| Peer-Reviewed

Copula Estimation Method of the Running Accuracy of Ball Bearing

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

References
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Cite This Article
  • 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
  • Vehicel & Transportation Engineering Institute, Henan University of Science and Technology, Luoyang, China

  • Henan Key Lab for Machinery Design and Transmission System, Luoyang, China

  • Henan Key Lab for Machinery Design and Transmission System, Luoyang, China

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

  • Henan Key Lab for Machinery Design and Transmission System, Luoyang, China

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