Nonlinear Analysis of Bifurcation Phenomenon for a Simple Flexible Rotor System Supported by a Full-Circular Journal Bearing

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Tatsuya Miura ◽  
Tsuyoshi Inoue ◽  
Hiroshi Kano
Keyword(s):  
Normal Form ◽  
Dynamical Equation ◽  
Journal Bearing ◽  
Stability Limit ◽  
Rotor System ◽  
Flexible Rotor ◽  
Normal Form Theory ◽  
Bifurcation Phenomenon ◽  
The Stability ◽  
Manifold Theory

This paper demonstrates nonlinear theoretical analysis of a flexible rotor system supported by a full-circular journal bearing focusing on the bifurcation phenomenon in the vicinity of the stability limit (bifurcation point). A third-order polynomial approximation model is used for the representation of the oil film force of the journal bearing. The reduced-order model, with modes concerning the bifurcation, is deduced using the center manifold theory. The dynamical equation in the normal form relating the bifurcation which leads to the oil whirl is obtained using the normal form theory. The influences of various parameters are investigated based on the analysis of a deduced dynamical equation in the normal form. Furthermore, the validity of the derived analytical observation is confirmed by comparing it with the numerically obtained frequency response result.

Nonlinear Simulation Analysis and Experiment of Fluid Plain Journal Bearing With Incompressible Fluid

2003 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Koji Yoshioka ◽  
Kouhei Okuno ◽  
Hiroaki Tanaka ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Journal Bearing ◽  
Simulation Analysis ◽  
Journal Bearings ◽  
Stable Region ◽  
Flexible Rotor ◽  
Nonlinear Simulation ◽  
Fluid Forces ◽  
The Stability

Recently, in many areas such as computers and information equipments etc., the fluid journal bearings are required to rotate at higher speed. To satisfy this requirement, the strictly stability analysis of the journal is indispensable. In this paper, we investigate the stability analysis of the dynamic behavior of the fluid plain journal bearing with an incompressible fluid considering the nonlinear terms of fluid forces. The stability analysis is examined by the numerical simulations on each model of a rigid rotor and a flexible rotor. The stable regions by nonlinear analysis are compared with the regions by classical linear analysis. Performing the nonlinear simulation analysis, it becomes clear that there is rather a stable region which amplitude does not grow up abruptly, and this phenomenon can not only be pointed out, but also is judged to be unstable by linear stable analysis. Finally, the experiment using actual bearings is performed and compared with the numerical results.

On an Independent Period-1 Motion in a Flexible Rotor System

2019 ◽  
Author(s):  
Yeyin Xu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Internal Resonance ◽  
Mapping Method ◽  
Rotor System ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Phase Trajectories ◽  
Stability And Bifurcation ◽  
The Stability ◽  
Nonlinear Rotor System

Abstract This paper investigates stable and unstable period-1 motions in a rotor system through the discrete mapping method. The discrete mapping of a nonlinear rotor system is for stable and unstable period-1 motions. The stability and bifurcation of periodic motions are determined. Numerical simulations of periodic motions are completed and phase trajectories, displacement orbits and velocity plane are illustrated. The period-1 motion near the internal resonance is determined with large vibration in the nonlinear rotor system.

Stability and Bifurcation of Nonlinear Bearing-Flexible Rotor System with a Single Disk

2010 ◽  
Vol 148-149 ◽  
pp. 141-146
Author(s):  
Di Hei ◽  
Yong Fang Zhang ◽  
Mei Ru Zheng ◽  
Liang Jia ◽  
Yan Jun Lu
Keyword(s):  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Rotor System ◽  
Dynamic Responses ◽  
Flexible Rotor ◽  
Runge Kutta Method ◽  
Stability And Bifurcation ◽  
Single Disk ◽  
The Stability ◽  
Predictor Corrector

Dynamic model and equation of a nonlinear flexible rotor-bearing system are established based on rotor dynamics. A local iteration method consisting of improved Wilson-θ method, predictor-corrector mechanism and Newton-Raphson method is proposed to calculate nonlinear dynamic responses. By the proposed method, the iterations are only executed on nonlinear degrees of freedom. The proposed method has higher efficiency than Runge-Kutta method, so the proposed method improves calculation efficiency and saves computing cost greatly. Taking the system parameter ‘s’ of flexible rotor as the control parameter, nonlinear dynamic responses of rotor system are obtained by the proposed method. The stability and bifurcation type of periodic responses are determined by Floquet theory and a Poincaré map. The numerical results reveal periodic, quasi-periodic, period-5, jump solutions of rich and complex nonlinear behaviors of the system.

