scholarly journals Fractal analysis for biosurface comparison and behaviour prediction

2009 ◽  
Vol 63 (3) ◽  
pp. 239-245 ◽  
Author(s):  
Bozica Bojovic ◽  
Zoran Miljkovic ◽  
Bojan Babic ◽  
Djuro Koruga
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Surface Profile ◽  
Scanning Probe ◽  
Real Surface ◽  
Behavior Prediction ◽  
Functional Behavior ◽  
Probe Microscope ◽  
The Given

Fractal analysis was used in previous authors' researches for characterizations of grinded ceramics surface textures by surface profile fractal dimension. In this paper the 'skyscrapers' method was chosen for calculating fractal dimension of surface, using the image processing toolbox, as well as a custom-developed algorithm of Matlab environment. This method entails recording the surface as an image, by using a scanning probe microscope. In the given contact lens case, fractal dimension values confirm changes of the surface roughness during the cleaning and wearing processes. Examination of real surface roughness could provide comparison and functional behavior prediction.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

A Three-Dimensional Fractal Analysis Method for Ground Monocrystal Sapphire Surface

2014 ◽  
Vol 1017 ◽  
pp. 187-192
Author(s):  
Qiu Yan Wang ◽  
Zhi Qiang Liang ◽  
Xi Bin Wang ◽  
Wen Xiang Zhao ◽  
Yong Bo Wu ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Ground Surface ◽  
Surface Characteristics ◽  
Surface Phenomenon ◽  
Analysis Method ◽  
Characterization Methods ◽  
Box Counting

Conventional characterization methods of grinding surface using surface roughness parameters, e.g., Ra, depend on either the resolution of the measuring instrument or the length of the sample. But fractal dimension (FD) as a scale-independent fractal parameter is effective to evaluate the ground surface at any length scale and represent lots of surface phenomenon at its relevant length scales. In this paper, a three-dimensional (3D) box-counting fractal analysis method is used to investigate ground surface morphology of monocrystal sapphire by calculating 3D fractal dimension of the ground surface. The results obtained show that fractal dimension decreases with the increasing surface roughness. For the ground surface with higher fractal dimension, its microtopography is more exquisite with minor defects. Once the fractal dimension become smaller, deep cracks and pronounced defects are exhibited in ground surface. Moreover, the ground surface obtained in ductile mode has much higher fractal dimension than that in brittle mode. Therefore, the fractal analysis method has the potential to reveal the ground surface characteristics of monocrystal sapphire.

scholarly journals Experimental verification of a numerical surface roughness model for metallic bodies under large plastic strain

2019 ◽  
Vol 252 ◽  
pp. 05005
Author(s):  
Paweł Sidun
Keyword(s):  
Surface Roughness ◽  
Plastic Strain ◽  
Experimental Verification ◽  
Surface Profile ◽  
Surface Force ◽  
Numerical Calculations ◽  
Real Surface ◽  
Friction Process ◽  
Arithmetic Average ◽  
The Impact

The present work describes selected aspects of numerical modelling of the process of bonding metal alloys with consideration for micro-roughness, as well as experimental verification. The plastic-elastic contact between two deformable bodies was investigated in a DEFROM FEM environment, and verified at the test stand. The present paper demonstrates selected results of contact modelling investigated using aluminium-copper samples, in relation to their elastic-plastic range. The real surface profile helped to create a mathematical model of surface roughness measured using a laser microscope. Dependency between a blade of a tool and a feed was used to build a numerical model of roughness based on the arithmetic average value of the roughness profile. The work presents also a process of simplification of real surface roughness for the needs of numerical calculations. The paper investigates an impact of wave roughness at obtained values on effective plastic strain and stress. Additionally, numerical analysis shows a need to enter a new roughness wave correction factor assuming a zero value of the coefficient of friction. This is due to the interaction of metallic surfaces within the plastic contact zone. The obtained results allow the estimation of the impact of surface force interaction expressed by the wave coefficient factor. The experimental verification of numerical calculations allowed the estimation of the actual impact of the micro-cutting process in the entire friction process. Further analysis of obtained results permits the author to explain the surface phenomena occurring during the friction process, such as adhesion or diffusion, and outline the development direction of numerical methods.

