A dynamic model of ball bearing for simulating localized defects on outer race using cubic hermite spline

2014 ◽  
Vol 28 (9) ◽  
pp. 3433-3442 ◽  
Author(s):  
P. G. Kulkarni ◽  
A. D. Sahasrabudhe
Keyword(s):  
Dynamic Model ◽  
Ball Bearing ◽  
Outer Race ◽  
Localized Defects ◽  
Hermite Spline

scholarly journals Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Measurement Data ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Rolling Elements ◽  
Localized Defects

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

A 4-DOF dynamic model for ball bearing with multiple defects on raceways

2020 ◽  
pp. 146441932097287
Author(s):  
Xianghong Gao ◽  
Changfeng Yan ◽  
Yaofeng Liu ◽  
Pengfei Yan ◽  
Junbao Yang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Characteristic Frequency ◽  
Ball Bearing ◽  
Elastohydrodynamic Lubrication ◽  
Radial Clearance ◽  
Multiple Defects ◽  
Single Defect ◽  
Localized Defects ◽  
Fourier Function ◽  
Fault Characteristic

Localized defects in ball bearing components would cause additional vibration and it is imperative to reveal the vibration mechanism. The relationship between fault characteristic frequency (fBPFI and fBPFO) and multiple defect parameters of ball bearing were given in this paper. Considering elastohydrodynamic lubrication (EHL), radial clearance, time-varying displacement and excitation force generated from multiple defects, a 4 degree-of-freedom (DOF) dynamic model for ball bearing with multiple defects on inner or outer raceway was established, and the model has been verified by experiments. Vibration signals of ball bearing with different defects parameters were simulated, the effects of the angle between two defects ( θIAD and θOAD), the number of defects ( NDI and NDO) and the location of defects on outer raceway on dynamic response were studied. Comparing simulated signals with experimental results, it is shown that more impulses of acceleration signals are generated by multiple defects than that by single defect, meanwhile time delay due to two defects on raceways could also be found, fault characteristic frequency and their harmonics frequencies appeared in the envelope spectrums. Harmonics frequencies of fBPFI are modulated mainly by 2 fs instead of fs in frequency domain for multiple defects on inner raceway. The amplitudes of fBPFO and fBPFI change as Fourier curve when θOAD and θIAD varied within a certain range, and a series of Fourier function are given to describe the mathematic relationship.

Dynamic modeling and simulation of inter-shaft bearings with localized defects excited by time-varying displacement

2019 ◽  
Vol 25 (8) ◽  
pp. 1436-1446 ◽  
Author(s):  
Jing Tian ◽  
Yan-Ting Ai ◽  
Cheng-Wei Fei ◽  
Feng-Ling Zhang ◽  
Yat-Sze Choy
Keyword(s):  
Dynamic Model ◽  
Defect Size ◽  
Time Varying ◽  
Radial Load ◽  
Dynamic Features ◽  
Outer Race ◽  
Counter Rotation ◽  
Localized Defects ◽  
Bearing Vibration ◽  
Inner Race

To accurately describe the dynamic features of inter-shaft bearings with localized defect under operation, the dynamic model of inter-shaft bearing with localized defects was established with respect to time-varying displacement excitation. Based on fault simulations on a birotor experimental rig, the developed dynamic model of inter-shaft bearing is validated to have high accuracy (over 99%) when localized defects happen on inner and outer race with co- and counter-rotation, which indicates that the model can be adopted to simulate the faults of inter-shaft bearing instead of experiment. Through investigation of the square-root (SR) amplitudes of bearing vibration with different defect sizes, radial loads, and rotational directions, we find that the SR amplitudes of bearing vibration increase with increasing defect size and radial load for both co- and counter-rotation. The amplitudes of counter-rotation are larger than those of co-rotation for inner race and outer race, and the amplitude of inner race defect are larger than that of outer race defect for the same defect size or same radial load. This work reveals the SR variation of bearing vibration with localized surface defects under different defect sizes and radial loads, and accurately describes the dynamic characteristics of inter-shaft bearing with localized defects. The efforts of this study open a door to adopt a dynamic model in the future to evaluate and monitor the health condition of inter-shaft bearings in an aeroengine or other rotating machinery.

