Intermittent Chaotic Dynamics of Rail Axle Supported by Roller Bearings

2009 ◽  
Author(s):  
S. P. Harsha ◽  
C. ‘Nat’ Nataraj
Keyword(s):  
High Speed ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Radial Clearance ◽  
High Speed Rail ◽  
Frequency Spectra ◽  
Roller Bearings ◽  
Nonlinear Springs ◽  
Rolling Elements

In this paper, intermittent chaotic analysis of high speed rail axle supported by roller bearings has been analyzed. In the analytical formulation, the contacts between rolling elements and races are considered as nonlinear springs, whose stiffness values are obtained by using Hertzian elastic contact deformation theory. The results show the appearance of instability and chaos in the dynamic response as the speed of the axle-bearing system is changed. Period doubling and mechanism of intermittency have been observed which lead to chaos. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the radial clearance. Poincare´ maps, time response and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

The Effect of Surface Waviness and Number of Rolling Elements on the Dynamic Behavior of a Rotor-Bearing System

2007 ◽  
Author(s):  
S. P. Harsha ◽  
C. Nataraj
Keyword(s):  
Chaotic Behavior ◽  
Nonlinear Dynamic Analysis ◽  
Wave Number ◽  
Surface Waviness ◽  
Nonlinear Load ◽  
Nonlinear Springs ◽  
Rotor Bearing ◽  
Rolling Elements ◽  
Bearing System ◽  
Effect Of Surface

In the paper, the effects of the number of rolling elements and wave number of surface waviness on the nonlinear dynamic analysis of a rotor-bearing system has been studied. In the analytical formulation, the contacts between rolling elements and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The results are presented in the form of Fast Fourier Transformations (FFT) and Poincare´ maps, which show that the vibration characteristics of the rotor and its bearings change when the bearings operate in different regions of their nonlinear load deflection characteristics. The appearance of regions of periodic, sub-harmonic and chaotic behavior has been observed to be strongly dependent on number of rolling elements.

Bearing Skidding Detection for High Speed and Aero Engine Applications

2021 ◽  
Author(s):  
Azzedine Dadouche ◽  
Rami Kerrouche
Keyword(s):  
High Speed ◽  
Power Losses ◽  
Severe Damage ◽  
Roller Bearings ◽  
Custom Made ◽  
Rolling Element ◽  
Aero Engine ◽  
Oil Flow ◽  
Rolling Elements ◽  
Surface Distress

Abstract Rolling-element bearings (REB) can develop severe damage due to skidding (slipping) between the rolling elements and bearing races. Skidding can be described as gross sliding between the bearing surfaces in relative motion and can result in significant surface distress such as smearing, especially at light loads and high rotational speeds. Under these conditions, skidding occurs between the rolling elements and the bearing races, leading to increased wear (higher friction coefficient), elevated bearing temperature, significant power losses and reduced service life of the bearing. The main objective of this study is to investigate the significance of various sensing technologies (induction, vibration, ultrasound, acoustic and optical) in detecting skidding in standard series roller bearings as well as custom-made roller bearings for aero engine applications. The bearings have a bore diameter of 60 mm and 90 mm, respectively. Jet and under race lubrication techniques have been used to supply oil to the bearings under test. The custom-made aero engine test bearing features special channels to allow under race lubrication of the rollers/races contacts as well as the cage land. The effect of radial load, rotational speed and oil flow on roller skidding have also been investigated and analyzed. Tests have been performed on a dedicated high speed experimental bearing facility and data was recorded using a commercially-available data acquisition system.

scholarly journals Kinematic Correction for Roller Skewing

1982 ◽  
Vol 104 (1) ◽  
pp. 175-184
Author(s):  
M. Savage ◽  
S. H. Loewenthal
Keyword(s):  
High Speed ◽  
Roller Bearings ◽  
Transverse Curvature ◽  
Constant Radius ◽  
Rolling Elements ◽  
Convex Curvature ◽  
Cylindrical Roller

A theory of kinematic stabilization of rolling cylinders is developed for high-speed cylindrical roller bearings. This stabilization requires race and roller crowning to produce changes in the rolling geometry as the roller shifts axially. These changes put a reverse skew in the rolling elements by changing the rolling taper. Twelve basic possible bearing modifications are identified in this paper. Four have single transverse convex curvature in the rollers while eight have rollers with compound transverse curvature composed of a central cylindrical band of constant radius surrounded by symmetric bands with both slope and transverse curvature.