A comparison of fractal methods for evaluation of hydraulic fracturing surface roughness

2020 ◽  
Vol 60 (1) ◽  
pp. 184 ◽  
Author(s):  
Abbas Movassagh ◽  
Xi Zhang ◽  
Elaheh Arjomand ◽  
Manouchehr Haghighi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Hydraulic Fracturing ◽  
Fractal Analysis ◽  
Roughness Length ◽  
Variation Method ◽  
Fracture Surfaces ◽  
Wide Range ◽  
Surface Profiles ◽  
Fractal Methods

Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.

Quantitative Analysis for Micro Geometrical Characteristic of Rough Surface Profile Based on Fractal Theory

2010 ◽  
Vol 154-155 ◽  
pp. 19-22
Author(s):  
Xiu Juan Yang ◽  
Zhi Qian Xu ◽  
Xiang Zhen Yan
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Quantitative Analysis ◽  
Rough Surface ◽  
Vertical Section ◽  
Fractal Theory ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Geometrical Characteristic ◽  
Accuracy Requirement

In this paper, a quantitative analysis for the micro geometrical characteristic of rough surface profile is researched with the fractal theory. Firstly, the fractal dimensions of profile curves under different surface roughness are obtained by using the vertical section method, and then the theoretical relationship between the surface roughness and the fractal dimension is built. Secondly, according to the surface profile curve composed of many triangle peaks, the angles and heights of them are calculated to study the micro geometrical size. Through their variation laws changing with the fractal parameters, the calculation formulas of their average values related to fractal dimension are obtained by using mathematics regression tools. Finally, combing three theoretical relationships built above, the geometrical characteristic of the rough surface profile can be calculated with the surface roughness and accuracy requirement known.

Fractal analysis with scanning probe microscopy

1992 ◽  
Vol 50 (2) ◽  
pp. 1046-1047
Author(s):  
Paul E. West ◽  
Sid Marchesse-Rugona ◽  
Zhuoning Li
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Physical Properties ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Optical Microscope ◽  
Two Dimensional ◽  
Atomic Force ◽  
Dimensional Measurements ◽  
Surface Profiles

Surface roughness determined qualitatively by direct visualization can be correlated to several physical properties. However, finding a suitable method of quantifying surface roughness, until recently, has been difficult. The concept of Fractal Dimension, recently popularized by Mandelbrot(1982) has been extremely successful in quantifying surface roughness and relating it to such measurable physical properties such as; cleanability, catalytic activity, rate of corrosion, and even flavor.Atomic Force Microscopes permit direct three dimensional measurements of surface microstructure. AFM images are obtained by measuring the motion of a sharp stylus as it is scanned across a surface. Because the AFM directly measures three dimensional topograms, it is ideally suited for two dimensional and three dimensional fractal analysis. Other microscope techniques such as the scanning electron or optical microscope give only two dimensional magnification and fractal measurements are not easily made.The Atomic Force Microscope enables us to obtain the fractal dimension of surface profiles as well as surface areas. For surface profiles we use a box counting method (Mandelbrot 1986, Chesters et al. 1989).

Surface Roughness Effects on Fluid Flow between Two Rotating Cylinders

2015 ◽  
Vol 642 ◽  
pp. 275-280
Author(s):  
Sutthinan Srirattayawong ◽  
Shian Gao
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Profile ◽  
Fluid Film ◽  
Real Surface ◽  
Contact Center ◽  
Roughness Effects ◽  
Fluid Film Thickness ◽  
Lubricant Viscosity

In general, the thin fluid film problems are explained by the classical Reynolds equation, but this approach has some limitations. To overcome them, the method of Computational Fluid Dynamics (CFD) is used in this study, as an alternative to solving the Reynolds equation. The characteristics of the two cylinders contact with real surface roughness are investigated. The CFD model has been used to simulate the behavior of the fluid flows at the conjunction between two different radius cylinders. The non-Newtonian fluid is employed to calculate the lubricant viscosity, and the thermal effect is also considered in the evaluation of the lubricant properties. The pressure distributions, the fluid film thickness and the temperature distributions are investigated. The obtained results show clearly the significance of the surface roughness on the lubricant flow at the contact center area. The fluctuated flow also affects the pressure distribution, the temperature and the lubricant viscosity in a similar pattern to the rough surface profile. The surface roughness effect will decrease when the film thickness is increased.

