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Open AccessArticle
A Hybrid Fractal-NURBS Model for Characterizing Material-Specific Mechanical Surface Contact
by
Leilei Zhang
Leilei Zhang 1,
Yingkun Mu
Yingkun Mu 1,
Kui Luo
Kui Luo 1,
Guang Ren
Guang Ren 1 and
Zisheng Wang
Zisheng Wang 2,*
1
Department of Automation, Moutai Institute, Renhuai 564500, China
2
Department of Industrial Engineering, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
Machines 2026, 14(1), 49; https://doi.org/10.3390/machines14010049 (registering DOI)
Submission received: 26 November 2025
/
Revised: 25 December 2025
/
Accepted: 29 December 2025
/
Published: 30 December 2025
Abstract
The reliability of mechanical systems hinges on analyzing the actual surface-to-surface contact area, which critically influences dynamic behavior, friction, material performance, and thermal dissipation. Uneven surfaces lead to incomplete contact, where only a fraction of asperities touch, creating a nominal contact area. This study proposes a novel fractal contact model for various mechanical behaviors between mechanical contact surfaces, integrating the Weierstrass–Mandelbrot fractal function and nonuniform rational B-spline interpolation (NURBS) to model material-dependent actual contact conditions. Furthermore, this research delved into the changes in thermal conductivity across the surfaces of metal materials within a simulated setting. It maintained a contact ratio ranging from 0.038% to 15.2%, a factor that remained unaffected by contact pressure. Both experimental and simulated findings unveiled an actual contact rate spanning from 0.44% to 1.06%, thereby underscoring the distinctive interface behaviors specific to different materials. The proposed approach provides fresh perspectives for investigating material–contact interactions and tackling associated engineering hurdles.
Share and Cite
MDPI and ACS Style
Zhang, L.; Mu, Y.; Luo, K.; Ren, G.; Wang, Z.
A Hybrid Fractal-NURBS Model for Characterizing Material-Specific Mechanical Surface Contact. Machines 2026, 14, 49.
https://doi.org/10.3390/machines14010049
AMA Style
Zhang L, Mu Y, Luo K, Ren G, Wang Z.
A Hybrid Fractal-NURBS Model for Characterizing Material-Specific Mechanical Surface Contact. Machines. 2026; 14(1):49.
https://doi.org/10.3390/machines14010049
Chicago/Turabian Style
Zhang, Leilei, Yingkun Mu, Kui Luo, Guang Ren, and Zisheng Wang.
2026. "A Hybrid Fractal-NURBS Model for Characterizing Material-Specific Mechanical Surface Contact" Machines 14, no. 1: 49.
https://doi.org/10.3390/machines14010049
APA Style
Zhang, L., Mu, Y., Luo, K., Ren, G., & Wang, Z.
(2026). A Hybrid Fractal-NURBS Model for Characterizing Material-Specific Mechanical Surface Contact. Machines, 14(1), 49.
https://doi.org/10.3390/machines14010049
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