硬涂层粗糙表面接触分形建模研究

doi:10.3901/JME.2025.23.280

摘要/Abstract

摘要： 在涂层球接触模型的基础上，基于7个假设，首先推导了涂层球接触刚度模型，进而研究建立了考虑弹性完全塑性硬涂层粗糙表面接触分形模型与法向接触刚度分形模型，并对所建模型进行了仿真计算分析，研究了涂层厚度比、涂层与基体材料性能以及涂层基体表面分形参数对硬涂层粗糙表面接触行为与法向接触刚度的影响，结果表明：在给定载荷条件下，硬涂层粗糙表面接触比无涂层粗糙表面接触具有更小的实际接触面积和更大的法向接触刚度；涂层较厚的硬涂层粗糙表面接触具有较小的实际接触面积；涂层与基体材料弹性模量比对硬涂层粗糙表面接触行为与法向接触刚度的影响随着分形维数的增大而减小；涂层较硬的硬涂层粗糙表面接触具有较小实际接触面积和较大的法向接触刚度；基体表面较光滑的硬涂层粗糙表面具有较大的实际接触面积和较大的法向接触刚度。仿真结果还表明，所建模型可以逼近一般粗糙表面接触分形MB模型以及基于MB模型的结合面法向接触刚度分形模型，并取得了与硬涂层粗糙表面接触统计模型一致的结论，说明了所提出的建模方法的可行性与所建模型的正确性。

关键词: 涂层微凸体, 硬涂层粗糙表面, 接触载荷, 接触面积, 接触刚度, 分形模型

Abstract: Based on the contact model of coated sphere and 7 assumptions, the contact stiffness model for coated asperity is derived firstly, and then the contact fractal model and normal contact stiffness fractal model for rough surfaces with elastic-perfectly plastic hard coatings are proposed. The proposed models are simulated for investigating the effects of coating thickness ratio, coating and substrate material properties, and substrate surface roughness on the contact behavior and the normal contact stiffness of rough surfaces with hard coating. The simulating results demonstrated the following conclusions. Under a given load rough surfaces with hard coatings exhibits a smaller actual contact area and a greater normal contact stiffness compared to those of uncoated rough surfaces. The thicker the hard coating, the smaller the actual contact area of coated rough surfaces. The influence of the elastic modulus ratio between the coating and substrate on the contact behavior and normal contact stiffness diminishes as the fractal dimension increases. Rough surfaces with harder coatings exhibit a smaller actual contact area and greater normal contact stiffness. Rough surfaces with hard coatings on smoother substrate surfaces display a larger actual contact area and greater normal contact stiffness. The simulation results also demonstrate that the proposed models closely approximate the general rough surface contact fractal MB model and the normal contact stiffness fractal model for uncoated rough surfaces (based on the MB model). The consistency between the conclusions of the proposed fractal model and those of the statistical contact model for hard-coated rough surfaces validates the feasibility of the proposed modeling approach and the correctness of the developed models.

Key words: coating asperities, rough surface with hard coating, contact load, contact area, contact stiffness, fractal model

中图分类号:

TH113

廉义章, 张学良, 廖山钧. 硬涂层粗糙表面接触分形建模研究[J]. 机械工程学报, 2025, 61(23): 280-291.

LIAN Yizhang, ZHANG Xueliang, LIAO Shanjun. Research on Contact Fractal Model of Rough Surfaces with Hard Coatings[J]. Journal of Mechanical Engineering, 2025, 61(23): 280-291.

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