MATHEMATICAL MODELING OF THE THERMOELASTIC STATE OF AN ISOTROPIC HALF-SPACE UNDER THE INFLUENCE OF A FRICTIONAL HEAT SOURCE
DOI:
https://doi.org/10.32718/agroengineering2025.29.172-178Keywords:
thermoelasticity, isotropic half-space, frictional heating, Lame stress function, thermocontact criterion, equivalent stressAbstract
This paper presents an analytical study of the thermoelastic state of an isotropic half-space subjected to a frictional heat source acting on its boundary surface. The relevance of this research stems from the need to enhance the accuracy of stress-strain assessments for machine components and structural elements that operate under intense frictional contact and substantial thermal loads. Examples include braking systems, bearing units, and frictional assemblies. The nonuniform temperature distribution caused by frictional heating leads to high thermal gradients and the formation of a complex thermoelastic stress state in the near-surface region of the material.
The aim of the study is to derive analytical expressions for the components of the thermal stress tensor in an isotropic half-space, while taking into account thermocontact conditions. Additionally, it analyzes the influence of surface roughness on the level of equivalent stresses. The investigation is conducted within the framework of classical thermoelasticity, based on the assumptions of no body forces, internal heat sources, or external mechanical loads. The axisymmetric thermoelastic state is described using the thermoelastic displacement potential and the Lame stress function.
To solve the formulated boundary-value problem, Hankel and Laplace integral transforms are employed. This approach enables the derivation of closed-form analytical expressions for the thermal stress components and ensures that the boundary conditions on the half-space surface are satisfied exactly. A dimensionless thermocontact parameter is introduced to characterize the thermal contact conditions and surface roughness at the friction interface. It is demonstrated that this parameter significantly affects the distribution and magnitude of thermal stresses in the near-surface zone.
To quantitatively assess the intensity of the thermoelastic state, the Huber-Mises-Hencky energy criterion is utilized. Numerical analysis of the obtained analytical solutions is conducted, and the results are presented as graphical representations of equivalent stresses along the depth of the half-space. The analysis reveals that an increase in the surface roughness parameter leads to a decrease in the overall level of thermal stresses. However, a local maximum of equivalent stress persists at the friction surface.
The scientific novelty of this work lies in the analytical integration of the thermocontact criterion into the study of the thermoelastic state of an isotropic half-space. The practical significance of the results lies in their applicability to the engineering analysis and design of thermally loaded friction components, thereby enhancing their strength and durability.
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