Stability analysis of a whirling rigid rotor supported by stationary grooved FDBs considering the five degrees of freedom of a general rotor-bearing system

This paper proposes a method to determine the stability of a whirling rotor supported by stationary grooved fluid dynamic bearings (FDBs), considering the five degrees of freedom of a general rotor-bearing system. Dynamic coefficients are calculated by using the finite element method and the perturbation method, and they are represented as periodic harmonic functions. Because of the periodic time-varying dynamic coefficients, the equations of motion of the rotor supported by FDBs can be represented as a parametrically excited system. The solution of the equations of motion can be assumed to be a Fourier series, allowing the equations of motion to be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Hill’s infinite determinant is calculated by using these algebraic equations to determine the stability. Increasing rotational speed increases Kxx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{xx}$$\end{document} and Kθxθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{{\theta_{x} \theta_{x} }}$$\end{document}, which decreases the stability of the stationary grooved FDBs; increasing whirl radius increases the stability of the FDBs because the resulting increases in the averages and variations of Cxx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{xx}$$\end{document} and Cθxθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{{\theta_{x} \theta_{x} }}$$\end{document} increase the stability faster than the corresponding increases of Kxx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{xx}$$\end{document} and Kθxθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{{\theta_{x} \theta_{x} }}$$\end{document} decrease the stability. The proposed method was verified by investigating the convergence and divergence of the whirl radius after the equations of motion were solved using the fourth-order Runge–Kutta method.