MATHEMATICAL MODELING OF HEAT TRANSFER PROCESSES IN THE FRICTION ZONE OF ROUGH SURFACES
DOI:
https://doi.org/10.32718/agroengineering2025.29.166-171Keywords:
frictional heating, surface roughness, contour contact area, thermal conductivity, integral transformations, temperature field, half-spaceAbstract
The paper presents an analytical study of transient heat transfer processes occurring in the frictional contact zone of rough solid bodies with a circular contour contact area. The mathematical model combines the heat conduction equation for a half-space with a modified contact interaction law that accounts for the real micro-geometry of the surface through the roughness parameter β. It is shown that the value of β determines the size of the contour contact region and significantly affects the actual pressure distribution, which, for rough surfaces, differs markedly from the classical Hertz solution. A quasi-Hertzian pressure profile is employed to accurately describe the increase in real contact area under low loads and elevated roughness levels.
To solve the transient problem, the Hankel and Laplace integral transforms are applied, yielding an analytical expression for the temperature field at any point within the half-space. Based on the obtained formulas, a numerical analysis of the influence of the roughness parameter β, the pressure distribution, and the frictional heat flux on the peak temperature and its spatial distribution is conducted. It is established that an increase in β leads to a decrease in the maximum temperature in the contact center due to the enlargement of the contour contact area and the corresponding redistribution of thermal energy.
The results demonstrate good agreement with published analytical and experimental findings by other authors concerning the influence of surface micro-geometry on frictional heating. The proposed model can be applied to the thermal assessment of frictional components such as disc brakes, clutches, sliding and rolling bearings. The approach improves the accuracy of predicting temperature peaks, which is crucial for enhancing the reliability and durability of tribological systems.
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