An Analytic Model for Ball Bearing Vibrations to Predict Vibration Response to Distributed Defects

Abstract

An analytic method for predicting the spectral character of vibrations generated by an important class of defects in ball bearings is described. This family of bearing problems comprises those operating modes in which the magnitude of the ball-race contact force varies continuously and periodically as the bearing rotates. Defects of this type include race misalignment and off-sized rolling elements. The analytic technique is based on solving Lagrangian equations for the time-varying displacement of the bearing race in response to the rotating system of ball forces.

Roller bearing dynamics under transient thermal-mixed non-Newtonian elastohydrodynamic regime of lubrication

“…These equations ignore the mass of rolling elements, as in most analyses [1,8,11,13,17,18]. Otherwise, an m-degrees of freedom model would be required with discretisation of the supported shaft mass proportionately to these radial degrees of freedom.…”

“…This results in bearing-induced vibration, which is also affected by a host of geometrical and topographical parameters. These include the presence of off-sized rolling elements [10], surface waviness of contacting solids [5,6,11], faults such as pits and cracks on the contacting surfaces [7,11] and dynamic variation in bearing stiffness as the result of the orbiting rolling element complement, known as the variable compliance effect [5,6,12]. This is an inherent property of a bearing, even for idealised smooth mating surfaces.…”

“…Most dynamic analyses are based on 2 degrees-of-freedom models in the radial lateral directions of bearings [11,12]. Others include axial vibration of bearings in shaft-bearing systems subjected to thrust forces [13], or up to 5 degrees-of-freedom when moment loading and centrifugal effects [9,14] are taken into account.…”

Effect of Localized Defect on the Vibration Behavior of Cylindrical Roller Bearing-Rotor System

“…Tondon et al [7] proposed an analytical model for predicting the vibration frequencies of rolling bearings and amplitude of frequency component due to localised defect under radial and axial load. Mayer et al [8] studied effect on vibration due to distributed defect of bearing on rotor bearing system. Patil et al [9].…”

Vibration Characteristics of Tapered Roller Bearings with Roller Diameter error

“…The effect of off-sized roller, in particular, error in roller diameter on bearing vibration has been investigated by several researchers. However, most of them carried out investigation with regard to ball or cylindrical roller bearings [2][3][4][5][6][7]. Although TRBs are widely used in heavy load applications, the effect of geometric error on the performance of TRBs has not been sufficiently considered.…”