Kogut Etsion Research Articles

Nano-sized single-asperity friction behavior: Insight from molecular dynamics simulations

Friction phenomenon plays an essential role in contact pairs, from macroscale to nanoscale friction. Nano-sized friction behavior is different from macroscopic friction behavior due to discreteness of atoms. Taking α-Fe as paradigm material, single-asperity friction molecular dynamics (MD) simulations are conducted. The MD results show that the multi-slip phenomenon exists during the tangential loading process of nano-sized single asperity. Meanwhile, the macroscopic friction coefficient model is not suitable for nano-sized friction, while the macroscopic Kogut-Etsion (KE) contact radius model can approximately describe nano-sized contact radius. Besides, the Mindlin model can hardly describe the initial tangential stiffness under large normal loadings due to the neglect of plastic deformation. Therefore, it is suggested to modify the macroscopic friction models by considering the plastic deformation mechanism and asperity size effect to improve the full-scale description ability.

Friction Mechanism and Characteristics of Reticle Based on Contact Theory

Abstract With the development of integrated circuits, the structure of chips becomes more and more complex, and the processing cost increases accordingly. To improve the productivity of lithography, the acceleration of the reticle stage should be increased to reduce the positioning time. However, the increase of acceleration will cause the relative slip between the reticle and the vacuum chuck, which seriously affects the accuracy and the product yield of lithography. To suppress the slippage, the friction mechanism and the characteristics between the reticle and the chuck are studied in this article. First, based on the Kogut–Etsion contact model and the Majumdar–Bhushan (MB) fractal contact model, the maximum static friction coefficient model between nano-scale surfaces was established. Then, the surface morphology parameters of reticle and chuck adsorption surface were obtained by atomic force microscopy (AFM) scanning. Finally, the maximum static friction force experiments show that the MB model is more suitable for the study of friction mechanism between reticle and vacuum chuck, and the model is more instructive for the suppression of reticle slip.

A Fluid–Solid–Heat Coupling Analysis for Water-Lubricated Rubber Stern Bearing Considering the Deflection of Propeller Shaft

The novelty of the present study is that it investigates the effect of propeller shaft deflection, caused by the propeller self-weight and interfacial mixed forces, on the fluid–solid–heat (FSH) coupling performance of water lubricated rubber stern bearing (WLRSB). In the FSH coupling model, the generalized average Reynolds equation and the Kogut–Etsion asperity contact model are used to determine the hydrodynamic and the elastic–plastic contact behaviors of WLRSB. In the thermal analysis, the journal, water film, and rubber bushing are considered as an integrated system (JWR system) using the Euler method. To prove the correctness of the developed model, the predicted results are verified by comparisons with the experimental results given in the literature. In addition, to assess the effect of the force-driven deflection during FSH simulation, comparisons of the FSH predictions between the aligned journal case and the deflected journal case are carried out. The results indicate that, especially under a heavy load condition, the deflection of the stern shaft should be incorporated into the lubrication gap between the journal–rubber interface during the analysis of FSH performance of the JWR system.

On the normal contact stiffness and contact resonance frequency of rough surface contact based on asperity micro-contact statistical models

Contact stiffness is an important parameter for describing the interface characteristics in many engineering applications. In this paper, five different statistical micro-models including the Greenwood-Williamson (GW), Zhao-Maietta-Chang (ZMC), Kogut-Etsion (KE), Jackson-Green (JG) and Brake are employed to predict the normal contact stiffness for rough surface contact. It is found that the expressions of contact stiffness obtained using the statistical micro-models are very complex and the direct relationship between the contact stiffness and normal load is not available. Accordingly, an explicit approximated expression for contact stiffness is established in terms of normal load based on the results of numerical simulations. The normal contact stiffness as a function of normal load can be approximated using a power law, in which the coefficient and power are related to surface roughness parameters, material properties as well as nominal contact area. The close agreement between the predicted results and full numerical simulations verify the accuracy of the established explicit expression. The contact stiffness calculated using the predictive expressions are also compared with available experimental results from both ultrasonic method and contact resonance method. Further, the explicit expression of contact resonance frequency for rough surface contact with respect to the normal load is also provided, which can be used to evaluate the contact resonance frequency. The predicted contact resonance frequency is also validated through comparing with experimental results.

