Analysis of the stress state of a layer on two cylindrical embedded supports with plain bearings

Abstract

Cylindrical bushings and plain bearings in mechanical and aircraft engineering are important structural elements that perform various functions, ensuring the reliability, durability, and safety of structures. This paper analyzes the stress state of a part on two embedded supports. Sliding bearings are used between the supports and the body of the part. The model is reduced to a layer with two embedded thick-walled cylindrical tubes. Smooth contact conditions are set between the layer and the pipes, as well as on the inner surfaces of the pipes (modeling a sliding bearing), and stresses are set on the flat surfaces of the layer. The spatial problem of elasticity is based on the Lamé equations. The layer is considered in the Cartesian coordinate system, the pipes in the local cylindrical coordinate system. When the boundary conditions are met, an infinite system of integro-algebraic equations is created. The redistribution formulas of the basic solutions of the analytical-numerical generalized Fourier method are applied to the created system of equations. As a result of mathematical transformations, an infinite system of linear algebraic equations is obtained, to which the reduction method is applied. After determining the unknowns, the stress-strain state is obtained. A numerical analysis of the stress state was performed for a layer of D16T aircraft alloy and polyamide sliding bushings. The result is compared with the work where the pipes are rigidly connected to the support. The numerical analysis suggests that the presence of contact-type conditions redistributes the stress state, increasing the maximum stresses. The proposed approach to solving the problem can be applied to structures whose design scheme coincides with the formulation of the problem presented.