Control of Period-Doubling and Chaos in Varying Compliance Resonances for a Ball Bearing

2019 ◽  
Vol 87 (2) ◽  
Author(s):  
Zhiyong Zhang ◽  
Xiaoting Rui ◽  
Rui Yang ◽  
Yushu Chen
Keyword(s):  
Ball Bearing ◽  
Dynamic Stiffness ◽  
Period Doubling ◽  
Rolling Bearing ◽  
Type I ◽  
Ball Bearings ◽  
Bifurcation Instability ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Varying Compliance

Abstract Varying compliance (VC) is an inevitable parametrical excitation to rolling bearing systems due to time-varying stiffness from rolling element revolution. Period-doubling instability in the VC primary resonances of ball bearing is presented in many studies. Recently, this instability was demonstrated to be a probable indicator of occurrence of strong one to two internal resonances and chaotic motions, which has potential effects on the stability and safety of the bearing-rotor system. However, few studies have directly attempted to suppress this bifurcation instability. Here, a dynamic stiffness evaluating method is presented for assessing the threshold of the period-doubling and complex motions in VC primary resonances of ball bearings, where the elaborate evolution of the bifurcating process is obtained by harmonic balance and alternating frequency/time domain (HB-AFT) method and using Floquet theory. Our analysis indicates that by introducing certain additional stiffness, the period-doubling and corresponding subharmonic internal resonances can be suppressed. Besides, the evolution and mechanism of type I intermittency chaos in ball bearings will be clarified in depth. It is also shown that extensive chaotic motions for large bearing clearances (e.g., 40 μm) can vanish perfectly by action of additional stiffness.

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.

Simulation and Analysis of Vibration of Rolling Bearing

2013 ◽  
Vol 588 ◽  
pp. 257-265 ◽  
Author(s):  
Robert Kostek
Keyword(s):  
Failure Modes ◽  
Ball Bearing ◽  
Period Doubling ◽  
Rolling Bearing ◽  
Self Similarity ◽  
Chaotic Vibrations ◽  
Deep Groove ◽  
Wide Range ◽  
Deep Groove Ball Bearing ◽  
Non Linear

This article presents a non-linear model of deep groove ball bearing and results of simulation. Vibrations of this bearing are studied for a wide range of clearance. An evolution from periodic to chaotic vibrations is visible due to increase of clearance. A number of phenomena associated with non-linear dynamics are observed, for instance: bistability, chaotic vibrations, windows of periodical vibrations, jump of amplitude, period-doubling cascade leading to chaos, bifurcation directly leading to chaos, and self-similarity of a Poincaré section. Moreover, amplitudes of vibrations are presented as functions of clearance. This provides an opportunity to select failure modes. Unfortunately, relations clearance amplitude and amplitude - clearance are ambiguous.

scholarly journals Mechanism and Characteristics of Global Varying Compliance Parametric Resonances in a Ball Bearing

2020 ◽  
Vol 10 (21) ◽  
pp. 7849
Author(s):  
Zhiyong Zhang ◽  
Thomas Sattel ◽  
Yujie Zhu ◽  
Xuan Li ◽  
Yawei Dong ◽  
...  
Keyword(s):  
Ball Bearing ◽  
Primary Resonance ◽  
Period Doubling ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Bearing Clearance ◽  
Parametric Resonances ◽  
Rolling Elements ◽  
The Stability ◽  
Varying Compliance

Varying compliance (VC) is an unavoidable form of parametric excitation in rolling bearings and can affect the stability and safety of the bearing and its supporting rotor system. To date, we have investigated VC primary resonance in ball bearings, and in this paper other parametric VC resonance types are addressed. For a classical ball bearing model with Hertzian contact and clearance nonlinearities between the rolling elements and raceway, the harmonic balance and alternating frequency/time domain (HB–AFT) method and Floquet theory are adopted to analyze the VC parametric resonances and their stabilities. It is found that the 1/2-order subharmonic resonances, 2-order superharmonic resonances, and various VC combination resonances, such as the 1-order and 2-order summed types, can be excited, thus resulting in period-1, period-2, period-4, period-8, period-35, quasi-period, and even chaotic VC motions in the system. Furthermore, the bifurcation and hysteresis characteristics of complex VC resonant responses are discussed, in which cyclic fold, period doubling, and the second Hopf bifurcation can occur. Finally, the global involution of VC resonances around bearing clearance-free operations (i.e., adjusting the bearing clearance to zero or one with low interference) are provided. The overall results extend the investigation of VC parametric resonance cases in rolling bearings.

