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Two-stage method for fractal dimension calculation of the mechanical equipment rough surface profile based on fractal theory

Author

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  • Liu, Yao
  • Wang, Yashun
  • Chen, Xun
  • Zhang, Chunhua
  • Tan, Yuanyuan

Abstract

The determination of fractal dimension of rough surface profile curve is important for characterizing the fractal features of rough surface microscopic topography. There are many methods to calculate the fractal dimension, such as the power spectrum method (PSM), the structure function method (SFM), the variation method, the R/S analysis method, the wavelet transform method and etc., among which the PSM and SFM are widely used methods. This study aims to improve the computational accuracy of the fractal dimension of the profile curve. For this purpose, the two-stage method based on PSM and SFM are proposed. Firstly, we analyze the principle of calculating the fractal dimension of profile curve using PSM and SFM. Then, based on PSM and SFM, we propose a two-stage method for determining the fractal dimension of profile curve. Simulation results show that the two-stage method for fractal dimension of profile curve can greatly reduce the error compared with the original PSM and SFM. Finally, the fractal dimensions of the profile curve of the cuboid specimen are calculated by the original PSM and SFM and the two-stage method respectively. The experimental results show that the proposed method provides more precise results for determining the fractal dimension.

Suggested Citation

  • Liu, Yao & Wang, Yashun & Chen, Xun & Zhang, Chunhua & Tan, Yuanyuan, 2017. "Two-stage method for fractal dimension calculation of the mechanical equipment rough surface profile based on fractal theory," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 495-502.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:495-502
    DOI: 10.1016/j.chaos.2017.09.012
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    Citations

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    Cited by:

    1. Roman Kaminskiy & Nataliya Shakhovska & Jana Kajanová & Yurii Kryvenchuk, 2021. "Method of Distinguishing Styles by Fractal and Statistical Indicators of the Text as a Sequence of the Number of Letters in Its Words," Mathematics, MDPI, vol. 9(19), pages 1-16, September.
    2. Zhang, Shuai & Li, Yingjun & Wang, Guicong & Qi, Zhenguang & Zhou, Yuanqin, 2024. "A novel method for calculating the fractal dimension of three-dimensional surface topography on machined surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Liu, Yao & Wang, Yashun & Chen, Xun & Yu, Huangchao, 2018. "A spherical conformal contact model considering frictional and microscopic factors based on fractal theory," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 96-107.
    4. Chen, Zhiying & Liu, Yong & Zhou, Ping, 2018. "A comparative study of fractal dimension calculation methods for rough surface profiles," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 24-30.
    5. Zuo, Xue & Tang, Xiang & Zhou, Yuankai, 2020. "Influence of sampling length on estimated fractal dimension of surface profile," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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