scholarly journals Using the Gottwald and Melbourne’s 0-1 test and the Hugichi fractal dimension to detect chaos in defective and healthy ball bearings

2018 ◽  
Vol 241 ◽  
pp. 01017 ◽  
Author(s):  
C. A. Kitio Kwuimy ◽  
T. Haj Mohamad ◽  
C. Nataraj
Keyword(s):  
Fractal Dimension ◽  
Experimental Model ◽  
Chaotic Behavior ◽  
Ball Bearings ◽  
Behavior Dynamics ◽  
Rolling Elements ◽  
Dynamic Map

The paper considers the identification of chaotic behavior dynamics using the data extracted from an experimental model of rotor supported on rolling elements. A description of the methodis provided as well as an illustration using a standard dynamic map. The 0-1 test for chaos and the Higuchi dimension are shown to be effective tool in the identification of chaotic behavior of the systembearing with and without faults.

Dynamic Analysis of Ball Bearings Due to Clearance Effect

2009 ◽  
Author(s):  
S. H. Upadhyay ◽  
S. C. Jain ◽  
S. P. Harsha
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Peak Frequency ◽  
System Response ◽  
Ball Bearings ◽  
Outer Race ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Machine Systems ◽  
The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

Chaos in Healthy Ball Bearings

2007 ◽  
Author(s):  
Shahab H. Ghafari ◽  
Eihab M. Abdel-Rahman ◽  
Farid Golnaraghi ◽  
Fathy Ismail
Keyword(s):  
Large Amplitude ◽  
Chaotic Behavior ◽  
Vibration Characteristics ◽  
Small Range ◽  
Ball Bearings ◽  
Periodic Vibration ◽  
Free Bearing

This paper explores the effect of internal clearance on vibration characteristics of ball bearings. It is found that a fault-free bearing exhibits periodic vibration within a small range of internal clearance. However for larger values of internal clearance and large amplitude excitations, fault-free bearings exhibit chaotic behavior.

Vibration Analysis of Deep Groove Ball Bearings With Local Defect Using a New Displacement Excitation Function

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Chengcheng Li ◽  
Yi Qin ◽  
Yi Wang ◽  
Haizhou Chen
Keyword(s):  
Excitation Function ◽  
Mechanical Equipment ◽  
Local Defect ◽  
Ball Bearings ◽  
Defect Zone ◽  
Proposed Model ◽  
Deep Groove ◽  
Impulse Function ◽  
Rolling Elements ◽  
Vibration Signal Analysis

Abstract Bearings are vital parts of many mechanical equipment, the vibration signal analysis of bearings with local defects is important in guiding the fault diagnosis. In this paper, a dynamic analysis method is proposed to investigate the vibration response of the deep groove ball bearings (DGBBs) with local defect using a new displacement excitation function based on the Hertz contact theory and Newton's second law. The DGBB is modeled as a two degrees-of-freedom system, and an additional friction force in the defect zone, the influence of centrifugal force, the gravity of rolling elements, and lubrication traction/slip force between rolling elements and raceway are considered. And this model is used to study the dynamic signals of DGBB under different fault sizes and rotation speeds. Results indicate that the simulation signal has many continuous impacts and change over the time which is closer to the actual situation compared with the one-shot impulse function such as rectangular or half-sine or piecewise function when the rolling elements passed through the defect zone. Finally, the validity of the proposed model is verified by experiments. The simulated and experimental results indicate that the proposed model would achieve a more appropriate and accurate dynamic simulation.

Ceramics in Rolling Element Bearings

1979 ◽  
Author(s):  
C. F. Bersch ◽  
Philip Weinberg
Keyword(s):  
Fatigue Life ◽  
Silicon Nitride ◽  
Cooling System ◽  
Extreme Environment ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Turbine Engine ◽  
Rolling Element ◽  
Rolling Elements ◽  
History Of

The feasibility of using hot-pressed silicon nitride (HPSN) for rolling elements and for races in ball bearings and roller bearings has been explored. HPSN offers opportunities to alleviate many current bearing problems including DN and fatigue life limitations, lubricant and cooling system deficiencies, and extreme environment demands. The history of ceramic bearings and the results of various element tests, bearing tests in rigs, and bearing tests in a turbine engine will be reviewed. The advantages and problems associated with the use of HPSN in rolling element bearings will be discussed.

scholarly journals CHAOTIC BEHAVIOR OF BHALEKAR–GEJJI DYNAMICAL SYSTEM UNDER ATANGANA–BALEANU FRACTAL FRACTIONAL OPERATOR

Fractals ◽  
2021 ◽  
pp. 2240005
Author(s):  
SHABIR AHMAD ◽  
AMAN ULLAH ◽  
ALI AKGÜL ◽  
THABET ABDELJAWAD
Keyword(s):  
Fractal Dimension ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Existence Theory ◽  
Complex Behavior ◽  
Nonlinear Functional ◽  
Proposed Model ◽  
Fractal Derivative ◽  
2D And 3D

In this paper, a new set of differential and integral operators has recently been proposed by Abdon et al. by merging the fractional derivative and the fractal derivative, taking into account nonlocality, memory and fractal effects. These operators have demonstrated the complex behavior of many physical, which generally does not predict in ordinary operators or sometimes in fractional operators also. In this paper, we investigate the proposed model by replacing the classic derivative by fractal–fractional derivatives in which fractional derivative is taken in Atangana–Baleanu Caputo sense to study the complex behavior due to nonlocality, memory and fractal effects. Through Schauder’s fixed point theorem, we establish existence theory to ensure that the model posseses at least one solution. Also, Banach fixed theorem guarantees the uniqueness of solution of the proposed model. By means of nonlinear functional analysis, we prove that the proposed model is Ulam–Hyers stable under the new fractal–fractional derivative. We establish the numerical results of the considered model through Lagrangian piece-wise interpolation. For the different values of fractional order and fractal dimension, we study the chaos behavior of the proposed model via simulation at 2D and 3D phase. We show the effect of fractal dimension on integer and fractional order through simulations.

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.

Hysteretic Resonances and Intermittency Chaos in Ball Bearings

2018 ◽  
Author(s):  
Zhiyong Zhang ◽  
Xiaoting Rui ◽  
Yushu Chen ◽  
Wenkai Dong ◽  
Lei Li
Keyword(s):  
Ball Bearing ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Bearings ◽  
Rotor Systems ◽  
Revolute Joints ◽  
Rolling Elements ◽  
Varying Compliance

Ball bearings are essential parts of mechanical systems to support the rotors or constitute the revolute joints. The time-varying compliance (VC), bearing clearance and the Hertzian contact between the rolling elements and raceways are three fundamental nonlinear factors in a ball bearing, hence the ball bearing can be considered as a nonlinear system. The hysteresis and jumps induced by the nonlinearities of rolling bearings are typical phenomena of nonlinear vibrations in the rolling bearing-rotor systems. And the corresponding hysteretic impacts have direct effects on the cleavage derivative and fatigue life of the system components. Therefore, the behaviors of hysteresis and jumps are given full attentions and continued studies in the theoretical and engineering fields. Besides, many researchers have done a lot of calculations to depict the various characteristics of bifurcations and chaos in the rolling bearings and their rotor systems, but few researches have been addressed on the inherent mechanism of the typical intermittency vibrations in rolling bearings. With the aid of the HB-AFT (the harmonic balance method and the alternating frequency/time domain technique) method and Floquet theory, this paper will investigate deeply the resonant hysteresis and intermittency chaos in ball bearings.

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.

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