Predictive Dynamic Model of a Deep Groove Ball Bearing With a Flexible Outer Ring

2008 ◽  
Author(s):  
Alexandre Laurent ◽  
David Lenoir ◽  
Louis Jezequel ◽  
Bruno Mevel
Keyword(s):  
Dynamic Model ◽  
Ball Bearing ◽  
Dynamic Equilibrium ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Outer Ring ◽  
Integration Scheme ◽  
Deep Groove ◽  
Deep Groove Ball Bearing

An explicit dynamic model of a deep groove ball bearing under a radial load is proposed. All components are treated as rigid bodies whereas the bearing outer ring flexibility is taken into account using fixed interface component mode synthesis (CMS). The classical lubricated Hertzian contact theory is used to calculate elastic deflections and non-linear contact forces. The dynamic loading of the outer ring interface nodes is ensured using C2-continuous rational cubic splines. A Runge-Kutta-Felhberg 4th/5th order integration scheme is used to solve the dynamic equilibrium of all components. Time and frequency domain analyses are then carried out to investigate the dynamic behaviour of the ball bearing. The accuracy of these works is validated by comparison with the results of an analytical model and a model based on finite elements proposed in prior researchs.

High frequency vibration analysis of ball bearings under radial loads

2016 ◽  
Vol 230 (4) ◽  
pp. 579-588
Author(s):  
Yang Zhao ◽  
Guihua Dong ◽  
Heng Liu ◽  
Fengtao Wang ◽  
Meng Li ◽  
...  
Keyword(s):  
Dynamic Model ◽  
High Frequency ◽  
Vibration Amplitude ◽  
Ball Bearing ◽  
High Frequency Vibration ◽  
Rotating Speed ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Bearing Load

The paper investigates the role of radial load and rotating speed on the high frequency vibration of a deep groove ball bearing. Firstly, a bearing dynamic model with 6-DOF balls was established, considering the interactions between balls, races and the cage. The dynamic model was solved by fourth order varying steps Runge-Kutta integration. The frequency spectrums of dynamic response of races were analyzed with yule-walker and FFT. Secondly, a verification experiment was done with different radial loads and speeds. Finally, compared with the numerical and experimental results, the similar trend of the high frequency vibration was emerged. Higher vibration frequencies result with increasing bearing load; higher vibration amplitude cause by more quickly rotating speed. That is because the nature frequencies of the races are excited by the contact and shock between balls and races when balls leave from the non-load to the load zone. The frequency spectrums were also affected by the interaction between the balls and cage.

Ball Bearing Vibration Analysis Including Localized and Distributed Defects

2003 ◽  
Author(s):  
Jussi T. Sopanen ◽  
Aki M. Mikkola
Keyword(s):  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Natural Frequencies ◽  
Computer Code ◽  
Hertzian Contact ◽  
Outer Ring ◽  
Proposed Model ◽  
Deep Groove ◽  
Localized Defects ◽  
Bearing Rings

This study proposes the dynamic model of a deep groove ball bearing with six degrees of freedom. The model includes descriptions of non-linear Hertzian contact deformation and elastohydrodynamic fluid film. The geometry, material properties and diametral clearance of the bearing are given as the input to the proposed model. The bearing force and torque components are calculated from the relative displacements and velocities between bearing rings. Distributed defects such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. The effect of the diametral clearance of the bearing on the natural frequencies and vibration response of the rotor bearing system is studied. The diametral clearance is found to have a significant effect on the level of vibration as well as on the natural frequencies. Low-order waviness, also known as out-of-roundness, is found to generate vibration at frequencies of the waviness order multiplied by the rotation speed. Localized defects in the inner and outer ring are found to generate vibrations at bearing defect frequencies. The simulation results are in line with the analytical and experimental results available in literature. The proposed ball bearing model could be used in the general multibody or rotor dynamics computer code as an interference element between the rotor and the housing.

