Fractal Network Model for Contact Conductance

1991 ◽  
Vol 113 (3) ◽  
pp. 516-525 ◽  
Author(s):  
A. Majumdar ◽  
C. L. Tien
Keyword(s):  
Fractal Dimension ◽  
Network Model ◽  
Rough Surfaces ◽  
Surface Profile ◽  
Contact Conductance ◽  
Fractal Surfaces ◽  
Real Area Of Contact ◽  
Similar Images ◽  
Fractal Network

The topography of rough surfaces strongly influences the conduction of heat and electricity between two surfaces in contact. Roughness measurements on a variety of surfaces have shown that their structure follows a fractal geometry whereby similar images of the surface appear under repeated magnification. Such a structure is characterized by the fractal dimension D, which lies between 2 and 3 for a surface and between 1 and 2 for a surface profile. This paper uses the fractal characterization of surface roughness to develop a new network model for analyzing heat conduction between two contacting rough surfaces. The analysis yields the simple result that the contact conductance h and the real area of contact At are related as h ~ AtD/2 where D is the fractal dimension of the surface profile. Contact mechanics of fractal surfaces has shown that At varies with the load F as At ~ Fη where η ranges from 1 to 1.33 depending on the value of D. This proves that the conductance and load are related as h ~ FηD/2 and resolves the anomaly in previous investigations, which theoretically and experimentally obtained different values for the load exponent. The analytical results agreed well with previous experiments although there is a tendency for overprediction.

scholarly journals A mixed lubrication analysis of a thrust bearing with fractal rough surfaces

2019 ◽  
Vol 234 (4) ◽  
pp. 608-621
Author(s):  
Xiaohan Zhang ◽  
Yang Xu ◽  
Robert L Jackson
Keyword(s):  
Fractal Dimension ◽  
Roughness Length ◽  
Thrust Bearing ◽  
Rough Surfaces ◽  
Mixed Lubrication ◽  
Bearing Surface ◽  
Fractal Surfaces ◽  
Lubrication Regime ◽  
Surface Data ◽  
Mixed Lubrication Regime

Fractal descriptions of rough surfaces are widely used in tribology. The fractal dimension, D, is an important parameter which has been regarded as instrument and scale independent, although recent findings bring this into question. A thrust bearing is analyzed in the mixed lubrication regime while considering the fractal nature. Surface data obtained from a thrust bearing surface are characterized and used to calculate the fractal dimension value by the roughness-length method. Then these parameters are used to generate different rough surfaces via a filtering algorithm. By comparing the predicted performance between the measured surface and generated fractal surfaces, it is found that the fractal dimension must be used carefully when characterizing the tribological performance of rough surfaces, and other parameters need to be found.

Fractal Model of Elastic-Plastic Contact Between Rough Surfaces

1991 ◽  
Vol 113 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A. Majumdar ◽  
B. Bhushan
Keyword(s):  
Size Distribution ◽  
Rough Surfaces ◽  
Surface Profile ◽  
Scanning Tunneling ◽  
Roughness Parameters ◽  
The Real ◽  
Real Area Of Contact ◽  
Fractal Roughness ◽  
Contact Spots ◽  
Real Area

Roughness measurements by optical interferometry and scanning tunneling microscopy on a magnetic thin-film rigid disk surface have shown that its surface is fractal in nature. This leads to a scale-dependence of statistical parameters such as r.m.s height, slope and curvature, which are extensively used in classical models of contact between rough surfaces. Based on the scale-independent fractal roughness parameters, a new model of contact between isotropic rough surfaces is developed. The model predicts that all contact spots of area smaller than a critical area are in plastic contact. When the load is increased, these plastically deformed spots join to form elastic spots. Using a power-law relation for the fractal size-distribution of contact spots, the model shows that for elastic deformation, the load P and the real area of contact Ar are related as P~Ar(3−D)/2, where D is the fractal dimension of a surface profile which lies between 1 and 2. This result explains the origins of the area exponent which has been the focus of a number of experimental and theoretical studies. For plastic loading, the load and area are linearly related. The size-distribution of spots also suggests that the number of contact spots contributing to a certain fraction of the real area of contact remains independent of load although the spot sizes increase with load. The model shows that the load-area relation and the fraction of the real area of contact in elastic and plastic deformation are quite sensitive to the fractal roughness parameters.

Study on Reconstruction of Fractal Rough Surfaces

2013 ◽  
Vol 278-280 ◽  
pp. 527-530
Author(s):  
Nan Zhang ◽  
Li Hua Wang ◽  
Yu Song He ◽  
Zi Lu
Keyword(s):  
Rough Surfaces ◽  
Three Dimensional ◽  
Computer Models ◽  
Contact Analysis ◽  
Solid Model ◽  
Fractal Surfaces ◽  
Contact Conductivity ◽  
Surface Contact

The geometric topography of the engineering surfaces play key roles in many issue of engineering and science including the analysis of friction, wear, lubrication, sealing and contact conductivity, especially microcosmic surface contact, thus the characterization of surface is one of the most important topics of tribology. Using the technology of CAD/CAE, a three-dimensional solid model of the fractal surfaces was established and meshed to provide the computer models for microcosmic contact analysis between two rough surfaces in this paper.

