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J I Inayathussain - One of the best experts on this subject based on the ideXlab platform.
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geometric coupling effects on the bifurcations of a flexible Rotor Response in active magnetic bearings
2009Co-Authors: J I InayathussainAbstract:Abstract This work reports on a numerical investigation on the bifurcations of a flexible Rotor Response in active magnetic bearings taking into account the nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the actuator forces that are nonlinear function of the coil current and the air gap. For the values of design and operating parameters of the Rotor-bearing system investigated in this work, numerical results showed that the Response of the Rotor was always synchronous when the values of the geometric coupling parameter α were small. For relatively larger values of α, however, the Response of the Rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of periods-2, -3, -6, -9, and -17, quasi-periodicity and chaos. Numerical results further revealed the co-existence of multiple attractors within certain ranges of the speed parameter Ω. In practical rotating machinery supported by active magnetic bearings, the possibility of synchronous Rotor Response to become non-synchronous or even chaotic cannot be ignored as preloads, fluid forces or other external excitation forces may cause the Rotor’s initial conditions to move from one basin of attraction to another. Non-synchronous and chaotic vibrations should be avoided as they induce fluctuating stresses that may lead to premature failure of the machinery’s main components.
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bifurcations in the Response of a flexible Rotor in squeeze film dampers with retainer springs
2009Co-Authors: J I InayathussainAbstract:Abstract Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the Rotor-bearing system, there have however been some cases of Rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the Response of a flexible Rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the Rotor Response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous Response was seen to decrease with the increase of α; in fact non-synchronous Rotor Response was totally absent for α = 0.4 . With the exception of the case α = 0.1, the speed range of non-synchronous Response was also seen to decrease with the increase of K. Multiple Responses of the Rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the Rotor Response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical Rotor systems. These results provide some insights into the range of design parameters for squeeze-film dampers with retainer springs to ensure synchronous Rotor Response within a specified operating speed range.
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chaos via torus breakdown in the vibration Response of a rigid Rotor supported by active magnetic bearings
2007Co-Authors: J I InayathussainAbstract:This work reports on a numerical study undertaken to investigate the Response of an imbalanced rigid Rotor supported by active magnetic bearings. The mathematical model of the Rotor-bearing system used in this study incorporates nonlinearity arising from the electromagnetic force—coil current—air gap relationship, and the effects of geometrical cross-coupling. The Response of the Rotor is observed to exhibit a rich variety of dynamical behavior including synchronous, sub-synchronous, quasi-periodic and chaotic vibrations. The transition from synchronous Rotor Response to chaos is via the torus breakdown route. As the Rotor imbalance magnitude is increased, the synchronous Rotor Response undergoes a secondary Hopf bifurcation resulting in quasi-periodic vibration, which is characterized by a torus attractor. With further increase in the Rotor imbalance magnitude, this attractor is seen to develop wrinkles and becomes unstable resulting in a fractal torus attractor. The fractal torus is eventually destroyed as the Rotor imbalance magnitude is further increased. Quasi-periodic and frequency-locked sub-synchronous vibrations are seen to appear and disappear alternately before the emergence of chaos in the Response of the Rotor. The magnitude of Rotor imbalance where sub-synchronous, quasi-periodic and chaotic vibrations are observed in this study, albeit being higher than the specified imbalance level for rotating machinery, may possibly occur due to a gradual degradation of the Rotor balance quality during operation.
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bifurcations of a flexible Rotor Response in squeeze film dampers without centering springs
2005Co-Authors: J I InayathussainAbstract:Abstract Squeeze-film dampers are often utilized in high-speed rotating machinery to provide additional external damping to the Rotor-bearing system for the purpose of reducing the synchronous Response of the Rotor especially while traversing critical speeds, or to eliminate Rotor instability problems. The application of these dampers are widely found in aircraft gas turbine engines that are usually mounted on rolling element bearings, which are known to provide almost negligible damping to the system. Although the squeeze-film damper is an inherently stable machine element, its operation at certain parameters may give rise to undesirable non-synchronous vibration. The effects of the design and operating parameters, namely the bearing parameter, B, gravity parameter, W, and mass ratio, α, on the bifurcations in the Response of a flexible Rotor supported by squeeze-film dampers without centering springs were examined using direct numerical integration. Specifically, the effects of these parameters on the onset speed of bifurcation and the extent of non-synchronous Response of the Rotor within the range of speed parameter, Ω, between 0.5 and 5.0 were determined. Numerical simulation results showed the occurrence of period-2, period-4 and quasi-periodic vibrations in the Response of the Rotor as the speed parameter, Ω, was varied from 0.5 to 5. The results further showed that increasing B resulted in the increase of the onset speed of bifurcation, and a decrease in the range of Ω where non-synchronous Response was observed. With the exception of the case of W = 0.0, the increase of W was found to increase the onset speed of bifurcation and also the range of Ω where non-synchronous Response was observed. The effect of increasing α resulted in a decrease in the range of Ω where non-synchronous Response existed. The increase of α also caused the onset speed of bifurcation to increase, except for the case of B = 0.05, W = 0.0, where the onset speed of bifurcation was observed to decrease as α was increased. The numerical results presented in this work were obtained for an unbalance parameter, U, of 0.1, which is considered to be at the upper end of the acceptable range of balance quality specifications for practical Rotor systems. The non-synchronous vibrations that were observed in the Rotor Response, for the range of practical design and operating parameters investigated in this work, are detrimental to the performance of rotating machinery as they cause alternating stresses in the Rotor that may eventually lead to fatigue failure.