A statistical model of elastic-plastic contact between rough surfaces

In a mechanical interface, the contact surface topography has an important influence on the contact stiffness. In the contact processes of asperities, elastic-plastic change can lead to discontinuity and lack of smoothness at a critical contact point. The result is a large difference between the elastic-plastic deformation and the actual asperity deformation. Based on Hertz contact theory, the heights of asperities on a rough surface obey a Gaussian distribution. To take into consideration the continuity of elastic-plastic asperity deformation, we divide the elastic-plastic deformation into three stages: pre-elastic-plastic, mid-elastic-plastic, and post-elastic-plastic deformation. This establishes an elastic-plastic contact model of asperity at a continuous critical point. The contact model of a single asperity fits well with the Kogut–Etsion model and the Zhao–Maietta–Chang model, and the variation trend is consistent. At a lower plastic index, the present model coincides with classical models of contact area and contact load. At a higher plastic index, the simulation results of the present model differ from the Greenwood–Williamson model and the Chang–Etsion–Bogy model but are similar to results from the Kogut–Etsion and Zhao–Maietta–Chang models. This study provides a more accurate microscopic contact model for rough surfaces and a theoretical framework for interface design and analysis.

Model for Elastic–Plastic Contact Between Rough Surfaces

This paper studies elastic–plastic contact between Greenwood–Williamson (GW) rough surfaces, on which there are many asperities with the same radius whose height obeys the Gaussian distribution. A new plasticity index is defined as the ratio of the standard deviation of the height of asperities on the rough surface to the single-asperity critical displacement (the transition point from the elastic to the elastic-fully plastic deformation regime), which is linearly proportional to the GW plasticity index to the power of 2. The equations for the load/area–separation relationship of rough surfaces are presented based on Wang and Wang's smooth model of singe-asperity elastic–plastic contact, which is an improvement of the Kogut–Etsion (KE) empirical model based on finite element analysis (FEA) data. The load/area–separation relationship can be described by empirical Gaussian functions. The load–area relationship of rough surfaces is approximately linear. The average pressure is only function of the new plasticity index. According to Wang and Wang's conclusion that Etsion et al. single-asperity elastic–plastic loading (EPL) index is approximately equal to the ratio of the single-asperity residual plastic contact displacement to the single-asperity total elastic–plastic contact displacement, the equations for the relationship between Kadin et al. modified plasticity index (MPI) and separation of rough surfaces are also presented. In addition, the MPI is approximately linearly proportional to the separation between rough surfaces for a given new plasticity index ranging from 5 to 30. When the new plasticity index is smaller than 5, due to the large proportion of the elastic deformation in the total deformation, the MPI slightly deviate from linearity.

Model for a Sphere–Flat Elastic–Plastic Adhesion Contact

This paper presents a cubic model for the sphere–flat elastic–plastic contact without adhesion. In the cubic model, the applied load and the contact area are described by the cubic polynomial functions of the displacement to the power of 1/2 during loading and unloading, and the applied load is also expressed as the cubic polynomial function of the contact area to the power of 1/3 during loading. Utilizing these cubic polynomial functions, the elastic–plastic load (EPL) index, which is defined by the ratio between the dissipated energy due to plastic deformations and the work done to deform the sphere during loading, is calculated analytically. The calculated EPL index is just the ratio between the residue displacement after unloading and the maximum elastic–plastic displacement after loading. Using the cubic model, this paper extends the Johnson–Kendall–Roberts (JKR) model from the elastic regime to the elastic–plastic regime. Introducing the Derjaguin–Muller–Toporov (DMT) adhesion, the unified elastic–plastic adhesion model is obtained and compared with the simplified analytical model (SAM) and Kogut–Etsion (KE) model.