EVALUATION OF FRACTAL DIMENSION MEASUREMENTS BY FREQUENCY ANALYSIS METHODS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 680-686 ◽  
Author(s):  
MIGUEL AGUILAR ◽  
MANUEL PANCORBO ◽  
ELOY ANGUIANO
Keyword(s):  
Computer Simulation ◽  
Fractal Dimension ◽  
Frequency Analysis ◽  
Fractal Surfaces ◽  
New Methods ◽  
Analysis Methods ◽  
Mathematical Algorithms ◽  
Computer Generation

A study of the quality and accuracy of the methods, based on frequency analysis, for fractal characterization of surfaces is carried out. The study is based on computer simulation of fractal surfaces images and then a discussion of the mathematical algorithms used for computer generation of fractal surfaces is also made. The main conclusion is that the studies of fractal characterization by frequency analysis reported in previous papers as well as the conclusions about the performance of the different methods are doubtful and questionable. We propose new methods for frequency analysis that in some cases yield the more accurate results.

The Characteristic Fractal Parameter for the Characterization of Rough Surfaces

2005 ◽  
Author(s):  
Shirong Ge ◽  
Hua Zhu ◽  
Gang Li
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Rough Surfaces ◽  
Roughness Parameter ◽  
Geometric Meaning ◽  
Statistical Parameters ◽  
Characterization Methods ◽  
Fractal Parameter ◽  
Scale Coefficient

The issues about the characterization of rough surfaces are always of concern to tribologist. Because the statistical parameters used conventionally are not ideal to characterize rough surfaces, it is very necessary to investigate the new characterization methods and characterization parameters. In this paper, the fractal geometry is applied, and a roughness parameter called the characteristic fractal parameter τ* is put forth by combining fractal dimension D and scale coefficient C. Its definition, geometric meaning and mathematical express are given. Four surfaces with different roughness formed by turning, milling, grinding and sandpaper polishing machining are characterized with the characteristic fractal parameter τ*. And the results of characterizing these surfaces are compared with that of Ra. It is proved that the characteristic fractal parameter is not only more objective but also more sensitive to characterize rough surfaces than the conventional characterization parameter Ra.

Fractal Characterization of Corroded Surface Profile in Reinforcing Steel Bars

2010 ◽  
Vol 163-167 ◽  
pp. 3118-3121 ◽  
Author(s):  
Yi Dong Xu ◽  
Chun Xiang Qian
Keyword(s):  
Fractal Dimension ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Corrosion Damage ◽  
Absolute Measurement ◽  
Reinforcing Steel ◽  
Multi Scale ◽  
Steel Bars ◽  
Fractal Characteristics

Based on fractal geometry theory and surface roughness characterization technology, this paper presents the fractal characterization of nonuniform corrosion degree of corroded reinforcing steel bars. The surface profile curves of different corroded reinforcing steel bars were obtained and their fractal dimensions were calculated in order to describe the fractal characteristics. As is shown by the results, the surface profile curves of rebar have statistical fractal feature. However, fractal dimension is not sensitive to small changes in profile curves. By combining fractal dimension D with scale parameter C, characteristic profile parameter r* is derived to characterize the surface profile of corroded reinforcing steel bars sensitively, which realized the unity of multi-scale similarity measurement and absolute measurement. The results of this analysis will become the basis for corrosion damage evolution of corroded reinforcing steel bars.

Optimum Roughness for Minimum Adhesion

2008 ◽  
Author(s):  
D.-L. Liu ◽  
J. Martin ◽  
N. A. Burnham
Keyword(s):  
Surface Roughness ◽  
Rough Surfaces ◽  
Optimal Size ◽  
Fractal Surfaces ◽  
Single Asperity ◽  
Roughness Exponent ◽  
Asperity Model ◽  
Roughness Exponents ◽  
Adhesive Forces

Surface roughness has a significant affect on adhesion. We used a single-asperity model to describe a smooth tip in contact with a rough surface and predicted that an optimal size of asperity will yield a minimum of adhesion. Experimentally, adhesive forces on silicon wafers with varying roughness were measured using AFM cantilevers with varying tip radii. It was found that minima do exist, and for all tip radii, the adhesion falls significantly for roughness greater than 1–2 nm and drops at higher roughness for larger tips. In addition to RMS roughness, the roughness exponent is another important parameter for the characterization of rough surfaces and its affect on adhesion was also investigated. We developed computer programs to simulate a set of fractal rough surfaces with differing roughness exponents. The adhesive forces between an AFM tip and the fractal surfaces were calculated and the adhesion was seen to decrease as the roughness exponent increases. This work should help minimize MEMS stiction and progress the understanding of nanoscale contact mechanics.

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