An improved model for investigating the vibration characteristics of ball bearing owing to outer race waviness under high speed

2021 ◽  
Vol 69 (2) ◽  
pp. 89-101
Author(s):  
Pingping Hou ◽  
Liqin Wang ◽  
Zhijie Xie ◽  
Qiuyang Peng
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Vibration Measurement ◽  
Vibration Frequencies ◽  
Outer Race ◽  
Response Characteristics ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Initial Clearance ◽  
Improved Model

In this study, an improved model for a ball bearing is established to investigate the vibration response characteristics owing to outer race waviness under an axial load and high speed. The mathematical ball bearing model involves the motions of the inner ring, outer ring, and rolling elements in the radial XY plane and axial z direction. The 2Nb + 5 nonlinear differential governing equations of the ball bearing are derived from Lagrange's equation. The influence of rotational speed and outer race waviness is considered. The outer race waviness is modeled as a superposition of sinusoidal function and affects both the contact deformation between the outer raceway and rolling elements and initial clearance. The MATLAB stiff solver ODE is utilized to solve the differential equations. The simulated results show that the axial vibration frequency occurred at l fc and the radial vibration frequencies appeared at l fc fc when the outer race waviness of the order (l) was the multiple of the number of rolling elements (k Nb) and that the principal vibration frequencies were observed at l fc fc in the radial x direction when the outer race waviness of the order (l) was one higher or one lower than the multiple of the number of rolling elements (k Nb 1). At last, the validity of the proposed ball bearing model was verified by the high-speed vibration measurement tests of ball bearings.

A Simulation Study on the Effects of Race Surface Waviness on Cage Dynamics in High-Speed Ball Bearings

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Linkai Niu
Keyword(s):  
Wear Rate ◽  
Dynamic Model ◽  
High Speed ◽  
Wave Amplitude ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Cage Effect ◽  
Surface Waviness ◽  
Slip Ratio ◽  
Wear Rates

The effects of the race surface waviness on the cage dynamics, including cage slip ratios, cage instabilities, and time-averaged cage wear rates, in high-speed ball bearings are investigated. A dynamic model of high-speed ball bearings considering the cage effect and the race surface waviness is proposed. Based on the proposed dynamic model, the effects of the maximum wave amplitude (MWA) and the wave order (WO) of race surface waviness on cage slip ratio, cage instability, and time-averaged cage wear rate are investigated. The results show that the race surface waviness has a great effect on the cage dynamics. The waviness would increase the random impacts between balls and cage pockets and thus cause more instable motion of the cage. Although the ball skidding and the cage slip ratio decrease with the increase of MWA, the cage instability and the cage wear rate become severe when MWA increases. In addition, the effect of WO on cage dynamics is nonlinear. The current investigation could provide a theoretical tool for an in-depth understanding of the dynamics in a high-speed ball bearing.

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.

Effect of Waviness on Vibration and Acoustic Features of Rolling Element Bearing

2012 ◽  
Author(s):  
Yimin Shao ◽  
Pei Wang ◽  
Zaigang Chen
Keyword(s):  
Dynamic Model ◽  
Computational Cost ◽  
Element Model ◽  
Mapping Method ◽  
Rolling Element Bearing ◽  
Acoustic Features ◽  
Rigid Displacement ◽  
Outer Race ◽  
Deep Groove ◽  
Rolling Element

Waviness of rolling element bearings, as one of the most concerned factors, would greatly influence the dynamic and acoustic performances of machines. In this paper, a new algorithm of vibro-acoustic coupling, which is based on the displacement mapping method by applying the displacement history obtained from a 6-DOF bearing dynamic model to be as the boundary condition of the finite element model of the bearing housing, is developed to predict the effect of waviness on the vibration and acoustic features of the bearing. The displacement excitation of the circumferential surface of bearing housing can be obtained by vector synthesis of bearing rigid displacement from the 6-DOF bearing dynamic model. This new method enables not only the reduction in computational cost, but also simulation of the bearing waviness under different sizes. A 6308 deep groove ball bearing model with outer race waviness is taken as an example case to examine the effectiveness of the new algorithm. The simulation results show that the new algorithm is able to predict the vibration and acoustic features of the bearing with waviness.

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