Acta Mechanica Slovaca 2016, 20(3):30-36 | DOI: 10.21496/ams.2016.021

Comparison of Different Methods for Estimating Fractal Dimension with the Method of Statistics

Matej Babič

Jožef Stefan Institute

This paper presents three methods for calculating the fractal dimension and its application in Mechanical Engineering. The microstructure of hardened specimens is very complex and we cannot describe it with classical Euclidian geometry. Thus we use a new method, fractal geometry. We present the method of box-counting, homeomorphic model and the R/S method to calculate fractal dimensions. We compare how these three different methods have an impact on the mechanical properties of robot laser hardened specimens. We use the statistical method of multiple regression to describe the percentage of black pixels of SEM images of robot laser hardened specimens. Robot laser hardening is a technology of heat treatment process. Today, technologists who operate various CNC machines only have a knowledge based on practical experience. Each technologist must consider numerous CNC machine parameters to obtain the desired results. Because this is a very time-consuming process, we used a statistical method, which allows us to obtain results more quickly. Heat treatment is known as a quicker way to access information according to the desired specifications. It was necessary to use a statistical method based on individual samples to disclose the percentage of black pixels of SEM images of robot laser hardened specimens. With this statistical method, we increase the production of the process of laser hardening, because we decrease the time of the process and increase the topographical properties of materials.

Keywords: Statistics, fractal dimension, hardening, multiple regression

Published: October 31, 2016  Show citation