Ball Motion and Sliding Friction in Ball Bearings

1959 ◽  
Vol 81 (1) ◽  
pp. 1-12 ◽  
Author(s):  
A. B. Jones
Keyword(s):  
High Speed ◽  
Sliding Friction ◽  
Interfacial Slip ◽  
Ball Bearings ◽  
Angular Contact Ball Bearing ◽  
Friction Forces ◽  
Inertia Effects ◽  
Closed Form Solutions ◽  
Gyroscopic Effects ◽  
Ball Motion

In modern high-speed ball bearings the pressure areas, which result from elastic deformations at the ball-race contacts, are appreciably curved and interfacial slip can occur at most points within the pressure areas. These slippages give rise to friction forces acting on the ball which are held in equilibrium by reactions from the races and the inertia effects of the motion of the ball. A method is derived for determining the motion of the ball and sliding friction in a high-speed, angular-contact ball bearing under thrust load in terms of the inertia effects on the ball and the frictional resistances resulting from interfacial slip at the contact areas. Possible elastic compliance at the interface, hysteresis, and dynamical perturbations of ball motion are neglected. The solution of eight, simultaneous equations involving double integrals for which closed-form solutions cannot be found is required. A solution for a particular case requires the services of a high-speed computer. For the case where gyroscopic effects on the ball can be neglected, certain simplifications and assumptions can be made which enable the solution of a particular problem using conventional computation means.

Motion of Unbalanced Balls in High-Speed Angular Contact Ball Bearings

1990 ◽  
Vol 112 (1) ◽  
pp. 105-110 ◽  
Author(s):  
H. Kawamura ◽  
K. Touma
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Three Dimensional ◽  
Ball Bearings ◽  
Axial Loads ◽  
Angular Contact Ball Bearing ◽  
High Speeds ◽  
Dimensional Ball ◽  
Ball Motion ◽  
Bearing Ball

This paper reports on an experimental study of the three-dimensional ball motion of an unbalanced ball in a 50-mm bore angular contact ball bearing operating at high speeds under axial loads. One bearing ball, which was unbalanced by making a small hole in it, was magnetized and the motion of the ball was determined using Hall-elements. The bearing was tested under various loads and speeds up to 12,000 rpm. The influence of unbalance eccentricity on the unbalanced ball’s motion was investigated.

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.

Prediction of Ball Motion in High-Speed Thrust-Loaded Ball Bearings

1976 ◽  
Vol 98 (3) ◽  
pp. 463-469 ◽  
Author(s):  
C. R. Gentle ◽  
R. J. Boness
Keyword(s):  
Computer Program ◽  
High Speed ◽  
Ball Bearing ◽  
Viscoelastic Behavior ◽  
Specific Situation ◽  
Fluid Models ◽  
Ball Bearings ◽  
Theoretical Predictions ◽  
Ball Motion

This paper describes the development of a computer program used to analyze completely the motion of a ball in a high-speed, thrust-loaded ball bearing. Particular emphasis is paid to the role of the lubricant in governing the forces and moments acting on each ball. Expressions for these forces due to the rolling and sliding of the ball are derived in the light of the latest fluid models, and estimates are also made of the cage forces applicable in this specific situation. It is found that only when lubricant viscoelastic behavior is considered do the theoretical predictions agree with existing experimental evidence.

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.

scholarly journals Film Stiffness Analysis for Angular Contact Ball Bearings Considering Thermal Effect

2015 ◽  
Vol 9 (1) ◽  
pp. 156-159 ◽  
Author(s):  
Chun L. Lei ◽  
Zhi Y. Rui ◽  
Qin Wu ◽  
Jun F. Guo ◽  
Li N. Ren
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Ball Bearing ◽  
Elastohydrodynamic Lubrication ◽  
Calculation Model ◽  
Frictional Heat ◽  
Ball Bearings ◽  
Angular Contact Ball Bearing ◽  
Calculation Results ◽  
Film Stiffness

In order to more accurately calculate the film stiffness of angular contact ball bearing, it is necessary to establish the film stiffness calculation model that is consistent with reality. The frictional heat exists in high-speed ball bearings, and can impact on oil film thickness and stiffness. The calculation model of film stiffness of an angular contact ball bearing taking account of the effects of viscous heating was proposed based on the elastohydrodynamic lubrication theory. The central film thickness and film stiffness have been determined. An example was calculated with this derived equation and the result was compared with that given in other literatures. The calculation results show that the central film thickness decreases and the film stiffness increases when friction heating are considered.

Computational-experimental research of the stiffness of high-speed spindles

2020 ◽  
pp. 33-39
Author(s):  
I.A. Zverev
Keyword(s):  
Elastic Deformation ◽  
Experimental Research ◽  
Rotational Speed ◽  
High Speed ◽  
Ball Bearing ◽  
Deformation Model ◽  
Ball Bearings ◽  
Radial Load ◽  
Angular Contact Ball Bearing ◽  
Spindle Unit

The stiffness indices of high-speed spindle units on angular contact ball bearings at high rotational speeds are investigated. It is found, that the spindle rotational speed, radial load, bearing temperature, type and magnitude of the preload in the bearings significantly affect the stiffness of the spindle unit. Keywords: high-speed spindle unit, angular contact ball bearing, elastic-deformation model. [email protected]

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