Lund’s Elliptic Orbit Forced Response Analysis: The Keystone of Modern Rotating Machinery Analysis

2001 ◽  
Author(s):  
R. Gordon Kirk
Keyword(s):  
Linear Response ◽  
Vibration Analysis ◽  
Rotating Machinery ◽  
Forced Response ◽  
Design Tool ◽  
Elliptic Orbit ◽  
Response Analysis ◽  
Flexible Rotor ◽  
Response Sensitivity ◽  
Machinery Design

Abstract A total understanding of rotating machinery vibration analysis requires evaluation of critical speed placement, forced response sensitivity to imbalance, linear onset of instability prediction and full non-linear response analysis. Of these four areas of analysis, only the first three are applied as a basic design tool in modern turbo-machinery analysis. The prediction of multi-mass flexible rotor steady-state elliptic orbit response, including bearing damping and support flexibility, has been and remains in this author’s opinion, to be the basic workhorse and keystone of machinery design. This has now been true for over 35 years. The person responsible for developing this basic method of analysis has been a longtime friend of many engineers worldwide. This paper is written to acknowledge this contribution, one of many in fact, made by Jorgen W. Lund and is presented in memory of his life’s work at this occasion of honoring his contributions to our profession. The utility of the analysis will be discussed and the powerful insight it gives to complex machinery dynamic behavior will be illustrated.

Lund’s Elliptic Orbit Forced Response Analysis: The Keystone of Modern Rotating Machinery Analysis

2003 ◽  
Vol 125 (4) ◽  
pp. 455-461 ◽  
Author(s):  
R. Gordon Kirk
Keyword(s):  
Rotating Machinery ◽  
Forced Response ◽  
Design Tool ◽  
Elliptic Orbit ◽  
Response Analysis ◽  
Flexible Rotor ◽  
Response Sensitivity ◽  
Personal Reflections ◽  
Short Section ◽  
Machinery Design

A total understanding of rotating machinery vibration analysis requires evaluation of critical speed placement, forced response sensitivity to imbalance, linear onset of instability prediction and full non-linear response analysis. Of these four areas of analysis, only the first three are applied as a basic design tool in modern turbo-machinery analysis. The prediction of multi-mass flexible rotor steady-state elliptic orbit response, including bearing damping and support flexibility, has been and remains in this author’s opinion, to be the basic workhorse and keystone of machinery design. This has now been true for over 35 years. The person responsible for developing this basic method of analysis has been a longtime friend of many engineers worldwide. This paper is written to acknowledge this contribution, one of many in fact, made by Jørgen W. Lund and is presented in memory of his life’s work at this occasion of honoring his contributions to our profession. A short section on the methods and understanding gained from the basic analysis will be presented. Finally, some personal reflections will be given concerning Jørgen Lund.

Conceptual Analysis of the Non-Linear Forced Response of Aerodynamically Unstable Bladed-Discs

2013 ◽  
Author(s):  
Roque Corral ◽  
Juan Manuel Gallardo ◽  
Rahul Ivaturi
Keyword(s):  
Time Domain ◽  
Linear Response ◽  
Harmonic Excitation ◽  
Friction Model ◽  
Forced Response ◽  
Response Analysis ◽  
Non Linear ◽  
Aerodynamic Instability ◽  
Time Domain Response ◽  
The Time Domain

The response of aerodynamically unstable tuned bladed-discs with non-linear friction dissipation at blade-root attachments due to harmonic external excitation is studied. The bladed-disc is modeled using a simple mass-spring system and the effect of friction is modeled using a micro-slip friction model. The response is computed in time domain using a Runge-Kutta scheme. The time domain response is decomposed to obtain the evolution of traveling waves in the bladed-disc. Parametric studies have been conducted to study the non-linear response at different vibration amplitudes at high and low engine orders of excitation. It is seen that the non-linearity due to friction gives rise to a complicated interaction between the synchronous response of the system due to harmonic excitation and the non-synchronous response of the system due to aerodynamic instability. For low excitation levels the system behaves as in the pure flutter regime where a single, or at most a few, aerodynamically unstable modes may be found in the final state when a limit cycle is reached. When the forcing is large enough the aerodynamic instability is suppressed and only the non-linear response of the excited mode may be seen. It is concluded that the superimposition of the flutter and forced response analysis in terms of vibration amplitude is not valid and leads to prediction of vibration amplitudes significantly larger than that obtained when both phenomena are simulated together.

Regeneration-Induced Forced Response in Axial Turbines

2013 ◽  
Author(s):  
Jens Aschenbruck ◽  
Christopher E. Meinzer ◽  
Linus Pohle ◽  
Lars Panning-von Scheidt ◽  
Joerg R. Seume
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Response Analysis ◽  
Geometrical Parameters ◽  
Turbine Stage ◽  
Structural Dynamic ◽  
Air Turbine ◽  
Axial Turbines ◽  
Interaction Approach ◽  
Stagger Angle

The regeneration of highly loaded turbine blades causes small variations of their geometrical parameters. To determine the influence of such regeneration-induced variances of turbine blades on the nozzle excitation, an existing air turbine is extended by a newly designed stage. The aerodynamic and the structural dynamic behavior of the new turbine stage are analyzed. The calculated eigenfrequencies are verified by an experimental modal analysis and are found to be in good agreement. Typical geometric variances of overhauled turbine blades are then applied to stator vanes of the newly designed turbine stage. A forced response analysis of these vanes is conducted using a uni-directional fluid-structure interaction approach. The effects of geometric variances on the forced response of the rotor blade are evaluated. It is shown that the vibration amplitudes of the response are significantly higher for some modes due to the additional wake excitation that is introduced by the geometrical variances e.g. 56 times higher for typical MRO-induced variations in stagger-angle.

scholarly journals A Knowledge-based Master-model Approach with Application to Rotating Machinery Design

2011 ◽  
Vol 19 (4) ◽  
pp. 295-305 ◽  
Author(s):  
M. Sandberg ◽  
I. Tyapin ◽  
M. Kokkolaras ◽  
O. Isakasson ◽  
J.-O. Aidanpää ◽  
...  
Keyword(s):  
Rotating Machinery ◽  
Knowledge Based ◽  
Master Model ◽  
Machinery Design ◽  
Model Approach

Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

2021 ◽  
Author(s):  
Akira Saito ◽  
Junta Umemoto ◽  
Kohei Noguchi ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Linear Systems ◽  
Piecewise Linear ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Response Analysis ◽  
Piecewise Linear Systems ◽  
Two Degree Of Freedom

scholarly journals Vibration Analysis of Rotor - Coupling - Bearing System With Misaligned Shafts

1996 ◽  
Author(s):  
A. Sreenivasa Rao ◽  
A. S. Sekhar
Keyword(s):  
Theoretical Model ◽  
Finite Elements ◽  
Vibration Analysis ◽  
Rotating Machinery ◽  
Value Analysis ◽  
Flexible Coupling ◽  
Eigen Value ◽  
Shaft Misalignment ◽  
Reaction Forces ◽  
Bearing System

The shaft misalignment, even being a common fault in rotating machinery, is not sufficiently studied. The present work addresses effects of misalignment in rotating machinery. An attempt to give a theoretical model for a rotor-coupling-bearing system has been done. The rotor-bearing system including the flexible coupling is modelled using the finite elements. The reaction forces and moments developed due to flexible coupling misalignment both for parallel and angular are derived and introduced in the model. Vibration analyses such as eigen value analysis and unbalance response are carried out for the rotor system with misaligned shafts.

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