Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Shengye Lin ◽  
Shuyun Jiang
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Fixed Position ◽  
Angular Contact Ball Bearing ◽  
Face To Face ◽  
Radial Stiffness ◽  
Proposed Model ◽  
Stiffness Characteristics

This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.

Dynamic Characteristics of Motorized Spindle With Tandem Duplex Angular Contact Ball Bearings

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Shengye Lin ◽  
Shuyun Jiang
Keyword(s):  
Transfer Matrix ◽  
Dynamic Characteristics ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Motorized Spindle ◽  
Angular Contact Ball Bearing ◽  
Stiffness Coefficients ◽  
Proposed Model

Abstract The purpose of this study is to investigate the dynamics of motorized spindle, in which the tilting effect of tandem duplex angular contact ball bearing is considered. First, the quasi-static model of the duplex angular contact ball bearing is developed based on the Jones's bearing model. Then, the model is numerically solved using the Newton–Raphson method to obtain 16 stiffness coefficients (including the tilting ones). Later, a modified transfer matrix method is used to establish the dynamic model of the motorized spindle system with 16 stiffness coefficients. Finally, experiments have been performed to detect the stiffness of the tandem duplex angular contact ball bearing and the unbalance response of the motorized spindle. Results show that the modified transfer matrix method can be used to analyze the dynamic behavior of the motorized spindle supported on tandem duplex angular contact ball bearings, the tilting effect of the tandem duplex angular contact ball bearing affects the dynamic behaviors of the motorized spindle, and the theoretical dynamic characteristics using the proposed model agree with the experimental ones.

Theoretical and Experimental Study on Stiffness Characteristics of a Wire Race Ball Bearing

2012 ◽  
Vol 569 ◽  
pp. 461-465
Author(s):  
De Fu Zhong ◽  
Jiang Bo Yuan ◽  
Xiao Biao Shan ◽  
Tao Xie
Keyword(s):  
Stiffness Matrix ◽  
Ball Bearing ◽  
Experimental System ◽  
Contact Theory ◽  
Axial Stiffness ◽  
Rotary Table ◽  
Hertz Contact ◽  
Radial Stiffness ◽  
Compound Load ◽  
Stiffness Characteristics

A new mathematical model on the stiffness matrix of the bearing was established by using the non-conforming Hertz contact theory. In this model, the case of compound load and the coupling effects was considered. The numerical arithmetic to estimate the displacements under the compound loads is discussed. As a sample, a wire race ball bearing used in a certain type of three-axis aircraft simulating rotary table was provided. The curves of axial stiffness and radial stiffness were obtained in MATLAB. The experimental system for measuring the stiffness was built. The experimental results verify the validity of the theoretical model.

Study on Modeling Method and Characteristics of Bearing System with High Rotation Speed

2013 ◽  
Vol 842 ◽  
pp. 391-396
Author(s):  
Li Gang Cai ◽  
Gen Li ◽  
Ya Hui Cui ◽  
Tie Neng Guo ◽  
Yong Sheng Zhao
Keyword(s):  
Ball Bearing ◽  
Rotation Speed ◽  
Modeling Method ◽  
Ball Bearings ◽  
Angular Contact Ball Bearing ◽  
Gyroscopic Moment ◽  
High Rotation Speed ◽  
Stiffness Characteristics ◽  
Load Conditions ◽  
Bearing System

This paper established a general mathematical modeling method based on stress analysis of the angular contact ball bearing under high rotation speed. The influence of the centrifugal force and gyroscopic moment generated in the rotation process is taken into account in this mathematical model. This paper conducted in-depth research for these aspects: the stiffness characteristics of angular contact ball bearings under different load conditions and different rotational speed, internal contact deformation and the change of bearing parameters.

Temperature Rise Prediction of Oil-Air Lubricated Angular Contact Ball Bearings Using Artificial Neural Network

2019 ◽  
Vol 12 (3) ◽  
pp. 248-261
Author(s):  
Baomin Wang ◽  
Xiao Chang
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Temperature Rise ◽  
High Speed ◽  
Ball Bearing ◽  
Influence Factors ◽  
Ball Bearings ◽  
Ann Model ◽  
Angular Contact Ball Bearing ◽  
Artificial Neural

Background: Angular contact ball bearing is an important component of many high-speed rotating mechanical systems. Oil-air lubrication makes it possible for angular contact ball bearing to operate at high speed. So the lubrication state of angular contact ball bearing directly affects the performance of the mechanical systems. However, as bearing rotation speed increases, the temperature rise is still the dominant limiting factor for improving the performance and service life of angular contact ball bearings. Therefore, it is very necessary to predict the temperature rise of angular contact ball bearings lubricated with oil-air. Objective: The purpose of this study is to provide an overview of temperature calculation of bearing from many studies and patents, and propose a new prediction method for temperature rise of angular contact ball bearing. Methods: Based on the artificial neural network and genetic algorithm, a new prediction methodology for bearings temperature rise was proposed which capitalizes on the notion that the temperature rise of oil-air lubricated angular contact ball bearing is generally coupling. The influence factors of temperature rise in high-speed angular contact ball bearings were analyzed through grey relational analysis, and the key influence factors are determined. Combined with Genetic Algorithm (GA), the Artificial Neural Network (ANN) model based on these key influence factors was built up, two groups of experimental data were used to train and validate the ANN model. Results: Compared with the ANN model, the ANN-GA model has shorter training time, higher accuracy and better stability, the output of ANN-GA model shows a good agreement with the experimental data, above 92% of bearing temperature rise under varying conditions can be predicted using the ANNGA model. Conclusion: A new method was proposed to predict the temperature rise of oil-air lubricated angular contact ball bearings based on the artificial neural network and genetic algorithm. The results show that the prediction model has good accuracy, stability and robustness.

