On the Unstable Vibrations of a Shaft Carrying an Unsymmetrical Rotor

1964 ◽  
Vol 31 (3) ◽  
pp. 515-522 ◽  
Author(s):  
Toshio Yamamoto ◽  
Hiroshi O¯ta
Keyword(s):  
Natural Frequencies ◽  
Rotating Shaft ◽  
Unstable Region ◽  
Critical Speeds ◽  
Rotating Speed ◽  
Lateral Vibrations ◽  
Shaft System

In a rotating shaft system carrying an unsymmetrical rotor, there is always one unstable region in the neighborhood of the rotating speed at which the sum of two natural frequencies of the system is equal to twice the rotating speed of the shaft. In this unstable region two unstable lateral vibrations with frequencies P1 and P2 take place simultaneously and grow up steadily. Generally, frequencies P1 and P2 are not equal to the rotating speed ω of the shaft and the sum of these P1 + P2 is always equal to 2ω. Of course there are other unstable regions which appear at the major critical speeds.

On the Unstable Vibrations of a Shaft With Unsymmetrical Stiffness Carrying an Unsymmetrical Rotor

1968 ◽  
Vol 35 (2) ◽  
pp. 313-321 ◽  
Author(s):  
T. Yamamoto ◽  
H. O¯ta ◽  
K. Ko¯no
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
Relative Orientation ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Damping Coefficients ◽  
Shaft System ◽  
Analytical Results ◽  
Negative Damping ◽  
The Asymmetry

In a rotating shaft system carrying an unsymmetrical rotor, or in a rotating shaft system with inequality in stiffness, there are unstable regions in the neighborhood of both the major critical speed ωc and the rotating speed ωd at which the sum of two natural frequencies of the system is equal to twice the rotating speed of the shaft. The unstable vibrations appearing in these unstable regions are treated for the system consisting of a rotor with unsymmetrical inertia and a shaft with unequal stiffness which rotates with the rotor. Simultaneous effects of the unsymmetrical rotor and the unsymmetrical shaft are appreciated and quantitative analytical results are obtained which relate the width of the unstable regions and the negative damping coefficients of the unstable vibrations to the asymmetry in inertia, the inequality in stiffness, and the relative orientation between the inequalities in inertia and stiffness. Furthermore, elimination of two kinds of unstable regions is realized theoretically and experimentally.

The Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

1975 ◽  
Vol 97 (3) ◽  
pp. 881-886 ◽  
Author(s):  
D. R. Chivens ◽  
H. D. Nelson
Keyword(s):  
Natural Frequencies ◽  
Numerical Solutions ◽  
Geometric Model ◽  
Analytical Investigation ◽  
Rotating Shaft ◽  
Disk System ◽  
Critical Speeds ◽  
Transverse Bending ◽  
Wide Range ◽  
Dimensional Parameters

An analytical investigation into the influence of disk flexibility on the transverse bending natural frequencies and critical speeds of a rotating shaft-disk system is presented. The geometric model considered consists of a flexible continuous shaft carrying a flexible continuous circular plate. The partial differential equations governing the system motion and the associated exact solution form are developed. Numerical solutions are presented covering a wide range of non-dimensional parameters and general conclusions are drawn.

Analysis of the rub-impact forces between a controlled nonlinear rotating shaft system and the electromagnet pole legs

2021 ◽  
Vol 93 ◽  
pp. 792-810
Author(s):  
N.A. Saeed ◽  
Emad Mahrous Awwad ◽  
Mohammed A. EL-meligy ◽  
Emad Abouel Nasr
Keyword(s):  
Rotating Shaft ◽  
Shaft System ◽  
Impact Forces

Vibration of Flexibly Mounted Gyroscopes

1973 ◽  
Vol 15 (3) ◽  
pp. 225-231
Author(s):  
L. Maunder
Keyword(s):  
Natural Frequencies ◽  
Critical Speeds ◽  
Supporting Structure ◽  
Vibrational Characteristics

Flexibility in the supporting structure of two-axis or single-axis gyroscopes is shown to have a radical effect on vibrational characteristics. The analysis determines the ensuing natural frequencies and critical speeds.

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