• Title, Summary, Keyword: Fractal

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Morphological Analysis of Wear Particles using Fractal Parameters

  • Cho, Y.S.;Park, H.S.
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • pp.457-458
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    • 2002
  • The fractal dimension is the characteristics that can quantitatively define the irregularity in natural. It is useful in describing the morphology or various rubbed surface for hydraulic piston motor instead of the stylus profiling method. But fractal parameters had not constructed on the morphological characteristic or rubbed surface because of the insufficient knowledge about a conception of fractal dimension. In this study, for the purpose or applying fractal I parameters practically, we have suggested way to establish the morphological characteristic of rubbed surface with fractal parameters, and we carried out an experiment on the lubricant friction and wear by using Ball-ON-Disk type tester. Materials were the brass and the bronze which are used to slipper-pad in the hydraulic piston motor. We searched for fractal parameters or surface structure with the digital image processing, Surface fractal dimension can be determined by sum of intensity difference of surface pixel. Using the image processing and fractal parameters for rubbed surface in the friction and wear test, morphology of rubbed sur race can be effectively obtained by fractal dimensions.

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A Fundamental Study of Fractal Characteristics for a Crack Growth Profile (성장균열 형상에 대한 기초적 프랙탈 특성연구)

  • 권오헌
    • Journal of the Korean Society of Marine Engineering
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    • v.22 no.4
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    • pp.522-528
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    • 1998
  • This paper presents a fundamental fractal characteristics of the growing crack that has an irregularity producing a zigzag crack contour. This irregularity is analysed by a fractal geometry in a box counting method that is a very simple technique. First the fractal dimensions and actual fractal extensive crack length are obtained. Also a fractal fracture energy relation with a fractal dimension is found so as to get fractal crack behaviors. Thus it can be shown that the fractal dimension has a possibility as a fracture parameter in a real crack growth length meaning.

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Application of Fractal Geometry on the Static Growing Crack of STS316 CT Specimen with a Side Groove (측면 홈을 가지는 STS316 CT시험편의 정적 성장균열에 대한 프랙탈 기하학의 응용)

  • Yun, Yu-Seong;Kwon, Oh-Heon
    • Journal of the Korean Society of Safety
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    • v.17 no.4
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    • pp.38-44
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    • 2002
  • The application of fractal concept provides an useful method in the study for the quantitative analysis of irregular variations like the fracture surfaces and crack profiles. Fractal curves have characteristics that represents a self-similarity based on the fractal dimension. The fractal dimensions were obtained by the box counting method. In this report, we obtained the nearly stable fractal dimensions of fracture crack profiles for STS316 with CT specimen as the crack advances and the relationships between crack length and fractal dimension. Moreover fractal fracture parameter that corresponds to J-R curve is shown by the relationships between fractal dimension and crack extension. From the results, we concluded that crack extension of high toughness material also shows the fractal characteristics, which can be used in order to evaluate the crack life precisely.

Crack Growth Behaviors of Cement Composites by Fractal Analysis

  • Won, Jong-Pil;Kim, Sung-Ae
    • KCI Concrete Journal
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    • v.14 no.1
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    • pp.30-35
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    • 2002
  • The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

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Application of Fractal Geometry to Architectural Design

  • Lee, Myung-Sik
    • Architectural research
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    • v.16 no.4
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    • pp.175-183
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    • 2014
  • Contemporary architecture tends to deconstruct modern architecture based on rationalization just like reductionism and functionalism and secedes from it. It means change from mechanical to organic and ecological view of the world. According to these changes, consideration of a compositive relationship presented variety and complexity in architecture. Thus, the modern speculation based on rationalism cannot provide an alternative interpretation about complicated architectural phenomena. At this point in time, the purpose of this study is to investigate the possibilities of the fractal as an alternative tool of analysis and design in contemporary architecture. In this study, two major aspects are discussed. First, the fractal concepts just like 'fractal dimension', 'box-counting dimension' and 'fractal rhythm' can be applied to analysis in architecture. Second, the fractal formative principles just like 'scaling', 'superimposition trace', 'distortion' and 'repetition' can be applied to design in architecture. Fractal geometry similar to nature's patterned order can provide endless possibilities for analysis and design in architecture. Therefore further study of fractal geometry should be conducted synthetically from now on.

