Stability Analysis on a Crack Rotor System in the Special Speeds

2013 ◽  
Vol 675 ◽  
pp. 116-120 ◽  
Author(s):  
Feng Lan Wang
Keyword(s):  
Experimental Study ◽  
Stability Analysis ◽  
Theoretical Analysis ◽  
Stability Problem ◽  
Critical Speed ◽  
Transverse Crack ◽  
Crack Depth ◽  
Rotor System ◽  
Single Disk ◽  
The Stability

In this paper, the single disk rotor system with a transverse open and close crack has been taken as an example; the stability problem on the system in the special speeds has been discussed by theoretical analysis and experimental study. First, the conditions, positions and areas of the stable vibrations and the unstable vibrations on a rotor system with a transverse crack have been studied quantitatively theoretically. Not only the conclusions of other authors are verified，but also that the unstable vibrations are found in the regions near the rotational speed at 2/5and 2/7 of the critical speed in the large crack and the small damping case. Then the influence of some factors such as the crack depth parameters and the damping on stability of the system is qualitatively discussed.

Theoretical Analysis and Experimental Model Study on Stability of a Crack Rotor System

2013 ◽  
Vol 328 ◽  
pp. 651-656 ◽  
Author(s):  
Feng Lan Wang
Keyword(s):  
Theoretical Analysis ◽  
Experimental Model ◽  
Critical Speed ◽  
Transverse Crack ◽  
Crack Depth ◽  
Rotor System ◽  
Model Study ◽  
Single Disk ◽  
The Stability ◽  
Opening And Closing

In this paper, the single disk rotor system with a transverse open and close crack has been taken as an example; square wave function has been adopted to express opening and closing characteristics of a transverse crack. The stability on the system has been discussed by theoretical analysis and experimental model study. The conclusions have shown that the unstable vibrations are found in the regions near the rotational speed at 2/3, 2/5and 2/7 of the critical speed in the large crack and the small damping case. The influence of some factors such as the crack depth and the damping on stability of the system is qualitatively discussed.

scholarly journals Experimental Study on the Nonlinear Vibrations and n× Amplitudes of a Rotor With a Transverse Crack

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Jean-Jacques Sinou
Keyword(s):  
Experimental Study ◽  
Theoretical Analysis ◽  
Monitoring System ◽  
Nonlinear Response ◽  
Transverse Crack ◽  
Nonlinear Vibrations ◽  
Rotor System ◽  
Experimental Results ◽  
Frequency Components ◽  
On Line

In this paper, the nonlinear response of a rotor system containing a transverse crack is analyzed experimentally in order to propose a nondestructive detection of cracks in the rotor. More particularly, the evolutions of the n× superharmonic frequency components at the various subcritical resonant peaks and the decrease in the subcritical resonant speeds are investigated for various crack depths. The experimental results that are presented in this study confirm the theoretical analysis of many researchers and provide a possible basis for an on-line monitoring system.

scholarly journals Dynamic Stability Analysis of Periodically Time-Varying Rotor System with a Transverse Crack

Engineering ◽  
2011 ◽  
Vol 03 (07) ◽  
pp. 719-725 ◽  
Author(s):  
Costin D. Untaroiu ◽  
Alexandrina Untaroiu ◽  
Mihail Boiangiu
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Transverse Crack ◽  
Rotor System ◽  
Time Varying

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.

Three-dimensional stability analysis for slurry-filled trench wall in cohesionless soil

1996 ◽  
Vol 33 (5) ◽  
pp. 798-808 ◽  
Author(s):  
Jiin-Song Tsai ◽  
Jia-Chyi Chang
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Slip Surface ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Soil Mass ◽  
Cohesionless Soil ◽  
Cohesionless Soils ◽  
Slurry Trench ◽  
The Stability

On the basis of the limiting equilibrium and arching theory, a three-dimensional analysis is proposed for slurry-supported trenches in cohesionless soils. This analytical approach is developed by considering the trench stability problem as a vertical soil cut within a fictitious half-silo with a rough wall surronding. Arching effects are considered not only in the vertical direction but also in the horizontal direction. A shell-shaped slip surface of the sliding soil mass is defined by Mohr-Coulomb criterion. The factor of safety is defines as the ratio of the resisting force induced by slurry pressure to the horizontal force required to maintain the stability of the trench wall. Results of the proposed method have been compared with those of two existing analytical methods for a typical trench stability problem. Key words: stability analysis, slurry trench wall, cohesionless soil.

