Generalized fractal analysis and its applications to engineering surfaces (original) (raw)
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Fractal Simulation on Machined Surfaces
The characterization of machined surfaces is a very important activity in any manufacturing process. There are instruments that characterize the surface and its roughness using scale dependent statistical parameters such as variation of height, slope and its curvature. However it has been found that these parameters are strongly dependent on the resolution of roughness measuring instrument. Consequently, instruments with different resolutions and scan lengths yield different values of these statistical parameters for the same surface. The conventional methods of characterization are therefore fraught with inconsistencies. The underlying problem is that although rough surfaces contain roughness at a large number of length scales, the characterization parameters depend only on a few particular length scales, such as the instrument resolution or the sampling length. A logical solution to this problem is to use scale-invariant parameters to characterize rough surfaces. Fractal geometry is a potential tool for characterizing this type of random patterns observed in nature and hence its suitability for surface finish measurements and studying the effect of operating conditions and tool geometry in the finish obtained on a machined surface and simulate the pattern using of fractals. Thus this study can be extended to predict the surface pattern when machining conditions.
Surface Evaluation by Estimation of Fractal Dimension and Statistical Tools
The Scientific World Journal, 2014
Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text ...
Fractal Characterisation of Worn Surfaces
Tribological behaviour – friction, wear and lubrication – of machine elements highly depend on the operating state and also the original topography of working pair. In our study wear experiments and surface roughness measurements before and after wear were performed. Investigations extended to wear in the course of the non-lubricated ceramic-steel, ferrodo-steel and bronze-steel material pairs. Fractal dimension of topographies before and after wear were calculated using power spectral density, height-difference correlation and scale-analysis methods. The aim of this study was to compare the capability of three different surface characterisation techniques through the analysis of worn surfaces and also to examine the changes of fractal character of topographies in wear.
Fractal Relation with Conventional Roughness Parameters for Surface Topography Generated in Grinding
2005
Surface roughness plays an important role in product quality and manufacturing process planning. Surface topography is generally characterized by statistical parameters such as centerline average (Ra), root mean square average (Rq), mean line peak spacing (Rsm) etc. Since surface topography is non-stationary and multi-scaled, these parameters are not sufficient to describe the characteristics of the surface. Fractal dimension, on the other hand, describes surface roughness invariant with length scale and fractals can be extremely useful when applied to tribology. Obtaining fractal descriptions of engineering surfaces requires surface topography information to be measured, digitized and processed. The present work describes the evaluation of the fractal dimensions of the surface profiles generated by grinding with different machining conditions such as work-piece speed, longitudinal feed and radial in-feed. The measured roughness parameters and fractal dimension are analyzed using AN...
Comparison of fractal and profilometric methods for surface topography characterization
Applied Surface Science, 2008
In this study microstructural and roughness characterization of surface of aluminium foils used in lithographic printing process was performed by contact and non-contact profilometric methods and fractal analysis. Significant differences in roughness parameters values inferred from stylus method in respect to those inferred from the non-contact measurements were observed. The investigation of correlation between various fractal dimensions obtained from gray-scale SEM micrographs and binary images resulting from median filtering of the original SEM micrographs as well as selected relevant roughness parameters shows that there is a strong correlation between certain roughness parameters and particular fractal dimensions. This correlations permit better physical understanding of fractal characteristics and interpretation of the dynamics of surface roughness change through processing. Generally these correlations are more suitable for parameters obtained by stylus method than those inferred from the laser-based measurements. #
Fractal models of surface topography and contact mechanics
Mathematical and Computer Modelling, 1998
In many tribological applications, some geometrical parameters defined in Euclidean space such as the developed area, surface bearing, void and material volume are very difficult to measure independently of the unit of measurement. The values of these parameters increase when the scale of measurement is decreased. Fractal geometry can be used as an adapted space for rough morphology in which roughness can be considered as a continuous but nondifferentiable function and dimension D of this space is an intrinsic parameter to characterize the surface topography. In the first part of this work, the fractal theory is used as a mathematical model for random surface topography, which can be used as input data in contact mechanics modeling. The result shows that the fractal model is realistic and the fractal dimension can be used as an indicator of the real values of different scale-dependent parameters such as length, surfaces, and volume of roughness. In the second part, we have analyzed through experiments, the contact between fractal random surfaces and a smooth plane, the experimental results show that the fractal dimension can be used as an invariant parameter to analyse the distribution law of the contact points area.
Applied Surface Science, 2014
An analysis of several methods of extraction of fractal parameters from the simulated, artificial surfaces and AFM images of the real, polycrystalline diamond films is presented in the paper. The methods involve: the cube count method, the roughness method, the autocorrelation function method, and the structure function method. By comparing the four methods, the roughness method is found to be superior for its high numerical accuracy, whereas the cube count method appears to be inferior in that aspect. The changes in the fractal dimension and the anisotropy ratio values observed over deposition time are also shown and discussed in the paper.
Fractal characterization by frequency analysis. I. Surfaces
Journal of Microscopy, 1993
A study of the quality and accuracy of the methods based on frequency analysis for the fractal characterization of surfaces as measured by scanning tunnelling microscopy (or profilometry) is made. The study is based on computer simulation of images of fractal surfaces. A discussion of the mathematical algorithms used for computer generation of fractal surfaces then follows. The main conclusion is that studies of fractal characterization by frequency analysis reported in previous papers in the STM field, as well as conclusions about the performance of the various methods, are doubtful. New methods for frequency analysis that in some cases produce more reliable results are proposed.