FRACTAL HEDGEHOGS

  • Rani, Mamta;Kumar, Vinod
    • The Pure and Applied Mathematics
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    • v.9 no.2
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    • pp.91-105
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    • 2002
  • The study of fractal hedgehogs is a recent development in the ambit of fractal theory and nonlinear analysis. The intent of this paper is to present a study of fractal hedgehogs along with some of their special constructions. The main result is a new fractal hedgehog theorem. As a consequence, a fractal projective hedgehog theorem of Martinez-Maure is obtained as a special case, and several fractal hedgehogs and similar images are discussed.

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Fractal Characteristic Analysis Applied to Fracture Parameter (프랙탈 특성 해석의 파괴역학적 적용)

  • 권오헌;구동희
    • Journal of the Korean Society of Safety
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    • v.13 no.4
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    • pp.71-78
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    • 1998
  • Real crack and fracture surfaces have irregularities producing zigzag contours. These irregularities are analysed by a fractal geometry which has been by a Mandelbrot. We obtained a fractal dimension which is one of the fractal characteristics. It is also estimated by an vertical section method that fractal characteristics in the fractured surfaces can be obtained as the crack grows. Moreover fractal fracture energy that corresponds to an energy release rate is shown to find relationships between fractal dimensions and crack behaviors. From these results, we concluded that a fractal characteristics analysis for a crack can be applied to a fracture mechanics.

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Statistical Characteristics of Fractal Dimension in Turbulent Prefixed Flame (난류 예혼합 화염에서의 프랙탈 차원의 통계적 특성)

  • Lee, Dae-Hun;Gwon, Se-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.1
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    • pp.18-26
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    • 2002
  • With the introduction of Fractal notation, various fields of engineering adopted fractal notation to express characteristics of geometry involved and one of the most frequently applied areas was turbulence. With research on turbulence regarding the surface as fractal geometry, attempts to analyze turbulent premised flame as fractal geometry also attracted attention as a tool for modeling, for the flame surface can be viewed as fractal geometry. Experiments focused on disclosure of flame characteristics by measuring fractal parameters were done by researchers. But robust principle or theory can't be extracted. Only reported modeling efforts using fractal dimension is flame speed model by Gouldin. This model gives good predictions of flame speed in unstrained case but not in highly strained flame condition. In this research, approaches regarding fractal dimension of flame as one representative value is pointed out as a reason for the absence of robust model. And as an extort to establish robust modeling, Presents methods treating fractal dimension as statistical variable. From this approach flame characteristics reported by experiments such as Da effect on flame structure can be seen quantitatively and shows possibility of flame modeling using fractal parameters with statistical method. From this result more quantitative model can be derived.

Application of Fractal Parameter for Morphological Analysis of Wear Particle (마멸입자 형상분석을 위한 프랙탈 파라미터의 적용)

  • 조연상;류미라;김동호;박흥식
    • Tribology and Lubricants
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    • v.18 no.2
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    • pp.147-152
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    • 2002
  • The morphological analysis of wear particle is a very effective means fur machine condition monitoring and fault diagnosis. In order to describe morphology of various wear particle, the wear test was carried out under friction experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing. These descriptors to analyze shape and surface of wear particle are shape fractal dimension and surface fractal dimension. The boundary fractal dimension can be derived from the boundary profile and surface fractal dimension can be determined by sum of intensity difference of surface pixel. The morphology of wear particles can be effectively obtained by two fractal parameter.

End-milling Force Estimation by Fractal Interpolation (프랙탈 보간에 의한 엔드밀링 절삭력 예측)

  • Jeong, Jin-Seok;Chin, Do-Hun;Yoon, Moon-Chul
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.5 no.1
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    • pp.7-12
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    • 2006
  • Recently, the fractal interpolation methods have been widely introduced and used to estimate and analyze various theoretical and experimental data. Because of the chaotic behaviors of dynamic cutting force data, some method for end-milling force analysis must be used. The fractal analysis used in this paper is fractal linear interpolation and fractal dimension. Also, several methods for computing fractal dimensions have been used in which the fractal dimension of the typical dynamic end-milling force was calculated according to number of data points that are generally lower than 200 data points sampled. This fractal analysis shows a possible prediction of end-milling force that has some dynamic chatter property or stationary property in endmilling operation.

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