Фізико-математичне моделювання процесу відновлення підшипників ковзання з використанням полімерів

Abstract

The article considers the problem of increasing the service life and accuracy of sliding bearings by improving their restoration technologies using polymer and polymer composite materials. It is shown that under operating loads, friction and wear, the violation of the geometric accuracy of the bearing surfaces significantly affects the performance of the unit, causing an increase in contact stresses, vibrations and energy losses. The feasibility of using polymer coatings as an alternative to traditional repair methods, which are accompanied by significant thermal effects and residual deformations, is substantiated. The aim of the work is to develop a physical and mathematical model of the restoration process of sliding bearings with a polymer coating, which provides quantitative prediction of contact characteristics, stress-strain state and durability of the friction unit based on a limited number of physically justified parameters. Within the framework of the study, a contact model of the interaction of the system “shaft - polymer layer - metal sleeve” was formed, taking into account the assumptions of the linear theory of elasticity, smooth contact and isotropic properties of materials. The proposed mathematical description is based on the equations of equilibrium of a continuous medium, the relations of stresses and strains for the linear-elastic matrix of a polymer material and the generalized Hertzian contact formulation. An analytical expression for the contact pressure diagram, which is characterized by a smooth load distribution with a maximum in the central contact zone and zero values at the boundaries of the contact region, was obtained. This form of distribution is consistent with the physical nature of elastic contact and the results of known tribological studies. The influence of the composition of the polymer composition on the effective modulus of elasticity, contact stresses and the width of the contact zone was analyzed. It is shown that changing the fillers and matrix of the polymer material allows for targeted control of contact characteristics and reduction of wear intensity. As a final element of the model, a criterion for the operability and durability of a sliding bearing is proposed, which combines the results of contact analysis with a generalized wear law and allows for predicting the service life of the unit at the design or repair stage.