KE Model Research Articles

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.

A comprehensive model analysis of activity coefficients and thermodynamic properties of EAE-1DMA2P blended solvent

Solubility has an important influence on industrial applications of amine solvents. The CO2 equilibrium solubilities of EAE-1DMA2P solvents were obtained in 1:2, 1.5:1.5, and 2:1 ratios at 298–333 K and CO2 partial pressures of 8–100 kPa. Using these data, the accurate prediction of CO2 equilibrium solubility of EAE-1DMA2P solvent was achieved by constructing an activity coefficient model with an AARD of only 0.79%. In addition, by constructing the solubility prediction model of EAE-1DMA2P system based on an empirical model, KE model, Austgen model, Li-Shen model, Hu-Chakma model, Helei Liu model, and Liu et al. model the results were compared to confirm introduction of the activity coefficient has effectively improved the accuracy of the model prediction. Based on thermodynamic parameters of solubility, ΔrGm and ΔrHm, EAE-1DMA2P solvent was screened against other solvents. The results showed that EAE-1DMA2P solvent had excellent absorption, reaction rate and low desorption energy consumption, confirming its potential in CO2 capture.

A Moment-Based Depth-Averaged K-ε Model for Predicting the True Turbulence Intensity over Bedforms

Turbulence models are critical for depth-averaged flow models in at least two ways: (i) as closures for momentum equations and (ii) as indicators of the spatial variability in the turbulence intensity field, which is crucial for sediment transport and bedform evolutions. This paper introduces a novel moment-based depth-averaged k-ε turbulence (MDAKE) model that could be considered as a revised version for the standard k-ε Rastogi–Rodi (SDAKE) model and can be used to estimate the true values for the depth-averaged turbulence kinetic energy in more complex and varied flow conditions with accelerating–decelerating flow fields. The study in hand shows that the SDAKE model tends to overestimate the true depth-averaged turbulent kinetic energy (k¯u) by 50 to 130% in the benchmark case of uniform flow over a flatbed. Further, the SDAKE model assumes that the bed shear velocity is an appropriate scale for the generation terms of both turbulent kinetic energy and dissipation. When bed topographic features vary, a shear flow zone is formed and the assumption is invalid. Since most of the turbulence is generated by shear flow zones away from the bed, the SDAKE model’s estimates for the depth-averaged turbulent kinetic energy field are out of phase with measurements for the flow over a train of bedforms. Therefore, a newly developed depth-averaged KE model based on the moment concept (MDAKE) is presented here. The model replaces bed shear velocity with the integral moment velocity scale (u1). The calibrated MDAKE model is used to predict turbulent kinetic energy over a train of bedforms. The results of the MDAKE model are in phase and generally in reasonable agreement with the measurements.

A Normal Contact Stiffness Statistical Model of Joint Interface considering Hardness Changes

Based on Kogut and Etsion’s finite element contact model (KE model) and citing the hardness geometric limit proposed by Jackson et al., the deformation stage of an asperity is re-divided, and a normal contact stiffness model of joint interface is established by using a statistical theory. The simulation results show that the normal contact stiffness of joint interface is a nonlinear function of the mean surface separation and decreases with the increase of the mean surface separation under different plasticity indexes. By comparing the normal contact stiffness model of joint interface considering hardness changes with the normal contact stiffness model of joint interface without considering hardness changes, it is found that, with the increase of the plasticity index, the difference between calculated results becomes larger.

Research on Normal Contact Stiffness of Rough Joint Surfaces Machined by Turning and Grinding

In order to accurately obtain the contact stiffness of rough joint surfaces machined by turning and grinding, a research simulation is carried out by using the finite element method. Based on the surface modeling method under the combined machining mode, the three-dimensional (3D) solid model is constructed. Then, the finite element results of the normal contact stiffness were obtained through contact analysis. The comparative analysis was carried out with the analytical results of the KE model and the experimental results. The comparison results show that three results have the same trend of change. However, the maximum relative error of the finite element results is 6.03%, while that of the analytical results for the KE model is 60.07%. After that, the finite element results under different machining parameters are compared. The normal contact stiffness increases with the increase in the turning tool arc radius, grinding depth, and fractal dimension, but decreases with the increase in the turning feed rate and scale coefficient. The rationality of the results is explained by the distribution of the asperities and the contact deformation law of the asperities on the rough surface.

