Open AccessThe Methodology of Distinguish Between Random and Chaotic Machine Tool Oscillations
Author(s) -
Sanel Gredelj
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1208/1/012009
Subject(s) - correlation dimension , lyapunov exponent , chaotic , statistical physics , aperiodic graph , mathematics , entropy (arrow of time) , fractal dimension , nonlinear system , correlation integral , dimension (graph theory) , chaos theory , computer science , fractal , artificial intelligence , correlation , mathematical analysis , physics , quantum mechanics , pure mathematics , geometry , combinatorics
Machine tool oscillations are irregular or aperiodic. Most often, these oscillations are chaotic but, in some cases, they can be quasi-periodic or random. The methodology for characterizing oscillations in the first of two steps uses the nonparametric hypothesis tests which the observed oscillations confirmed as irregular. The methodology for the final characterization of oscillations is based on chaos quantifiers. A time series defined as the measured values of oscillations in the time domain is the basis for calculating the quantifiers of chaos. There are four quantifiers of chaos: the Lyapunov exponent, Kolmogorov entropy, fractal dimension and correlation dimension. The correlation dimension and Kolmogorov entropy are important for distinguishing between random and chaotic oscillations. Other quantifiers of chaos are not used for this purpose. The methodology requires a multidisciplinary approach based on combining Nonlinear Dynamics and Probability Theory and Statistics. The methodology can be applied to many oscillating phenomena. Therefore, the paper mainly used the term oscillations, not vibrations, chatter, etc.