Periodic, Quasi-Periodic, and Chaotic Motions to Diagnose a Crack on a Horizontally Supported Nonlinear Rotor System

Symmetry

Mohamed S. Mohamed¹  S. K. Elagan¹  N. A. Saeed² 

[1] Department of Mathematics and Statistics, College of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia;Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt;

关键词: transverse crack;    crack diagnosis;    quasi-periodic motion;    chaotic motion;    frequency spectrum;    torus bifurcation;   

DOI  :  10.3390/sym12122059

来源: DOAJ

【 摘 要 】

This work aims to diagnose the crack size of a nonlinear rotating shaft system based on the qualitative change of the system oscillatory characteristics. The considered system is modeled as a two-degree-of-freedom horizontally supported nonlinear Jeffcott rotor system. The influence of the crack size on the system whirling motion for the primary, superharmonic, and subharmonic resonance cases are investigated utilizing the bifurcation diagram, Poincaré map, frequency spectrum, and whirling orbit. The obtained numerical results revealed that the cracked system whirling motion is subjected to a continuous qualitative change as the crack size increases for the superharmonic resonance case, where the system can exhibit period-1, period-2, quasi-periodic, period-3, period-doubling, chaotic, and period-2 motions, sequentially. In addition, an asymmetry is observed in the system whirling orbit due to both the shaft weight and shaft crack. Moreover, it is found that the disk eccentricity does not affect the nature of these motions. Accordingly, we illustrated a simple method to diagnose the existence of such a crack and to quantify its size via monitoring the system lateral vibrations at the superharmonic resonance. Finally, all the obtained numerical results are concluded and a comparison with already published work is included.

【 授权许可】

Unknown