[论文解读] A magnification-based multi-asperity (MBMA) model of rough contact where the Greenwood-Williamson and Persson theories meet

Xu Guo, Benben Ma+1 more|arXiv (Cornell University)|Dec 18, 2017

Adhesion, Friction, and Surface Interactions参考文献 19被引用 4

一句话总结

该论文提出了一种基于放大倍数的多尖峰（MBMA）模型，统一了Greenwood-Williamson（G-W）尖峰模型与Persson的压力扩散理论，用于粗糙表面接触。通过将形态学多分辨率分析整合到分层尖峰表示中，该模型能够准确预测整个压缩范围内的接触面积和压力分布，弥合了G-W模型在小尺度下的精确性与Persson理论在全接触状态下的性能之间的差距。

ABSTRACT

Contact analysis without adhesion is still a challenging problem, mainly owing to the multiscale and self-fractal characteristics of rough surfaces. Up to now, theories for analyzing contact behavior of rough surfaces in literature can be generally categorized into two groups: the asperity-based Hertz contact models initiated by Greenwood and Williamson (G-W model), which is shown more accurate under small indentation distance, and the magnification-based pressure diffusion theory initiated by Persson, which is shown to work well under full contact conditions. The aim of this paper is to propose a theoretical model that can effectively formulate the contact status of rough surfaces during the entire compression process. This is achieved by integrating the idea of magnification, or evolving resolution into an asperity representation of rough surfaces, and a magnification-based multi-asperity model is thus established. In the derived model, the originally complex contact problem is decomposed into a family of sub-problems each defined on a morphologically simpler contact islands. Benefiting from the explicit results given by Greenwood and Williamson, the proposed method is relatively easy for numerical implementation. Compared to other G-W type models, the proposed method has especially shown its strength in the computation of the contact area. Moreover, the G-W and Persson models are found well connected by the proposed method. For its validation, the proposed model is well compared with existing numerical, theoretical and experimental results. In particular, the proposed model has shown its excellency through comparison with representative theoretical, numerical and experimental data compiled in the contact challenge test by Mueser et al.

研究动机与目标

• 解决由于自仿射分形形态导致的多尺度粗糙表面接触建模挑战。
• 克服现有模型的局限性：G-W模型适用于小压陷，Persson模型适用于全接触条件。
• 构建一个统一的理论框架，无缝连接基于尖峰的模型与基于放大倍数的方法。
• 实现在全压缩过程中接触面积与压力分布的精确且数值高效的计算。
• 通过实验、数值和理论基准对模型进行验证，包括Mueser接触挑战数据集。

提出的方法

• 提出一种基于放大倍数的方法，通过动态调整分辨率来表征多尺度下的粗糙表面。
• 将全局接触问题分解为一系列在形态学上不同的接触岛上的简化子问题。
• 在每个子问题的相应分辨率层级上应用Greenwood-Williamson（G-W）赫兹尖峰模型。
• 利用Persson理论中的压力扩散概念，模拟不同尺度间尖峰之间的相互作用。
• 整合所有分辨率层级的结果，以计算总的真实接触面积与压力分布。
• 利用每个尺度下G-W模型的解析解，确保计算的高效性与精确性。

实验结果

研究问题

• RQ1 如何构建一个统一的理论模型，以同时捕捉粗糙表面的初始尖峰接触与全接触区域的过渡？
• RQ2 与标准G-W模型相比，基于放大倍数的方法在接触面积预测精度方面能提升多少？
• RQ3 所提出的模型能否弥合Greenwood-Williamson理论与Persson理论之间的理论鸿沟？
• RQ4 MBMA模型在全压缩范围内对实验与数值数据的拟合表现如何？
• RQ5 多尺度分辨率在提升粗糙接触建模的物理一致性与数值可处理性方面起到何种作用？

主要发现

• MBMA模型通过将多尺度分辨率整合到基于尖峰的框架中，成功统一了Greenwood-Williamson与Persson理论。
• 该模型在预测真实接触面积方面表现出卓越的准确性，尤其在部分接触向全接触过渡的区域。
• 与标准G-W模型相比，MBMA模型在所有压缩水平下均显著提升了接触面积计算的精度。
• 该模型与Mueser接触挑战实验数据高度一致，证实了其强大的预测能力。
• 由于在每个分辨率层级上采用G-W模型的解析解，该方法实现了高效的数值实现。
• 该模型揭示了G-W理论与Persson理论所描述区域之间的平滑过渡，验证了二者理论上的关联性。