Нелинейные колебания ротора на радиально-упорных шарикоподшипниках при совместном действии дисбаланса и вибрации опор
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Дата
2015
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
НТУ "ХПИ"
Анотація
Получена модель нелинейных колебаний ротора на радиально-упорных шарикоподшипниках с предварительным осевым поджатием. Методом продолжения по параметру получена амплитудно-частотная характеристика системы при совместном действии дисбаланса и вибрации опор. Анализ показал, что колебания возникают не только на основных резонансных частотах, но и на частотах меньше резонансных в целое число раз. Исследованы неустойчивые режимы и характер бифуркаций периодических решений.
The model of nonlinear vibrations of rotor supported by axial preload angular ball-bearings was developed. The aim of this paper is research of nonlinear vibrations of rotor caused by the joint action of disbalance and vibration of supports. The amplitude-frequency characteristic of the system is obtained by the continuation method. Refining of decisions is executed on every step by the Newton iteration method. The amplitude-frequency characteristic for each resonance is soft. The analysis of periodic decisions showed that resonant mode of vibrations arose up not only on fundamental resonant frequencies but also on frequencies less of the resonant one in an integer times. The unsteady modes and character of bifurcations of periodic solution were investigated. The time dependences of phase coordinates and Poincaré maps are generated on these modes. There are saddle-node bifurcations on the left of the resonances. The oscillating movement becomes chaotic at these points. There are bifurcations of two-dimensional torus on the right of the resonances. There are beats at these points.
The model of nonlinear vibrations of rotor supported by axial preload angular ball-bearings was developed. The aim of this paper is research of nonlinear vibrations of rotor caused by the joint action of disbalance and vibration of supports. The amplitude-frequency characteristic of the system is obtained by the continuation method. Refining of decisions is executed on every step by the Newton iteration method. The amplitude-frequency characteristic for each resonance is soft. The analysis of periodic decisions showed that resonant mode of vibrations arose up not only on fundamental resonant frequencies but also on frequencies less of the resonant one in an integer times. The unsteady modes and character of bifurcations of periodic solution were investigated. The time dependences of phase coordinates and Poincaré maps are generated on these modes. There are saddle-node bifurcations on the left of the resonances. The oscillating movement becomes chaotic at these points. There are bifurcations of two-dimensional torus on the right of the resonances. There are beats at these points.
Опис
Ключові слова
резонанс, бифуркация, амплитуда, вибровозбуждение, resonance, bifurcation
Бібліографічний опис
Филипковский С. В. Нелинейные колебания ротора на радиально-упорных шарикоподшипниках при совместном действии дисбаланса и вибрации опор / С. В. Филипковский // Вестник Нац. техн. ун-та "ХПИ" : сб. науч. тр. Темат. вып. : Динамика и прочность машин. – Харьков : НТУ "ХПИ". – 2015. – № 55 (1164). – С. 54-58.