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.

Nonlinear Dynamic Analysis of an Asymmetric Ball Bearing Rotor System

2019 ◽  
Author(s):  
Doğancan Bahan ◽  
Ender Ciğeroğlu
Keyword(s):  
Ball Bearing ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Ball Bearings ◽  
Algebraic Equations ◽  
Rotor Systems ◽  
Nonlinear Algebraic Equations

Abstract Performance of ball bearing–rotor systems are highly dependent on and often limited by characteristics of ball bearings. Several studies are available in the literature, investigating varying compliance and subharmonic resonances of ball bearings. Most of the studies are carried out with rigid rotors to focus on modelling of the bearings. There exist few studies which take flexibility of rotors into account. Furthermore, even if the rotor flexibility is modelled, most of the time symmetrical rotors are considered. However, rotors are rarely symmetric in realistic applications due to different locations of bearings and different weights of rotor components (compressors, turbines etc.). In this study, an asymmetric, balanced, flexible rotor supported by ball bearings considering Hertzian contact and radial clearance is investigated. Rotor shaft is modelled with Nelson finite rotor elements using Timoshenko beam theory and disks are considered as rigid masses. Harmonic Balance Method (HBM) is used to obtain nonlinear algebraic equations in the frequency domain and Alternating Frequency Time (AFT) method is utilized to find Fourier coefficients of nonlinear bearing forces. In order to decrease the number of nonlinear equations to be solved, Receptance Method (RM) is applied. Resulting set of nonlinear algebraic equations is solved by using Newton’s method with arclength continuation. Several case studies are performed and effects of asymmetry on nonlinear periodic vibration response of rotors are studied.

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.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

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.

scholarly journals Suppression of Complex Hysteretic Resonances in Varying Compliance Vibration of a Ball Bearing

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Zhiyong Zhang ◽  
Thomas Sattel ◽  
Aditya Suryadi Tan ◽  
Xiaoting Rui ◽  
Shaopu Yang ◽  
...  
Keyword(s):  
Ball Bearing ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Dynamical Mechanism ◽  
Nonlinear Characteristics ◽  
Bearing Clearance ◽  
Rolling Elements ◽  
Bearing Stiffness ◽  
Hysteretic Characteristics ◽  
The Stability

It is traditionally considered that, due to the Hertzian contact force-deformation relationship, the stiffness of rolling bearings has stiffening characteristics, and gradually researchers find that the supporting characteristics of the system may stiffen, soften, and even coexist from them. The resonant hysteresis affects the stability and safety of the system, and its jumping effect can make an impact on the system. However, the ball bearing contains many nonlinearities such as the Hertzian contact between the rolling elements and raceways, bearing clearance, and time-varying compliances (VC), leading great difficulties to clarify the dynamical mechanism of resonant hysteresis of the system. With the aid of the harmonic balance and alternating frequency/time domain (HB-AFT) method and Floquet theory, this paper will investigate the hysteretic characteristics of the Hertzian contact resonances of a ball bearing system under VC excitations. Moreover, the linearized dynamic bearing stiffness of the system will be presented for assessing the locations of VC resonances, and the nonlinear characteristics of bearing stiffness will also be discussed in depth. Our analysis indicates that the system possesses many types of VC resonances such as the primary, internal, superharmonic, and even combination resonances, and the evolutions of these resonances are presented. Finally, the suppression of resonances and hysteresis of the system will be proposed by adjusting the bearing clearance.

Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid Rotor Supported by Two or More Ball Bearings Considering Five Degrees of Freedom

2001 ◽  
Vol 124 (1) ◽  
pp. 82-90 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Nonlinear Load ◽  
Rolling Elements ◽  
Nonlinear Equations Of Motion

This research presents a nonlinear model to analyze the ball bearing vibration due to the waviness in a rigid rotor supported by two or more ball bearings. The waviness of a ball and each races is modeled by the superposition of sinusoidal function, and the position vectors of inner and outer groove radius center are defined with respect to the mass center of the rotor in order to consider five degrees of freedom of a general rotor-bearing system. The waviness of a ball bearing is introduced to these position vectors to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. Numerical results of this research are validated with those of prior researchers. The proposed model can calculate the translational displacement as well as the angular displacement of the rotor supported by two or more ball bearings with waviness. It also characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing, and the sideband frequencies resulting from nonlinearity of the waviness interaction.

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).

