AN IMPROVED ENGINEERING MODEL FOR CALCULATING THE RADIAL STIFFNESS OF ROLLER BEARINGS

Abstract

The paper presents an analysis of quasi-static models for calculating stiffness and substantiates the choice of the most effective engineering model for calculating the radial stiffness of roller bearings. The analysis of quasi-static models for calculating the stiffness of roller bearings is carried out, which consists in numerical-analytical modeling of force-displacement ratios under conditions of contact interaction. It is noted that for roller bearings, semi-empirical dependencies proposed by Palmgren, Jones and Harris are more often used. For all numerical-analytical quasistatic models of roller bearings, a generalizing relationship between force and displacement at contact is introduced within the framework of the Hertz contact theory, where the stiffness characteristics are determined by the solution of the corresponding contact problem. The numerical values of constants obtained by several authors on the basis of empirical approaches or an approximate solution of the contact Hertz problem for steel bearings are given. In this paper, an analysis of quasi-static models for calculating stiffness is presented and the choice of the most effective engineering model for calculating the radial stiffness constants of roller bearings is substantiated. To solve the contact problem of a separate rolling element and rolling tracks, a finite element periodic model consisting of two halves of the rolling element is used, which are in contact separately with part of the inner and outer bearing rings, respectively, and have physically justified boundary conditions. The labor and computer time required to implement the proposed approach is less than when using the finite element method to determine the stiffness "in the forehead" for each individual bearing, which makes this model an effective engineering model for calculating the stiffness of roller bearings.