Volume 4, Issue 1, January 2019, Page: 11-20
Copula Estimation Method of the Running Accuracy of Ball Bearing
Li Lihong, Vehicel & Transportation Engineering Institute, Henan University of Science and Technology, Luoyang, China; Henan Key Lab for Machinery Design and Transmission System, Luoyang, China
Li Jishun, Henan Key Lab for Machinery Design and Transmission System, Luoyang, China
Xue Yujun, Henan Key Lab for Machinery Design and Transmission System, Luoyang, China
Yu Tongshuai, Vehicel & Transportation Engineering Institute, Henan University of Science and Technology, Luoyang, China
Yu Yongjian, Henan Key Lab for Machinery Design and Transmission System, Luoyang, China
Received: Jan. 22, 2019;       Accepted: Feb. 28, 2019;       Published: May 11, 2019
DOI: 10.11648/j.ajmie.20190401.12      View  181      Downloads  24
Abstract
The bearing is an assembly consisting of multiple elements and its performance is shown mainly as its running accuracy which is influenced by many factors including its elements’ geometrical precision. The influence of elements geometrical precision on bearing running accuracy is joint effect when multiple elements are assembled together. So there must be dependent relationships between bearing running accuracy and the joint action of multiple elements. Such relationship was very complicated and difficultly described by mathematical formula. But, the elements’ geometrical precision follow statistics law, and so, statistics can be applied to analyzing elements’ dimension distribution law and construct joint distribution function. The copula function can be introduced to establish the transmit relationships that join the running accuracy to multiple elements geometrical precision. Based on the copula estimation of distribution algorithm, the mathematic modeling of the radial and face run out distribution of the bearing and elements dimension precision distribution can be built to forecast bearings running accuracy.
Keywords
Bearings, Running Accuracy, Copula Function, Dimension Precision
To cite this article
Li Lihong, Li Jishun, Xue Yujun, Yu Tongshuai, Yu Yongjian, Copula Estimation Method of the Running Accuracy of Ball Bearing, American Journal of Mechanical and Industrial Engineering. Vol. 4, No. 1, 2019, pp. 11-20. doi: 10.11648/j.ajmie.20190401.12
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
NELSEN R B. An Introduction to Copulas(Second Edition) [M]. New York: Springer-Verlag, 2006.
[2]
Lu, Wang. A high-dimensional vine copula approach to movement of China's financial markets. 2013 20th International Conference on Management Science and Engineering, 2013: 1538-1543.
[3]
CUI Yu¡wei, YUAN Pengcheng, NI Anning, JUAN Zhicai. Travel time reliability estimating methodology in transportation networks based on Copula function. Application Research of Computers, 2014, 31(5):1385-1389.
[4]
LIN Jingli, YANGWeiming, YAN Gongjun. Cooperative collision warning based on Copula method. Application Research ofComputers, 2012, 29(10):3761-3764.
[5]
Xiaolei Ma, Sen Luan, Bowen Du, Bin Yu. Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors. Sensors 2017, 17, 2160.
[6]
Selma Jayech. The contagion channels of July-August-2011 stock market crash: A DAG-copula based approach. European Journal of Operational Research 249 (2016) 631-646
[7]
JOSHUA V R, TIl S. A General Approach to Integrated Risk Management with Skewed, Fat-tailed Risks [J]. Journal of Financial Economics, 2006, 79(3): 569-614.
[8]
TU Zhibin, HUANG Mingfeng, LOU Wenjuan. Dynamic wind load combination of tall buildings based on Copula functions [J]. Journal of Zhejiang University (engineering science), 2014, 48(8):1370-1375.
[9]
Dian-Qing Li, Lei Zhang, Xiao-Song Tang, Wei Zhou, Jin-Hui Li, Chuang-Bing Zhou. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability. Computers and Geotechnics 68 (2015) 184-195.
[10]
XU A. Statistical Analysis of Competing Failure Modesin Accelerated Life Testing Based on Assumed Copulas [J]. Chinese Journal of Applied Probability and Statistics, 2012 , 28(6): 51-62.
[11]
TANG Jiayin, HE Ping, LIANG Hongqin, WANG Qin. Comprehensive Reliability Assessment of Long-life Products with Correlated Multiple Failure Modes. Journal of mechanical engineering, 2013, 49(12):176-182.