A Static Friction Model for Unlubricated Contact of Random Rough Surfaces at Micro/Nano Scale.

A novel static friction model for the unlubricated contact of random rough surfaces at micro/nano scale is presented. This model is based on the energy dissipation mechanism that states that changes in the potential of the surfaces in contact lead to friction. Furthermore, it employs the statistical theory of two nominally flat rough surfaces in contact, which assumes that the contact between the equivalent rough peaks and the rigid flat plane satisfies the condition of interfacial friction. Additionally, it proposes a statistical coefficient of positional correlation that represents the contact situation between the equivalent rough surface and the rigid plane. Finally, this model is compared with the static friction model established by Kogut and Etsion (KE model). The results of the proposed model agree well with those of the KE model in the fully elastic contact zone. For the calculation of dry static friction of rough surfaces in contact, previous models have mainly been based on classical contact mechanics; however, this model introduces the potential barrier theory and statistics to address this and provides a new way to calculate unlubricated friction for rough surfaces in contact.

Stimulation of CO2 solubility in reversible ionic liquids activated by novel 1-(2-aminoethyl piperazine) and bis (3-aminopropyl) amine

The quest of energy efficient post combustion CO2 capture through an integrated process approach leads to the development of various novel solvents which can yield the necessary outputs. In line with this, the current work explores the experimental and simulation analysis of vapor liquid equilibrium of CO2 in novel aqueous 3-aminoproyl triethoxysilane (TESA) solvent blends enhanced by amine activators. Specific amine activators, viz. 1-(2-aminoethyl) piperazine (AEP) and bis (3-aminopropyl) amine (APA) were considered. The experiments were carried out over the temperature range of (303.2–323.2) K and pressure of (4–350) kPa. In order to realize the effect of activator, AEP/ APA concentration was gradually increased from 0.5 to 1.0 mol/kg with a total solvent concentration of ≈3 mol/kg. Along with this, qualitative 13C NMR and FTIR analysis were also performed to assess the proposed reaction scheme. The experimental vapour liquid equilibrium data (VLE) were correlated by modified Kent-Eisenberg equilibrium model considering gas phase non-ideality as well as non-rigorous statistical non-linear model. The equilibrium constants associated to deprotonation of protonated TESA, AEP and APA as well as carbamate formation reactions of these amines with CO2 are function of solvent concentration, temperature and CO2 partial pressure. These are regressed to fit the experimental VLE data. The modified KE model is further prolonged to estimate the concentration profiles of various molecular and ionic species involved in the reactive system.

Statistical Model of Normal Contact Stiffness of Fixed Joint Surface during Unloading after First Loading

Based on Kogut and Etsion’s model (KE model), a statistical method is used to establish a model of normal contact stiffness of fixed joint surface during unloading after first loading. Simulation results show that, for the elastoplastic contact, normal contact stiffness of joint surface is the nonlinear function of mean surface separation during loading and unloading and decreases as the separation increases. For different plasticity indexes, the normal contact stiffness of joint surface varies differently following the change of mean surface separation during loading and unloading.

A simple approximation to the electron-phonon interaction in population dynamics.

The modeling of coupled electron-ion dynamics including a quantum description of the nuclear degrees of freedom has remained a costly and technically difficult practice. The kinetic model for electron-phonon interaction provides an efficient approach to this problem, for systems evolving with low amplitude fluctuations, in a quasi-stationary state. In this work, we propose an extension of the kinetic model to include the effect of coherences, which are absent in the original approach. The new scheme, referred to as Liouville-von Neumann + Kinetic Equation (or LvN + KE), is implemented here in the context of a tight-binding Hamiltonian and employed to model the broadening, caused by the nuclear vibrations, of the electronic absorption bands of an atomic wire. The results, which show close agreement with the predictions given by Fermi's golden rule (FGR), serve as a validation of the methodology. Thereafter, the method is applied to the electron-phonon interaction in transport simulations, adopting to this end the driven Liouville-von Neumann equation to model open quantum boundaries. In this case, the LvN + KE model qualitatively captures the Joule heating effect and Ohm's law. It, however, exhibits numerical discrepancies with respect to the results based on FGR, attributable to the fact that the quasi-stationary state is defined taking into consideration the eigenstates of the closed system rather than those of the open boundary system. The simplicity and numerical efficiency of this approach and its ability to capture the essential physics of the electron-phonon coupling make it an attractive route to first-principles electron-ion dynamics.

