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.

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.

Dynamic Analysis of Ball Bearings Due to Clearance Effect

2009 ◽  
Author(s):  
S. H. Upadhyay ◽  
S. C. Jain ◽  
S. P. Harsha
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Peak Frequency ◽  
System Response ◽  
Ball Bearings ◽  
Outer Race ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Machine Systems ◽  
The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

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.

Analysis of a Rolling-Element Idler Gear Bearing Having a Deformable Outer-Race Structure

1963 ◽  
Vol 85 (2) ◽  
pp. 273-278 ◽  
Author(s):  
A. B. Jones ◽  
T. A. Harris
Keyword(s):  
Fatigue Life ◽  
High Speed ◽  
Roller Bearing ◽  
Rolling Element Bearing ◽  
Outer Ring ◽  
Outer Race ◽  
Rolling Element ◽  
Rolling Elements ◽  
Planet Gear ◽  
Bearing Rings

Conventional calculations of ball and roller bearing carrying capacity and fatigue life assume that the raceway bodies are rigid structures and that all elastic deformation occurs at the rolling elements’ contact with the raceways. In many instances, and particularly with aircraft applications, the bearing rings and their supports cannot be considered rigid. One such application is the planet gear in a transmission. This report develops a theory whereby the effects of the elastic distortions of the outer race of a rolling-element bearing on the internal load distribution and fatigue life of the bearing can be considered. The theory has been programmed for a high-speed, digital computer. An example of calculation for a planet gear roller bearing whose outer race is integral with the gear and of relatively thin section is given. The distortions of the flexible outer ring cause a significantly lower bearing fatigue life (L10) than would occur if the outer ring were rigid and considering a practical range of bearing diametral clearances. Mr. Jones developed the theoretical analysis for this paper and Mr. Harris provided the programming and the experimental data.

Dynamic Analysis of a High-Speed Rotor-Ball Bearing System Under Elastohydrodynamic Lubrication

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Yu-Yan Zhang ◽  
Xiao-Li Wang ◽  
Xiao-Qing Zhang ◽  
Xiao-Liang Yan
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Power Spectra ◽  
Elastohydrodynamic Lubrication ◽  
Lubricated Contacts ◽  
Rolling Elements ◽  
Stiffness And Damping ◽  
Bearing System

The nonlinear dynamic behaviors of a high-speed rotor-ball bearing system under elastohydrodynamic lubrication (EHL) are investigated. First, the numerical curve fittings for stiffness and damping coefficients of lubricated contacts between rolling elements and races are undertaken, and then the fitted formulae are introduced to the equations of motion of the rotor-ball bearing system to investigate its nonlinear characteristics. Furthermore, the time responses, power spectra, phase trajectories, orbit plots, and bifurcation diagrams for cases of ignoring and considering the lubrication condition in bearings are inspected and compared. The results indicate that, when lubrication is taken into account, the amplitudes of vibration displacements and velocities of the rotor system increase, and the appearance of different regions of periodic, quasi-periodic, and chaotic behavior is strongly dependent on the speed and load.

scholarly journals Analysis of an Arched Outer-Race Ball Bearing Considering Centrifugal Forces

1973 ◽  
Vol 95 (3) ◽  
pp. 265-271 ◽  
Author(s):  
B. J. Hamrock ◽  
W. J. Anderson
Keyword(s):  
Thermal Effects ◽  
High Speed ◽  
Ball Bearing ◽  
Centrifugal Forces ◽  
Angular Contact Ball Bearing ◽  
Outer Race ◽  
Contact Loads ◽  
Thrust Load ◽  
Raphson Method ◽  
Life Evaluations

A thrust load analysis of an arched outer-race ball bearing which considers centrifugal forces but which neglects gyroscopics, elastohydrodynamics, and thermal effects was performed. A Newton-Raphson method of iteration was used in evaluating the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center (V and W). Fatigue life evaluations were made. The similar analysis of a conventional bearing can be directly obtained from the arched bearing analysis by simply letting the amount of arching be zero (g = 0) and not considering equations related to the unloaded half of the outer race. The analysis was applied to a 150-mm angular contact ball bearing. Results for life, contact loads, and angles are shown for a conventional bearing (g = 0) and two arched bearings (g = 0.127 mm (0.005 in.), and 0.254 mm (0.010 in.)). The results indicate that an arched bearing is highly desirable for high speed applications. In particular, for a DN value of 3 million (20000 rpm) and an applied axial load of 4448 N (1000 lb), an arched bearing shows an improvement in life of 306 percent over that of a conventional bearing. At 4.2 million DN (28000 rpm), the corresponding improvement is 340 percent. It was also found for low speeds, the arched bearing does not offer the advantages that it does for high speed applications.

