Chaos of a Flexible Rotor in Journal Bearings

1995 ◽  
Author(s):  
R. D. Brown ◽  
G. Drummond
Keyword(s):  
Theoretical Models ◽  
Journal Bearings ◽  
Rotating Machinery ◽  
Rigid Rotor ◽  
Flexible Rotor ◽  
Hydrodynamic Bearings ◽  
Stress Reversals ◽  
Oil Films ◽  
Rigid Rotors ◽  
Rotor Model

Abstract Nonlinear systems can give rise to chaotic behaviour, essentially unpredictable. Oil film forces arising from hydrodynamic bearings in rotating machinery can be extremely nonlinear under conditions of large unbalance. Chaotic response has been demonstrated in theoretical models of rigid rotors supported in hydrodynamic bearings. The behaviour of a rigid rotor can be extended by looking at a flexible rotor model supported on journal bearings and subject to large unbalance levels. The introduction of a flexible shaft yields chaotic regions which are less extensive than those obtained from a rigid rotor model. This is not surprising as the nonlinearity in the model is confined to the oil films at the end of the shaft. However if this level of unbalance is experienced in service then shaft fatigue could occur because of the sustained nature of the non-synchronous response and the effect of the resulting stress reversals.

scholarly journals Blade Loss Simulation of Multi Mass Rotor Model With Nonlinear Tilt Pad Journal Bearings

1995 ◽  
Author(s):  
R. K. Gadangi ◽  
A. B. Palazzolo
Keyword(s):  
Natural Frequency ◽  
Transient Response ◽  
Critical Speed ◽  
Journal Bearings ◽  
Rigid Rotor ◽  
Flexible Rotor ◽  
Equilibrium Location ◽  
Rotor Model ◽  
Limiting Value ◽  
Bearing System

Prediction of rotor vibrations due to large imbalance requires nonlinear solution of the supporting bearings. This paper presents a methodology and results for the effects of large, sudden imbalance on the response of a multi mass rotor model supported on tilt pad journal bearings. For a given imbalance, response is obtained for rotor speeds below, above and at the rotor natural frequency. The maximum peak to peak amplitude is larger at the critical speed than at a speed above or below the critical. The imbalance response is compared with two other methods used for predicting the transient response of a rotor bearing system. The rigid rotor and nonlinear bearing model shows a response similar in shape to that obtained with a flexible rotor and nonlinear bearing model, but the magnitude is different, which reached a limiting value as the imbalance was increased. The flexible rotor and linearized bearing model predicts a similar trend as the flexible rotor and nonlinear bearing model, with increasing speed for a given imbalance, but the shape and magnitude of the orbit is completely different. The motion of rotor to static equilibrium location for the flexible rotor and nonlinear bearing model showed oscillations which diminished with time, while the rigid rotor and nonlinear bearing model does not show any oscillations.

Stability analysis of a rigid rotor on tilting-pad journal bearings

2000 ◽  
Vol 214 (3) ◽  
pp. 243-251 ◽  
Author(s):  
J. M. M. Guijosa ◽  
Z. C. Feng
Keyword(s):  
Previous Analysis ◽  
Journal Bearings ◽  
Rotating Machinery ◽  
Superior Performance ◽  
Limiting Factor ◽  
Loss Of Stability ◽  
Rigid Rotor ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings ◽  
Insight Into

Tilting-pad journal bearings are used in many rotating machinery applications. They are known to have superior performance in comparison with fixed geometry cylindrical bearings. Previous analysis by other investigators on the rotor stability has shown that the pad inertia is the main limiting factor on the bearing performance. In this paper, that analysis is extended to examine the bifurcation types that are associated with the loss of stability in order to gain insight into whether the linear stable regions are robust under finite perturbations. The effect of pad friction force on the rotor stability is also examined. Furthermore, the analysis is extended to bearings with four pads.

Optimal Clearance Configuration of Fluid-Film Journal Bearings for Stability Improvement

2004 ◽  
Vol 126 (1) ◽  
pp. 125-131 ◽  
Author(s):  
Koichi Matsuda ◽  
Yoichi Kanemitsu ◽  
Shinya Kijimoto
Keyword(s):  
Performance Index ◽  
Fourier Coefficients ◽  
Journal Bearings ◽  
Rotating Machinery ◽  
Fluid Film ◽  
System Stability ◽  
Rigid Rotor ◽  
System A ◽  
Improve Stability ◽  
Machinery System

This paper aims to optimize a clearance configuration of fluid-film journal bearings. In order to improve stability of a rotating-machinery system, a performance index is given by summing the squared values of the attitude-angles over a region of eccentricity. A Fourier series is used to represent an arbitrary clearance configuration of a bearing, and the problem is to find the Fourier coefficients to minimize the performance index. The problem is numerically solved by a kind of the conjugate gradient method to yield a unique clearance configuration. The optimal clearance configuration is computed for various ratios of length to diameter of a bearing. A rigid-rotor system is used to verify that the designed bearing improves the system stability compared with that of a full circular bearing and to show that this optimization is more effective for shorter bearings.

