Theoretical and Experimental Analysis of a Base-Excited Rotor

2006 ◽  
Vol 1 (3) ◽  
pp. 257-263 ◽  
Author(s):  
N. Driot ◽  
C. H. Lamarque ◽  
A. Berlioz
Keyword(s):  
Dynamic Behavior ◽  
Theoretical Study ◽  
Multiple Scales ◽  
Ritz Method ◽  
Flexible Rotor ◽  
Coupled Equations ◽  
Points Of View ◽  
Lateral Displacements ◽  
Support Excitation ◽  
Form Approach

In this study, the dynamic behavior of a flexible rotor system subjected to support excitation (imposed displacements of its base) is analyzed. The effect of an excitation on lateral displacements is investigated from theoretical and experimental points of view. The study focuses on behavior in bending. A mathematical model with two gyroscopic and parametrical coupled equations is derived using the Rayleigh-Ritz method. The theoretical study is based on both the multiple scales method and the normal form approach. An experimental setup is then developed to observe the dynamic behavior permitting the measurement of lateral displacements when the system’s support is subjected to a sinusoidal rotation. The experimental results are favorably compared with the analytical and numerical results.

Investigations on a Base Excited Rotor

2005 ◽  
Author(s):  
N. Driot ◽  
C. H. Lamarque ◽  
A. Berlioz
Keyword(s):  
Dynamic Behavior ◽  
Ritz Method ◽  
Multiple Scale ◽  
Point Of View ◽  
Theoretical Point ◽  
Coupled Equations ◽  
Lateral Displacements ◽  
Support Excitation ◽  
Set Up ◽  
Form Approach

In this study, the dynamic behavior of a flexible rotor system under support excitation (imposed displacements of its base) is analyzed. The effect of an excitation on lateral displacements is investigated from an experimental and a theoretical point of view. The study focuses on the behavior in bending. An experimental set-up is developed to observe the dynamic behavior that permits to measure the lateral displacements when the support of the system is submitted to a sinusoidal rotation. A mathematical model with two gyroscopic coupled equations is then derived using Rayleigh-Ritz method. The theoretical study is based on both the multiple scale method and the normal form approach. The experimental results are favorably compared with the analytical and numerical results.

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.

scholarly journals Dynamic Performances of Foil Bearing Supporting a Jeffcot Flexible Rotor System Using FEM

Lubricants ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 14
Author(s):  
Benyebka Bou-Saïd ◽  
Mustapha Lahmar ◽  
Ahcène Mouassa ◽  
Bachir Bouchehit
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Point Of View ◽  
Flexible Rotor ◽  
Auxiliary Power ◽  
Partitioned Approach ◽  
Non Linear ◽  
Auxiliary Power Units ◽  
Dynamic Performances ◽  
Air Film

Aerodynamic bearings have received considerable attention in recent decades and are increasingly being used in applications where high speed, low loads and high precision are required. Aerodynamic applications mainly concern auxiliary power units (APU) and air-conditioning machines (ACM). From the industrial point of view, the static and dynamic characteristics of these bearings rotating at very high speed must be determined. According to the literature, studies carried out on this type of bearing consider the elastic deformations of the foils due to the pressure generated in the air film. The linear approach is from time to time adopted for the prediction of the dynamic behavior of these bearings, which is not always justified. This paper aims to present a step towards a better mastery of the non-linear dynamic behavior of a flexible rotor-air bearing system. We will focus on finite element modeling (FEM) of the non-linear isothermal elasto-aerodynamic lubrication problem in the case of a radial bearing operating in a dynamic regime. We will present the effects of rotational speed, unbalance eccentricity, and rotor mass on the non-linear response of rigid and compliant bearings. We use a partitioned approach which treats fluid and structure as two computation domains solved separately; reducing the development time needed for a monolithic code which is difficult to manage when the geometries or the physical properties of the problem to be treated become complex.

Vibration-Based Crack Identification of Generally Supported Beam Structures

2010 ◽  
Vol 163-167 ◽  
pp. 2723-2726
Author(s):  
Yu Xiang Zhang ◽  
Fu Hou Xu ◽  
Cui Qin Wu
Keyword(s):  
Particle Swarm Optimization ◽  
Dynamic Behavior ◽  
Optimization Algorithm ◽  
Numerical Experiments ◽  
Particle Swarm Optimization Algorithm ◽  
Ritz Method ◽  
Crack Identification ◽  
Search Technique ◽  
Cracked Beam ◽  
Swarm Optimization

An effective crack identification method has been developed based on the dynamic behavior of a cracked beam. The nature frequencies of a generally supported beam with crack are calculated by Rayleigh-Ritz method. The crack is then identified from the changes of the nature frequencies caused by the appearance of crack. A hybrid PSO (Particle Swarm Optimization) algorithm is employed as a global search technique to back-calculate the damage. Numerical experiments are carried out on beams with different crack damage. The results demonstrate that the proposed method is able to effectively and reliably locate and quantify the crack in the beam with elastically restraint against translation and rotation.

scholarly journals A Theoretical Investigation of an Overhung Flexible Rotor Mounted on Uncentralized Squeeze-Film Damper Bearings and Flexible Supports

