Abstract

It is shown that friction fracture surfaces can be self-affine with a local fractal dimension. However, the intersection of such a self-affine surface with a plane gives similar contour lines, which are undoubtedly self-similar. The above considerations regarding the fractal properties of fracture surfaces give reason to believe that a rough surface in contact with metallic bodies in the process of friction is also self-similar. This article presents the fractal dimensions of the transient contact regimes (from elastic to elastoplastic and from elastoplastic to plastic contact) for self-affinity curves, which are the curves of the reference surface at various combinations of material parameters: Poisson’s ratio, hardness, and modulus of elasticity. In the calculations, the Minkowski dimension, calculated by the cellular method, was taken as the fractal dimension of curved reference surfaces. This method, based on the consideration of contact interaction, formed the basis of the method for calculating the contact characteristics of bodies, taking into account their macroshape and the roughness of friction surfaces. The results of the study are of great importance for the development of engineering methods for calculating homogeneous and inhomogeneous rough bodies.

中文翻译：

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分析粗糙摩擦表面的分形结构以建立摩擦接触的瞬态机制

摘要

结果表明，摩擦断裂面可以是具有局部分形维数的自仿射。然而，这样的自仿射曲面与平面的相交给出了相似的轮廓线，这无疑是自相似的。上述关于断裂表面分形性质的考虑使我们有理由相信，在摩擦过程中与金属体接触的粗糙表面也是自相似的。本文介绍了自仿射曲线的瞬态接触状态（从弹性到弹塑性以及从弹塑性到塑性接触）的分形维数，这些曲线是参考表面在各种材料参数组合下的曲线：泊松比、硬度和弹性模量。计算中，采用元胞法计算出的闵可夫斯基维数作为弯曲参考面的分形维数。该方法基于考虑接触相互作用，形成了计算物体接触特性的方法的基础，同时考虑了物体的宏观形状和摩擦表面的粗糙度。研究结果对于均匀和非均匀粗糙体计算工程方法的发展具有重要意义。