Stability of a Rigid Rotor Supported on Rough Oil Journal Bearings

1990 ◽  
Vol 112 (1) ◽  
pp. 73-77 ◽  
Author(s):  
B. C. Majumdar ◽  
M. K. Ghosh
Keyword(s):  
Surface Roughness ◽  
Journal Bearings ◽  
Variance Ratio ◽  
Rigid Rotor ◽  
Roughness Parameters ◽  
Roughness Effect ◽  
Composite Surface ◽  
The Stability ◽  
Orientation Pattern ◽  
Rigid Rotors

This investigation deals with the stability of rigid rotors supported on finite rough oil journal bearings using perturbation method. The effect of various surface roughness parameters, viz., composite surface roughness, roughness orientation pattern and variance ratio on the stability has been studied. In general, surface roughness effect when incorporated into the analysis does not show a significant change in the stability for surfaces having same roughness structure. However, the effect of variance ratio (i.e., surfaces having different roughness structure) on stability is quite marked.

Imbalance Estimation for Speed-Varying Rigid Rotors Using Time-Varying Observer

1999 ◽  
Vol 123 (4) ◽  
pp. 637-644 ◽  
Author(s):  
Shiyu Zhou ◽  
Jianjun Shi
Keyword(s):  
Active Vibration Control ◽  
Estimation Method ◽  
Time Varying ◽  
Rigid Rotor ◽  
Augmented System ◽  
Active Balancing ◽  
Active Vibration ◽  
Rotor Dynamic ◽  
Rigid Rotors ◽  
Rotor Model

Rigid rotor dynamic model is widely used to model rotating machinery. In this paper, a speed-varying transient rigid rotor model is developed in the state space form. The states of this model are augmented to include imbalance forces and moments. A time-varying observer can then be designed for the augmented system by using canonical transformation. After obtaining an estimation of the imbalance forces and moments as the states of the augmented system, the estimated imbalance can be directly calculated. This estimation method can be used in the active vibration control or active balancing schemes for a rigid rotor.

Enhanced Campbell Diagram With the Concept of H∞ in Rotating Machinery: Lee Diagram

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Chong-Won Lee ◽  
Yun-Ho Seo
Keyword(s):  
Frequency Response ◽  
Modal Analysis ◽  
Rotating Machinery ◽  
Time Varying ◽  
Rigid Rotor ◽  
Response Matrix ◽  
Rotating Machines ◽  
Campbell Diagram ◽  
Infinity Norm ◽  
Rotor Model

The Campbell diagram, a frequency-speed diagram, has been widely used for prediction of possible occurrence of resonances in the phase of design and operation of rotating machinery since its advent in 1920s. In this paper, a set of new frequency-speed diagrams, which is referred to as the Lee diagram, is newly proposed, where the conventional Campbell diagram is incorporated with the concept of the infinity norm of directional frequency response matrix (dFRM) associated with a rotor with rotating and stationary asymmetry in general. The dFRM is constructed based on complete modal analysis of a linear periodically time-varying rotor model formulated in the complex coordinates. It is shown that the Lee diagram is powerful in that it can identify the modes of symmetry, rotating and stationary asymmetry, and extract only a few critical resonances out of the, otherwise, overcrowded ones without a measure of priority as in the Campbell diagram. In order to demonstrate the power of the Lee diagram in design and operation of rotating machines, three examples are treated: a typical anisotropic rigid rotor, a simple general rotor, and a two-pole generator.

scholarly journals Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

Molecules ◽  
2020 ◽  
Vol 25 (17) ◽  
pp. 3963
Author(s):  
Jizhou Wu ◽  
Jie Ma ◽  
Yuqing Li ◽  
Wenliang Liu ◽  
Peng Li ◽  
...  
Keyword(s):  
Long Range ◽  
Spectroscopic Technique ◽  
Rigid Rotor ◽  
Simple Analysis ◽  
Rotational Constants ◽  
Vibrational Levels ◽  
Photoassociation Spectroscopy ◽  
Rotor Model ◽  
Good Agreement

This article demonstrates new observation of the high-resolution ro-vibrational bichromatic photoassociation spectra (BPAS) of Cs2 in the 0u+ long-range state below the asymptotes 6S1/2 + 6P1/2. By combining with a modulation spectroscopic technique, precise references of the frequency differences have been engineered through the BPAS, with which the rotational constants of low-lying vibrational levels of the Cs20u+ long-range state have been accurately determined by fitting the frequency differences to the non-rigid-rotor model. The rotational constants for the newly observed seven ro-vibrational levels are summarized and disagreement for the level ῦ = 498 is clarified. The rotational constants of different vibrational levels demonstrate strong perturbations of the related energy structures. A simple analysis is performed and shows good agreement with experimental results.

Numerical and experimental study on the dynamic bearing properties of a four-pad and eight-pad tilting pad journal bearings in a vertical rotor

2021 ◽  
pp. 1-24
Author(s):  
Gudeta Berhanu Benti ◽  
David Jose Rondon ◽  
Rolf Gustavsson ◽  
Jan-Olov Aidanpää
Keyword(s):  
Dynamic Properties ◽  
Mean Value ◽  
Journal Bearings ◽  
Navier Stokes ◽  
Rigid Rotor ◽  
Navier Stokes Equation ◽  
Vertical Rotor ◽  
Tilting Pad ◽  
Fifth Order ◽  
Tilting Pad Journal Bearings

Abstract In this paper, the dynamics of tilting pad journal bearings with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier-Stokes equation. A nonlinear bearing model is developed and used in the steady state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16 % and 38 %, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excite the system at the third and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed.

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