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Article

A Hybrid Fractal-NURBS Model for Characterizing Material-Specific Mechanical Surface Contact

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.
Keywords: mechanical surface; contact rate; finite element method; NURBS mechanical surface; contact rate; finite element method; NURBS

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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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