Oscillatory Occurrences in Ball Bearings

1952 ◽  
Vol 56 (504) ◽  
pp. 885-908 ◽  
Author(s):  
M. S. Frenkel
Keyword(s):  
Ball Bearing ◽  
Maximum Speed ◽  
System Of Equations ◽  
Ball Bearings ◽  
Angular Contact Ball Bearing ◽  
Simple Motion ◽  
Ball Motion

In this paper it is shown how, in an angular contact ball bearing, the motion of a ball depends on the dimensions, loading and speed of the bearing. In general, ball motion in an angular contact bearing differs from the simple motion usually visualised by including oscillatory occurrences, shown here analytically, graphically and visually. These oscillatory occurrences are shown to lead to premature fatigue of the bearing metal, as a function of the speed of rotation, thereby imposing the present limitations on maximum speed and “ life.”It is further shown that only when the dimensions of an angular contact ball bearing are related in a certain way, a motion is produced in which the oscillatory phenomena are eliminated. These relations are given as functions of loading and speed in a system of equations and limiting conditions (hereafter referred to as “ Relations of the Dimensions ”).

scholarly journals Study on Simplified Model and Numerical Solution of High-Speed Angular Contact Ball Bearing

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Guang Zeng ◽  
Chunjiang Zhao ◽  
Xiaokai Yu ◽  
Biao Sun ◽  
Zhigang Xiao ◽  
...  
Keyword(s):  
High Speed ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Ball Bearing ◽  
Calculation Model ◽  
Ball Bearings ◽  
Initial Value ◽  
Angular Contact Ball Bearing ◽  
Bee Colony ◽  
Simplified Calculation

For the calculation model of high-speed angular contact bearing has many variables, the large root difference exists, and the Newton iterative method solving the convergence depends on the initial value problems; thus, the simplified calculation model is proposed and the algorithm is improved. Firstly, based on the nonlinear equations of variables recurrence method of the high-speed angular contact ball bearing calculation model, it is proved that the ultimate fundamental variables of calculation model are the actual inner and outer contact angles, the axial and radial deformations. According to this reason, the nonlinear equations are deformed and deduced, and the number of equations is reduced from 4Z + 2 to 2Z + 2 (Z represents the number of rolling bodies); a simplified calculation model is formed. Secondly, according to the small dependence of the artificial bee colony algorithm on the initial value, an improved artificial bee colony algorithm is proposed for the large root difference characteristics of high-speed ball bearings. The validity of the improved algorithm is verified by standard test function. The algorithm is used to solve the high-speed angular contact ball bearing calculation model. Finally, the deformations of high-speed angular contact ball bearings are compared and verified by experiments, and the results of improved algorithm show good agreement with the experiments results.

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.

Modeling of Flexible Coupling to Connect Misaligned Flexible Rotors Supported on Ball Bearings

2014 ◽  
Author(s):  
T. C. Gupta ◽  
K. Gupta
Keyword(s):  
Dynamic Response ◽  
Stiffness Matrix ◽  
Ball Bearing ◽  
Radial Clearance ◽  
Fe Model ◽  
Ball Bearings ◽  
Flexible Coupling ◽  
Flexible Rotors ◽  
Deep Groove ◽  
Coupling Stiffness

Parallel or/and angular misalignment between rotors connected by flexible coupling causes deformation of coupling elements and rotor shafts both. The forces and moments from flexible coupling act on driver and driven rotors simultaneously and depend upon dynamic response of coupled rotor system. The authors’ aim in the present work is to propose a methodology to incorporate the coupling stiffness matrix and coupling loads into the finite element model of flexibly coupled flexible rotors supported on deep groove ball bearings. The coefficients of coupling stiffness matrix and coupling loads are nonlinear and depend upon the amount of parallel and angular misalignments. To segregate the effect of nonlinear stiffness of coupling on the dynamic response of the system, the stiffness of ball bearing is initially considered to be linear. Thereafter, ball bearing nonlinearities arising from radial clearance, Hertzian deformation of balls and races, and varying compliance effect are included into the FE model of the system. Considering different types of misalignments in succession and combination, the dynamic response is characterized by the presence of 1N, 2N and other super or sub harmonics. The misalignment in one plane is found to affect the dynamic response in both the orthogonal planes. Comparing to the stiffness of flexible coupling, the stiffness of ball bearing is of higher order and therefore, nonlinear coupling forces and moments have dominant influence on the dynamic response of the system.

Wear analysis of angular contact ball bearing in multiple-bearing spindle system subjected to uncertain initial angular misalignment

2020 ◽  
pp. 1-32
Author(s):  
Zhongchi Yang ◽  
Yu Zhang ◽  
Ke Zhang ◽  
Songhua Li
Keyword(s):  
Ball Bearing ◽  
Spindle Speed ◽  
Wear Depth ◽  
Ball Bearings ◽  
Wear Model ◽  
Angular Misalignment ◽  
Angular Contact Ball Bearing ◽  
Spindle System ◽  
Dispersion Degree ◽  
Spinning Speed

Abstract The effects of the uncertainty of angular misalignment on the wear of angular contact ball bearings in the spindle system are investigated. The wear model of bearing raceways is derived based on Archard model. The angular misalignment caused by mounting error is assumed to comply with normal distribution, Monte Carlo method is used to extract angular misalignment sample. Based on the spindle system model, the spinning speed, pitch angle and contact force of ball elements in each angular contact ball bearing are calculated. The wear depth of bearing raceways is analyzed. The results show that the uncertainty of the initial angular misalignment leads to significant dispersion of wear depth of ball bearings, but the dispersion degree is related to spindle speed, angular misalignment cases, and bearing mounting position. Increasing the spindle speed increases the wear depth but decreases the wear depth dispersion.

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