Noise calculation method of deep groove ball bearing caused by vibration of rolling elements considering raceway waviness

2021 ◽  
pp. 095440622110458
Author(s):  
Minjie Sun ◽  
Haojie Xu ◽  
Qi An
Keyword(s):  
Ball Bearing ◽  
Axial Direction ◽  
Rolling Bearing ◽  
Mechanical Analysis ◽  
Machining Accuracy ◽  
Surface Waviness ◽  
Random Surface ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Rolling Elements

Raceway waviness error is the main reason to cause rolling elements to vibrate along axial direction and emit noise. In this paper, the mechanical analysis on deep groove ball bearing is carried out. With auto-correlation function, random surface waviness of both inner and outer raceways is simulated. A contact model of rolling elements and raceways considering surface waviness is established. Combining with the theory of acoustic equation, a calculation model is established for the noise caused by vibration of rolling elements and inner ring. The results show that with the decrease of machining accuracy, the noise of rolling elements increases due to axial vibration; with the increase of rotation speed, the noise also increases. Besides, the spectrum of radiation noise of inner raceway with different waviness amplitudes is given. The results indicate that the 3-D waviness on raceway surface has an influence on the vibration and the noise emitted by both rolling elements and inner ring, and provide guidance for sound control in deep groove rolling bearing.

scholarly journals Analisa Getaran Akibat Kerusakan Deep Grove Ball Bearing Seri 6003RS

2019 ◽  
Vol 9 (02) ◽  
pp. 39-43
Author(s):  
Muhamad Riva’i ◽  
Nanda Pranandita
Keyword(s):  
Ball Bearing ◽  
Rolling Bearing ◽  
Internal Diameter ◽  
Outer Diameter ◽  
Outer Race ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Rolling Element ◽  
Rolling Elements ◽  
Vibration Measuring

Measurement of the damage of elements in bearing can be by measuring the vibration generated in the form of a frequency signal when the pad is rotating. Measurement of vibration on the bearing by using vibration measuring instrument. Damage to the rolling bearing includes damage to the cage, outer ring, inner ring and balls. The rolling bearings used in this study are deep groove ball bearing type 6003 RS with internal diameter (d) = 17 mm, outer diameter (D) = 35 mm, bearing thickness (B) = 10, number of rolling elements (Nb) = 10 pieces, and the diameter of the rolling element (Bd) = 4.75 mm. In the rotation of the bearing (Fr) = 2003 rpm (33.38 Hz) we found the experimental results of bearings that have been damaged in the outer race at 138 Hz frequency, inner race damage at 196 Hz frequency, (ball) at a frequency of 88.8 Hz and cage damage at a frequency of 13.8 Hz.

A dynamic model of an overhung rotor with ball bearings

2011 ◽  
Vol 225 (4) ◽  
pp. 310-321 ◽  
Author(s):  
O Cakmak ◽  
K Y Sanliturk
Keyword(s):  
Ball Bearing ◽  
Element Model ◽  
Contact Dynamics ◽  
Ball Bearings ◽  
Cage Structure ◽  
Order Tracking ◽  
Rolling Elements ◽  
Localized Defects ◽  
Gyroscopic Effects ◽  
Multi Body

A ball bearing comprising rolling elements, inner and outer rings, and a cage structure can be described as a multi-body system (MBS). In order to predict the dynamic behaviour and resonance characteristics of a rotor–ball bearing system, it can be modelled and analysed as a MBS with flexible and rigid parts. In this study, a ball bearing is modelled with MBS approach using MSC ADAMS commercial software. The Hertzian theory is used for modelling the contact dynamics between the balls and the rings. The ball bearing model is then assembled with the rotor model which comprised a shaft and a disc positioned at the free end of the shaft. The ball bearing model is used with both flexible and rigid shaft assumptions in order to highlight the differences between the two cases. For the flexible shaft case, the MBS model also included a finite element model of the shaft. As expected, it is necessary to include the flexibility of the shaft in the model in order to to predict the changes in the modal characteristics of the system as a function of the rotor speed. Furthermore, including the gyroscopic effects leads to observe the forward and backward travelling modes with different natural frequencies. The effects of the bearing diametral clearance and localized defects on the inner and outer rings are modelled and analysed using the model developed. Also, the effects of the rotor unbalance on the vibration level of the whole system are examined. A test rig – consisting of two ball bearings, a shaft, and a disc – is also designed and developed so as to validate the theoretical model using experimental data. Order tracking and modal analyses are carried out and Campbell diagrams are obtained. Finally, the theoretical and the experimental results are compared and a refined MBS model is obtained for further analyses.

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