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| Research on the Normal Contact Stiffness of Rough Surfaces Based on the Ubiquitiform Theory |
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Abstract Based on the ubiquitiform theory and Hertz contact theory, the morphology of the rough surface is described by the ubiquitiformal islands to establish the elastic contact model of the joint surface, which characterizes the normal contact stiffness of the joint surface. Assuming that the height of the asperity of the rough contact surface satisfies the Gaussian distribution, by establishing the asperity micro-contact model, the ubiquitiformal complexity D of the rough surface and the minimum infimum of the measurement size δmin are introduced. Then the normal contact stiffness of the rough surface is derived on basis of ubiquitiformal model. Different with fractal model, the limited self-similar or self-affine structures with only integer dimensions. The ubiquitiformal complexity shows the complexity of the surface topography. the infimum of measuring size can reflect the details of the surface topography, and the surface topography is determined by the ubiquitiformal complexity and the minimum infimum of the area. After comparing and analyzing the results of Literature, it is found that the contact stiffness of the joint surface obtained by using the ubiquitiform island model is more consistent with the experimental results than fractal model. Numerical example results are carried out on the normal contact stiffness of rough surfaces with different ubiquitiformal complexity D, the minimum infimum of the measurement size δmin. It is shown that in the same area scale interval, the normal contact stiffness of rough surfaces increases with the increase of ubiquitiformal complexity, and vice versa; when other conditions remain unchanged, the normal contact stiffness of rough surface It increases with the decrease of the minimum infimum. When the ubiquitiformal complexity is larger, the change of the minimum infimum has more obvious influence on the contact stiffness. These results should provide theoretical guidance to evaluate the normal contact stiffness of rough surfaces and to improve accuracy of contact machine in engineering application.
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Received: 03 June 2021
Published: 19 April 2022
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2022, Vol. 43 
