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<p>In this study, a novel normal contact model for a joint surface, considering the contact angles between asperities, was established based on anisotropic fractal theory. Through theoretical modeling and experimental verification, the quantitative effects of the fractal parameters and loading cycles on the normal contact stiffness and the actual contact area of the joint surface were discussed. The results show that the proposed model improves the prediction accuracy of the contact stiffness. The contact stiffness initially increased and then decreased with the increase in the fractal dimension <i>D</i>, reaching a maximum value when <i>D</i> = 2.6. Multiple loadings significantly improved the contact stiffness, with the improvement primarily influenced by the fractal dimension and the number of loading cycles. By contrast, the fractal roughness <i>G</i> had little effect on the lifting capacity of the contact stiffness. After three loading cycles, the stiffness reached more than 90% of the maximum stiffness and stabilized at 1.2 times the first loading stiffness when <i>D</i> exceeded 2.6. These findings provide a basis for the rational design of precision machine tool assembly processes.</p>

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Modeling of normal stiffness of the joint surface considering contact angles between asperities based on the fractal theory

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • Yongchang Li,
  • Guangpeng Zhang,
  • Shuai Liu,
  • Kang Ji,
  • Yang Li

摘要

In this study, a novel normal contact model for a joint surface, considering the contact angles between asperities, was established based on anisotropic fractal theory. Through theoretical modeling and experimental verification, the quantitative effects of the fractal parameters and loading cycles on the normal contact stiffness and the actual contact area of the joint surface were discussed. The results show that the proposed model improves the prediction accuracy of the contact stiffness. The contact stiffness initially increased and then decreased with the increase in the fractal dimension D, reaching a maximum value when D = 2.6. Multiple loadings significantly improved the contact stiffness, with the improvement primarily influenced by the fractal dimension and the number of loading cycles. By contrast, the fractal roughness G had little effect on the lifting capacity of the contact stiffness. After three loading cycles, the stiffness reached more than 90% of the maximum stiffness and stabilized at 1.2 times the first loading stiffness when D exceeded 2.6. These findings provide a basis for the rational design of precision machine tool assembly processes.