Copula Estimation Method of the Running Accuracy of Ball Bearing

Li Lihong; Li Jishun; Xue Yujun; Yu Tongshuai; Yu Yongjian

doi:doi:10.11648/j.ajmie.20190401.12

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Copula Estimation Method of the Running Accuracy of Ball Bearing

Li Lihong, Li Jishun, Xue Yujun, Yu Tongshuai, Yu Yongjian

Published in American Journal of Mechanical and Industrial Engineering (Volume 4, Issue 1)

Received: 22 January 2019 Accepted: 28 February 2019 Published: 11 May 2019

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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.

Published in	American Journal of Mechanical and Industrial Engineering (Volume 4, Issue 1)
DOI	10.11648/j.ajmie.20190401.12
Page(s)	11-20
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Bearings, Running Accuracy, Copula Function, Dimension Precision

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APA Style

Li Lihong, Li Jishun, Xue Yujun, Yu Tongshuai, Yu Yongjian. (2019). Copula Estimation Method of the Running Accuracy of Ball Bearing. American Journal of Mechanical and Industrial Engineering, 4(1), 11-20. https://doi.org/10.11648/j.ajmie.20190401.12

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ACS Style

Li Lihong; Li Jishun; Xue Yujun; Yu Tongshuai; Yu Yongjian. Copula Estimation Method of the Running Accuracy of Ball Bearing. Am. J. Mech. Ind. Eng. 2019, 4(1), 11-20. doi: 10.11648/j.ajmie.20190401.12

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AMA Style

Li Lihong, Li Jishun, Xue Yujun, Yu Tongshuai, Yu Yongjian. Copula Estimation Method of the Running Accuracy of Ball Bearing. Am J Mech Ind Eng. 2019;4(1):11-20. doi: 10.11648/j.ajmie.20190401.12

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@article{10.11648/j.ajmie.20190401.12,
  author = {Li Lihong and Li Jishun and Xue Yujun and Yu Tongshuai and Yu Yongjian},
  title = {Copula Estimation Method of the Running Accuracy of Ball Bearing},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {4},
  number = {1},
  pages = {11-20},
  doi = {10.11648/j.ajmie.20190401.12},
  url = {https://doi.org/10.11648/j.ajmie.20190401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20190401.12},
  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.},
 year = {2019}
}

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TY  - JOUR
T1  - Copula Estimation Method of the Running Accuracy of Ball Bearing
AU  - Li Lihong
AU  - Li Jishun
AU  - Xue Yujun
AU  - Yu Tongshuai
AU  - Yu Yongjian
Y1  - 2019/05/11
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmie.20190401.12
DO  - 10.11648/j.ajmie.20190401.12
T2  - American Journal of Mechanical and Industrial Engineering
JF  - American Journal of Mechanical and Industrial Engineering
JO  - American Journal of Mechanical and Industrial Engineering
SP  - 11
EP  - 20
PB  - Science Publishing Group
SN  - 2575-6060
UR  - https://doi.org/10.11648/j.ajmie.20190401.12
AB  - 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.
VL  - 4
IS  - 1
ER  -

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Author Information

Li Lihong

Vehicel & Transportation Engineering Institute, Henan University of Science and Technology, 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

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Plain Text BibTeX RIS

APA Style

Li Lihong, Li Jishun, Xue Yujun, Yu Tongshuai, Yu Yongjian. (2019). Copula Estimation Method of the Running Accuracy of Ball Bearing. American Journal of Mechanical and Industrial Engineering, 4(1), 11-20. https://doi.org/10.11648/j.ajmie.20190401.12

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ACS Style

Li Lihong; Li Jishun; Xue Yujun; Yu Tongshuai; Yu Yongjian. Copula Estimation Method of the Running Accuracy of Ball Bearing. Am. J. Mech. Ind. Eng. 2019, 4(1), 11-20. doi: 10.11648/j.ajmie.20190401.12

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AMA Style

Li Lihong, Li Jishun, Xue Yujun, Yu Tongshuai, Yu Yongjian. Copula Estimation Method of the Running Accuracy of Ball Bearing. Am J Mech Ind Eng. 2019;4(1):11-20. doi: 10.11648/j.ajmie.20190401.12

Copy | Download

@article{10.11648/j.ajmie.20190401.12,
  author = {Li Lihong and Li Jishun and Xue Yujun and Yu Tongshuai and Yu Yongjian},
  title = {Copula Estimation Method of the Running Accuracy of Ball Bearing},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {4},
  number = {1},
  pages = {11-20},
  doi = {10.11648/j.ajmie.20190401.12},
  url = {https://doi.org/10.11648/j.ajmie.20190401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20190401.12},
  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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Copula Estimation Method of the Running Accuracy of Ball Bearing
AU  - Li Lihong
AU  - Li Jishun
AU  - Xue Yujun
AU  - Yu Tongshuai
AU  - Yu Yongjian
Y1  - 2019/05/11
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmie.20190401.12
DO  - 10.11648/j.ajmie.20190401.12
T2  - American Journal of Mechanical and Industrial Engineering
JF  - American Journal of Mechanical and Industrial Engineering
JO  - American Journal of Mechanical and Industrial Engineering
SP  - 11
EP  - 20
PB  - Science Publishing Group
SN  - 2575-6060
UR  - https://doi.org/10.11648/j.ajmie.20190401.12
AB  - 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.
VL  - 4
IS  - 1
ER  -

Copy | Download