FRACTAL CHARACTERISTIC AND DOMAIN EXTENSION FACTOR STUDY ON CONTACT MODEL OF ROUGH SURFACE

Machine joint surface has an important impact on the performance of mechanical systems. Based on fractal theory, joint surface is assumed to be the contact between absolute smooth surface and rough surface. Through the analysis of the contact process, the contact mechanics model, the contact stiffness model and the three-dimensional surface micro-contact model are studied. To obtain fractal characteristic, the factors and laws affecting the contact characteristics are indicated through digital simulation. The concept of micro-convex body hierarchy is proposed. The critical values are related to the scale of micro-convex bodies and affected by the property parameters of the material. It is proved that the critical point is smooth and continuous, the parameter characteristics of the critical point are determined and the error between prediction and practice is reduced. In the integral calculation of the model, the experimental constants are also established to facilitate the calculation. The results show that the contact process of rough surface is consistent with the actual contact. It makes up the deficiency of KE model by considering the interaction between micro-convex bodies.

Decentralized rural electrification in Kenya: Speeding up universal energy access

This paper undertakes a comprehensive spatial mapping of the existing energy infrastructure in Kenya. With the perspective of the current energy status and local resources, the study develops a rural electrification spatial model for Kenya (RE_RU_KE tool) to identify optimal strategies for the different locations. The model considers the potential of conventional approaches (diesel gensets), clean technologies (solar, wind, hydro mini-grids), hybrid systems and the option of central grid extension to electrify remote areas in Kenya at the lowest possible cost. The model output is contrasted to the national Rural Electrification Master Plan (REM) of Kenya. While both the REM and RE_RU_KE tool target the off-grid rural electrification options, their methodological approaches are intrinsically different. The comparison between both results aims to enable valuable synergies and highlight the potential complementarities that can create added value for stakeholders involved in rural electrification planning. In particular, RE_RU_KE model output highlights the substantial role that renewable energy systems can play in decentralized generation providing universal energy access to rural households at a competitive cost.

A Static Friction Model for Elastic-plastic Contacting Surfaces Using Statistically Homogenized Technique

An improved static friction model is developed for elastic-plastic contacting surfaces. Two random variables of asperity height and curvature for Gaussian isotropic contacting surfaces are assumed to govern asperities distribution and they satisfy a joint probability distribution function. Based on the contact parametric representation of the KE model proposed by Kogut and Etsion, the expected macroscopic values of normal stress and shear stress are obtained by using statistically homogenized technique. Then the effect of roughness, the energy of adhesion and material properties on static friction coefficients are studied and the results show similar trend with literatures. A comparison of the present model with the SV friction model proposed by Sista and Vemaganti shows that the adhesion force has a more significant effect for smoother surface and SV model is more suitable for heavily loaded contacts. The static friction coefficient is related to the ratio of hardness to elastic modulus H/E. At the same roughness and normal load, lower H/E leads to lower critical interference ωc, higher plasticity index ψ, and smaller static friction coefficient.

Verification of a 3D CFD model for vertical slot fish-passes

In the present work, we verified a 3D computational fluid dynamics model for vertical slot fish-passes (VSFs) that employs the renormalization-group k-epsilon turbulence model (RNG KE) and the volume of fluid (VOF) method. We compared model calculations with experiments in two pool designs T1 and T2 of an experimental VSF and with 2D calculations using the shallow water equations (SWE) and the standard k-epsilon (2D SKE) model. Calculations of the 3D model showed (1) good agreement with experiments and 2D calculations in predicting mean flow velocities, (2) better performance in the determination of the water surface in the VSF, which is attributed to the accurate VOF method, (3) superior prediction of turbulence characteristics than the 2D model, which is due to the 3D RNG KE model that overcomes the problem of turbulence overestimation of the 2D SKE model, and to the fact that the 3D model takes into account the 3D features of the flow in the fish pass. Moreover, the present 3D calculations showed that the common assumptions in VSFs that (1) the flow is 2D, and (2) the simulation of 4 pools of a VSF is sufficient to obtain satisfactory results, are not always valid. Flow can be considered as 2D only in pool design T2 and for certain geometries and flow characteristics in pool design T1; while, eventually, all the pools of a fish pass need to be modeled to ensure accurate results. Finally, the present work illustrates the need to perform fish experiments simultaneously with flow experiments.