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on the bifurcations of a rigid Rotor Response in squeeze film dampers
2003Co-Authors: J I Inayathussain, Hiroshi Kanki, Njuki W MureithiAbstract:Abstract The effectiveness of squeeze-film dampers in controlling vibrations in rotating machinery may be limited by the nonlinear interactions between large Rotor imbalance forces with fluid-film forces induced by dampers operating in cavitated conditions. From a practical point of view, the occurrence of nonsynchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the Rotor, which in turn may rapidly induce fatigue failure. The bifurcations in the Response of a rigid Rotor supported by cavitated squeeze-film dampers resulting from such interactions are presented in this paper. The effects of design and operating parameters, namely the bearing parameter (B), gravity parameter (W), spring parameter (S) and unbalance parameter (U), on the bifurcations of the Rotor Response are investigated. Spring parameter (S) values between 0 and 1 are considered. A spring parameter value of S=0 represents the special case of dampers without centering springs. With the exception of the case S=1, jump phenomena appeared to be a common bifurcation that occurred at certain combinations of B, W and U irrespective of the value of S. Period-doubling and secondary Hopf bifurcations which occurred for low values of S (⩽0.3) were not observed for the higher values S⩾0.5. For very low stiffness values (S
Tae Ho Kim - One of the best experts on this subject based on the ideXlab platform.
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thermal management and Rotordynamic performance of a hot Rotor gas foil bearings system part i measurements
2011Co-Authors: Luis Sa Andres, Keu Ryu, Tae Ho KimAbstract:Implementation of gas foil bearings (GFBs) into micro gas turbines requires careful thermal management with accurate measurements verifying model predictions. This two-part paper presents test data and analytical results for a test Rotor and GFB system operating hot (157°C maximum Rotor outer diameter (OD) temperature). Part I details the test rig and measurements of bearing temperatures and Rotor dynamic motions obtained in a hollow Rotor supported on a pair of second generation GFBs, each consisting of a single top foil (38.14 mm inner diameter) uncoated for high temperature operation and five bump strip support layers. An electric cartridge (maximum of 360°C) loosely installed inside the Rotor (1.065 kg, 38.07 mm OD, and 4.8 mm thick) is a heat source warming the Rotor-bearing system. While coasting down from 30 krpm to rest, large elapsed times (50―70 s) demonstrate Rotor airborne operation, near friction free, and while traversing the system critical speed art ∼13 krpm, the Rotor peak motion amplitude decreases as the system temperature increases. In tests conducted at a fixed Rotor speed of 30 krpm, while the shaft heats, a cooling gas stream of increasing strength is set to manage the temperatures in the bearings and Rotor. The effect of the cooling flow, if turbulent in character, is most distinctive at the highest heater temperature. For operation at a lower heater temperature condition, however, the cooling flow stream demonstrates a very limited effectiveness. The measurements demonstrate the reliable performance of the Rotor-GFB system when operating hot. The test results, along with full disclosure on the materials and geometry of the test bearings and Rotor, serve to benchmark a predictive tool. A companion paper (Part II) compares the measured bearing temperatures and the Rotor Response amplitudes to predictions.
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forced nonlinear Response of gas foil bearing supported Rotors
2008Co-Authors: Luis San Andres, Tae Ho KimAbstract:Abstract Microturbomachinery implements gas foil bearings (GFBs) in oil-free compact units with reduced maintenance and lower life cycle costs. Challenges for GFBs include intermittent contact and wear at startup and shutdown, and potential for large amplitude Rotor whirl at high-speed operation. Subsynchronous motions are common in FBs, though hastily attributed to hydrodynamic bearing instability. In actuality, an FB load capacity depends mainly on its support structure, which shows a strong hardening effect. Presently, an FB force is modeled as a third-order structural element with nonlinear stiffnesses derived from measurements. Predictions of the performance of a rigid Rotor supported on bump-type FBs and comparisons to Rotor Response measurements follow. The predictions evidence a Duffing oscillator dynamic behavior with multiple frequency Responses, sub- and super-harmonic, within certain ranges of Rotor speed. Predicted Rotor amplitudes replicate accurately the measured Responses, with a main whirl frequency locked at the system natural frequency. The predictions and measurements validate the simple FB model, i.e. a minute gas film with effective infinite stiffness, with applicability to large amplitude Rotordynamic motions. For the first time in the open literature, a simple physical model reproduces the richness and complexity of measured Rotor–GFB motions.