scholarly journals Stability Problem of Wave Variable Based Bilateral Control: Influence of the Force Source Design

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Dapeng Tian ◽  
Bao Zhang ◽  
Honghai Shen ◽  
Jiaquan Li
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Time Delay ◽  
Robust Stability ◽  
Scattering Theory ◽  
Stability Problem ◽  
Bilateral Control ◽  
Wave Variable ◽  
Small Gain ◽  
The Stability

The wave variable has been proposed to achieve robust stability against the time delay in bilateral control system. However, the influence of the force source on the overall system is still not clear. This paper analyzes this problem and proposes a supplement to the stability analysis for wave variable based bilateral control. Based on the scattering theory, it is pointed out that the design of force source decides the passivity of the two-port network of slave robot. This passivity influences the stability of overall system. Based on the characteristic equation and small gain theorem, it is clear that inappropriate designed force source in encoding the wave variable destroys the stability in the presence of time delay. A wave domain filter makes up for the broken stability. The principle of this reparation is explained in this paper. A reference is also provided by the analysis to design the parameter of the wave domain filter. Experiments prove the correctness and validity.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

Experimental Verification of Critical Speed Ranges for Elastic Closed Loop Linkage Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 126-130 ◽  
Author(s):  
S. Nagarajan ◽  
D. A. Turcic
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Critical Speed ◽  
Closed Loop ◽  
Local Maximum ◽  
Experimental Methods ◽  
Strain Response ◽  
Maximum Value ◽  
Speed Range ◽  
The Stability

In this work critical speed ranges are determined and verified for an elastic four bar crank rocker mechanism where all links are modeled as elastic members. The procedure used for the dynamic stability analysis is described in Nagarajan and Turcic (1991). The speed range of interest where the stability analysis is performed is 195–390 rpm. The values of the critical speeds obtained in the above speed range are then verified using independent theoretical and experimental methods of analysis. The steady state strain response is obtained both theoretically and experimentally for a number of speeds in the speed range of 195–390 rpm. From these responses plots different strain characteristics versus operating speeds are obtained. These plots exhibit peaks in the response at certain speeds indicating that the dynamic response at these speeds reaches a local maximum value. The critical speed ranges determined are found to correspond quite closely to the speeds where the peaks occur. This indicates that the critical speed ranges are indeed speeds where the response of the system is larger when compared to neighboring speeds and that the methods of determining them are accurate for the application considered.

An experimental study of Couette instability of stratified fluids

1974 ◽  
Vol 66 (4) ◽  
pp. 725-737 ◽  
Author(s):  
E. M. Withjack ◽  
C. F. Chen
Keyword(s):  
Experimental Study ◽  
Critical Speed ◽  
Outer Cylinder ◽  
Spiral Wave ◽  
Angular Speed ◽  
Wave Form ◽  
Salt Solutions ◽  
Taylor Vortices ◽  
Critical Wavelength ◽  
The Stability

The stability of Couette flow of stratified salt solutions is investigated in an apparatus with both the inner and outer cylinders rotating. The ratio of the radius of the inner cylinder to that of the outer cylinder is 0·2. The flow is visualized by means of shadowgraph and dye-trace methods. Compared with homogeneous fluids, the effect of the stabilizing density gradient is to increase the critical speed of the inner cylinder and to decrease the critical wavelength for a given angular speed of the outer cylinder. When the cylinders are rotating in the same direction, in the critical state, the instabilities appear along the inner cylinder in a spiral wave form which is itself not very stable. With counterrotating cylinders, the instabilities appear as regularly spaced vortices which, for the most part, are neither symmetric Taylor vortices nor simple spirals. In addition, these vortices rotate as a whole at a speed generally smaller than that of the inner cylinder. From shadowgraph observations, stability curves are constructed for three density gradients. The critical wavelength and the rotational periods of the vortices are also determined.

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.

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