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A spherical conformal contact model considering frictional and microscopic factors based on fractal theory

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  • Liu, Yao
  • Wang, Yashun
  • Chen, Xun
  • Yu, Huangchao

Abstract

Spherical conformal contact is widely used in engineering structures. The existing solution of the spherical conformal contact problem always ignores the microscopic characteristics or friction of the spherical surfaces. Therefore, the current paper presents a spherical fractal model to characterize the contact state of spherical pairs considering the microscopic topography of rough spherical surface and the factor of friction. Firstly, a method of characterizing the microscopic topography of rough spherical surface is proposed based on three-dimensional Weierstrass–Mandelbrot function. The fractal contact model of the single asperity is developed by Hertz theory in combination with elasticity. Then, the macroscopic parameters are introduced to construct the contact surface coefficient. The area distribution function under conformal contact region is obtained. Considering the friction factor of the conformal contact region, the microcontact model of the spherical conformal contact is developed based on fractal theory. Finally, the formula between (elastic, elastic-plastic, plastic) contact area, (elastic, elastic-plastic, plastic) contact load and the key parameters (fractal parameters and macro parameters) are derived based on the proposed model. The relationship between the actual contact area and the normal load of the contact region is established. Numerical results show that the proposed model is more accurate for the analysis of the spherical surface contact area and contact load.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:96-107
    DOI: 10.1016/j.chaos.2018.04.017
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    References listed on IDEAS

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    1. Mahjani, Mohamad Ghassem & Moshrefi, Reza & Sharifi-Viand, Ahmad & Taherzad, Ahad & Jafarian, Majid & Hasanlou, Fatemeh & Hosseini, Maryam, 2016. "Surface investigation by electrochemical methods and application of chaos theory and fractal geometry," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 598-603.
    2. 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.
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    Cited by:

    1. Wang, Gengxiang & Faes, Matthias G.R. & Cheng, Fuan & Shi, Tengfei & Gao, Peng, 2022. "Extension of dashpot model with elastoplastic deformation and rough surface in impact behavior," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Li, Zhiwei & Wang, Jianjian & Yuan, Meng & Wang, Zhongyu & Feng, Pingfa & Feng, Feng, 2022. "An indicator to quantify the complexity of signals and surfaces based on scaling behaviors transcending fractal," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Feng Feng & Meng Yuan & Yousheng Xia & Haoming Xu & Pingfa Feng & Xinghui Li, 2022. "Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal," Mathematics, MDPI, vol. 10(7), pages 1-17, March.

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