1982 ◽  
Author(s):  
R. A. Cookson ◽  
Xin-Hai Feng
Keyword(s):  
Theoretical Study ◽  
Effective Means ◽  
Complex Model ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Squeeze Film Damper ◽  
Surrounding Structure ◽  
Turbine Disc ◽  
Flexible Supports ◽  
Selection Of

Previous investigations have shown that the uncentralized type of squeeze-film damper is an effective means of reducing the transmission of unbalance forces into the supporting structure. In this theoretical study a more complex model, which includes an overhung “fan” disc and a noncentral “turbine” disc, has been employed. This model represents the conventional gas turbine somewhat closer than does the previously studied single disc system. This investigation has shown that it is possible to minimize the force transmitted into the surrounding structure by a careful selection of squeeze-film damper characteristics, although it may be found that some larger amplitudes of motion accompany the minimized transmissibility.

Theoretical study of the photoacoustic signal produced in a relaxing gas

1986 ◽  
Vol 64 (9) ◽  
pp. 1098-1106 ◽  
Author(s):  
M. Rebelo Da Silva
Keyword(s):  
Theoretical Study ◽  
Sound Propagation ◽  
Photoacoustic Signal ◽  
Rigid Wall ◽  
Gas Cell ◽  
Collisional Relaxation ◽  
Coupled Equations ◽  
Flow Through ◽  
Relaxing Gas ◽  
Lateral Walls

The photoacoustic signal generated in a photoacoustic gas cell with rigid wall boundaries is calculated by solving the coupled equations for sound propagation and thermal diffusion in a viscous and relaxing gas. For a cylindrical geometry, monochromatic radiation, and sinusoidal modulation, when a condition of zero heat flow through the lateral walls of the cell is verified, a general expression is found that can be applied whatever the deactivation scheme is for collisional relaxation in the gas. Both resonant and nonresonant modes of operation are considered.

Nonlinear Dynamic Analysis of a Flexible Rotor Supported by Externally Pressurized Porous Gas Journal Bearings

2002 ◽  
Vol 124 (3) ◽  
pp. 553-561 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cheng-Ying Lo ◽  
Cha’o-Kuang Chen
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Flexible Rotor ◽  
Bearing Number ◽  
Rotor Mass

This paper studies the nonlinear dynamic analysis of a flexible rotor supported by externally pressurized porous gas journal bearings. A time-dependent mathematical model for externally pressurized porous gas journal bearings is presented. The finite difference method and the Successive Over Relation (S.O.R.) method are employed to solve the modified Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and quasi-periodic response of the rotor and journal center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and bearing number. The results of this study contribute to a further understanding of the nonlinear dynamics of gas-lubricated, externally pressurized, porous rotor-bearing systems.

Longitudinal–Flexural–Torsional Dynamic Behavior of Liquid-Filled Pipelines: An Analytic Solution

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Dimitrios G. Pavlou
Keyword(s):  
Dynamic Behavior ◽  
Analytic Solution ◽  
Integral Transform ◽  
Equation System ◽  
Time And Space ◽  
Partial Differential ◽  
Coupled Equations ◽  
Contraction Ratio ◽  
The Time Domain ◽  
Poisson Contraction

Abstract The 14 partial differential equation system describing the longitudinal–flexural–torsional dynamic behavior of liquid-filled pipelines contains coupled equations due to mutual boundary conditions and Poisson contraction ratio terms. Solutions of the above system are available in the frequency-domain or in the time-domain (method of characteristics (MOC)). In this paper, an analytic solution in the domain of time and space is achieved. Double integral transform, namely, finite sine Fourier transform (FSFT) and Laplace transform, is applied to the derived system of the 14 fourth-order partial differential equations, yielding an algebraic system in terms of the transformed variables. The inversion of the FSFT is an easy task, but the analytic inversion of the Laplace transforms is very challenging. Both integral transform inversions of the 14 transformed variables are successfully performed, and an analytic matrix formula in the domain of time and space along with numerical results is obtained.

Stability Analysis of an Industrial Gas Compressor Supported by Tilting-Pad Bearings Under Different Lubrication Regimes

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Alejandro Cerda Varela ◽  
Ilmar Ferreira Santos
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Lubrication Regimes ◽  
Lubrication Regime ◽  
Stable Operating ◽  
Tilting Pad ◽  
The Stability ◽  
Tilting Pad Journal Bearing

This work is aimed at a theoretical study of the dynamic behavior of a rotor-tilting pad journal bearing (TPJB) system under different lubrication regimes, namely, thermohydrodynamic (THD), elastohydrodynamic (EHD), and hybrid lubrication regime. The rotor modeled corresponds to an industrial compressor. Special emphasis is put on analyzing the stability map of the rotor when the different lubrication regimes are included into the TPJB modeling. Results show that, for the studied rotor, the inclusion of a THD model is more relevant when compared to an EHD model, as it implies a reduction on the instability onset speed for the rotor. Also, results show the feasibility of extending the stable operating range of the rotor by implementing a hybrid lubrication regime.

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