动精度;表面粗糙度过高会导致运动副磨损加剧,过低则会降低间隙表面微凸体对碰撞能量的吸收。此外,磨损加剧了间隙表面轮廓不规则度,导致机构动态响应的不稳定性增大,运动精度降低。     

Roughness modeling in up-face milling

In this study, we aimed to optimize cutting parameters to minimize surface roughness in up-face milling. An experimental system method has been used to analyze the evolution of surface roughness in connection with cutting parameters, and to develop mathematical models for roughness and optimal cutting parameter calculation. Roughness results show that lower cutting speeds give poor surface quality. This is due to the formation of a built-up edge. On the other hand, higher cutting speeds result in more roughness due to vibrations. So, an optimal value of cutting speed must be used to minimize roughness. We found good correlation in experimental values of roughness .     

Dynamic modeling of oblique non-uniform piezoelectric MC in liquid with various percentages of glycerin in the presence of rough surface

One of the most useful applications of an AFM is imaging of biological particles in a liquid medium. The increase of the topography accuracy in a liquid medium requires accurate dynamic modeling of a Microcantilever (MC). This article investigates the accurate dynamic modeling of the non-uniform AFM piezoelectric MC with rectangular geometry in the amplitude mode in liquid medium for rough surfaces. To increase the accuracy of the modeling, the Modified couple stress (MCS) theory in the liquid medium according to the Timoshenko beam model has been used. Moreover, the differential quadrature (DQ) method has been used for solving equations, because in comparison with the other methods it has a high speed in solving equations and is accurate in the number of fewer elements. In addition, the accurate force modeling has been established by considering the shear forces caused by liquid on the sides of the piezoelectric MC by solving the Navier-Stokes equations, and by considering the hydrodynamic force, squeeze force and applied forces between the sample surface and the MC tip. The results illustrate that utilizing higher vibration modes affect the quality of rough surface topography with the step roughness in the liquid medium and increase the quality of surfaces topography in the tapping mode, especially in the second MC vibration mode. Moreover, it should be noted that the sensitivity of the MC vibration amplitude to the piezoelectric MC angle is higher in comparison with other investigated parameters.