Stability of High Speed Rotors With Internal Friction

1974 ◽  
Vol 96 (3) ◽  
pp. 960-968 ◽  
Author(s):  
J. M. Vance ◽  
J. Lee
Keyword(s):  
Internal Friction ◽  
Differential Equations ◽  
Numerical Solution ◽  
High Speed ◽  
Critical Speed ◽  
Rotating Machinery ◽  
Rigid Foundation ◽  
Flexible Rotor ◽  
Mathematical Methods ◽  
The Stability

The problem of nonsynchronous whirl induced by internal friction is shown to be important when rotating machinery is designed for operation at supercritical speeds. Mathematical methods are used to determine the stability speed threshold of nonsyncronous whirl instability for an unbalanced flexible rotor on a rigid foundation. This threshold of instability is shown to be the same as the threshold for balanced rotors established by previous investigations. The location of the external damping (foundation or rotor) is shown to be important in determining stability when the foundation is made very rigid. The effect of shaft stiffness orthotropy on nonsynchronous whirl induced by internal friction is also investigated. Results from the stability analyses are verified by numerical solution of the differential equations. It is concluded that rotors can be safely operated up to speeds about eighty percent above the significant critical speed if the external damping is larger than the internal friction, and that shaft stiffness orthotropy has an insignificant effect on friction-induced whirl.

Internal Rotor Friction Induced Instability in High-Speed Rotating Machinery

1993 ◽  
Author(s):  
James F. Walton ◽  
Michael R. Martin
Keyword(s):  
Internal Friction ◽  
Natural Frequency ◽  
High Speed ◽  
Critical Speed ◽  
Rotating Machinery ◽  
Rotor System ◽  
Analytical Models ◽  
Interference Fit ◽  
Internal Rotor

Abstract Results of a program to investigate internal rotor friction destabilizing effects are presented. Internal-friction-producing joints were shown to excite the rotor system first natural frequency, when operating either below or above the first critical speed. The analytical models used to predict the subsynchronous instability were also confirmed. The axial spline joint demonstrated the most severe subsynchronous instability. The interference fit joint also caused subsynchronous vibrations at the first natural frequency but these were bounded and generally smaller than the synchronous vibrations. Comparison of data from the two test joints showed that supersynchronous vibration amplitudes at the first natural frequency were generally larger for the interference fit joint than for the axial spline joint. The effects of changes in imbalance levels and side loads were not distinguishable during testing because amplitude-limiting bumpers were required to restrict orbits.

STABILITY OF STOCHASTIC SYSTEMS WITH MEMORY

2005 ◽  
Vol 05 (02) ◽  
pp. 223-232 ◽  
Author(s):  
V. D. POTAPOV
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Stochastic Systems ◽  
Wide Band ◽  
Statistical Simulation ◽  
Statistical Moments ◽  
Fading Memory ◽  
The Stability ◽  
Systems With Memory ◽  
With Memory

Many processes in physics, biology, ecology, mechanics etc. can be modeled by Volterra integro-differential equations (VIDEs) with "fading memory". Often the behaviour of corresponding systems is perturbed by random noises. One of the main problems for the theory of stochastic Volterra integro-differential equations (SVIDEs) is connected with their stability. The present paper is devoted to the numerical solution of the stability problem for linear SVIDEs. The method is based on the statistical simulation of input random wide-band stationary processes, which are assumed in the form of "colored" noises. For each realization the numerical solution of VIDEs is found. The conclusion about the stability of the considered system SVIDE with respect to statistical moments is made on the basis of Liapunov exponents, which are calculated for statistical moments of the solution.

The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

High-Speed Rotor Suspension Formed by Fully Floating Hydrodynamic Radial and Thrust Bearings

1964 ◽  
Vol 86 (2) ◽  
pp. 149-160 ◽  
Author(s):  
Juraj Dworski
Keyword(s):  
Gas Turbine ◽  
High Speed ◽  
Critical Speed ◽  
Vibrational Excitation ◽  
Turbine Rotor ◽  
Continuous Operation ◽  
Flexible Rotor ◽  
Actual System ◽  
Apparent Absence ◽  
Thrust Bearings

The hydrodynamic suspension of a 44,000-rpm gas turbine rotor is described with emphasis on interaction between the flexible rotor and its supports. Bearings with relatively large clearances are shown to allow continuous operation at the rotor first critical-speed of 22,000 rpm. The apparent absence of hydrodynamic system instabilities is attributed to the use of simple floating-sleeve bearings. A parametric study of the influence of bearing clearances upon vibrational excitation relief is presented together with test data collected on actual system hardware.

Optimization Design and Experimental Study of a Two-disk Rotor System Based on Multi-Island Genetic Algorithm

2019 ◽  
Vol 36 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Jingjing Huang ◽  
Longxi Zheng ◽  
Chris K Mechefske ◽  
Bingbing Han
Keyword(s):  
Genetic Algorithm ◽  
Vibration Amplitude ◽  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Optimization Method ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimum Position ◽  
Transient Experiments

Abstract Based on rotor dynamics theory, a two-disk flexible rotor system representing an aero-engine with freely supported structure was established with commercial software ANSYS. The physical model of the two-disk rotor system was then integrated to the multidisciplinary design optimization software ISIGHT and the maximum vibration amplitudes experienced by the two disks when crossing the first critical speed were optimized using a multi-island genetic algorithm (MIGA). The optimization objective was to minimize the vibration amplitudes of the two disks when crossing the first critical speed. The position of disk 1 was selected as the optimization variable. The optimum position of disk 1 was obtained at the specified constraint that the variation of the first critical speed could not exceed the range of ±10 %. In order to validate the performance of the optimization design, the proof-of-transient experiments were conducted based on a high-speed flexible two-disk rotor system. Experimental results indicated that the maximum vibration amplitude of disk 1 when crossing the first critical speed declined by 60.9 % and the maximum vibration amplitude of disk 2 fell by 63.48 % after optimization. The optimization method found the optimum rotor positions of the flexible rotor system which resulted in minimum vibration amplitudes.

