An Adhesion Model for Elastic-Contacting Fractal Surfaces in the Presence of Meniscus

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Y. F. Peng ◽  
Y. B. Guo ◽  
Y. Q. Hong
Keyword(s):  
Relative Humidity ◽  
Thin Liquid Film ◽  
Surface Model ◽  
Fractal Surface ◽  
Fractal Function ◽  
Adhesive Interaction ◽  
Dugdale Model ◽  
Fractal Surfaces ◽  
Fractal Parameters ◽  
Adhesion Model

The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a microsized interface. The present research concerns the elastic adhesion of rough fractal surfaces in the presence of a thin liquid film. A rough fractal surface is characterized with a two-variable Weierstrass–Mandelbrot fractal function. The microcontact model of the single asperity is established in terms of the fractal parameters. The adhesion model from meniscus is developed with the Dugdale approximation of the Laplace pressure to consider the adhesive interaction within/outside the contact area. Then the Maugis–Dugdale model and its extension are used to solve the elastic adhesive interaction for the two approaching fractal surfaces by incorporating the fractal surface model. Simulations of the external force versus the interface stiffness, surface roughness, and relative humidity are performed, respectively. The simulation results show that the interface stiffness, surface topography, and relative humidity can heavily influence the interface adhesion of rough surfaces with meniscus.

An Elastic Adhesion Model for Contacting Cylinder and Perfectly Wetted Plane in the Presence of Meniscus

2007 ◽  
Vol 129 (2) ◽  
pp. 231-234 ◽  
Author(s):  
Y. F. Peng ◽  
G. X. Li
Keyword(s):  
Relative Humidity ◽  
Normal Load ◽  
Adhesive Contact ◽  
Laplace Pressure ◽  
Contact Radius ◽  
Adhesive Interaction ◽  
Applied Normal Load ◽  
Adhesion Model ◽  
The Relationship

The present research concerns the elastic contacting adhesion of a cylinder with a perfectly wetted plane in the presence of a meniscus. The Laplace pressure due to the meniscus is simplified utilizing Maugis–Dugdale approximation. Then the Baney and Hui solution and its extension are used to solve the adhesive interaction of the cylinder and the plane. Simulations of the relationship between the adhesive contact radius and the applied normal load are performed, and the influence of the relative humidity on the relationship is also discussed.

scholarly journals Climate pattern-scaling set for an ensemble of 22 GCMs – adding uncertainty to the IMOGEN version 2.0 impact system

2018 ◽  
Vol 11 (2) ◽  
pp. 541-560 ◽  
Author(s):  
Przemyslaw Zelazowski ◽  
Chris Huntingford ◽  
Lina M. Mercado ◽  
Nathalie Schaller
Keyword(s):  
Climate Change ◽  
Relative Humidity ◽  
Land Surface ◽  
Land Surface Model ◽  
Individual Performance ◽  
Balance Model ◽  
Surface Model ◽  
Near Surface ◽  
Global Circulation Models ◽  
Version 2.0

Abstract. Global circulation models (GCMs) are the best tool to understand climate change, as they attempt to represent all the important Earth system processes, including anthropogenic perturbation through fossil fuel burning. However, GCMs are computationally very expensive, which limits the number of simulations that can be made. Pattern scaling is an emulation technique that takes advantage of the fact that local and seasonal changes in surface climate are often approximately linear in the rate of warming over land and across the globe. This allows interpolation away from a limited number of available GCM simulations, to assess alternative future emissions scenarios. In this paper, we present a climate pattern-scaling set consisting of spatial climate change patterns along with parameters for an energy-balance model that calculates the amount of global warming. The set, available for download, is derived from 22 GCMs of the WCRP CMIP3 database, setting the basis for similar eventual pattern development for the CMIP5 and forthcoming CMIP6 ensemble. Critically, it extends the use of the IMOGEN (Integrated Model Of Global Effects of climatic aNomalies) framework to enable scanning across full uncertainty in GCMs for impact studies. Across models, the presented climate patterns represent consistent global mean trends, with a maximum of 4 (out of 22) GCMs exhibiting the opposite sign to the global trend per variable (relative humidity). The described new climate regimes are generally warmer, wetter (but with less snowfall), cloudier and windier, and have decreased relative humidity. Overall, when averaging individual performance across all variables, and without considering co-variance, the patterns explain one-third of regional change in decadal averages (mean percentage variance explained, PVE, 34.25±5.21), but the signal in some models exhibits much more linearity (e.g. MIROC3.2(hires): 41.53) than in others (GISS_ER: 22.67). The two most often considered variables, near-surface temperature and precipitation, have a PVE of 85.44±4.37 and 14.98±4.61, respectively. We also provide an example assessment of a terrestrial impact (changes in mean runoff) and compare projections by the IMOGEN system, which has one land surface model, against direct GCM outputs, which all have alternative representations of land functioning. The latter is noted as an additional source of uncertainty. Finally, current and potential future applications of the IMOGEN version 2.0 modelling system in the areas of ecosystem modelling and climate change impact assessment are presented and discussed.