A new model for correlation and prediction of equilibrium CO2 solubility in N‐methyl‐4‐piperidinol solvent

In this work, the equilibrium CO2 solubility in the aqueous tertiary amine, N‐methyl‐4‐piperidinol (MPDL) was measured over a range of temperatures, CO2 partial pressures and amine concentrations. The dissociation constant of the MPDL solution was determined as well. A new thermodynamic model was developed to predict the equilibrium CO2 solubility in the MPDL‐H2O‐CO2 system. This model, equipped with the correction factor (Cf), can give reasonable prediction with an average absolute deviation of 2.0%, and performs better than other models (i.e., KE model, Li‐Shen model, and Hu‐Chakma). The second‐order reaction rate constant (k2) of MPDL and the heat of CO2 absorption (–ΔHabs) into aqueous MPDL solutions were evaluated as well. Based on the comparison with some conventional amines, MPDL revealed a high‐equilibrium CO2 loading, reasonably fast absorption rate when compared with other tertiary amines, and a low energy requirement for regeneration. It may, therefore, be considered to be an alternative solvent for CO2 capture. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3395–3403, 2017

Theoretical calculations and experimental study of spur gears churning power loss based on finite element analysis

The influencing factors of spur gear churning loss include the kinematical viscosity, peripheral velocity and operating temperature of lubricant, module of gear, number of teeth, gear width, oil immersion depth of gear and local gravity values. The coexistence of these factors forms complex functions, and these functions are difficult to determine a direct analytic solution. For the reason, the theoretical analysis of spur gear churning power loss is carried on by using the boundary layer theory of fluid mechanics based on the partial simplification of above factors, and the churning flow partial differential equations are established. By using the multiphase flow VOF model and eddy current Ke model in FLUENT software, the numerical simulation analysis is carried out. Finally, the simulation results are experimentally verified. The results show that under the condition of low rotation speed, the value of churning power loss can be efficiently predicted by using this simulation method.

An elastic–plastic asperity contact model and its application for micro-contact analysis of gear tooth profiles

This paper presents a continuous elastic–plastic asperity contact model with or without the consideration of friction to investigate the micro-contact properties of gear tooth profiles. The model for normal or side contact analysis is established according to Hertz contact theory and the asperity morphology feature, which yields to similar results as obtained from the model proposed by Chang W.R., Etsion I., and Bogy D.B. (CEB model) and the model proposed by Kogut L. and Etsion I. (KE model). More importantly, this model avoids the constant average contact stress as predicted by the CEB model, and the noncontinuous contact stress and deformation within the ultimate strength as given by the KE model. As a application of the present theoretical model in micro-contact analysis of rough tooth profiles, a finite element model (FE model) for elastic–plastic asperity in normal or side contact is established according to the measured surface parameters of a spur gear pair. It is shown that the extreme point of Von Mise stress of the asperities along the normal vector is ascertained by FE model, and that the extreme point is relative to the initial occurrence of the asperities plastic deformation. Compared with the present theoretical model, the similar normal contact stress along the contact radius is attained by FE model. Though the contact stress isogram in the specific plane in normal or side contact of the asperities is a circle or ellipse respectively when the plastic deformation is expanded from the inside of the asperities to their surfaces, it is in line with the distribution of elastic and plastic region of the theoretical model. Compared with CEB model, KE model, and FE model, the consistent results are attained by the present theoretical model in elastic–plastic asperity contact analysis. The results indicate that the theoretical model is applicable to the elastic–plastic asperity contact analysis on the rough surface of a spur gear drive.

