Modeling surface structure of tribotechnical materials


  • I. Drach Khmelnitskyi National University
  • M. Dykha Khmelnitskyi National University
  • O. Babak Khmelnitskyi National University
  • O. Kovtun Khmelnitskyi National University



surface relief; statistical models; stochastic models; fractal models; energy spectral density function


Modern tribology makes it possible to correctly calculate, diagnose, predict and select appropriate materials for friction pairs, to determine the optimal mode of operation of the tribo-joint. The main parameter for solving friction problems and other problems of tribology is the topography of the surface. The main purpose of the models in these tasks is to display the tribological properties of engineering surfaces. In the framework of the classical approach, the topography of the surface is studied on the basis of its images from the point of view of functional and statistical characteristics: the evaluation of the functional characteristics is based on the maximum roughness along the height and the average roughness along the center line, and the statistical characteristics are estimated using the power spectrum or the autocorrelation function. However, these characteristics are not only surface properties. They depend on the resolution of the device for measuring the surface geometry and the length of the scan. However, the degree of complexity of a surface shape can be represented by a parameter called the fractal dimension: a higher degree of complexity has a larger value of this parameter. Fractal dimensionality is a characteristic of surface relief and makes it possible to explain tribological phenomena without the influence of resolution. This article provides an overview of mathematical approaches to the description of the relief of engineering surfaces, in particular statistical, stochastic and topological modeling, their limitations, advantages and disadvantages. The implementation of the principles of the theory of fractal structures is discussed, which makes it possible to introduce the degree of imbalance of the tribological system into the analysis of structure formation in the surface and near-surface layers of materials and to describe the development of friction and wear processes. This is the basis for controlling the structure of the surface layers of materials with given properties. The concept of fractals, used for the quantitative description of the dissipative structure of the tribojunction zone, makes it possible to establish a connection between its fractal dimension and mechanical properties, as well as critical states of deformation of metals and alloys. The course of research and stages of fractal modeling, the classification of methods of fractal analysis of the structure of engineering contact surfaces are considered. A critical analysis of modern models based on the energy-spectral density function, which are quite similar to fractal models, is presented. Readers are expected to gain an overview of research developments in existing modeling methods and directions for future research in the field of tribology


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How to Cite

Drach, I., Dykha, M., Babak, O., & Kovtun, O. (2024). Modeling surface structure of tribotechnical materials. Problems of Tribology, 29(1/111), 16–24.