Dynamics and stability analysis of a flexible liquid-filled rotor in a constant thermal environment

2021 ◽  
pp. 107754632110224
Author(s):  
Guangding Wang ◽  
Wenjun Yang ◽  
Huiqun Yuan
Keyword(s):  
Thermal Environment ◽  
Rotor System ◽  
Flexible Rotor ◽  
Rotatory Inertia ◽  
Rayleigh Beam ◽  
Comparison Results ◽  
The Stability ◽  
Spinning Speed ◽  
Thermoelastic Theory ◽  
Good Agreement

In this study, the dynamics and stability of a flexible rotor containing liquid in a constant thermal environment are investigated. According to thermoelastic theory, the thermal axial force exerted on the rotor is calculated by using the analytical method. A spinning Rayleigh beam is used as a simplified model of the rotor. Applying the Hamilton principle, the governing equation of motion for the flexible liquid-filled rotor system is derived. Using the obtained model, the stability prediction model and the critical spinning speed for the rotor system are formulated. To demonstrate the validity of the developed model, the present analysis is compared with the results reported in the previous study, and good agreement is observed from the comparison results. Finally, numerical results based on the obtained model are performed for a better understanding of the parameters including filling parameters, mode number, rotatory inertia and thermal effect on the stability, and critical spinning speed of the rotor system.

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.

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.

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.

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.

Nonlinear Analysis of Bifurcation Phenomenon for a Simple Flexible Rotor System Supported by a Full-Circular Journal Bearing

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Tatsuya Miura ◽  
Tsuyoshi Inoue ◽  
Hiroshi Kano
Keyword(s):  
Normal Form ◽  
Dynamical Equation ◽  
Journal Bearing ◽  
Stability Limit ◽  
Rotor System ◽  
Flexible Rotor ◽  
Normal Form Theory ◽  
Bifurcation Phenomenon ◽  
The Stability ◽  
Manifold Theory

This paper demonstrates nonlinear theoretical analysis of a flexible rotor system supported by a full-circular journal bearing focusing on the bifurcation phenomenon in the vicinity of the stability limit (bifurcation point). A third-order polynomial approximation model is used for the representation of the oil film force of the journal bearing. The reduced-order model, with modes concerning the bifurcation, is deduced using the center manifold theory. The dynamical equation in the normal form relating the bifurcation which leads to the oil whirl is obtained using the normal form theory. The influences of various parameters are investigated based on the analysis of a deduced dynamical equation in the normal form. Furthermore, the validity of the derived analytical observation is confirmed by comparing it with the numerically obtained frequency response result.

Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System

2003 ◽  
Vol 125 (3) ◽  
pp. 307-316 ◽  
Author(s):  
Y. S. Ho ◽  
H. Liu ◽  
L. Yu
Keyword(s):  
Periodic Motion ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mass Eccentricity ◽  
The Stability

This paper is concerned with the effect of a thrust active magnetic bearing (TAMB) on the stability and bifurcation of an active magnetic bearing rotor system (AMBRS). The shaft is flexible and modeled by using the finite element method that can take the effects of inertia and shear into consideration. The model is reduced by a component mode synthesis method, which can conveniently account for nonlinear magnetic forces and moments of the bearing. Then the system equations are obtained by combining the equations of the reduced mechanical system and the equations of the decentralized PID controllers. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the AMBRS subjected to the influences of both journal and thrust active magnetic bearings and mass eccentricity simultaneously. In the stability analysis, only periodic motion is investigated. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by using Floquet theory. The results indicate that the TAMB and mass eccentricity have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion. Therefore, sufficient attention should be paid to these factors in the analysis and design of a flexible rotor system equipped with both journal and thrust magnetic bearings in order to ensure system reliability.

scholarly journals Estimation of the Dynamic Parameters of the Bearings in a Flexible Rotor System Utilizing Electromagnetic Excitation by a Built-In Motor

Actuators ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 1
Author(s):  
Yinsi Chen ◽  
Ren Yang ◽  
Naohiro Sugita ◽  
Jianpeng Zhong ◽  
Junhong Mao ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Rotor System ◽  
Radial Excitation ◽  
Maximum Relative Error ◽  
Fe Model ◽  
Dynamic Parameters ◽  
Flexible Rotor ◽  
Electromagnetic Excitation ◽  
Excitation Force ◽  
Good Agreement

Estimation of the dynamic parameters of bearings is essential in order to be able to interpret the performance of rotating machinery. In this paper, we propose a method to estimate the dynamic parameters of the bearings in a flexible rotor system. By utilizing the electromagnetic excitation generated by a built-in PM motor and finite element (FE) modeling of the rotor, safe, low-cost, and real-time monitoring of the bearing dynamics can be achieved. The radial excitation force is generated by injecting an alternating d-axis current into the motor windings. The FE model of the rotor and the measured frequency responses at the motor and bearing locations are used to estimate the dynamic parameters of the bearings. To evaluate the feasibility of the proposed method, numerical simulation and experiments were carried out on a flexible rotor system combined with a bearingless motor (BELM) having both motor windings and suspension windings. The numerical simulation results show that the proposed algorithm can accurately estimate the dynamic parameters of the bearings. In the experiment, the estimates made when utilizing the excitation force generated by the motor windings are compared with the estimates made when utilizing the excitation force generated by the suspension windings. The results show that most of the stiffness and damping coefficients for the two experiments are in good agreement, within a maximum error of 8.92%. The errors for some coefficients are large because the base values of these coefficients are small in our test rig, so these coefficients are sensitive to deviations. The natural frequencies calculated from the dynamic parameters estimated from the two experiments are also in good agreement, within a maximum relative error of 3.04%. The proposed method is effective and feasible for turbomachines directly connected to motors, which is highly significant for field tests.

Modelling of Misaligned Rotor Systems in Aero-Engines

2012 ◽  
Author(s):  
Jun Li ◽  
Jie Hong ◽  
Yanhong Ma ◽  
Dayi Zhang
Keyword(s):  
Dynamic Model ◽  
Rotor System ◽  
Flexible Rotor ◽  
Lagrange Equations ◽  
Rotor Systems ◽  
Nonlinear Properties ◽  
Aero Engine ◽  
Series Of Experiments ◽  
Aero Engines ◽  
Good Agreement

Based on the analysis of structural and dynamic characteristics, a dynamic model of flexible rotor system under misalignment and unbalance excitation in aero-engine was developed through Lagrange equations. The model describes the mechanism and influencing factors of nonlinear properties of misaligned rotors. Then some numerical simulations were performed in order to get the vibration response in time and frequency domain. The results suggest that the rotor system and its coupling may behave in a complex and nonlinear way with the excitation of misalignment and unbalance. The response of the system contains 1× and 2× harmonics, and the spectrum signature closely relate to the misalignment magnitude and the distribution of unbalance mass. A series of experiments were also designed to verify the dynamic model. Their characteristics of response are in good agreement.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

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