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Title:A new method for estimating the Hurst exponent H for 3D objects
Authors:ID Babič, Matej (Author)
ID Kokol, Peter (Author)
ID Guid, Nikola (Author)
ID Panjan, Peter (Author)
ID Inštitut za kovinske materiale in tehnologije (Copyright holder)
Files:.pdf Materiali_in_Tehnologije_2014_Babic_et_al._a_New_Method_for_Estimating_the_Hurst_Exponent_H_for_3D_Objects.pdf (468,97 KB)
MD5: C53078CBAFAD01C4EC55097647221D06
 
URL http://mit.imt.si/Revija/izvodi/mit142/babic.pdf
 
Language:English
Work type:Scientific work
Typology:1.01 - Original Scientific Article
Organization:FERI - Faculty of Electrical Engineering and Computer Science
Abstract:Mathematics and computer science are very useful in many other sciences. We use a mathematical method, fractal geometry, in engineering, specifically in laser techniques. Characterization of the surface and the interfacial morphology of robot-laser-hardened material is crucial to understand its properties. The surface microstructure of robot-laser-hardened material is rough. We aimed to estimate its surface roughness using the Hurst parameter H, which is directly related to the fractal dimension. We researched how the parameters of the robot-laser cell impact on the surface roughness of the hardened specimen. The Hurst exponent is understood as the correlation between the random steps X1 and X2, which are followed by time for the time difference t. In our research we understood the Hurst exponent H to be the correlation between the random steps X1 and X2, which are followed by the space for the space difference d. We also have a space component. We made test patterns of a standard label on the point robot-laser-hardened materials of DIN standard GGG 60, GGG 60 L, GGG 70, GGG 70 L and 1.7225. We wanted to know how the temperature of point robot-laser hardening impacts on the surface roughness. We developed a new method to estimate the Hurst exponent H of a 3D-object. This method we use to calculate the fractal dimension of a 3D-object with the equation D = 3 - H.
Keywords:fractal structure, Hurst exponent, robot, hardening, laser
Publication status:Published
Publication version:Version of Record
Year of publishing:2014
Number of pages:str. 203-208
Numbering:Letn. 48, št. 2
PID:20.500.12556/DKUM-65165 New window
ISSN:1580-2949
UDC:620.1/.2
ISSN on article:1580-2949
COBISS.SI-ID:78019329 New window
NUK URN:URN:SI:UM:DK:6Q9PCGVW
Publication date in DKUM:14.03.2017
Views:1685
Downloads:159
Metadata:XML DC-XML DC-RDF
Categories:Misc.
:
BABIČ, Matej, KOKOL, Peter, GUID, Nikola and PANJAN, Peter, 2014, A new method for estimating the Hurst exponent H for 3D objects. Materiali in tehnologije [online]. 2014. Vol. 48, no. 2, p. 203–208. [Accessed 20 January 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=65165
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Record is a part of a journal

Title:Materiali in tehnologije
Shortened title:Mater. tehnol.
Publisher:Inštitut za kovinske materiale in tehnologije
ISSN:1580-2949
COBISS.SI-ID:106193664 New window

Secondary language

Language:Slovenian
Title:Nova metoda za ocenjevanje Hurstovega eksponenta H za 3D-objekte
Abstract:Matematika in računalništvo sta zelo uporabni veji drugih vrst znanosti. Uporabili bomo matematično metodo - fraktalno geometrijo - v inženirstvu, natančneje, v laserski tehniki. Karakterizacija površine in morfologija robotsko lasersko kaljenih materialov ima ključni pomen za razumevanje lastnosti materialov. Površina robotsko lasersko kaljenega materiala je hrapava. To hrapavost pa bi radi ocenili s Hurstovim eksponentom H, ki ga dobimo direktno iz fraktalne geometrije, kot meritev hrapavosti površine. Raziskali smo, kako parameter robotske celice vpliva na hrapavost kaljenih vzorcev. Hurstov eksponent H razumemo kot korelacijo med korakoma X1 in X2, ki ga dobimo med časovno razliko t. V naši raziskavi razumemo Hurstov eksponent H kot relacijo med korakoma X1 in X2, ki ga dobimo med prostorsko komponento. Osredinili smo se na točkovno robotsko lasersko kaljenje vzorcev standardne oznake po DIN-standardu GGG 60, GGG 60 L, GGG 70, GGG 70 L in 1.7225. Želeli smo izvedeti, kako temperatura točkovnega robotskega laserskega kaljenja vpliva na hrapavost površine. Razvili smo novo metodo za ocenjevanje Hurstovega eksponenta H za 3D-objekte. To metodo smo uporabili za računanje fraktalne dimenzije 3D-objektov po formuli D = 3 - H.
Keywords:obdelava materiala, fraktalna struktura, Hurstov eksponent, robot, laser, kaljenje


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