SIMULATION OF CO CHEMISORPTION ON Pt SUPPORTED ON FRACTAL SURFACES

2005 ◽  
Vol 04 (03) ◽  
pp. 769-785 ◽  
Author(s):  
GIANINA DOBRESCU ◽  
IUDIT FANGLI ◽  
MIRCEA RUSU
Keyword(s):  
Active Sites ◽  
Energy Surface ◽  
Weak Interactions ◽  
Fractal Surface ◽  
High Concentration ◽  
Co Chemisorption ◽  
Fractal Surfaces ◽  
Lennard Jones ◽  
Planar Surfaces ◽  
Co Chemisorption On Pt

CO chemisorption on Pt supported on fractal surfaces was simulated in order to compute chemisorption dimension and active sites fractal dimension. Pt deposition was simulated using different models on both fractal and planar surfaces. The potential energy surface with two adsorption positions model was used to compute Pt–CO interaction and a Lennard–Jones 6–12 potential was used to simulate CO–CO interaction. Two Pt phases on fractal surface, one at low concentration — the dispersed phase and the second at high concentration — the aggregated phase characterized by weak interactions with support are obtained. The results are in accord with experimental data of CO chemisorption on Pt supported on γ-alumina. Computed data obtained for planar support are compared with those obtained on fractal support. The effect of fractal support on chemisorption data is underlined.

scholarly journals Coefficients of Restitution Based on a Fractal Surface Model

2003 ◽  
Vol 70 (3) ◽  
pp. 339-345 ◽  
Author(s):  
Chung-Jen Lu ◽  
Ming-Chang Kuo
Keyword(s):  
Surface Topography ◽  
Material Properties ◽  
Plastic Material ◽  
Coefficient Of Restitution ◽  
Surface Model ◽  
Fractal Surface ◽  
Normal Contact ◽  
Perfectly Plastic ◽  
Fractal Models ◽  
Elastic Perfectly Plastic

Equations of rigid-body mechanics provide a means to predict the post-collision behavior without recourse to highly complex, detailed analysis of deformations during contact. Before the prediction can be completed, the coefficient of restitution, which relates the rebound velocity to the incident velocity, must be estimated properly. The coefficient of restitution depends on the surface topography in addition to the material properties and incident velocity. Recent investigations showed that surface topography can be characterized properly by fractal models. This paper proposes a normal contact model for a fractal surface in contact with a rigid smooth half-space. The fractal surface is constructed based on the Cantor set and composed of elastic-perfectly plastic material. Asymptotic continuous expressions for the load-displacement relations during loading and unloading are derived. Based on these results, we study the effects of surface roughness, material properties and incident velocity on the coefficient of restitution.

Prediction of Surface Roughness Profiles for Milling Process with Fractal Parameters Based on LS-SVM

2010 ◽  
Vol 97-101 ◽  
pp. 1186-1193 ◽  
Author(s):  
Ben Gan ◽  
Yi Jian Huang ◽  
Gui Xia Zheng
Keyword(s):  
Surface Roughness ◽  
Cutting Parameters ◽  
Milling Process ◽  
Face Milling ◽  
Cutting Conditions ◽  
Vertical Scaling ◽  
Support Vector ◽  
Fractal Function ◽  
Milling Operations ◽  
Fractal Parameters

Least squares support vector machines (LS-SVM) were developed for the analysis and prediction of the relationship between the cutting conditions and the corresponding fractal parameters of machined surfaces in face milling operation. These models can help manufacturers to determine the appropriate cutting conditions, in order to achieve specific surface roughness profile geometry, and hence achieve the desired tribological performance (e.g. friction and wear) between the contacting surfaces. The input parameters of the LS-SVM are the cutting parameters: rotational speed, feed, depth of milling. The output parameters of the LS-SVM are the corresponding calculated fractal parameters: fractal dimension D and vertical scaling parameter G. The LS-SVM were utilized successfully for training and predicting the fractal parameters D and G in face milling operations. Moreover, Weierstrass-Mandelbrot（W–M ）fractal function was integrated with the LS-SVM in order to generate an artificially fractal predicted profiles at different milling conditions. The predicted profiles were found statistically similar to the actual measured profiles of test specimens and there is a relationship between the scale-independent fractal coefficients(D and G).

Free Surface Model Derived From the Analytical Solution of Stokes Flow in a Wedge

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
R. W. Hewson
Keyword(s):  
Free Surface ◽  
Stokes Flow ◽  
Thin Liquid Film ◽  
Industrial Process ◽  
Surface Model ◽  
Coating Flows ◽  
Element Simulation ◽  
Extraction Processes ◽  
Full Solution ◽  
Free Surface Model

The formation of a thin liquid film onto a moving substrate is a commonly encountered industrial process, and one that is encountered in lubrication, oil extraction processes, and coating flows. The formation of such a film is analyzed via the analytical Stokes flow solution for the flow in a wedge bounded on one side by a free surface and on the other by a moving surface. The full solution is obtained by numerically integrating a set of ordinary differential equations from far downstream, in the region of the final film thickness. The results show excellent agreement with the results obtained by the Bretherton equation, the Ruschak equation, the Coyne and Elrod model, and a two-dimensional free surface finite element simulation of the problem.

