A Numerical Approach to the Stability of Rotor-Bearing Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 356-363 ◽  
Author(s):  
K. Athre ◽  
J. Kurian ◽  
K. N. Gupta ◽  
R. D. Garg
Keyword(s):  
Eigenvalue Problem ◽  
Characteristic Polynomial ◽  
Eigenvalue Problems ◽  
Numerical Technique ◽  
Numerical Approach ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems ◽  
Rotor Bearing ◽  
The Stability ◽  
Bearing System

The stability characteristics of a rotor-bearing system which indicate the threshold of instability are generally obtained by applying the Routh-Hurwitz criterion to the characteristic polynomial. Usually the characteristic polynomial is obtained analytically from the characteristic determinant. In the case of the generalized eigenvalue problems, this is practically impossible. To study the stability characteristics of a floating bush bearing, the characteristic polynomial is constructed from the generalized eigenvalue problem using a recently developed numerical technique. Results obtained through this computer package are compared with those already available in the literature.

Filtering Algorithm for Real Eigenvalue Bounds of Interval and Fuzzy Generalized Eigenvalue Problems

2016 ◽  
Vol 2 (4) ◽  
Author(s):  
Nisha Rani Mahato ◽  
S. Chakraverty
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Triangular Fuzzy Number ◽  
Generalized Eigenvalue Problem ◽  
Real Eigenvalue ◽  
Eigenvalue Bounds ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems ◽  
Precise Bound ◽  
Fuzzy Parameter

This paper deals with an interval and fuzzy generalized eigenvalue problem involving uncertain parameters. Based on a sufficient regularity condition for intervals, an interval filtering eigenvalue procedure for generalized eigenvalue problems with interval parameters is proposed, which iteratively eliminates the parts that do not contain an eigenvalue and thus reduces the initial eigenvalue bound to a precise bound. The same iterative procedure has been proposed for generalized fuzzy eigenvalue problems. In general, the solution of dynamic problems of structures using the finite element method (FEM) leads to a generalized eigenvalue problem. Based on the proposed procedures, various structural examples with an interval and fuzzy parameter such as triangular fuzzy number (TFN) are investigated to show the efficiency of the algorithms stated. Finally, fuzzy filtered eigenvalue bounds are depicted by fuzzy plots using the α-cut.

scholarly journals Analytical and Experimental Investigation of the Stability of the Rotor-Bearing System of a New Small Turbocharger

1987 ◽  
Author(s):  
H. R. Born
Keyword(s):  
Experimental Investigation ◽  
Dynamic Stability ◽  
Squeeze Film ◽  
Test Results ◽  
Flow Capacity ◽  
Squeeze Film Dampers ◽  
Rotor Bearing ◽  
The Stability ◽  
Turbine Design ◽  
Bearing System

This paper presents an overview of the development of a reliable bearing system for a new line of small turbochargers where the bearing system has to be compatible with a new compressor and turbine design. The first part demonstrates how the increased weight of the turbine, due to a 40 % increase in flow capacity, influences the dynamic stability of the rotor-bearing system. The second part shows how stability can be improved by optimizing important floating ring parameters and by applying different bearing designs, such as profiled bore bearings supported on squeeze film dampers. Test results and stability analyses are included as well as the criteria which led to the decision to choose a squeeze film backed symmetrical 3-lobe bearing for this new turbocharger design.

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

scholarly journals Dynamic Characteristics and Experimental Research of a Two-Span Rotor-Bearing System with Rub-Impact Fault

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Rui Zhu ◽  
Guang-chao Wang ◽  
Qing-peng Han ◽  
An-lei Zhao ◽  
Jian-xing Ren ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Critical Speed ◽  
Great Influence ◽  
Experimental Platform ◽  
Rotating Machine ◽  
Rotor Bearing ◽  
Before And After ◽  
Analysis System ◽  
The Stability ◽  
Bearing System

Rotor rub-impact has a great influence on the stability and safety of a rotating machine. This study develops a dynamic model of a two-span rotor-bearing system with rubbing faults, and numerical simulation is carried out. Moreover, frictional screws are used to simulate a rubbing state by establishing a set of experimental devices that can simulate rotor-stator friction in the rotor system. Through the experimental platform and its analysis system, the rubbing experiment was conducted, and the vibration of the rotor-bearing system before and after the critical speed is observed. Rotors running under normal condition, local slight rubbing, and severe rubbing throughout the entire cycle are simulated. Dynamic trajectories, frequency spectrum diagrams, chart of axis track, and Poincare maps are used to analyze the features of the rotor-bearing system with rub-impact faults under various parameters. The vibration characteristics of rub impact are obtained. Results show that the dynamic characteristics of the rotor-bearing system are affected by the change in velocity and degree of impact friction. The findings are helpful in further understanding the dynamic characteristics of the rub-impact fault of the two-span rotor-bearing system and provide reference for fault diagnosis.

scholarly journals Research on Periodic Motion Stability of Rotor-Bearing System with Dual-Unbalances

2011 ◽  
Vol 2-3 ◽  
pp. 728-732
Author(s):  
Chao Feng Li ◽  
Guang Chao Liu ◽  
Qin Liang Li ◽  
Bang Chun Wen
Keyword(s):  
Stability Analysis ◽  
Phase Difference ◽  
Periodic Motion ◽  
Initial Phase ◽  
Shooting Method ◽  
Small Eccentricity ◽  
Rotor Bearing ◽  
Large Eccentricity ◽  
The Stability ◽  
Bearing System

Multiple freedom degrees model of rotor-bearing system taking many factors into account is established, the Newmark-β and shooting method are combined during the stability analysis of periodic motion in such system. The paper focused on the influence law of two eccentric phase difference on the instability speed of rotor-bearing system. The results have shown that the instability speed rises constantly with the eccentric phase difference angle increasing in small eccentricity system. When the two unbalance be in opposite direction, the system reached its maximum instability speed. However, the unstable bifurcation generates mutation phenomenon for large eccentricity system with the eccentric phase difference angle increasing. In summary, the larger initial phase angle can inhibit system instability partly. The conclusions have provided a theoretical reference for vibration control and stability design of the more complex rotor-bearing system.

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