C Nataraj - One of the best experts on this subject based on the ideXlab platform.
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recurrence analysis of experimental time series of a Rotor Response with bearing outer race faults
2015Co-Authors: C Kitio A Kwuimy, M Samadani, P K Kankar, C NatarajAbstract:In this paper, the time series Response of a Rotor with bearing outer race faults is analyzed. The recurrence quantification analysis (RQA) parameters deduced from the recurrence plot (RP) of the system Response are used to delve into characterization of the specific and overall behavior of the system. Attention is focused on the variation of the RQA parameters for healthy and defective states of the system. The results of this investigation are encouraging for further application of the method of RP in the diagnostics and analysis of bearing faults. In fact, it is shown that appropriate classification of the RQA can be effectively used to detect outer race faults and serve as a discriminant for fault severity.Copyright © 2015 by ASME
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sequential recurrence analysis of experimental time series of a Rotor Response with bearing outer race faults
2015Co-Authors: C Kitio A Kwuimy, M Samadani, K Kappaganthu, C NatarajAbstract:Rolling elements bearings are one of the most common components used in expensive, high precision and critical machines such as gas turbines, rolling mills and gyroscopes. They can be subjected to various defects which could lead to catastrophic results. This includes inner and outer race defects and hence it is of interest to analyze the system Response under such defects. A better understanding of the system performance under such defects can be beneficial when performing system diagnostics and system design. In this paper we are focused on the outer race defect and perform a comparative nonlinear time series analysis of a healthy system and a defective system. We consider various levels of outer race defects. The analysis is based on the recurrence properties of the system in its reconstructed state space. After determining the appropriate time lags through the average mutual information technique and the corresponding embedding dimensions through the false neighbor technique, we perform a sequential analysis of the system by subdividing the time series into bins and investigating the system Response through recurrence quantification analysis parameters along with the entropy. This contributes to the enhancement of the science of diagnostics of outer race defects by analyzing the signature of various recurrence quantification analysis parameters as the system goes from a healthy state to a severely defective state.
Njuki W Mureithi - One of the best experts on this subject based on the ideXlab platform.
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on the bifurcations of a rigid Rotor Response in squeeze film dampers
2003Co-Authors: J I Inayathussain, Hiroshi Kanki, Njuki W MureithiAbstract:Abstract The effectiveness of squeeze-film dampers in controlling vibrations in rotating machinery may be limited by the nonlinear interactions between large Rotor imbalance forces with fluid-film forces induced by dampers operating in cavitated conditions. From a practical point of view, the occurrence of nonsynchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the Rotor, which in turn may rapidly induce fatigue failure. The bifurcations in the Response of a rigid Rotor supported by cavitated squeeze-film dampers resulting from such interactions are presented in this paper. The effects of design and operating parameters, namely the bearing parameter (B), gravity parameter (W), spring parameter (S) and unbalance parameter (U), on the bifurcations of the Rotor Response are investigated. Spring parameter (S) values between 0 and 1 are considered. A spring parameter value of S=0 represents the special case of dampers without centering springs. With the exception of the case S=1, jump phenomena appeared to be a common bifurcation that occurred at certain combinations of B, W and U irrespective of the value of S. Period-doubling and secondary Hopf bifurcations which occurred for low values of S (⩽0.3) were not observed for the higher values S⩾0.5. For very low stiffness values (S
Luis San Andres - One of the best experts on this subject based on the ideXlab platform.
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forced nonlinear Response of gas foil bearing supported Rotors
2008Co-Authors: Luis San Andres, Tae Ho KimAbstract:Abstract Microturbomachinery implements gas foil bearings (GFBs) in oil-free compact units with reduced maintenance and lower life cycle costs. Challenges for GFBs include intermittent contact and wear at startup and shutdown, and potential for large amplitude Rotor whirl at high-speed operation. Subsynchronous motions are common in FBs, though hastily attributed to hydrodynamic bearing instability. In actuality, an FB load capacity depends mainly on its support structure, which shows a strong hardening effect. Presently, an FB force is modeled as a third-order structural element with nonlinear stiffnesses derived from measurements. Predictions of the performance of a rigid Rotor supported on bump-type FBs and comparisons to Rotor Response measurements follow. The predictions evidence a Duffing oscillator dynamic behavior with multiple frequency Responses, sub- and super-harmonic, within certain ranges of Rotor speed. Predicted Rotor amplitudes replicate accurately the measured Responses, with a main whirl frequency locked at the system natural frequency. The predictions and measurements validate the simple FB model, i.e. a minute gas film with effective infinite stiffness, with applicability to large amplitude Rotordynamic motions. For the first time in the open literature, a simple physical model reproduces the richness and complexity of measured Rotor–GFB motions.
