Application of Genetic Algorithm in Numerical Solution of Analysis Model for Angular-Contact Ball Bearings

2011 ◽  
Vol 411 ◽  
pp. 11-15
Author(s):  
Hao Hao Shi ◽  
You Yun Zhang ◽  
Zhi Zhou ◽  
Peng Wang
Keyword(s):  
Genetic Algorithm ◽  
Ball Bearing ◽  
Contact Theory ◽  
Hertz Contact ◽  
Improved Genetic Algorithm ◽  
Analysis Model ◽  
Initial Value ◽  
Angular Contact Ball Bearing ◽  
Calculation Results ◽  
Raphson Method

In this paper, an angular contact ball bearing analysis model has been established based on Hertz contact theory. Solving nonlinear equations by improved genetic algorithm (IGA) and verified the effectiveness of the method through numerical experiment. The results proved that the adoption of IGA to solve the analysis model of angular contact ball bearing, can effectively resolve the problem of the Newton-Raphson method such as no convergence and need initial value, the calculation results is satisfied.

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.

Research on Genetic Algorithm-Based Solution Method for Variable Cycle Engine Model

2014 ◽  
Vol 668-669 ◽  
pp. 633-636
Author(s):  
Zheng Jia Wu ◽  
Rong Hua Meng ◽  
Ji Li
Keyword(s):  
Complex System ◽  
Genetic Algorithm ◽  
Solution Method ◽  
Initial Value ◽  
Engine Model ◽  
Computation Efficiency ◽  
Implicit Equations ◽  
Newton Raphson ◽  
The Mathematical Model ◽  
Raphson Method

Variable cycle engine is a complex system, which is usually mathematically modeled as a series of multi-dimensional nonlinear implicit equations. Processes for solution of these equations are often complicated; therefore, a genetic algorithm-based method was presented in this paper for the solution of the mathematical model. The method was also evaluated by such parameters as initial value sensitivity, computation efficiency, convergence and stability; and compared with Newton-Raphson method. It shows that genetic algorithm-based method is less sensitive to initial values, more capable in convergent and computing stability than Newton-Raphson method, however more time consuming.

scholarly journals Analysis of Contact Deformations in Support Systems Using Roller Prisms

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2644
Author(s):  
Krzysztof Nozdrzykowski ◽  
Zenon Grządziel ◽  
Paweł Dunaj
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Theory ◽  
Finite Element Analyses ◽  
The Finite Element Method ◽  
Hertz Contact ◽  
Contact Points ◽  
Calculation Results ◽  
Reaction Forces ◽  
Shaft Journal

This article presents the results of finite element analyses of the influence of reaction forces on stresses and strains at the contact points of the rollers of prism supports with cylindrical surfaces of the main journals of large-sized crankshafts. The analyses of strains and stresses, as well as the depth of their occurrences, in the case of the shaft journal and support rollers were carried out using Hertz contact theory and the finite element method. These calculation results proved to be highly consistent. Additionally, they provide a basis for stating that, in the case under consideration, permanent deformations do not significantly affect the values of the measured geometrical deviations nor the profile forms of the supported main crankshaft journals.

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.

Modeling high-speed angular contact ball bearing under the combined radial, axial and moment loads

2013 ◽  
Vol 228 (5) ◽  
pp. 852-864 ◽  
Author(s):  
Wen-Zhong Wang ◽  
Lang Hu ◽  
Sheng-Guang Zhang ◽  
Ling-Jia Kong
Keyword(s):  
Contact Angle ◽  
Contact Force ◽  
High Speed ◽  
Ball Bearing ◽  
Angular Contact Ball Bearing ◽  
Speed Condition ◽  
Newton Raphson ◽  
And Performance ◽  
Angular Displacements ◽  
Raphson Method

In this paper, a method based on coordinate equivalence was presented to investigate the characteristic parameters of angular contact ball bearing such as contact angle and contact force between ball and raceways subjected to the combined radial, axial and moment loads, with considering the effects of centrifugal force and gyroscopic moment in high-speed conditions. The radial, axial and angular displacements are solved based on Newton–Raphson method rather than as the known variables. The method simplifies the procedure involved in determining derivatives for Newton–Raphson method. The results show good agreement with existent model and can be used to analyze the bearing performance, especially for high-speed condition. It was also shown that the inertial loads resulting from the high-speed condition have significant effect on the contact angle and contact force between ball and raceways and have to be considered in the bearing design and performance analysis.

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.

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.

Effect of structural parameters and service conditions on the tilt angle of double row angular contact ball bearing

2021 ◽  
pp. 146441932110610
Author(s):  
Zhaoliang Cui ◽  
Rui He ◽  
Wanyu Wu ◽  
Fengtao Wang ◽  
Liu Heng
Keyword(s):  
Tilt Angle ◽  
Ball Bearing ◽  
Structural Parameters ◽  
Coincidence Degree ◽  
Radial Clearance ◽  
Initial Contact ◽  
Analysis Model ◽  
Angular Contact Ball Bearing ◽  
Double Row ◽  
Service Conditions

In this paper, for double row angular contact ball bearing, a five-degrees-of-freedom bearing analysis model based on quasi-statics is proposed. This model is used to study the influence of structural parameters and service conditions on the tilt angle and limit tilt angle of the bearing. The results show that the radial clearance will increase the ultimate tilt angle. The coincidence degree between the roller and the inner raceway will reduce the ultimate tilt angle, but the coincidence degree between the roller and the outer raceway has the opposite effect. The increase in the external load of the bearing will increase the tilt angle. The moment load has the greatest effect on the tilt angle. The rotation speed of the bearing has no effect on the tilt angle. The coincidence degree between the roller and the raceway will reduce the tilt angle; furthermore, the influence of the coincidence degree between roller and different ring on the tilt angle is also different when different rings are fixed. The tilt angle will decrease with the increase of the initial contact angle, and this effect is more and more obvious. The fixation of different ring has no effect on this influence.

The Research on the Quick Method for 6-DOF Parallel Robot Forward Kinematics

2012 ◽  
Vol 466-467 ◽  
pp. 849-853
Author(s):  
Zhao Yin Zhang
Keyword(s):  
Genetic Algorithm ◽  
Parallel Robot ◽  
High Accuracy ◽  
Point Of View ◽  
Forward Kinematics ◽  
Initial Value ◽  
Quick Method ◽  
Concurrent Control ◽  
Newton Raphson ◽  
Raphson Method

6-DOF parallel robot forward kinematics can be achieved by Newton-Raphson method with more accurancy, but the result depends on the offer of initial value. It can definitely calculate the result by genetic algorithm, however, more evolved algebra is needed to make it more accurate, and sometimes it hardly meets the requirement by concurrent control. This article points to use the result of genetic as the initial value of algorithm, and ultimately make use of iteration to complete the forward kinematics. High accuracy and speed are the main features of this calculation, and another one is interpreting from the implementation point of view, which is very practical and meet the concurrent control through experiment.

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