An Integrated Mechanical–Electrical Predictive Model of Electrical Contact Resistance between Two Rough Surfaces

This article introduces a novel approach for predicting the electrical contact resistance (ECR) between two rough surfaces based on a combination of contact modeling with surface topography analysis. Firstly, asperities distributed on rough surfaces are simulated as parabolas. An asperity shoulder-shoulder contact model is developed, which is similar to the well-known Kogut-Etsion (KE) model but requires extended capability regarding different degrees of contact misalignment. On the basis of such a contact model, Holm's principle is then incorporated to create a new theoretical formulation revealing the constitutive relations between the ECR and the deformation patterns of microcontacts arising at the contact interface. Then, a watershed approach is employed to get the contact surface topographies with which an iterative computational strategy is then proposed to alleviate the programming and computing efforts for implementing the calculation of the total ECR at the contact interface. To verify the feasibility of the proposed method, aiming at one case, the KE-based model is reviewed and compared numerically to the new model. The comparison shows good agreement between the two models. A slight difference is that the suggested model gives a relative lower estimation on the ECR value, which is mainly attributed to the different judgment of the deformation mechanism.

On the Contact of Curved Rough Surfaces: Contact Behavior and Predictive Formulas

The statistical microcontact models of Greenwood–Williamson (GW), Kogut–Etsion (KE), and Jackson–Green (JG) are employed along with the elastic bulk deformation of the contacting solids to predict the characteristics of rough elliptical point contact such as the pressure profile, real area of contact, and contact dimensions. In addition, the contribution of the bulk deformation and the asperity deformation to the total displacement is evaluated for different surface properties and loads. The approach involves solving the microcontact and separation equations simultaneously. Also presented are formulas that can be readily used for the prediction of the maximum contact pressure, contact dimensions, contact compliance, real area of contact, and pressure distribution.

On the Acceleration Limits for Sliding and Detachment Between Contacting Rough Surfaces for Micropart Manipulation in a Dry Environment

Micropart manipulation is an active research area encompassing a wide array of fields and applications. As the size of the parts to be manipulated by an automated system decreases, the dominant forces are different compared to macroscale ones. Thus, for accurately modeling and evaluating the motion dynamics of a micropart, microscale forces and their effects must be considered. This manuscript employs a nanomicroscale friction model based on the Kogut–Etsion model that along with microscale forces considers surface roughness and material hardness properties to identify the acceleration threshold that would cause a micropart to start sliding on a carrier surface or vertically detach from the carrier surface during gripperless manipulation in a dry environment. The microscale forces change significantly as a function of the surface roughness of the two contacting surfaces. The results indicate that there will always be critical acceleration values below which no sliding or detachment takes place. Also, for the same model parameters, the sliding acceleration is smaller than the detachment acceleration for softer materials and larger for harder materials. The sliding acceleration threshold is more sensitive to hardness changes at smaller surface roughness values as compared to larger surface roughness values. The material hardness has no effect on the detachment acceleration for the same surface roughness values. The knowledge of the acceleration thresholds and their relative magnitudes could be advantageously employed for the development of gripperless manipulation approaches for microcomponent or microdevice handling or for the development of microconveyor platforms for controlled micropart translocation.

An Elastic-Plastic Spherical Contact Model Under Combined Normal and Tangential Loading

Spherical contact under combined normal and tangential loading has been investigated by many researchers, and some physically based criteria were proposed to capture the sliding inception, e.g., the local yielding criterion of the Kogut-Etsion (KE) model and the tangential stiffness criterion of the Brizmer-Kligerman-Etsion (BKE) model. In this work, by utilizing the maximum frictional shear stress criterion for the sliding inception, a finite element model for obliquely loaded spherical contact has been developed, which realized a friction transition from the KE model to the BKE model, with an increasing normal approach. The stress, strain, tangential force, normal force, and contact area during tangential loading are investigated using different models. It was found that with an elastic normal displacement preload, material failure is initiated on the surface, while with an elastic-plastic normal displacement preload the failure is initiated under the surface and then extends to the surface with the increasing tangential load. With an elastic-plastic normal displacement preload, there is an obvious normal force release during tangential loading. Different from the full stick model, both the Coulomb friction model and the proposed model are partial slip models in nature. However, the Coulomb friction is more empirically determined with some arbitrary friction coefficient, whereas the proposed model is based on physics parameters. Furthermore, both the Coulomb friction model and the proposed model predict a lower tangential force at the same tangential displacement, a slower growth of the contact area under elastic normal displacement preload, and a faster growth of the contact area under an elastic-plastic normal displacement preload compared to the full stick model.

