A fractal model of rough surfaces based on ellipsoidal asperities
Industrial Lubrication and Tribology
ISSN: 0036-8792
Article publication date: 11 June 2024
Issue publication date: 26 June 2024
Abstract
Purpose
This study aims to use fractal theory to investigate the contact mechanics of two bidirectional anisotropic surfaces, taking into account the friction coefficient of the contact interface. This study introduces a model that centers on normal contact load and contact stiffness, providing an extensive framework to elucidate the interactions between these surfaces.
Design/methodology/approach
The research adopts the Weierstrass–Mandelbrot (W-M) function for simulating bidirectional surface profiles. Through the application of elastic-plastic contact theory, it evaluates the contact area and load of a singular asperity across elasticity, elastoplasticity and plasticity phases. The contact load and stiffness of the rough surface are determined using a refined asperity density distribution function, and these findings are juxtaposed with extant models to validate their precision and rationality.
Findings
The study delineates the influence of fractal dimension (D), surface roughness (G), ellipse eccentricity (e) and friction coefficient (µ) on the contact area, load and stiffness. It reveals that the contact area enlarges with the fractal dimension (D) yet diminishes with increased eccentricity (e), roughness (G) and friction coefficient (µ). These elements considerably affect the contact load and stiffness, underscoring their significance in comprehending surface interactions.
Originality/value
This study applies fractal theory to analyze the contact mechanics of bidirectional anisotropic surfaces, considering the geometry and mechanics of ellipsoidal asperities on rough surfaces to develop a contact mechanics model. This model clarifies the deformation of an asperity in normal contact, presenting a more rational alternative to current models.
Keywords
Acknowledgements
Funding: This work was funded by the Youth Program of Chinese Academy of Sciences (No. E224821231).
Conflict of interest: The authors declare that they have no conflict of interest.
Citation
Yu, H., Wang, Y. and Gao, C. (2024), "A fractal model of rough surfaces based on ellipsoidal asperities", Industrial Lubrication and Tribology, Vol. 76 No. 5, pp. 666-677. https://doi.org/10.1108/ILT-12-2023-0392
Publisher
:Emerald Publishing Limited
Copyright © 2024, Emerald Publishing Limited