Nonlinear Transient Analysis of Large Rotordynamic Systems

1991 ◽  
Vol 58 (2) ◽  
pp. 596-598 ◽  
Author(s):  
T. N. Shiau ◽  
A. N. Jean
Keyword(s):  
Degrees Of Freedom ◽  
Substantial Reduction ◽  
Computational Time ◽  
Solution Technique ◽  
Flexible Rotor ◽  
Nonlinear Characteristics ◽  
Rotor Systems ◽  
Nonlinear Transient ◽  
Nonlinear Components ◽  
Flexible Rotor Systems

A solution technique based on implicit numerical integration combined with a condensation technique is presented to predict the transient response of large flexible rotor systems with nonlinear characteristics. The analysis directly tackles the nonlinear second-order differential equations which describe the system motion. The condensation technique can lead to a reduced model in which only the coordinates associated with nonlinear components of the system are considered. Thus, a substantial reduction of computation can be expected if the nonlinear components of system are sparse. A flexible rotor system is studied to illustrate the merits of the procedures. The results show that, if the system is of a small number of coordinates associated with nonlinear components compared to that of entire system degrees-of-freedom, the computational time can be considerably reduced using this technique.

A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems

2017 ◽  
Author(s):  
Shibing Liu ◽  
Bingen Yang
Keyword(s):  
Optimization Problem ◽  
Optimization Method ◽  
Rotor System ◽  
Problem Solution ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Real Coded Genetic Algorithm ◽  
Minimum Number ◽  
Distributed Transfer Function ◽  
Flexible Rotor Systems

Flexible multistage rotor systems have a variety of engineering applications. Vibration optimization is important to the improvement of performance and reliability for this type of rotor systems. Filling a technical gap in the literature, this paper presents a virtual bearing method for optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. In the development, a distributed transfer function formulation is used to define the optimization problem. Solution of the optimization problem by a real-coded genetic algorithm yields the locations and dynamic coefficients of bearings, by which the prescribed operational requirements for the rotor system are satisfied. A numerical example shows that the proposed optimization method is efficient and accurate, and is useful in preliminary design of a new rotor system with the number of bearings unforeknown.

Prediction of Periodic Response of Flexible Mechanical Systems With Nonlinear Characteristics

1990 ◽  
Vol 112 (4) ◽  
pp. 501-507 ◽  
Author(s):  
Ting-Nung Shiau ◽  
An-Nan Jean
Keyword(s):  
Nonlinear Differential Equations ◽  
System Response ◽  
Algebraic Equations ◽  
Nonlinear Characteristics ◽  
Periodic Response ◽  
Rotor Systems ◽  
Nonlinear Algebraic Equations ◽  
Numerical Analytical Method ◽  
Harmonic Components ◽  
Nonlinear Components

A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotordynamic systems is addressed. Using this method, the set of nonlinear differential equations governing the motion of the rotor systems is transformed to a set of nonlinear algebraic equations. A condensation technique is proposed to reduce the nonlinear algebraic equations to those only related to the physical coordinates associated with nonlinear components. The method allows for the inclusion of searching for sub, super, ultra-sub and ultra-super harmonic components of the system response. Furthermore it can be used to locate limit cycles of an autonomous system. Three examples are employed to demonstrate the accuracy and the efficiency of the present method.

Imbalance Effects in Rotor Systems Under High Angular Accelerations

1994 ◽  
Author(s):  
R. D. Neilson ◽  
A. D. S. Barr ◽  
N. J. Blandford-Baker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Torsional Stiffness ◽  
Flexible Rotor ◽  
Disk System ◽  
Transient Vibration ◽  
Rotor Systems ◽  
Six Degrees Of Freedom ◽  
Transient Problems