[12]
HE Chengming, WU Wei, MENG Qingjun. A Copula-based Mechanical System Reliability Model and Its Application. ACTA ARMAMENTARII, 2012, 33(3):379-384.
[13]
WU Hong, WANG Weiping, WANG Lei, YANG Fen. Application of EDA in Path Planning of Cruise Missile. Electronics optics & control, 2010, 17(7):6-10.
[14]
ZHANG Qi-xin, WANG Shixing. Application of the EDA Algorithm in the Near Range Optimal Rendezvous for Spacecrafts. COMPUTER ENGINEERING£¦SCIENCE, 2012, 34(5):89-94.
[15]
Shui-Long Shen, Yong-Xia Wu, Ye-Shuang Xu, Takenori Hino. Huai-Na Wu a Evaluation of hydraulic parameters from pumping tests in multi-aquifers with vertical leakage in Tianjin. Computers and Geotechnics 68 (2015) 196-207.
[16]
XU Yuqin, ZHANG Linban. Modeling of wind speed correlation and analysis of probabilistically optimal power flow based on Copula function. Journal of Noah China ElectricPowerUniversity, 2013, 40(5):54-59.
[17]
Alireza Ahmadabadi, Burcu HudaverdiUcer. Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach. Comput Stat (2017) 32:1515-153.
[18]
Li Qiang. The Study of Financial Market Risk Measurement Based on Copula theory and GPD Model [D], Chongqing University, China, October 2012.
[19]
Zhong bo, Sun yoingbo. On the effect of copula for reliability of parallel system with dependent components. Journal of applied statistics and management, 2011, 30(2): 363-369.
[20]
JOSHUA V R, TIl S. A General Approach to Integrated Risk Management with Skewed, Fat-tailed Risks [J]. Journal of Financial Economics, 2006, 79(3): 569-614.
[21]
Gildas M, Stéphane G, Florence F. A Class of Multivariate Copulas Based on Products of Bivariate Copulas [J]. Journal of Multivariate Analysis, 2015, 140(8):363-376.
[22]
Nob Y, Choi K K, Du Liu. Reliability-Based Design Optimization of Problems with Correlated Input Variables Using a Gaussian Copula [J]. Struet Multidisc Optim, 2009, 38(6):1-16.
[23]
WU Quan-you, XUE Yu-jun, LI Ji-shun, YU Yong-jian. Effect of Roller Error on Movement Accuracy of Bearing Under the Load Restriction. Machinery Design Manufacture, 2016 (1):16-19,23.
[24]
HAO Daqing, LI Fulai, ZHANG wei. Measure- ment instrument for Runout of bearing outer rings. Bearing, 2014(5):57-58.
[25]
YU Yongjian1 LI Jishun2 CHEN Guoding and etc. Numerical Calculation and Experimental Research of Rotational Accuracy on Cylindrical Roller Bearing. Bearing, JOURNAL OF MECHANICAL ENGINEERING, 2016, 52(15):65-71.
[26]
Marcelo Brutti Righi, Paulo Sergio Ceretta. Forecasting Value at Risk and Expected Shortfall based on serial pair-copula constructions [J]. Expert Systems with Applications 42 (2015) 6380-6390.
[27]
Shouxiang Wang, Xingyou Zhang, Liyang Liu. Multiple stochastic correlations modeling for microgrid reliability and economic evaluation using pair-copula function. Electrical Power and Energy Systems 76 (2016) 44-52.
[28]
Luciana Dalla Valle, Maria Elena De Giuli, Claudia Tarantola, Claudio Manelli. Default probability estimation via pair copula constructions. European Journal of Operational Research, 249 (2016) 298-311.
[29]
SONG Fei, LI Jishun, LIU Yonggang. Influence of Raceway Roundness Error on Running Accuracy of Cylindrical Roller Bearings. Bearing, 2011(5):1-4.
[30]
Shi Wenxiang, Li Jishun, Liu Yonggang. Forecast and Simulation of Rotational Accuracy of Cylindrical Roller Bearing. Mechanical Science and Technology for Aerospace Engineering, 2012, 31(4):612-616.
Browse journals by subject