АСИМПТОТИЧЕСКИЙ ПОДХОД К РЕШЕНИЮ КОНТАКТНОЙ ЗАДАЧИ ДЛЯ ТЕЛА КАЧЕНИЯ С ТОНКИМ ДЕФОРМИРУЕМЫМ ОБОДОМ

Abstract

On the basis of an asymptotic approach to solving the elasticity theory boundary value problem for a thin strip rigidly linked to a non-deformable base, the differential equations are derived for determining the normal and shear loads distributed on the strip face free from fastening. These equations are used to solve the contact problem for a rigid cylinder with a thin elastic rim with a non-deformable horizontal rough support surface. The cylinder loading by a vertical force is considered for a given cylinder center settling. The calculated diagrams of contact pressure and shear contact stresses are obtained. In contrast to the previously used methods, the developed technique makes it possible to take into account the presence of adhesion and slip zones in the contact area, as well as to use a mathematically strict solution of the constitutive equations for contact pressure and shear contact stress. The value of the vertical force acting on the rigid cylinder for a given cylinder center displacement is determined. The stress tensor intensity distribution in the rim is established. The results of the developed technique application are compared with the calculated estimates obtained on the basis of the exact solution of the boundary value problem for a strip of arbitrary thickness and within the method, involving the use of the Winkler base simplified model. The dependences of the results error for the developed method on the thickness and Poisson's ratio of the rim material are obtained. The paper describes the effect of the rim-support surface friction coefficient on the contact pressure, shear contact pressure, and the maximum intensity of the stress tensor in the rim. It is concluded that it is reasonable to use the developed technique at solving contact problems for rolling elements with a relatively thin elastic rim.