Analysis of subharmonic and quasi-periodic vibrations of a Jeffcott rotor supported on a squeeze-film damper by the IHB method

• Published in: AIP advances 2022-05, Vol.12 (5), p.055328-055328-16
• Main Authors: Ri, Kwangchol, Jang, Junhyok, Yun, Cholil, Pak, Choljun, Kim, Kwangchol
• Format: Article
• Language: English
• Subjects: Bifurcation theory; Broken symmetry; Fourier transforms; Frequency domain analysis; Hopf bifurcation; Jacobi matrix method; Jacobian matrix; Mathematical analysis; Rotors; Runge-Kutta method; Stability analysis; Static eccentricity
• ISSN: 2158-3226; 2158-3226
• DOI: 10.1063/5.0088334

In rotors supported on a squeeze-film damper (SFD) with static eccentricity, subharmonic and quasi-periodic vibrations are generated by rotor unbalance. In this paper, subharmonic and quasi-periodic vibrations in a Jeffcott rotor supported on an SFD are analyzed using the modified incremental harmonic balance (IHB) method. Oil film forces in the damper are calculated using π film theory and short bearing approximation. These forces are first calculated in the time domain and then transformed into the frequency domain by Fourier transformation. The oil film forces in the frequency domain are multiplied by a transformation matrix to match the matrices used in the classical IHB method. To apply the continuation technique, the Jacobian matrix of residuals is calculated analytically. The stability analysis of the calculated solutions is analyzed using Floquet theory. Using this theory, saddle-node, symmetry breaking, period-doubling, and secondary Hopf bifurcations are detected. The phase plane, Poincaré sections, and time history at these bifurcation points are calculated using the Runge–Kutta method.