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Research on Cutting Tool Wear Based on Fractional Brownian Motion

Received: 6 January 2015    Accepted: 22 January 2015    Published: 1 February 2015
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Abstract

Cutting tool wear is a very complex process. Various factors have a direct or indirect effect on cutting tool wear, resulting in uncertainty, so it is difficult for experimental data and result to have good stability. However, Vibration analysis is a very important means for condition monitoring and fault diagnosis. This paper aims to study the methods of tool vibration signal processing, pattern recognition and trend prediction. Collected on tool vibration signal at different times, wavelet noise reduction is used to pretreat the vibration signals. Then, for the self-similar vibration signals, we propose the fractional Brownian motion (FBM) theory with long-range dependence (LRD). Combined with Wigner-Ville spectrum, characteristic parameter can be extracted, so the cutting tool wear state can be determined according to fractal dimension and average slope of the fitting curve of the logarithm power spectrum. Finally, we use FBM model to predict the trend of tool vibration signals. Experiments show that the methods have a good effect on tool wear state recognition and trend prediction.

Published in International Journal of Mechanical Engineering and Applications (Volume 3, Issue 1)
DOI 10.11648/j.ijmea.20150301.11
Page(s) 1-5
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), 2024. Published by Science Publishing Group

Keywords

Tool Wear, Fractal Dimension, Wigner-Ville Spectrum, FBM Model, Trend Prediction

References
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[2] P. Bhattacharyya, D. Sengupta, S. Mukhopadhyay, Cutting force-based real-time estimation of tool wear in face milling using a combination of signal processing techniques. Mechanical Systems and Signal Processing, 6(20), pp. 2665-2683, 2007.
[3] D. A. Stephenson, A. Ali, Tool temperatures in interrupted metal cutting, Winter Annual Meeting of the ASME, pp. 261–281, 1990.
[4] K.Iwata, T. Moriwaki, Application of acoustic emission measurement to in-process sensing of tool wear, Ann. CIRP 26 (1-2), pp. 19–23, 1977.
[5] D. Zhang, S. Dai, Y. Han, D. Chen, On-line monitoring of tool breakage using spindle current in milling, In:1st Asia–Pacific and 2nd Japan–China International Conference Progress of Cutting and Grinding, Shanghai, China, pp. 270–276, 1994.
[6] Hong W C, Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model, Energy Conversion and Management, 50(1), pp.105-117, 2009.
[7] Zhang Q, Lai K K, Niu D, Optimization Combination Forecast Method of SVM and WNN for Power Load Forecasting, IEEE Transactions on Computational Sciences and Optimization (CSO), pp.249-253, 2011.
[8] Lundahl T, Ohley W J, Kay S M, et al, Fractional Brownian motion: A maximum likelihood estimator and its application to image texture, IEEE Transactions on Medical Imaging, 5(3), pp.152-161, 1986.
[9] Jeon, Jae-Hyung, Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries, Physical review, 2(81), 2010.
[10] S. Ghofrani, D.C. McLernon, Auto-Wigner–Ville distribution via non-adaptive and adaptive signal decomposition, Signal Processing, 8(89), pp.1540-1549, 2009.
[11] Longjin Lv, Ren Fu-Yao, The application of fractional derivatives in stochastic models driven by fractional Brownian motion, Physical a-statistical mechanics and its applications, 21(389), pp.4809-4818, 2010.
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[13] Wang li-li, Numerical Calculation and Empirical Analysis of American Options Pricing Based On Fractional Brownian Motion, Huazhong University of science and technology, 2012.
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[15] M. Kious, A. Ouahabi, Detection process approach of tool wear in high speed milling, Measurement, 10(43), pp.1439-1446, 2010.
[16] H. Saglam, A. Unuvar, Tool condition monitoring in milling on cutting forces by a neural network, Int. J. Prod. Res., 41 (7), pp. 1519–1532, 2003.
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  • APA Style

