The unsteady contact interaction of a rotating stiff finite cylinder and elastic half-space with frictional heat generation

Abstract

There are several mathematical models that help describe the contacting process for bodies, but solving the majority of theoretical and practical problems is not impossible without considering the geometric characteristics of contact interaction. However, in the contact problems of thermoelasticity factors of finiteness of stiff dimensions and curvilinearity of its basis are not taken into account mostly.

In the example of an axisymmetric problem about pressing a finite rigid circular cylinder, rotating around its axis with constant angular velocity, into an elastic half-space, we consider the method that allows us to model and investigate a wide range of phenomena arising at the interaction of bodies: separation of contact surfaces, wedging, and simultaneous existence of adhesion and sliding zones. On the contact area, heat is generated by friction forces, and non-ideal heat contact between cylinder and half-space is mathematically modeled using "third body" – thin near-surfaces and intermediate layers of interacting bodies, the physical and mechanical properties of which differ from those of the contact pair, and by the microgeometry of their surfaces in the contact zone. For every contact body, the non-stationary equation of thermal conductivity with initial condition on temperature is solved, and the time variable appears as a parameter in the rest initial ratios. A Laplace integral transformation with respect to the time coordinate and a Hankel integral transformation with respect to the radial coordinate for the half-space and the method of straight lines cylinder are used to solve the problem. The temperature and thermal flux fields in the cylinder and in the half-space, the contact stresses, and the displacements of the half-space are determined. The inversion of the transforms of the desired functions was carried out numerically. Qualitatively distinct stages of the overall picture of unsteady interaction for the formulated problem have been identified. It was found that the course of the relevant processes is determined by specific loads and friction pair characteristics. It is noted that quasi-stationary contact problems should be considered when the initial data and the nature of the load cause the maximum values of the studied quantities of the corresponding characteristics to be exceeded in the stationary mode.

Pages of the article in the issue: 126 - 129

Language of the article: Ukrainian