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.

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.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

Feasibility investigation of a compressor rotor supported by gas foil bearings with inhomogeneous bump foils

2021 ◽  
pp. 135065012110046
Author(s):  
Hao Li ◽  
Haipeng Geng ◽  
Bo Wang ◽  
Wei Zheng
Keyword(s):  
Critical Speed ◽  
Rotor System ◽  
Experimental Result ◽  
Test Results ◽  
Rotating Speed ◽  
Foil Bearings ◽  
Dynamic Coefficients ◽  
High Order Harmonic ◽  
Compressor Rotor ◽  
Operating Points

In this paper, a rotordynamic experiment on a compressor rotor system is presented and the feasibility of gas foil bearings with inhomogeneous bump foils is verified. A push–pull device is designed to obtain the stiffness curve and the nominal clearance of foil bearings. Operating points and dynamic coefficients of the rotor system at each rotating speed are predicted. In rotordynamic analysis, an alternative model of the impeller is proposed and the critical speed is predicted by employing the finite element method, in which the dynamic coefficients of inhomogeneous foil bearings are taken into account. Compared with the experimental result, the accuracy of the prediction for the critical speed is verified to be about 14% error. Two sets of foil bearings with 22 and 41 μm nominal clearance are manufactured and tested. Test results indicate that the vibration amplitude can be greatly reduced by diminishing the bearing clearance. When foil bearings with 22 μm clearance are used, the high-order harmonic frequencies of rotor vibration are significantly inhibited, and the amplitude of the rotating frequency is obviously restricted. Thus, the foil bearing with inhomogeneous bump foils tested in this paper can meet the speed requirement of the compressor when the nominal clearance is set at 22 μm.

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
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