Dynamic Analysis of a High-Speed Rotor-Ball Bearing System Under Elastohydrodynamic Lubrication

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Yu-Yan Zhang ◽  
Xiao-Li Wang ◽  
Xiao-Qing Zhang ◽  
Xiao-Liang Yan
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Power Spectra ◽  
Elastohydrodynamic Lubrication ◽  
Lubricated Contacts ◽  
Rolling Elements ◽  
Stiffness And Damping ◽  
Bearing System

The nonlinear dynamic behaviors of a high-speed rotor-ball bearing system under elastohydrodynamic lubrication (EHL) are investigated. First, the numerical curve fittings for stiffness and damping coefficients of lubricated contacts between rolling elements and races are undertaken, and then the fitted formulae are introduced to the equations of motion of the rotor-ball bearing system to investigate its nonlinear characteristics. Furthermore, the time responses, power spectra, phase trajectories, orbit plots, and bifurcation diagrams for cases of ignoring and considering the lubrication condition in bearings are inspected and compared. The results indicate that, when lubrication is taken into account, the amplitudes of vibration displacements and velocities of the rotor system increase, and the appearance of different regions of periodic, quasi-periodic, and chaotic behavior is strongly dependent on the speed and load.

A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions

1960 ◽  
Vol 82 (2) ◽  
pp. 309-320 ◽  
Author(s):  
A. B. Jones
Keyword(s):  
General Solution ◽  
General Theory ◽  
High Speed ◽  
Ball Bearings ◽  
Precise Location ◽  
Roller Bearings ◽  
Load Paths ◽  
Elastic Yielding ◽  
Rolling Element ◽  
Rolling Elements

A completely general solution is obtained whereby the elastic compliances of a system of any number of ball and radial roller bearings under any system of loads can be determined. Elastic yielding of the shaft and supporting structure are considered as well as centrifugal and gyroscopic loading of the rolling elements under high-speed operation. The solution defines the loading and attitude of each rolling element in each bearing of the system as well as the displacement of each inner ring with respect to its outer ring. For ball bearings the precise location of the load paths in each raceway are found. Life estimates can be more accurately made since the fatigue effects can be evaluated over known paths in the raceways. The solution, which is accomplished numerically by iterative techniques, has been programmed for an IBM-704 digital computer.

scholarly journals Stability, Chaos Detection, and Quenching Chaos in the Swing Equation System

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shun-Chang Chang
Keyword(s):  
Power Systems ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Equation System ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Frequency Spectra ◽  
Chaos Detection ◽  
The Rich

The main objective of this study is to explore the complex nonlinear dynamics and chaos control in power systems. The rich dynamics of power systems were observed over a range of parameter values in the bifurcation diagram. Also, a variety of periodic solutions and nonlinear phenomena could be expressed using various numerical skills, such as time responses, phase portraits, Poincaré maps, and frequency spectra. They have also shown that power systems can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. In this study, the Lyapunov exponent and Lyapunov dimension were employed to identify the onset of chaotic motion. Also, state feedback control and dither signal control were applied to quench the chaotic behavior of power systems. Some simulation results were shown to demonstrate the effectiveness of these proposed control approaches.

