Chaotic Behavior of Rotor/Stator Systems With Rubs
01 Jul 1994-Journal of Engineering for Gas Turbines and Power-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 116, Iss: 3, pp 692-701
TL;DR: In this paper, the dynamic behavior of externally excited rotor/stator systems with occasional, partial rubbing conditions is described. And the results of numerical simulations are presented in the form of bifurcation diagrams, rotor lateral vibration time, base waves, and orbits.
Abstract: This paper outlines the dynamic behavior of externally excited rotor/stator systems with occasional, partial rubbing conditions. The observed phenomenon have one major source of a strong nonlinearity: transition from no contact to contact state between mechanical elements, one of which is rotating. This results in variable stiffness and damping, impacting, and intermittent involvement of friction. A new model for such a transition (impact) is developed. In case of the contact between rotating and stationary elements, it correlates the local radial and tangential ("super ball") effects with global behavior of the system. The results of numerical simulations of a simple rotor/stator system based on that model are presented in the form of bifurcation diagrams, rotor lateral vibration time—base waves, and orbits. The vibrational behavior of the considered system is characterized by orderly harmonic and subharmonic responses, as well as by chaotic vibrations. A new result (additional subharmonic regime of vibration) is obtained for the case of heavy rub of an anisotropically supported rotor. The correspondence between numerical simulation and previously obtained experimental data supports the adequacy of the new model of impact.
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01 Mar 2010
TL;DR: In this article, the reader can understand the dynamics of rotating machines by using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior of rotor vibration.
Abstract: This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.
395 citations
TL;DR: In this paper, an analytical study was carried out on the stability of the full annular rub solutions of an externally excited, modified Jeffcott rotor with a given rotor/stator clearance and cross-coupling influences.
Abstract: An analytical study is carried out on the stability of the fullannular rub solutions of an externally excited, modified Jeffcott rotorwith a given rotor/stator clearance and cross-coupling influences. Theobtained analytical stability conditions provide an opportunity for abetter understanding of the dynamical phenomena of rotor/stator systemswith rubs, such as jump phenomena and the transition between periodicand quasi-periodic full rub responses as well as between the fullannular rubs and the partial rubs. A systematic study on the influenceof the system parameters on these phenomena is carried out. It is foundthat the simultaneous presence of the coefficient of friction and thecross-coupling stiffness coefficient with a proper value may benefit thedynamics of the rotor/stator system with rubs.
89 citations
TL;DR: In this article, the effect of fractional order damping on the rotational speed ratio, derivative order of damping and mass eccentricity on the system dynamics were investigated using rotor trajectory diagrams, bifurcation diagrams and Poincare map.
79 citations
TL;DR: In this article, a model for the coupled torsional and lateral vibrations of unbalanced rotors that accounts for the rotor-to-stator rubbing is presented, which is solved using a predictive-corrective numerical integration algorithm.
76 citations
TL;DR: In this article, the nonlinear vibrations are considered in a two-degree of freedom rotordynamic system subjected to a bearing clearance effect, and the system response is extremely sensitive to changes in these parameters, and chaos can exist over large regions of parameter space.
Abstract: The nonlinear vibrations are considered in a two-degree of freedom rotordynamic system subjected to a bearing clearance effect The excitation is provided by an out-of-balance within the system, and the nonlinearity, in the form of a discontinuous stiffness, is effected by means of a radial clearance between the elastically supported rotor and the elastically supported outer ring Different nonlinear dynamics analysis techniques are employed to unveil the global dynamics of the rotor system In particular the system has been investigated with the help of time trajectories, phase portraits, bifurcation diagrams, Poincare maps, power spectrum analysis and the construction of basins of attraction A numerical study is presented which encompasses the effects of different system parameters in order to demonstrate the severity of the vibrations It is also shown that the response of the system can be extremely sensitive to changes in these parameters, and that chaos can exist over large regions of parameter space
76 citations
References
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01 Sep 1989TL;DR: The goal of this book is to present an elementary introduction on chaotic systems for the non-specialist, and to present and extensive package of computer algorithms for simulating and characterizing chaotic phenomena.
Abstract: The goal of this book qre to present an elementary introduction on chaotic systems for the non-specialist, and to present and extensive package of computer algorithms ( in the form of pseudocode) for simulating and characterizing chaotic phenomena. These numerical algorithms have been implemented in a software package called INSITE (Interactive Nonlinear System Investigative Toolkit for Everyone) which is being distributed separately.
1,859 citations
TL;DR: Vibrations dues au frottement entre rotor and stator dans les machines tournantes. Analyse de la litterature parue sur le sujet as discussed by the authors.
Abstract: Vibrations dues au frottement entre rotor et stator dans les machines tournantes. Analyse de la litterature parue sur le sujet
214 citations
TL;DR: In this article, a simple but exact computer model of the subharmonic vibration was developed based on the numerical integration of a finite difference formulation. But the model is not suitable for systems with low damping and extreme nonlinearity.
Abstract: Subharmonic vibration refers to the response of a dynamic system to excitation at a whole-number multiple (n) of its natural frequency by vibrating asynchronously at its natural frequency, that is, at (1/n) of the excitation. The phenomenon is generally associated with asymmetry in the stiffness vs. deflection characteristic of the system. It may be characterized as the “bouncing” of the rotor on the surface of the stiff support, energized by every nth unbalance impulse prior to contact. Second, third and fourth order subharmonic vibration responses have previously been observed in high speed rotating machinery with such an asymmetry in the bearing supports. An incident is reported where 8th and 9th order subharmonic vibration responses have been observed in a high speed rotor. A simple but exact computer model of the phenomenon has been evolved based on the numerical integration of a finite difference formulation. Response curves and wave forms of rotor deflection at individual speeds are computed. It is shown that the response is a series of pseudo-critical peaks at whole-number multiples of the rotational speed. Very high orders of subharmonic vibration are found to be possible for systems with low damping and extreme nonlinearity.
212 citations
TL;DR: A quasi-linear deterministic system arising throughout the physical sciences exhibits a family of sub-harmonic resonant peaks between which we delineate cascades of period-doubling bifurcations leading to chaotic regimes typical of a strange attractor as discussed by the authors.
122 citations
22 Sep 1991
18 citations