The Varying Compliance Resonance in a Ball Bearing Rotor System Affected by Different Ball Numbers and Rotor Eccentricities

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Rui Yang ◽  
Lei Hou ◽  
Yulin Jin ◽  
Yushu Chen ◽  
Zhiyong Zhang
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Influencing Factor ◽  
Rolling Bearing ◽  
Rotor System ◽  
Low Speed ◽  
Speed Range ◽  
Bearing Vibration ◽  
Varying Compliance ◽  
Theoretical Results

The varying compliance (VC) vibration directly reflects the oscillation intensity of a rolling bearing, and it can be fully revealed in the VC resonance. Moreover, we define the bearing vibration intensity as the bearing vibration information in this paper. Besides the rolling element number of the bearing, the rotor eccentricity is also an inevitable influencing factor for the VC vibration. This paper focuses on the VC resonance characteristics in a ball bearing rotor system. An analytical model is established, and the vibration responses of the system are calculated in a large speed range with the consideration of different ball numbers and different rotor eccentricities. The theoretical results show that the VC vibration is clearer in low-speed range where the VC resonance exist, while it is suppressed in high-speed range. In general, the intensity of the VC resonance decreases with the increase of ball numbers and is not sensible to the rotor eccentricities in low-speed range. Finally, a ball bearing rotor experiment system is setup, the VC resonance is clearly detected, and the high-quality bearing vibration information is obtained. The experimental results qualitatively agree with the theoretical results.

Temperature Rise Prediction of Oil-Air Lubricated Angular Contact Ball Bearings Using Artificial Neural Network

2019 ◽  
Vol 12 (3) ◽  
pp. 248-261
Author(s):  
Baomin Wang ◽  
Xiao Chang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Temperature Rise ◽  
High Speed ◽  
Ball Bearing ◽  
Influence Factors ◽  
Ball Bearings ◽  
Ann Model ◽  
Angular Contact Ball Bearing ◽  
Artificial Neural

Background: Angular contact ball bearing is an important component of many high-speed rotating mechanical systems. Oil-air lubrication makes it possible for angular contact ball bearing to operate at high speed. So the lubrication state of angular contact ball bearing directly affects the performance of the mechanical systems. However, as bearing rotation speed increases, the temperature rise is still the dominant limiting factor for improving the performance and service life of angular contact ball bearings. Therefore, it is very necessary to predict the temperature rise of angular contact ball bearings lubricated with oil-air. Objective: The purpose of this study is to provide an overview of temperature calculation of bearing from many studies and patents, and propose a new prediction method for temperature rise of angular contact ball bearing. Methods: Based on the artificial neural network and genetic algorithm, a new prediction methodology for bearings temperature rise was proposed which capitalizes on the notion that the temperature rise of oil-air lubricated angular contact ball bearing is generally coupling. The influence factors of temperature rise in high-speed angular contact ball bearings were analyzed through grey relational analysis, and the key influence factors are determined. Combined with Genetic Algorithm (GA), the Artificial Neural Network (ANN) model based on these key influence factors was built up, two groups of experimental data were used to train and validate the ANN model. Results: Compared with the ANN model, the ANN-GA model has shorter training time, higher accuracy and better stability, the output of ANN-GA model shows a good agreement with the experimental data, above 92% of bearing temperature rise under varying conditions can be predicted using the ANNGA model. Conclusion: A new method was proposed to predict the temperature rise of oil-air lubricated angular contact ball bearings based on the artificial neural network and genetic algorithm. The results show that the prediction model has good accuracy, stability and robustness.

Friction Tests of Ball Bearings with Comparison of Lubricants

2017 ◽  
Vol 866 ◽  
pp. 375-378
Author(s):  
Sathitbunanan Sumate ◽  
Wirote Ritthong
Keyword(s):  
Energy Efficiency ◽  
Electric Power ◽  
Ball Bearing ◽  
Maximum Load ◽  
Engine Oil ◽  
Ball Bearings ◽  
Hydraulic Oil ◽  
Proper Size ◽  
Transmission Fluid ◽  
Moving Parts

The ball bearings are the rotating components which are widely spread to moving parts for all machinery operation in general industry. This paper presents the ball bearing resistance tool which has a proper size and can handle the maximum load of 300 kg by using an electric power. The ball bearing resistance tool was used to test the bearings No. 6011 cm. The series of tests was performed in the ball bearings lubricated; engine oil SAE 10W/40, auto transmission fluid Dexron, and hydraulic oil. The rotational speeds for testing were vary; 500, 600 and 700 rpm respectively. At each speed, there were various weight; 50, 70, 90,110,130,150, and 170 kg respectively. The results show that the hydraulic oil generated the smallest coefficients of friction and energy efficiency for ball bearing operation.

