Abstract
This paper focuses on the stability and nonlinear response of a bearing-rotor system affected by a transverse crack and initial bending which was thought to be part of an unbalance or had been neglected before. The differences of breathing functions for the transverse breathing crack caused by initial bending is presented here, and the calculation of time-varying finite elements stiffness matrix of the cracked shaft is improved by replacing traditional the approximate crack segment with an exact area. After establishing the dynamic model of the cracked rotor with initial bending, vibrational characteristics such as amplitude-speed diagram, frequency spectrogram and bifurcations are investigated in detail. The eigenvalues of the transition matrix are calculated and analyzed as an indicator of dynamic stability with the growths of crack depth and initial bending. Many differences are found between the two cases of dynamic response of rotor system by numerical simulation. The frequency change with the growth of initial bending is opposite to the change with the growth of crack depth, and the shapes of amplitude-speed also having great different features. Stable regions are reduced and extended laterally by initial bending. All these results obtained in this paper will contribute to identify the bending fault and assess the stability of the bearing-rotor systems.
Highlights
It has been proven to have an important influence on the dynamic response of rotor systems, and more alternating stresses acting on the shaft may increase the probability of unpredicted crack or rubbing faults [3,4]
Numerical simulation is Machines 2021, 9, 79 difference from previous studies is that the initial bending and mass imbalance are separated in dynamic modeling and state transition of the crack
The change of the moment of inertia of the of the closed comparing theportion dynamic characteristics between the results calculated by the improved the position of neutral axis encased the initial bending are calculated and closed portion and theand position of neutral axis encased by theby initial bending are calcumodel with initial bending and former model, many differences can be found and used discussed in detail
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Accurate breathing functions and dynamical responses of cracked rotors with initial bending are presented here. Numerical simulation is Machines 2021, 9, 79 difference from previous studies is that the initial bending and mass imbalance are separated in dynamic modeling and state transition of the crack. The crack state is usually determined by the angle difference between rotation and whirl calculated as ∆φ = Ωt − φr or ∆φ = Ωt − φs − φ, where Ωt is the rotation angle of the shaft This difference in the current literature is due to the displacement of rotating shaft which can be obtained only after establishing the complete dynamic model of a rotor system. Another point that should be noted is that the rotating speed has an important crackon angle is delay other parameters beeffect found
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