Analysis of Normal Elastic Contact Stiffness of Rough Surfaces Based on Ubiquitiform Theory

Author:

Shang Shaofei1,Cao Xiaoshan1,Liu Zhiqiang1,Shi Junping1

Affiliation:

1. Department of Mechanics, School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an, Shaanxi 710048, China

Abstract

Abstract In this study, the normal stiffness of elastic contact between rough surfaces with asperities following Gaussian distribution is investigated using ubiquitiform theory, developed from fractal theory. In the generalized ubiquitiformal Sierpinski carpet model, the rough surface including contact asperity is controlled for, given the lower bound to scale invariance of rough surfaces. Considering the stiffness of a single asperity deduced from the Hertz contact model, we deduce the theoretical relation between the normal stiffness and the elastic contact of rough surfaces based on ubiquitiform theory. The results show that the normal contact stiffness of a rough surface increases as the normal load rises. If the ubiquitiformal complexity of a rough surface increases or the lower bound to scale invariance of a rough surface decreases, the normal contact stiffness of the rough surface should increase. The larger the ubiquitiformal complexity of a rough surface is, the more obvious the impact of the lower bound to scale invariance on the normal contact stiffness of the rough surface becomes. The results based on the ubiquitiformal model and the experimental results are in closer agreement. Therefore, the introduction of scale invariance is crucial to the surface contact problem.

Funder

National Natural Science Foundation of China

National Security Academic Fund of China

Publisher

ASME International

Subject

Surfaces, Coatings and Films,Surfaces and Interfaces,Mechanical Engineering,Mechanics of Materials

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