Prediction of Ball Motion in High-Speed Thrust-Loaded Ball Bearings

1976 ◽  
Vol 98 (3) ◽  
pp. 463-469 ◽  
Author(s):  
C. R. Gentle ◽  
R. J. Boness
Keyword(s):  
Computer Program ◽  
High Speed ◽  
Ball Bearing ◽  
Viscoelastic Behavior ◽  
Specific Situation ◽  
Fluid Models ◽  
Ball Bearings ◽  
Theoretical Predictions ◽  
Ball Motion

This paper describes the development of a computer program used to analyze completely the motion of a ball in a high-speed, thrust-loaded ball bearing. Particular emphasis is paid to the role of the lubricant in governing the forces and moments acting on each ball. Expressions for these forces due to the rolling and sliding of the ball are derived in the light of the latest fluid models, and estimates are also made of the cage forces applicable in this specific situation. It is found that only when lubricant viscoelastic behavior is considered do the theoretical predictions agree with existing experimental evidence.

Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Shengye Lin ◽  
Shuyun Jiang
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Fixed Position ◽  
Angular Contact Ball Bearing ◽  
Face To Face ◽  
Radial Stiffness ◽  
Proposed Model ◽  
Stiffness Characteristics

This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.

Oil Pumping in High Speed and High Loaded Ball Bearings

2004 ◽  
Author(s):  
Michael Flouros
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Research Programme ◽  
Aircraft Engine ◽  
Ball Bearings ◽  
European Research ◽  
Rolling Bearings ◽  
Engine Design ◽  
Oil Flow ◽  
Total Oil

Trends in aircraft engine design cause increased mechanical stress requirements for rolling bearings. Consequently high amounts of heat are rejected which results in high oil scavenge temperatures. The direction of oil flow in the bearing can considerably affect the heat transported by the oil. An RB199 turbofan bearing and its associated chamber were modified to carry out the survey. The test bearing was a 124mm PCD ball bearing. The bearing has a split inner-ring employing under-race lubrication by two individual jets. The total oil flow could be devided to any ratio through the jets. This had an impact on the oil scavenge temperatures and the scavenge flows on both sides of the bearing. Significant reduction in the ‘heat to oil’ was achieved when oil was fed at certain proportions (ratio). This work is part of the European Research programme Brite Euram ATOS (Advanced Transmission and Oil Systems).

scholarly journals Numerical simulation and experimental comparison of flaw evolution on a bearing raceway: Case of thrust ball bearing

2018 ◽  
Vol 5 (4) ◽  
pp. 427-434 ◽  
Author(s):  
M.Y. Toumi ◽  
S. Murer ◽  
F. Bogard ◽  
F. Bolaers
Keyword(s):  
Structural Damage ◽  
Ball Bearing ◽  
Rolling Contact ◽  
Experimental Comparison ◽  
Ball Bearings ◽  
Damage State ◽  
Element Analysis ◽  
Rolling Surface ◽  
Experimental Apparatus ◽  
Good Agreement

Abstract Bearings are essential elements in the design of rotating machines. In an industrial context, bearing failure can have costly consequences. This paper presents a study of the rolling contact fatigue damage applied to thrust ball bearings. It consists in building a dynamic three-dimensional numerical model of the cyclic shift of a ball on an indented rolling surface, using finite element analysis (FEA). Assessment of the evolution in size of a surface spall as a function of loading cycles is also performed using FEM coupled with fatigue laws. Results are in good agreement with laboratory tests carried out under the same conditions using a fatigue test cell dedicated to ball bearings. This study may improve knowledge about estimating the lifetime of rolling components after onset of a spall using FEA and accounting for structural damage state. Highlights The experimental apparatus and damaged thrust ball bearing are described. We model a portion of the thrust ball bearing featuring a spherical indent. Numerical results in terms of stress field are compared to analytical results from the literature. A fatigue software is used to assess the evolution of spalling size. Good agreement is obtained between experimental test campaigns at different loads and FEA results.

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