An Electrostatic Force Probe for Surface Profile Measurement in Noncontact Condition

2013 ◽  
Vol 7 (6) ◽  
pp. 714-719 ◽  
Author(s):  
So Ito ◽  
◽  
Zhigang Jia ◽  
Shigeaki Goto ◽  
Keiichiro Hosobuchi ◽  
...  
Keyword(s):  
Electrostatic Force ◽  
Surface Profile ◽  
Sample Surface ◽  
Contact Condition ◽  
Scanning Probe ◽  
Profile Measurement ◽  
Electrostatic Probe ◽  
Probe Microscope ◽  
Basic Characteristics ◽  
Surface Profile Measurement

A scanning probe microscope with an electrostatic force probe has been introduced for the dimensional measurement of the surface profile measurement. Since the intensity of the electrostatic force is strongly depended on the distance between a probe and the sample surface, the electrostatic force probe can be used for the measurement of the surface profile in non contact condition. In order to detect the electrostatic force between the probe tip and the sample surface, a method of the frequency modulation AFM has been employed. When the bias voltage is applied between the probe and the surface, the resonance frequency of the probe oscillation is shifted owing to the electrostatic force. In this paper, the basic characteristics of the electrostatic probe are investigated, experimentally. And then, the absolute distance between the probe tip and the sample surface is calculated by using the differences of the frequency shift of the probe. Finally, the measurement of surface profile is demonstrated in non-contact condition by utilizing the developed electrostatic force probe.

Paper 6: Assessment of Face Seal Performance Based on the Parameters of a Statistical Representation of Surface Roughness

1967 ◽  
Vol 182 (11) ◽  
pp. 101-107 ◽  
Author(s):  
L. A. Mitchell ◽  
M. D. Rowe
Keyword(s):  
Surface Roughness ◽  
Standard Deviation ◽  
Surface Profile ◽  
Real Surface ◽  
Face Seal ◽  
Statistical Representation ◽  
Adequate Information ◽  
Centre Line ◽  
Sealing Performance ◽  
The Mean

Most methods commonly used to describe real surface roughness do not provide adequate information to enable predictions to be made of fluid leakage between two surfaces. To carry out such an analysis it is essential to know the depths of the remaining valleys at all stages of compression. It is shown that, when the distributions of peak and valley levels are defined, load-compression and load-leakage relationships can be derived if wedge-shaped asperities of constant apex semi-angle are assumed. The results suggest that a convenient quantity for specifying the form of a surface profile is the ratio of the distance between the mean peak and mean valley levels to the standard deviation of the distributions ( d/σ). For the best sealing performance d/σ should be as large as possible, whilst the centre-line average (c.l.a.), which provides a measure of the scale of the roughness, should be as small as possible.

Fractal Analysis of Self-Sharpening Phenomenon in cBN Grinding

2008 ◽  
Vol 389-390 ◽  
pp. 42-47 ◽  
Author(s):  
Yoshio Ichida ◽  
Ryunosuke Sato ◽  
Masakazu Fujimoto ◽  
Nabil Ben Fredj
Keyword(s):  
Fractal Dimension ◽  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Surface Profile ◽  
Cutting Edge ◽  
The Self ◽  
Grinding Process ◽  
Scanning Electron

This paper presents a fractal analysis of the self-sharpening phenomenon of the grain cutting edges in cBN grinding. To clarify the self-sharpening mechanism due to the micro fracture of the cutting edges, the changes in three-dimensional profile of the cutting edges in the grinding process have been measured using a scanning electron microscope with four electron probes and evaluated on the basis of the fractal analysis. The fractal dimension for surface profile of the cutting edge formed by the micro fracture is higher than that of the cutting edge formed by the ductile attritious wear. Therefore, the complicated changes in shape of the cutting edge due to the self-sharpening can be evaluated quantitatively using the fractal dimension.

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