    Liang Jian-kai, Song Wan-qing, Li Qing. (2015). Research on Cutting Tool Wear Based on Fractional Brownian Motion. International Journal of Mechanical Engineering and Applications, 3(1), 1-5. https://doi.org/10.11648/j.ijmea.20150301.11

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    ACS Style

    Liang Jian-kai; Song Wan-qing; Li Qing. Research on Cutting Tool Wear Based on Fractional Brownian Motion. Int. J. Mech. Eng. Appl. 2015, 3(1), 1-5. doi: 10.11648/j.ijmea.20150301.11

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    AMA Style

    Liang Jian-kai, Song Wan-qing, Li Qing. Research on Cutting Tool Wear Based on Fractional Brownian Motion. Int J Mech Eng Appl. 2015;3(1):1-5. doi: 10.11648/j.ijmea.20150301.11

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  • @article{10.11648/j.ijmea.20150301.11,
      author = {Liang Jian-kai and Song Wan-qing and Li Qing},
      title = {Research on Cutting Tool Wear Based on Fractional Brownian Motion},
      journal = {International Journal of Mechanical Engineering and Applications},
      volume = {3},
      number = {1},
      pages = {1-5},
      doi = {10.11648/j.ijmea.20150301.11},
      url = {https://doi.org/10.11648/j.ijmea.20150301.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20150301.11},
      abstract = {Cutting tool wear is a very complex process. Various factors have a direct or indirect effect on cutting tool wear, resulting in uncertainty, so it is difficult for experimental data and result to have good stability. However, Vibration analysis is a very important means for condition monitoring and fault diagnosis. This paper aims to study the methods of tool vibration signal processing, pattern recognition and trend prediction. Collected on tool vibration signal at different times, wavelet noise reduction is used to pretreat the vibration signals. Then, for the self-similar vibration signals, we propose the fractional Brownian motion (FBM) theory with long-range dependence (LRD). Combined with Wigner-Ville spectrum, characteristic parameter can be extracted, so the cutting tool wear state can be determined according to fractal dimension and average slope of the fitting curve of the logarithm power spectrum. Finally, we use FBM model to predict the trend of tool vibration signals. Experiments show that the methods have a good effect on tool wear state recognition and trend prediction.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Research on Cutting Tool Wear Based on Fractional Brownian Motion
    AU  - Liang Jian-kai
    AU  - Song Wan-qing
    AU  - Li Qing
    Y1  - 2015/02/01
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ijmea.20150301.11
    DO  - 10.11648/j.ijmea.20150301.11
    T2  - International Journal of Mechanical Engineering and Applications
    JF  - International Journal of Mechanical Engineering and Applications
    JO  - International Journal of Mechanical Engineering and Applications
    SP  - 1
    EP  - 5
    PB  - Science Publishing Group
    SN  - 2330-0248
    UR  - https://doi.org/10.11648/j.ijmea.20150301.11
    AB  - Cutting tool wear is a very complex process. Various factors have a direct or indirect effect on cutting tool wear, resulting in uncertainty, so it is difficult for experimental data and result to have good stability. However, Vibration analysis is a very important means for condition monitoring and fault diagnosis. This paper aims to study the methods of tool vibration signal processing, pattern recognition and trend prediction. Collected on tool vibration signal at different times, wavelet noise reduction is used to pretreat the vibration signals. Then, for the self-similar vibration signals, we propose the fractional Brownian motion (FBM) theory with long-range dependence (LRD). Combined with Wigner-Ville spectrum, characteristic parameter can be extracted, so the cutting tool wear state can be determined according to fractal dimension and average slope of the fitting curve of the logarithm power spectrum. Finally, we use FBM model to predict the trend of tool vibration signals. Experiments show that the methods have a good effect on tool wear state recognition and trend prediction.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, P.R. China

  • College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, P.R. China

  • College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, P.R. China

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