A Comprehensive Elastic-Plastic Single-Asperity Contact Model

Generally, the contact of rough surfaces is modeled and analyzed through statistical approaches, including microgeometrical measurements and description of the asperities in contact (shape, size, spacing, and asperity height), developing theoretical expressions to describe the mechanical behavior of the asperities in contact, and finally extending it to the whole surface contacts. In some of the main contact models like the Kogut-Etsion model (KE model), Jackson-Green model (JG model), and Shankar-Mayuram model (SM model), an axisymmetrical hemispherical asperity in contact with a rigid flat surface is modeled and analyzed using finite element concepts and the resultant contact parameter relations are extended to rough surface contacts. The present work addresses the complete effect of Poisson's ratio and its influence in sub surface yielding, elastic-plastic transition and inception of fully plastic contact by accounting realistic material behavior which are not covered by the above models. A unified single-asperity model is proposed and, based on the results, empirical relations are developed to predict the contact parameters (dimensionless contact load and contact area), which are then extended to statistical rough surface contacts.

Method of analyzing the influence of network structure on information diffusion

Social phenomena are affected by the structure of networks consisting of personal relationships. In the present paper, the diffusion of information among people is examined. In particular, the relationship between the network structure and the dynamics is studied. First, several networks are generated using the proposed network model and other network models, such as the WS model and the KE model. By changing the parameters of the network models, networks with different structures are generated. The parameters of the network models determine the topology of the networks and the statistical indicators.Second, the role of network structure on information diffusion is investigated through numerical simulations using a simple information diffusion model of the networks. Two data mining methods are used to analyze the results. A neural network predicts the convergence rate and the time using six explanatory variables, and a decision tree reveals the statistical indicator that has a strong effect on the information diffusion. After these analyses, important statistical variables explaining the information diffusion are shown.

CFD prediction of local scour hole around bridge piers

In order to predict the local scour hole and its evaluation around a cylindrical bridge pier, the computational fluid dynamics (CFD) and theories of sediment movement and transport were employed to carry out numerical simulations. In the numerical method, the time-averaged Reynolds Navier-Stokes equations and the standard ke model were first used to simulate the three-dimensional flow field around a bridge pier fixed on river bed. The transient shear stress on river bed was treated as a crucial hydrodynamic mechanism when handling sediment incipience and transport. Then, riverbed volumetric sediment transport was calculated, followed by the modification of the river bed altitude and configuration. Boundary adaptive mesh technique was employed to modify the grid system with changed riverbed boundary. The evolution of local scour around a cylindrical bridge pier was presented. The numerical results represent the flow pattern and mechanism during the pier scouring, with a good prediction of the maximum scour hole depth compared with test results.

Numerical Study of Flow Past a Circular Cylinder Using Hybrid Turbulence Formulations

Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying Reynolds-averaged Navier―Stokes equations. The first scheme is a hybrid Reynolds-averaged Navier―Stokes and large eddy simulation model using the two-equation ke model with a Reynolds-averaged Navier―Stokes and large eddy simulation transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier―Stokes model, where the unresolved kinetic energy parameter f k is allowed to vary as a function of grid spacing and the turbulence length scale. Solutions from these models are compared to Reynolds-averaged Navier―Stokes results and experimental data for a stationary and rotating cylinder. The parameter f k varies between zero and one and has the characteristic to be equal to one in the viscous sublayer, and when the Reynolds-averaged Navier―Stokes turbulent viscosity becomes smaller than the large eddy simulation viscosity. The formulation, usage methodology, and validation example are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The models are compared to Reynolds-averaged Navier―Stokes results and experimental data for turbulent separated flows and laminar separated flows around stationary and rotating cylinders. For a stationary cylinder, the turbulent separated case is accurately simulated using the general two-equation ke turbulence model (eddy-viscosity model). PAB3D accurately predicts the drag coefficient C D , lift coefficient C L , and the Strouhal number St. The laminar separated case was a challenge for the Reynolds-averaged Navier―Stokes computation with an eddy-viscosity turbulence model. The Reynolds-averaged Navier―Stokes with large eddy simulation and partially averaged Navier―Stokes performed well and showed marked improvements over the Reynolds-averaged Navier―Stokes solution. The modified partially averaged Navier―Stokes model was the most accurate. For the rotating cylinder, the spin ratio varied from zero to one, and the partially averaged Navier―Stokes results were in good agreement with published experimental data. Reynolds-averaged Navier―Stokes with large eddy simulation and partially averaged Navier― Stokes capture both temporal and spatial fluctuations and produce large-scale structures that do not occur in the Reynolds-averaged Navier―Stokes simulation. The current results show promise for the capability of partially averaged Navier―Stokes in simulating unsteady and complex flow phenomena.