Bearing Skidding Detection for High Speed and Aero Engine Applications

2021 ◽  
Author(s):  
Azzedine Dadouche ◽  
Rami Kerrouche
Keyword(s):  
High Speed ◽  
Power Losses ◽  
Severe Damage ◽  
Roller Bearings ◽  
Custom Made ◽  
Rolling Element ◽  
Aero Engine ◽  
Oil Flow ◽  
Rolling Elements ◽  
Surface Distress

Abstract Rolling-element bearings (REB) can develop severe damage due to skidding (slipping) between the rolling elements and bearing races. Skidding can be described as gross sliding between the bearing surfaces in relative motion and can result in significant surface distress such as smearing, especially at light loads and high rotational speeds. Under these conditions, skidding occurs between the rolling elements and the bearing races, leading to increased wear (higher friction coefficient), elevated bearing temperature, significant power losses and reduced service life of the bearing. The main objective of this study is to investigate the significance of various sensing technologies (induction, vibration, ultrasound, acoustic and optical) in detecting skidding in standard series roller bearings as well as custom-made roller bearings for aero engine applications. The bearings have a bore diameter of 60 mm and 90 mm, respectively. Jet and under race lubrication techniques have been used to supply oil to the bearings under test. The custom-made aero engine test bearing features special channels to allow under race lubrication of the rollers/races contacts as well as the cage land. The effect of radial load, rotational speed and oil flow on roller skidding have also been investigated and analyzed. Tests have been performed on a dedicated high speed experimental bearing facility and data was recorded using a commercially-available data acquisition system.

Dynamic Response of an Unbalanced Rotor Supported on Bearing With Outer Race Waviness

2013 ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Dynamic Response ◽  
Chaotic Behavior ◽  
Mathematical Formulation ◽  
Rotational Frequency ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Unbalanced Rotor ◽  
Non Linear ◽  
Rolling Elements

The paper investigates the non-linear dynamic response of an unbalanced rotor supported on ball bearings with outer race waviness. The excitation is due to unbalanced force and waviness on outer race. The sources of non-linearities are both the radial clearance as well as the Hertzian contact between races and rolling elements. The nonlinear responses due to unbalanced rotor supported on bearings are investigated. The combined effects like non-linear stiffness and non-linear damping for unbalanced rotor with bearing waviness have been considered and analyzed in detail for a rotor bearing system. In the mathematical formulation, the contacts between the rolling elements and the races are considered as an oscillating spring-mass-damper system. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the number of waves in the outer race. The results show the appearance of instability and chaos in the dynamic response as the number of waves in the outer race is changed. The study indicates that the interaction of ball passage frequency (ωbp) due to outer race waviness and rotational frequency (X) due to the unbalanced rotor force. Poincaré maps and frequency responses are used to elucidate and to illustrate the diversity of the system behavior.

scholarly journals Dynamical complexities in a tri-trophic hybrid food chain model with Holling type II and Crowley–Martin functional responses

2010 ◽  
Vol 15 (3) ◽  
pp. 361-375 ◽  
Author(s):  
R. K. Upadhyay ◽  
S. N. Raw ◽  
V. Rai
Keyword(s):  
Chaotic Dynamics ◽  
Community Dynamics ◽  
Chaotic Behavior ◽  
Dominant Role ◽  
Period Doubling ◽  
Chain Model ◽  
Type Ii ◽  
Top Predator ◽  
Functional Responses ◽  
Predator Behavior

We study how predator behavior influences community dynamics of predatorprey systems. It turns out that predator behavior plays a dominant role in community dynamics. The hybrid model studied in this paper reveals that period-doubling and period-doubling reversals can generate short-term recurrent chaos (STRC), which mimics chaotic dynamics observed in natural populations. STRC manifests itself when deterministic changes in a system parameter interrupt chaotic behavior at unpredictable intervals. Numerical results reinforce an earlier suggestion that period-doubling reversals could control chaotic dynamics in ecological models. In ecological terms, the prey and intermediate predator populations may go to extinction in the event of a catastrophe. The top predator is always a survivor. In contrast to this, this is not the case when the constituent populations are interacting through Holling type II functional response. Even this top predator can go to extinction in the event of such catastrophes.

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