Asperity micro-contact models as applied to the deformation of rough line contact

Different statistical micro-contact models including Greenwood–Williamson (GW), Chang–Etsion–Bogy (CEB), Zhou–Maietta–Chang (ZMC), Kogut–Etsion (KE) and Jackson–Green (JG) are employed together with the bulk deformation of the bounding solids to predict dry rough line-contact characteristics such as the apparent pressure profile, contact width and real area of contact. The approach involves solving the micro-contact models and separation formulas simultaneously. Comparison of different contact models reveals that the use of elastic–plastic micro-contact models predicts a lower maximum normal pressure and a greater contact width and real contact area compared to the GW model. Further, based on the results of numerical simulations, useful relationships are provided for the prediction of the maximum contact pressure, contact width, real area of contact and pressure distribution.

Static Friction Research of LIGA-Microstructure: Comparison between Theory and Experiments

Micro electro mechanical system (MEMS) has been increasingly used in military application. For the reliability and specialty of military requirements, the material of the MEMS device is supposed to be metal and the device is moveable. Lithographic, Galvanoforming, Abformung (LIGA) technology capable of producing high aspect ratio structures in metals like nickel is one of the important fabrication technologies in military MEMS. There are many moveable MEMS device like micro-gear and micro-slider producing by LIGA technology. But the moveable devices cannot behave well because of the friction effect. In this paper, an improved elastic-plastic model including roughness effects and an experimental procedure that predict the static friction prosperity of LIGA-processed nickel is proposed. Firstly, we use the 3D optical profilometer to research the surface roughness of LIGA-processed nickel, the surface heights distribution was found to be nearly Gaussian distribution. Secondly, the static friction model, the Kogut-Etsion (KE) model is adopted to obtain the static friction coefficient. Finally, a special designed static friction coefficient measurement apparatus is used to conduct the friction experiments. The results indicate that the surface roughness affects the friction and the smoother surface leads to a higher friction coefficient. Also good agreement was found between simulations and experimental results.

Application of Elastic-Plastic Static Friction Models to Rough Surfaces With Asymmetric Asperity Distribution

Asymmetric height distribution in surface roughness is important in many engineering surfaces, such as in constant velocity (CV) joints, where specific manufacturing processes could result in such surfaces. Even if the initial surfaces exhibit symmetric roughness, the running-in and sliding processes could result in asymmetric roughness distributions. In this paper, the effect of asymmetric asperity height distribution on the static friction coefficient is investigated theoretically and experimentally. The asymmetry of the surface roughness is modeled using the Pearson system of frequency curves. Two elastic-plastic static friction models, the Kogut–Etsion (KE) and Cohen–Kligerman–Etsion (CKE) models are adapted to account for asymmetric roughness and employed to obtain the tangential and normal contact forces. Static friction experiments using CV joint roller and housing surfaces, which exhibit different levels of surface roughness, were performed and directly compared with the KE and CKE static friction models using both a symmetric Gaussian as well as Pearson distributions of asperity heights. It is found that the KE model with the Pearson distribution compares favorably with the experimental measurements.

A Finite Element Based Study on the Elastic-Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios (ω∕ωc) for the evolution of the elastic core and the plastic region within the asperity for different Y∕E ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the Y∕E ratio of the material.

Effect of strain hardening in elastic–plastic transition behavior in a hemisphere in contact with a rigid flat

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic–plastic material on the lines of the Kogut–Etsion Model (KE Model) and the Jackson–Green Model (JG Model). The present work extends the previous KE and JG works, accounting for the effect of realistic material behavior in terms of the varying yield strengths and the isotropic strain hardening behavior. The predicted results show that the transition behavior of the materials from the elastic–plastic to the fully plastic case is influenced by the yield strength and the tangent modulus ( E t) and such transition do not take place at specific values of interference ratios as suggested by the KE model. New empirical relations are proposed to determine the contact load and the contact area based on the analysis. Numerical results from the finite element modeling are also validated with an experimental ball on flat configuration approach.