结合面静摩擦因数尺度关联三维分形模型

doi:10.3901/JME.2021.09.127

摘要/Abstract

摘要： 针对现有结合面静摩擦因数分形模型的静摩擦因数随结合面法向接触载荷增大而增大，与试验研究结论及统计模型不一致的问题，基于尺度等级定义微凸体的大小，严格区分微凸体高度与变形，构建各尺度等级微凸体的法向接触载荷与接触面积之间关系及其发生弹性和弹塑性第一变形时所能承受的最大切向载荷即最大静摩擦力计算模型，进而建立结合面法向接触载荷与最大静摩擦力计算模型，在此基础上，依据结合面静摩擦因数定义，提出与微凸体尺度等级关联的考虑微凸体完全弹性、弹塑性和完全塑性三种变形机制的结合面静摩擦因数三维分形模型，数值仿真分析了结合面静摩擦因数与法向接触载荷和分形维数D等的关系，结果表明结合面静摩擦因数随着结合面法向接触载荷的增大而减小，随着分形维数的增大而增大，并试验实例验证了所建模型的正确性，解决了现有结合面静摩擦因数分形模型与统计模型和试验结果之间的不一致性。

关键词: 结合面, 静摩擦因数, 尺度关联, 分形模型

Abstract: In view of the fact that the static friction coefficient of the fractal model of the static friction coefficient of the existing interface increases with the increase of the normal contact load of the interface, which is inconsistent with the experimental results and the statistical model. The size of the micro convex body is defined based on the scale level, and the height and deformation of the micro convex body are strictly distinguished. The relationship between the normal contact load and the contact area of the micro convex body at each scale level and the calculation model of the maximum tangential load that the micro convex body can bear when the full elastic and the first elastic-plastic deformation occur are established. Finally, the calculation model of the relationship between the normal contact load and the maximum static friction force is established. On this basis, according to the definition of the static friction coefficient of the joint surface, a three-dimensional fractal model of the static friction coefficient of the joint surface is proposed, which is related to the scale level of the micro convex body and considers three deformation mechanisms of the micro convex body, i.e. complete elasticity, elastoplasticity and complete plasticity. The relationship between the static friction coefficient of the joint surface and the normal contact load and fractal dimension D is analyzed by numerical simulation. The results show that the static friction coefficient decreases with the increase of normal contact load and increases with the increase of fractal dimension. By comparing with the experiment, the correctness of the model is proved, and the inconsistency between the fractal model of static friction coefficient and the statistical model and the experimental results is solved.

Key words: joint interfaces, static friction factor, scale correlation, fractal model

中图分类号:

TH113

张学良, 张伟, 温淑花, 姚世生. 结合面静摩擦因数尺度关联三维分形模型[J]. 机械工程学报, 2021, 57(9): 127-138.

ZHANG Xueliang, ZHANG Wei, WEN Shuhua, YAO Shisheng. Three-dimensional Fractal Model with Scale Correlation for Static Friction Factor of Joint Interfaces[J]. Journal of Mechanical Engineering, 2021, 57(9): 127-138.

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