The Dynamic Analysis of SFD-Sliding Bearing Flexible Rotor System Based on Optimization Design

2012 ◽  
Vol 159 ◽  
pp. 355-360
Author(s):  
Ji Yan Wang ◽  
Rong Chun Guo ◽  
Xu Fei Si
Keyword(s):  
High Speed ◽  
Optimization Design ◽  
Critical Speed ◽  
Structural Parameters ◽  
Rotor System ◽  
Flexible Rotor ◽  
Optimization Analysis ◽  
Sliding Bearing ◽  
Critical Speeds ◽  
Design Variables

The paper establishes the mechanical model of SFD-sliding bearing flexible rotor system, adopting Runge-Kutta method to solve nonlinear differential equation, thus acquiring the unbalanced response curve and then gaining the first two critical speeds of the system. Meanwhile, the paper analyzes the sensitivity of the system on the first two critical speeds towards structural parameters, offering design variables to optimization analysis. Based on sensitivity analysis, genetic algorithm is employed to give an optimization analysis on critical speed, which aims to remove critical speed from working speed as much as possible. The critical speed ameliorates after the optimization which supplies theoretical basis as well as theoretical analysis towards the dynamic stability of high-speed rotor system and provides reference for the design of such rotor system.

Stability of Flexible Rotors With a LeBlanc Balancer

2011 ◽  
Author(s):  
Leonardo Urbiola-Soto ◽  
Marcelo Lopez-Parra
Keyword(s):  
High Speed ◽  
Particle Image ◽  
Flexible Rotor ◽  
Rotating System ◽  
Stability Behavior ◽  
Piv Technique ◽  
Flexible Rotors ◽  
Image Velocimetry ◽  
The Stability ◽  
Stability Limits

Although the liquid balancer has nearly a century of having been introduced by LeBlanc, little information is available on the dynamic response and stability behavior of this kind of device. Earlier author’s research using a high-speed camera and a Particle Image Velocimetry (PIV) technique showed the existence of a fluid backward traveling wave inside the balancer cavity. This damping phenomenon helps enhance the unbalance response of the rotating system and also raises the stability limits. This paper shows that a flexible rotor employing a LeBlanc balancer has remarkable increase in the threshold speed of instability for aerodynamic cross-coupling and viscous internal friction damping.

Numerical Analysis for the Stability of Cylinder Gas Film Seal

2013 ◽  
Vol 655-657 ◽  
pp. 526-530
Author(s):  
Gang Ma ◽  
Jun He ◽  
Xin Min Shen
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Reynolds Equation ◽  
Working Condition ◽  
Critical Mass ◽  
System Stability ◽  
Dynamics Analysis ◽  
Rotor Speed ◽  
Analysis Model ◽  
The Stability

Non-contacting gas film seal applies to the high speed working condition and a numerical method was presented for analyzing the effect of speed on the stability of cylinder gas film seal. The dynamics analysis model was established, solving the time-dependent Reynolds equation coupling with the dynamic equations. Through numerical simulation, the critical speed of cylinder gas film seal system and the diagram of critical mass versus rotor speed were obtained. The influence of the speed on dynamic stability was studied. The results show that the system stability becomes worse as rotor speed increases.

scholarly journals A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 806
Author(s):  
Ali Shokri ◽  
Beny Neta ◽  
Mohammad Mehdizadeh Khalsaraei ◽  
Mohammad Mehdi Rashidi ◽  
Hamid Mohammad-Sedighi
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Stability Property ◽  
Stability Region ◽  
Mathieu Equation ◽  
Variable Coefficients ◽  
Second Order ◽  
Implicit Schemes ◽  
The Stability

In this paper, a symmetric eight-step predictor method (explicit) of 10th order is presented for the numerical integration of IVPs of second-order ordinary differential equations. This scheme has variable coefficients and can be used as a predictor stage for other implicit schemes. First, we showed the singular P-stability property of the new method, both algebraically and by plotting the stability region. Then, having applied it to well-known problems like Mathieu equation, we showed the advantage of the proposed method in terms of efficiency and consistency over other methods with the same order.

scholarly journals MATHEMATICAL MODELLING OF PROBLEM ON NON-LINEAR FLUTTER OF VISCO-ELASTIC SHELLS

2014 ◽  
pp. 94-98
Author(s):  
Bakhtiyar Khudayarov
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Viscoelastic Property ◽  
Critical Speed ◽  
Galerkin Methods ◽  
Basic Direction ◽  
Viscoelastic Cylindrical Shell ◽  
Current Value

In this work is investigated the flutter of viscoelastic cylindrical shell streamlined by gas current. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integra-differential equations in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary Integro-Differential Equations (IDE). The IDE are solved by numerical method, which based on using of quadrature formula. The algorithm of the numerical solution on the basis of the method was described. Critical speeds for cylindrical shell flutter are defined. The influence of the viscoelastic property of the material, geometrical and aerodynamically non-linearity to the current value of critical speed and amplitude-frequency characteristics of the cylindrical shells was analyzed.

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