A Revised Continuous Observation Length Model of Rough Contact without Adhesion

Lan Zhang, Jing Wen, Ming Liu () and Guangzhen Xing
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Lan Zhang: College of Mechanical and Electrical Engineering, Harbin Engineering University, Nantong Ave 145, Harbin 150001, China
Jing Wen: College of Mechanical and Electrical Engineering, Harbin Engineering University, Nantong Ave 145, Harbin 150001, China
Ming Liu: College of Mechanical and Electrical Engineering, Harbin Engineering University, Nantong Ave 145, Harbin 150001, China
Guangzhen Xing: College of Mechanical and Electrical Engineering, Harbin Engineering University, Nantong Ave 145, Harbin 150001, China

Mathematics, 2022, vol. 10, issue 20, 1-18

Abstract: The real contact area of rough surfaces has significant importance in many engineering applications, such as tribology, wear, lubrication and seals. A continuous observation length-dependent mechanic model of rough contact without adhesion is proposed, which assumes that the rough surface is divided into ideal subplanes. However, the model ignores the elastoplastic deformation of asperities, and the standard deviation of ideal subplanes’ heights is assumed to vary linearly with continuous observation length, which is not precise for all the surface fractal dimensions. In this work, a revised continuous observation length model is proposed with elastic, elastoplastic and fully plastic stages. The expressions of force and real contact areas are derived. For surfaces with different fractal dimensions, the quadratic polynomial, cubic polynomial and power relationships between standard deviation and observation length are proposed, respectively. In addition, the influences of the dimensionless observation length, fractal dimension and equivalent elastic modulus on the real contact areas in different contact stages are also analyzed. It can be concluded that the quadrate real contact area decreases as the dimensionless observation length decreases, which can be applied to the percolation theory for leak seal problems.

Keywords: elastoplastic; isotropic; rough surface; contact mechanics model; the contact area (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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