Dynamic analysis of rotor-bearing system by considering the transverse crack on rotor

2019 ◽  
Author(s):  
N. Upadhyay ◽  
P. K Kankar
Keyword(s):  
Deformation Theory ◽  
Transverse Crack ◽  
Dynamic Behaviour ◽  
Ball Bearing ◽  
Equation Of Motion ◽  
Hertzian Contact ◽  
Rotating Speed ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Unbalance Force

In this study, a new improved theoretical model of rotorbearing system has been presented to analyse the behaviour of the system due to the transverse crack on the rotor. Firstly, a mathematical model of the system with a transverse crack on rotor has been developed. In the modelling, the rotor is taken as Timoshenko beam and the unbalance force also included, which vary with rotating speed. The rotor is supported by two healthy deep groove ball bearing at both ends. The contact between balls and races of the bearings is considered as nonlinear spring, whose stiffness is obtained by Hertzian contact deformation theory. After the modelling of the rotor, the equation of motion has been derived which represents the dynamic behaviour of the system. Bifurcation diagrams are used to investigate the influence of depth and size of the crack on the dynamic behaviour of rotor ball-bearings system. Results indicate that if the depth and size of the crack increase the system becomes highly chaotic and unstable.

Nonlinear Vibration Analysis of an Unbalanced Flexible Rotor Supported by Ball Bearings With Radial Internal Clearance

2008 ◽  
Author(s):  
T. C. Gupta ◽  
K. Gupta ◽  
D. K. Sehgal
Keyword(s):  
Ball Bearing ◽  
Natural Frequencies ◽  
Power Spectra ◽  
Hertzian Contact ◽  
Phase Portraits ◽  
Integration Scheme ◽  
Flexible Rotor ◽  
Deep Groove ◽  
Varying Compliance ◽  
Bearing System

In the present work, the nonlinear dynamic response of an unbalanced horizontal flexible rotor supported by deep groove ball bearing is studied. Nonlinearity effects in rolling element bearings arise from Hertzian contact force deformation relationship and clearance between rolling elements and races. The system is bi-periodically excited due to varying compliance of ball bearing and rotating unbalance. The flexible rotor bearing system is modeled by finite element method, taking into account the gyroscopic moments, rotary inertia, shear deformation, proportional damping, nonlinear stiffness and radial internal clearance of ball bearing. The implicit type numerical time integration scheme Newmark-β and Newton-Raphson methods are used to numerically solve the nonlinear equations of motion. The mathematical model is validated for the natural frequencies of the flexible shaft and whirl frequencies. On account of variation in the ball bearing stiffness, the variation in natural frequencies of the rotor ball bearing system is estimated. The influence of ball bearing nonlinearity on dynamic behavior is analyzed by time histories of steady state response, phase portraits and power spectra. Effect of radial internal clearance and varying compliance on the unbalance response of flexible rotor is studied in detail.

Analysis of Deep Groove Ball Bearing Design for Assembly

2013 ◽  
Vol 633 ◽  
pp. 77-86
Author(s):  
Radivoje Mitrovic ◽  
Aleksandar Subic ◽  
Ivana Atanasovska
Keyword(s):  
Ball Bearing ◽  
Experimental Testing ◽  
Theory Of Elasticity ◽  
Outer Ring ◽  
Ball Bearings ◽  
Element Analysis ◽  
Thin Ring ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Slight Deformation

This paper presents a comprehensive analysis of the assembly processes for single-row ball bearings. There are two different types of assembly processes, which depend on ball numbers and ball bearing ring designs. In the case of deep groove ball bearings, assembly is usually undertaken through slight deformation of the outer ring to increase clearance for insertion of the final ball. As a result, the outer ring takes an elliptical instead of a circular shape and requires deformation to be below a critical level to avoid fracture. Causal analysis of outer ring fracture during assembly is the main goal of the presented analysis, based on the expressions of the Theory of Elasticity for the thin ring exposed to bending, as well as Finite Element Analysis (FEA). The theoretical and numerical results have been verified by experimental testing.

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