An Experimental Investigation on the Response of a Flexible Rotor Mounted in Pressure Dam Bearings

1980 ◽  
Vol 102 (4) ◽  
pp. 842-850 ◽  
Author(s):  
R. D. Flack ◽  
M. E. Leader ◽  
E. J. Gunter
Keyword(s):  
Experimental Investigation ◽  
Rotor System ◽  
Flexible Rotor ◽  
The Stability

The response of a flexible rotor mounted in six bearing sets has been experimentally determined. One set of axial groove bearings and five sets of pressure dam bearings were tested. Conventional synchronous tracking was used in the analysis and other techniques utilizing an FFT analyzer were developed. The stability of the system was seen to strongly depend on the design of the step bearings. The dam bearings were also noted to lock into subsynchronous whip during deceleration after the system went unstable. The response of the system with varying degrees of unbalance is also analyzed and several structural resonances of the rotor system are discussed.

Chaos and bifurcation analysis of a flexible rotor supported by short journal bearings with non-linear suspension

2000 ◽  
Vol 214 (7) ◽  
pp. 931-947 ◽  
Author(s):  
H-T Yau ◽  
C-K Chen ◽  
C-L Chen
Keyword(s):  
Chaotic Motion ◽  
Power Spectra ◽  
Rotor System ◽  
Numerical Results ◽  
Operating Conditions ◽  
Flexible Rotor ◽  
Bifurcation And Chaos ◽  
Symmetric Motion ◽  
Bifurcation Phenomenon ◽  
Non Linear

The bifurcation and chaos of the unbalanced response of a bearing-rotor system with non-linear suspension are investigated on the basis of the assumption of an incompressible lubricant together with short bearing approximation. Numerical results show that, owing to the non-linear factors, the trajectory of the journal centre demonstrates steady state symmetric motion even when the trajectory of the bearing centre is in a state of disorder. Poincaré maps, bifurcation diagrams and power spectra are used to analyse the behaviour of the bearing centre in the horizontal and vertical directions under different operating conditions. A unidirectional bifurcation phenomenon is detected in the bearing-rotor system in this study. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. Numerical results show that the dimension of the bearing centre trajectory is fractal and greater than 2 in some operating conditions. This indicates that the bearing centre is in the state of chaotic motion at these operating conditions.

The Lower Bound of the Stability Threshold Speed of a Flexible Rotor System in Fluid-Film Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 351-353
Author(s):  
Wen Zhang
Keyword(s):  
Lower Bound ◽  
Theoretical Foundation ◽  
Simple Approach ◽  
Rotor System ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Stability Threshold ◽  
Fluid Film Bearings ◽  
Single Disk ◽  
The Stability

The paper is devoted to the estimation of the lower bound of the stability threshold speed (STS) of a flexible rotor system supported in fluid-film bearings. It is proved theoretically that the STS of any multi-degree-of-freedom flexible rotor system is always higher than the STS of the corresponding equivalent single disk rotor. The conclusion offers us a simple approach to estimate the STS of any actual rotor system and provides a theoretical foundation for the approach.

Rotordynamic Impact of Swirl Brakes on Labyrinth Seals With Smooth or Honeycomb Stators

1997 ◽  
Author(s):  
K. Kwanka
Keyword(s):  
Stability Limit ◽  
Labyrinth Seal ◽  
Flexible Rotor ◽  
Labyrinth Seals ◽  
Identification Procedure ◽  
Continuous Growth ◽  
Rotating Speed ◽  
Dynamic Coefficients ◽  
Flow Through ◽  
The Stability

The flow through labyrinth seals of turbomachinery generates forces which can cause self-excited vibrations of the rotor above the stability limit. The stability limit is reached at a specific rotating speed or power. The continuous growth in of power density and rotating speed necessitates an exact prediction of the stability limit of turbomachinery. Usually the seal forces are described with dynamic coefficients. A new, easy-to-handle identification procedure uses the stability behavior of a flexible rotor to determine the dynamic coefficients. Systematic measurements with a great number of labyrinth seal geometries lead to reasonable results and demonstrate the accuracy and sensitivity of the procedure. A comparison of the various methods used to minimize the excitation indicates which seal is more stable and will thus improve the dynamic behavior of the rotor.

Improving the Stability of Labyrinth Gas Seals

1997 ◽  
Vol 123 (2) ◽  
pp. 383-387 ◽  
Author(s):  
K. Kwanka
Keyword(s):  
Stability Limit ◽  
Labyrinth Seal ◽  
Flexible Rotor ◽  
Labyrinth Seals ◽  
Continuous Growth ◽  
Rotating Speed ◽  
Dynamic Coefficients ◽  
Flow Through ◽  
Gas Seals ◽  
The Stability

The flow through labyrinth seals of turbomachinery generates forces which can cause self-excited vibrations of the rotor above the stability limit. The stability limit is reached at a specific rotating speed or power. The continuous growth of power density and rotating speed necessitates an exact prediction of the stability limit of turbomachinery. Usually the seal forces are described with dynamic coefficients. A new, easy-to-handle identification procedure uses the stability behavior of a flexible rotor to determine the dynamic coefficients. Systematic measurements with a great number of labyrinth seal geometries lead to reasonable results and demonstrate the accuracy and sensitivity of the procedure. A comparison of the various methods used to minimize the excitation indicates which seal is more stable and will thus improve the dynamic behavior of the rotor.

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