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.

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.

Stability-Optimized Clearance Configuration of Fluid-Film Bearings

2006 ◽  
Vol 129 (1) ◽  
pp. 106-111 ◽  
Author(s):  
Koichi Matsuda ◽  
Shinya Kijimoto ◽  
Yoichi Kanemitsu
Keyword(s):  
Fourier Series ◽  
Load Capacity ◽  
Fluid Film ◽  
Eccentricity Ratio ◽  
Rotating Speed ◽  
Fluid Film Bearings ◽  
Wide Range ◽  
Jeffcott Rotor ◽  
The Stability ◽  
Frequency Ratios

The whirl instability occurs at higher rotating speeds for a full circular fluid-film journal bearing, and many types of clearance configuration have been proposed to solve this instability problem. A clearance configuration of fluid-film journal bearings is optimized in a sense of enhancing the stability of the full circular bearing at high rotational speeds. A performance index is chosen as the sum of the squared whirl-frequency ratios over a wide range of eccentricity ratios, and a Fourier series is used to represent an arbitrary clearance configuration of fluid-film bearings. An optimization problem is then formulated to find the Fourier coefficients to minimize the index. The designed bearing has a clearance configuration similar to that of an offset two-lobe bearing for smaller length-to-diameter ratios. It is shown that the designed bearing cannot destabilize the Jeffcott rotor at any high rotating speed for a wide range of eccentricity ratio. The load capacity of the designed bearings is nearly in the same magnitude as that of the full circular bearing for smaller length-to-diameter ratios. The whirl-frequency ratios of the designed bearing are very sensitive to truncating higher terms of the Fourier series for some eccentricity ratio. The designed bearings successfully enhance the stability of a full circular bearing and are free from the whirl instability.

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.

Identification of Bearing Force Coefficients From Measurements of Imbalance Response of a Flexible Rotor

2004 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar C. De Santiago
Keyword(s):  
High Performance ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Simple Method ◽  
Force Coefficients ◽  
Fluid Film Bearings ◽  
Support Force ◽  
Bearing Force ◽  
Rotor Structure ◽  
Motion Amplitude

Field identification of fluid film bearing parameters is critical for adequate interpretation of rotating machinery performance and necessary to validate or calibrate predictions from restrictive computational fluid film bearing models. This paper presents a simple method for estimating bearing support force coefficients in flexible rotor-bearing systems. The method requires two independent tests with known mass imbalance distributions and the measurement of the rotor motion (amplitude and phase) at locations close to the supports. The procedure relies on the modeling of the rotor structure and finds the bearing transmitted forces as a function of observable quantities (rotor vibrations at bearing locations). Imbalance response measurements conducted with a two-disk flexible rotor supported on two-lobe fluid film bearings allow validation of the identification method estimations. Predicted (linearized) bearing force coefficients agree reasonably well with the parameters derived from the test data. The method advanced neither adds mathematical complexity nor requires additional instrumentation beyond that already available in most high performance turbomachinery.

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.

Stability Analysis of Mechanical Seals With Two Flexibly Mounted Rotors

1998 ◽  
Vol 120 (2) ◽  
pp. 145-151 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fluid Film ◽  
Mechanical Seals ◽  
Stability Threshold ◽  
Seal Design ◽  
The Stability ◽  
Gyroscopic Effects

Dynamic stability is investigated for a mechanical seal configuration in which both seal elements are flexibly mounted to independently rotating shafts. The analysis is applicable to systems with both counterrotating and corotating shafts. The fluid film effects are modeled using rotor dynamic coefficients, and the equations of motion are presented including the dynamic properties of the flexible support. A closed-form solution for the stability criteria is presented for the simplifled case in which the support damping is neglected. A method is presented for obtaining the stability threshold of the general case, including support damping. This method allows instant determination of the stability threshold for a fully-defined seal design. A parametric study of an example seal is presented to illustrate the method and to examine the effects of various parameters in the seal design upon the stability threshold. The fluid film properties in the example seal are shown to affect stability much more than the support properties. Rotors having the form of short disks are shown to benefit from gyroscopic effects which give them a larger range of stable operating speeds than long rotors. For seals with one long rotor, counterrotating operation is shown to be superior because the increased fluid stiffness transfers restoring moments from the short rotor to the long.

scholarly journals Simply structured controllers for vibration suppression in long rotors

2021 ◽  
Author(s):  
Majid Aleyaasin
Keyword(s):  
Closed Loop ◽  
Vibration Suppression ◽  
Coupling Effect ◽  
Dynamic Stiffness ◽  
Fast Response ◽  
Rotor System ◽  
Fluid Film ◽  
High Rate ◽  
Vibration Sensors ◽  
Fluid Film Bearings

AbstractIn this paper suppression of the transient flexural vibrational disturbances in long rotors, with fluid film bearings, is investigated. The rotor is described by a series of distributed shafts connected by the lumped discs, and the system is mounted on lumped fluid film bearings. Upon determination of the dynamic stiffness matrix of the system, the best approximate transfer function matrix description of the rotor, is determined. Initially vibration suppression by simple diagonal Proportional + Integral (PI) controllers is studied and via direct search optimisation techniques the PI parameters which exhibit fast vibration suppression is found. The resulted high integration rate, and low proportional gain PI controller, theoretically provided fast suppression time. However, it is shown that due to the strong coupling effect in the rotor system, and high rate of integration, the closed loop relative stability is weak, and feasibility of controller is questionable. Therefore, an alternative simple first order controller without integration action, that is named “attenuation filter “is suggested that can produce stronger stability and produces significant (not full) vibration suppression. The closed loop multivariable control of the rotor system comprising two vibration sensors and two magnetic actuators using such attenuation filter, is then simulated. The response to step disturbances, has provided 95% suppression with significantly fast response. It is concluded that although the attenuation filter may not provide 100% suppression, but it more reliable since the integration of the error, that results weak stability is avoided.

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