Open Access

ARTICLE

A Normal Contact Stiffness Model of Joint Surface Based on Fractal Theory

Kuo Xu¹, Yuan Yuan^1,*, Lihua Zhang¹

1 Xi’An University of Technology, Xi’An, 710048, China.
* Corresponding Author: Yuan Yuan. Email: yuanyuan@xaut.edu.cn.

Computer Modeling in Engineering & Sciences 2019, 119(3), 459-480. https://doi.org/10.32604/cmes.2019.04677

Abstract

Based on the fractal theory, a normal contact stiffness model is established. In the model, the asperity is initially in elastic deformation under contact interference. As the interference is increased, a transition from elastic to elastoplastic to full plastic deformation occurs in this order. The critical elastic interference, the first elastoplastic critical interference and the second elastoplastic critical interference are scale-dependent. According to the truncated asperity size distribution function, the relations between the total normal contact stiffness and the total contact load are obtained. The results show the total normal contact stiffness depends on the range of frequency indexes of asperities. The normal contact stiffness in elastic deformation is major contribution to the total normal contact stiffness. When the first six frequency indexes are less than the critical elastic frequency index, the dimensionless load-stiffness relation approximately is F^*_r ~ (K^*_r)³. When the initial frequency index is greater than the critical elastic frequency index, the dimensionless load-stiffness relation approximately is F^*_r ~ K^*_r. The comparison between the theoretical results and the experimental results indicates that the theoretical results are consistent with the experimental data; therefore, the present fractal model of contact stiffness is reasonable.

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