Analysis of Ball Bearing Vibrations Caused by Outer Race Waviness

1998 ◽  
Vol 120 (4) ◽  
pp. 901-908 ◽  
Author(s):  
K. Ono ◽  
Y. Okada
Keyword(s):  
Experimental Investigation ◽  
Analytical Study ◽  
Ball Bearing ◽  
Analytical Investigation ◽  
Outer Race ◽  
Number Of Factors ◽  
Rolling Elements ◽  
Race Track ◽  
Bearing Vibration ◽  
Radial Gap

An analytical investigation of the shaft vibration caused by a ball bearing is presented in this paper. Bearing vibration could be caused by a number of factors, such as defects occurring on the race track or the rolling elements. A common problem with defective bearings is the generation of waviness on the outer race track during the manufacturing process. The vibration of an automobile drive shaft caused by rolling elements rolling over the waviness surface is transmitted to the passenger cabin, and produces undesirable noise. In this paper an analytical study is undertaken to evaluate the effect of waviness number, radial gap and shaft imbalance on the bearing vibration. An experimental investigation was carried out to confirm the analytical study. The results show that the analytical study and experimental investigation agree very well.

Numerical investigation of the oil–air distribution inside ball bearings with under-race lubrication

2021 ◽  
pp. 135065012110105
Author(s):  
Le Jiang ◽  
Yaguo Lyu ◽  
Wenjun Gao ◽  
Pengfei Zhu ◽  
Zhenxia Liu
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Volume Fraction ◽  
Volume Flow Rate ◽  
Ball Bearings ◽  
Outer Race ◽  
Rotating Speed ◽  
Oil Distribution ◽  
Hole Configuration ◽  
Inner Race

Oil distribution inside the under-race lubricated bearing is crucial for lubrication and cooling of high-speed ball bearings. An under-race lubricated ball bearing is modeled to numerically investigate the effects of operating parameters and feed hole configuration on the distribution behavior of lubricant oil. The results of the numerical simulation indicate that the average oil volume fraction changes with a convex trend as the outer race rotating speed increases, while it changes monotonically with the inner race rotating speed, oil volume flow rate, and oil temperature. The extent of oil spreading on the outer race, cage, ball, and inner race decreases successively. Optimizing the feed hole configuration according to the average oil volume fraction is helpful to achieve precise lubrication of the under-race lubricated ball bearing.

scholarly journals Vibration response of defect-ball-defect of rolling bearing with compound defects on both inner and outer races

2021 ◽  
Vol 1207 (1) ◽  
pp. 012006
Author(s):  
Wei Luo ◽  
Changfeng Yan ◽  
Junbao Yang ◽  
Yaofeng Liu ◽  
Lixiao Wu
Keyword(s):  
Rolling Bearing ◽  
Vibration Response ◽  
Radial Clearance ◽  
Rolling Bearings ◽  
Outer Race ◽  
Response Characteristics ◽  
Bearing Fault Diagnosis ◽  
Theoretical Criterion ◽  
Vibration Model ◽  
Rolling Elements

Abstract Aiming at the problem that the existing compound defects model of rolling bearings under radial load is difficult to reflect the actual contact between rolling elements and defects. A new model is proposed to accurately reflect the simultaneous or sequential contact between inner and outer race defects and rolling elements. Considering the coupled excitation between shaft and bearing and pedestal, time-varying displacement excitation, and radial clearance, a four degree-of-freedom vibration model of rolling bearing with compound faults on both inner and outer races is built. The vibration equations are calculated by the method of numerical way, and the model is verified by experiment. The vibration response characteristics of the Defect-Ball-Defect model are studied, which renders a theoretical criterion for bearing fault diagnosis.

A Study on Measuring Method for 3D Motion of Balls in High-Speed Ball Bearings

2011 ◽  
Vol 199-200 ◽  
pp. 449-455 ◽  
Author(s):  
Xiang Gao ◽  
Chen Yang Zhang
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Measuring Method ◽  
Detection Methods ◽  
Angular Contact Ball Bearing ◽  
Basic Principles ◽  
Real Motion ◽  
3D Motion ◽  
Outer Race ◽  
Hall Sensors

In order to simply and accurately measure the realistic motion of balls in a ball bearing, a method called the static oblique coordinates is proposed to measure the 3D motion of balls in an angular contact ball bearing. This measuring method utilizes Hall elements as the sensors which are assembled on the side of outer race and cage of the ball bearing with magnetized balls. The voltage signals of the Hall sensors are collected online and applied to calculate and analyze the variation of magnetic axis of the magnetized ball, from which the 3D motion of the balls can be calculated. The basic principles and experiment method of the measuring method are illustrated. This method has simple structure without damaging the bearing, by which the bearing’s real motion can be studied consequently with a high precision. The magnetization and magnetic pole detection methods in this study effectively solved the problem of magnetized balls’ magnetism un-uniformity which causes the measure signal chaos.

Sign in / Sign up

Export Citation Format

Share Document