Revisiting the Maugis–Dugdale Adhesion Model of Elastic Periodic Wavy Surfaces

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Qiang Wan
Keyword(s):  
Flat Surface ◽  
Adhesion Force ◽  
Adhesive Contact ◽  
Interaction Zone ◽  
Dugdale Model ◽  
Full Contact ◽  
Type Contact ◽  
Wavy Surfaces ◽  
Contact Models ◽  
Adhesion Model

The plane strain adhesive contact between a periodic wavy surface and a flat surface has been revisited based on the classical Maugis–Dugdale model. Closed-form analytical solutions derived by Hui et al. [1], which were limited to the case that the interaction zone cannot saturate at a period, have been extended to two additional cases with adhesion force acting throughout the whole period. Based on these results, a complete transition between the Westergaard and the Johnson, Kendall, and Roberts (JKR)-type contact models is captured through a dimensionless transition parameter, which is consistent with that for a single cylindrical contact. Depending on two dimensionless parameters, different transition processes between partial and full contact during loading/unloading stages are characterized by one or more jump instabilities. Rougher surfaces are found to enhance adhesion both by increasing the magnitude of the pull-off force and by inducing more energy loss due to adhesion hysteresis.

Modeling porous structures with fractal rough topography based on triply periodic minimal surface for additive manufacturing

2017 ◽  
Vol 23 (2) ◽  
pp. 257-272 ◽  
Author(s):  
Zhijia Xu ◽  
Qinghui Wang ◽  
Jingrong Li
Keyword(s):  
Additive Manufacturing ◽  
Minimal Surface ◽  
Surface Topography ◽  
Porous Structures ◽  
Fractal Surface ◽  
Content Type ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
Fractal Parameters ◽  
Triply Periodic Minimal Surface

Purpose The purpose of this paper is to develop a general mathematic approach to model the microstructures of porous structures produced by additive manufacturing (AM), which will result in fractal surface topography and higher roughness that have greater influence on the performance of porous structures. Design/methodology/approach The overall shapes of pores were modeled by triply periodic minimal surface (TPMS), and the micro-roughness details attached to the overall pore shapes were represented by Weierstrass–Mandelbrot (W-M) fractal representation, which was integrated with TPMS along its normal vectors. An index roughly reflecting the irregularity of fractal TPMS was proposed, based on which the influence of the fractal parameters on the fractal TPMS was qualitatively analyzed. Two complex samples of real porous structures were given to demonstrate the feasibility of the model. Findings The fractal surface topography should not be neglected at a micro-scale level. In addition, a decrease in the fractal dimension Ds may exponentially make the topography rougher; an increase in the height-scaling parameter G may linearly increase the roughness; and the number of the superposed ridges has no distinct influence on the topography. Furthermore, the synthesis method is general for all implicit surfaces. Practical implications The method provides an alternative way to shift the posteriori design paradigm of porous media to priori design mode through numeric simulation. Therefore, the optimization of AM process parameters, as well as the porous structure, can be potentially realized according to specific functional requirement. Originality/value The synthesis of TPMS and W-M fractal geometry was accomplished efficiently and was general for all implicit freeform surfaces, and the influence of the fractal parameters on the fractal TPMS was analyzed more systematically.

Fractal simulation of surface topography and prediction of its lubrication characteristics

2021 ◽  
Author(s):  
Jiang Zhao ◽  
zekun wang ◽  
Zhengminqing Li ◽  
Rupeng Zhu
Keyword(s):  
Film Thickness ◽  
Rough Surfaces ◽  
Surface Film ◽  
Fractal Theory ◽  
Morphological Characteristics ◽  
Fractal Surface ◽  
Statistical Parameters ◽  
Machined Surface ◽  
Fractal Parameters ◽  
Lubrication Characteristics

Abstract A machined surface has observable fractal characteristics, with infinite local and overall self-similar consistency. Therefore, the fractal theory is considered to provide a better description of the morphological characteristics of rough surfaces, which accurately reflects the randomness and multi-scale characteristics of rough surfaces and it is not comparable with the surface characteristics obtained based on statistical parameters limited by sampling length and device resolution. In this study, the Weierstrass-Mandelbrot (W-M) function was applied to construct a fractal reconstruction surface, and the mixed elastohydrodynamic lubrication model was used to investigate the lubrication characteristics of real and reconstructed surfaces under the same fractal parameters. The effects of the fractal parameters on the fractal surface lubrication characteristics were further analyzed. The results demonstrate that the lateral roughness fractal surface provides greater resistance to the entrained flow of lubricant, which leads to a larger average film thickness, than the longitudinal roughness and isotropic fractal surface. With the increase in fractal dimension, the surface roughness peak density increases, which reduces the surface film thickness by 47%, and the friction coefficient increases by 46%. The lubrication parameter fluctuates slightly with the change in the number of overlapping ridges M of the fractal surface. Generally, M has little effect on the surface lubrication characteristics.

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