Non-Linear Dynamic Model and Analysis of Ball Bearing with Localized and Distributed Defects Considering Ball Slip Condition

This paper presents a 6 DOF nonlinear vibration model to analyse the vibration responses caused by a deep groove ball bearing having localized defect of 2 mm circular diameter and surface waviness (waviness amplitude = 50 m and waviness orders = 9 and 20) on its races.The model includes the mass of the shaft, ball masses, housing mass, damping lubrication, centrifugal forces, and the slip condition.The equations of motions for this model have been derived using Newton's method.The Runge-Kutta method of the ode45 solver analyses the vibrational signals of bearings with various defects.Test bearings with localized defects and inner and outer race waviness orders 9, and 20 for theoretical analysis and waviness order 9 for experimental analysis were considered.The two races of the bearing were manually lapped to introduce artificial waviness.A coordinate measurement machine (CMM) is used to scan the artificially generated race waviness profile.The number of waves and their waviness amplitude were then determined by transferring the photos to CAD modeling software.Results of vibration responses obtained from simulation and experiments are compared and found to be in good agreement.Both theoretical and experimental results are used to estimate the cage frequency, shaft rotational frequency, and wave passage frequency (WVF or BPFI), as well as their sidebands at WVF fs = (nb*(fs-fc) fs).For waviness order 20, additional frequency peaks at sideband harmonics and sideband frequencies are determined.The results from analysis and experiments show peaks at the outer race defect frequency BPFO = n b *fc and its harmonics.Furthermore, peaks at ball slip frequency (f slip ) and its corresponding f slip sidebands are obtained in both theoretical and experimental spectra, suggesting ball slip over the races.