Nonstationary Oscillation of a Rotating Shaft With Nonlinear Spring Characteristics During Acceleration Through a Major Critical Speed (A Discussion by the Asymptotic Method and the Complex-FFT Method)

Abstract

Nonstationary oscillations during acceleration through a major critical speed of a rotating shaft with nonlinear spring characteristics are discussed. First, the first approximate solutions of steady-state and nonstationary oscillations are obtained by the asymptotic method. Second, the amplitude variation curves of each oscillation component are obtained by the complex-FFT method. It is clarified that the first approximation of the asymptotic method has comparatively large quantitative error in the case of nonstationary solutions. In addition, the influences of each nonlinear component in polar coordinate expression on nonstationary oscillations are investigated.

A computational investigation on the reducing lateral vibration of rotors with rolling-element bearings passing through critical speeds by means of tuning the stiffness of the system supports

“…The reason is that these equations are expressed in different reference frames, e.g. after performing the transformation from non-orthogonal to the orthogonal coordinate system in [10] or after the backward transformation from the reference frame coupled to the middle plane of the disc to the fixed coordinate system in [11] the equations of motion take the same form as derived in this article or published in [5][6][7]. After performing the missing transformations all moment equations of motion take the identical form independent on the method used for their derivation.…”

“…Then the terms of inertia moment for rotor spin motion would occur in both moment equations. Such equations of a flexibly supported disc performing a spherical movement with variable speed are used in [6][7][8][9]. The system has two degrees of freedom and therefore its vibration is governed by two equations.…”

A Full Spectrum Analysis Methodology Applied to an Anisotropic Overhung Rotor

“…Since the shaft is considered to be isotropic, the matrix is identical for the xz and the yz plane [6,13].…”

“…In addition, the asymmetry of the bearing stiffness will bring more complication to a rotor system. Even though there are many established publications about how to theoretically model an overhung rotor with anisotropic bearings [1][2][3][4][5][6], very few papers compared the theoretical models with experimental results. Ishida al etc.…”

“…Ishida al etc. [6] derived a sophisticated mathematical model to theoretically investigate the nonstationary vibration of a flexible rotor with nonlinear spring parameters during acceleration. They employed an asymptotic method to compute the first approximate solution to vibration response.…”