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.

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.

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.

scholarly journals Experimental Rig for Measuring Lubricant Film Thickness in Rolling Bearings

2014 ◽  
Vol 658 ◽  
pp. 381-386
Author(s):  
Xing Nan Zhang ◽  
Karolina Jablonka ◽  
Romeo Glovnea
Keyword(s):  
Film Thickness ◽  
Lubricant Film ◽  
Hertzian Contact ◽  
Lubricant Film Thickness ◽  
Rolling Bearings ◽  
The Past ◽  
Rolling Element ◽  
Rolling Elements ◽  
Experimental Rig ◽  
Made In

Electrical capacitance has been applied in the past for measuring the lubricant film thickness in rolling element bearings. The main difficulty arises from the fact that the measured capacitance is a combination of the capacitances of many rolling elements, which come in contact with both the inner and outer rings. Besides, the capacitance of the Hertzian contact itself and the surrounding area must also be separated. It results in a complex system which, in order to be solved for the film thickness at a particular location on the bearing many approximations have to be made. In the present study the authors use an experimental rig in which the capacitance of a single ball can be isolated. Moreover the capacitance of the ball – inner ring and ball – outer ring contacts can be measured separately.

scholarly journals A theoretical model for predicting the vibration response of outer race defective ball bearing

2018 ◽  
Vol 7 (2) ◽  
pp. 289
Author(s):  
Samir Shaikh ◽  
Sham Kulkarni
Keyword(s):  
Theoretical Model ◽  
Ball Bearing ◽  
Mathematical Formulation ◽  
Vibration Response ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Outer Race ◽  
Rolling Element ◽  
Rolling Elements ◽  
Extended Type

The theoretical model with 2 degree-of-freedom system is developed for predicting the vibration response and analyze frequency properties in an extended type defective ball bearing. In the mathematical formulation, the contact between the races and rolling element considered as non-linear springs. The contact forces produced during the collaboration of rolling elements are obtained by utilizing Hertzian contact deformation hypothesis. The second order nonlinear differential equation of motion is solved using a state space variable method with the help of MATLAB software and the vibration acceleration response of the defective ball bearing presented in the frequency spectrum. The effects of variation in speed and size of the defect on characteristic frequency of extended fault on the outer raceway of the ball bearing have been investigated. The theoretical results of the healthy (non defective) and defective bearing are compared with each other.

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.

Parameters research on time-varying stiffness of the ball bearing system without race control hypothesis

2021 ◽  
pp. 095440622110179
Author(s):  
Yongzhen Liu ◽  
Yimin Zhang
Keyword(s):  
Ball Bearing ◽  
Combined Loading ◽  
Time Varying ◽  
Noticeable Effect ◽  
Rotating Speed ◽  
Bearing Stiffness ◽  
Vibration Mechanism ◽  
Control Hypothesis ◽  
Full Consideration ◽  
Bearing System

When the ball bearing serving under the combined loading conditions, the ball will roll in and out of the loaded zone periodically. Therefore the bearing stiffness will vary with the position of the ball, which will cause vibration. In order to reveal the vibration mechanism, the quasi static model without raceway control hypothesis is modeled. A two-layer nested iterative algorithm based on Newton–Raphson (N-R) method with dynamic declined factors is presented. The effect of the dispersion of bearing parameters and the installation errors on the time-varying carrying characteristics of the ball-raceway contact and the bearing stiffness are investigated. Numerical simulation illustrates that besides the load and the rotating speed, the dispersion of bearing parameters and the installation errors have noticeable effect on the ball-raceway contact load, ball-inner raceway contact state and bearing stiffness, which should be given full consideration during the process of design and fault diagnosis for the rotor-bearing system.

Electric impedance of rolling bearings - Consideration of unloaded rolling elements

2021 ◽  
Vol 158 ◽  
pp. 106927
Author(s):  
T. Schirra ◽  
G. Martin ◽  
S. Puchtler ◽  
E. Kirchner
Keyword(s):  
Electric Impedance ◽  
Rolling Bearings ◽  
Rolling Elements

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

Motion of a Ball in a Ball Bearing

1973 ◽  
Vol 95 (1) ◽  
pp. 263-268
Author(s):  
H. Portig ◽  
H. G. Rylander
Keyword(s):  
Deformation Theory ◽  
Coulomb Friction ◽  
Ball Bearing ◽  
Digital Simulation ◽  
Equations Of Motion ◽  
Unsteady Motion ◽  
Hertzian Contact ◽  
Contact Deformation ◽  
Normal Forces ◽  
Simulation Language

A method is developed which allows the digital simulation of the unsteady motion of a single ball constrained only by two moving bearing races. Any desired motion of the races can be simulated. Normal forces acting on the ball are calculated by Hertzian contact deformation theory. If there is slippage between ball and races, Coulomb friction is assumed to occur. Solutions to the differential equations of motion were obtained on a computer with the digital simulation language MIMIC. The phenomenon of ball control as well as the behavior of the ball as it reached a controlled state from rest were observed. This analysis can produce more realistic results than methods that assume that the ball is controlled at all times, especially when the races are radially or angularly displaced with respect to each other.

Analysis of a Ball Bearing With Waviness Considering the Centrifugal Force and Gyroscopic Moment of the Ball

2003 ◽  
Vol 125 (3) ◽  
pp. 487-498 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Centrifugal Force ◽  
Contact Force ◽  
Ball Bearing ◽  
Vibration Frequencies ◽  
Governing Equations ◽  
Equilibrium Equations ◽  
Gyroscopic Moment ◽  
Rolling Elements ◽  
Force Contact ◽  
Force Displacement

This research presents an analytical method to calculate the characteristics of the ball bearing under the effect of the waviness in its rolling elements and the centrifugal force and gyroscopic moment of ball. The waviness of rolling elements is modeled by using sinusoidal function, and the centrifugal force and gyroscopic. moment of ball are included in the kinematic constraints and force equilibrium equations to produce the nonlinear governing equations. To improve the convergence of the numerical solution of the nonlinear governing equations, it includes the derivatives of the gyroscopic moment and load-deflection constant of each race in the Newton-Raphson formulation. The accuracy of this research is validated by comparing with the prior research, i.e., (i) the contact force, contact angle in case of considering only the centrifugal force and gyroscopic moment of ball, and (ii) the contact force and vibration frequencies in case of considering only the waviness, respectively. It investigates the stiffness, contact force, displacement and vibration frequencies of the ball bearing, considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

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