Combination resonances of a dual-rotor system with inter-shaft bearing

This paper focuses on the combination resonances of a dual-rotor system with inter-shaft bearing. The motion equations of the dual-rotor system are formulated by the Lagrange equation, in which the unbalanced excitations of the two rotors and the clearance of the inter-shaft bearing are taken into consideration. The HB-AFT method (harmonic balance-alternating frequency/time domain method) is employed to obtain all the periodic solutions including the unstable solutions of the system. The combination resonance characteristics of the system are analyzed in detail by using the frequency response curves and separated frequency responses of the dual-rotor system. Besides the two primary resonance peaks, three more combination resonance regions in the frequency response curves of the system are found, in which the jump and bi-stable phenomena are observed. The primary resonance is mainly dominated by the excitation frequency ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega_{1}$$\end{document} and ω2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega_{2}$$\end{document}, the combination resonance of the system is mainly dominated by the combined frequency component of 2ω2-ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\omega_{2} - \omega_{1}$$\end{document}, 4ω2-3ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\omega_{2} - 3\omega_{1}$$\end{document}, 3ω2-2ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\omega_{2} - 2\omega_{1}$$\end{document} and is almost independent of other frequency components. Furthermore, the effect of inter-shaft bearing clearance on the combination resonance regions is obtained, it is indicated that increasing the inter-shaft bearing clearance will not only affect the response amplitudes of the combination resonance and change the “softening and hardening characteristic” of the frequency response curves, but also show a certain “stiffness weakening effect” on the rotor system. The study in this paper is of great significance to select the parameters of the dual-rotor system reasonably so as to avoid harmful combination resonance.