To assess correctly the effects of transient vibration in a system with imbalance care is required in modelling the system. This is particularly true in cases of extreme imbalance e.g. a blade-off simulation in turbo-machinery. Generally, however, the imbalance is modelled as a simple mrΩ2 term applied when the blade is released but this does not include all possible terms. This paper presents the detailed equations of motion of a flexible rotor system with distributed imbalance. The equations are presented in a rotating coordinate system. The modelling includes coupling between the torsional, lateral and axial motions. A simpler model of a two disk system is then presented in fixed coordinates. The disks which can move laterally am connected by a massless shaft which has both lateral and torsional stiffness giving the system six degrees of freedom. An analysis is presented showing that the model is the same as the conventional model for steady state circular orbits. Results from a simplified blade-off simulation are then presented and compared to the standard mrΩ2 model. The conclusion drawn from these simulations is that the additional terms should be included for high angular acceleration transient problems.

Robust Optimization of Flexible Rotor Systems With Uncertain Parameters via Interval Analysis Method

2019 ◽  
Author(s):  
Jie Hong ◽  
ZheFu Yang ◽  
YaoYu Ni ◽  
YanHong Ma
Keyword(s):  
Interval Analysis ◽  
High Speed ◽  
Dynamic Performance ◽  
Practical Significance ◽  
Analysis Method ◽  
Flexible Rotor ◽  
Parameter Uncertainties ◽  
Rotor Systems ◽  
Interval Analysis Method ◽  
Flexible Rotor Systems

Abstract Uncertainties in the input parameters are inevitable in any design process. Along with the demands for higher rotational speed and higher efficiency of rotating machinery, parameter uncertainties (e.g. support stiffness, the effective bending stiffness of connecting structures) resulted from the increasing load on rotor systems lead to significant scatter of its dynamic performance. These parameters are “uncertain but bounded” which means the distributions are unknown, but the intervals are always got easier. This paper presents a method to robustly optimize the dynamic performance of flexible rotor systems taking into account parameter uncertainties via interval analysis method. Interval analysis methods for modal properties and dynamic response behavior of rotor systems are developed with the interval variables introduced into the equation of motion. The aim of the robust design method is to optimize the critical speed margins and dynamic load on bearings, in the meanwhile, minimizing the variability of the objective items by the means of reducing their sensitivity to parameter uncertainties. A numerical example is presented, results show that, for the high-speed flexible rotor systems, the optimal choices of design variables could reduce of sensitivity to rotor parameter uncertainties, thus optimizing the variability of dynamic performance, which has important practical significance in engineering.

Dynamic Behavior and Stability of a Rotor Under Base Excitation

2006 ◽  
Vol 128 (5) ◽  
pp. 576-585 ◽  
Author(s):  
M. Duchemin ◽  
A. Berlioz ◽  
G. Ferraris
Keyword(s):  
Dynamic Behavior ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Base Excitation ◽  
Flexible Rotor ◽  
Lagrange Equations ◽  
Rotor Systems ◽  
Simple Systems ◽  
Flexible Rotor Systems

The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.

Vibration Suppression of Rotating Shafts Passing Through Resonances by Switching Shaft Stiffness

1998 ◽  
Vol 120 (1) ◽  
pp. 170-180 ◽  
Author(s):  
J. Wauer ◽  
S. Suherman
Keyword(s):  
Vibration Suppression ◽  
Transient Behavior ◽  
Flexible Rotor ◽  
Nonstationary System ◽  
Rotor Systems ◽  
The Past ◽  
Limited Power ◽  
Rotating Shafts ◽  
Phase Angles ◽  
Flexible Rotor Systems

A method suggested in the past to suppress the vibrations of flexible rotor systems passing through critical speeds is reconsidered. An appropriate switching of the system stiffness (by using shape memory alloys, for instance) is utilized. To model the nonstationary system behavior more realistically, the rotor is driven by a limited power supply. A special feature is the inclusion of unequal bending stiffnesses of the shaft. The stationary and transient behavior of the motor and system characteristic and the deformation amplitudes and phase angles, are examined. Attention is focussed on the strategy for switching the stiffness to yield small resonance deflections.

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