Vibration monitoring and modelling of shaft/bearing assemblies under concentrated elastohydrodynamic condition

A five degrees of freedom analysis of a perfect precision grinding spindle supported by a pair of back to back angular contact ball bearings is performed. The ball to race contacts are simulated by a non-linear contact spring, representing the elastic deformation of the mating rolling members. Major frequencies associated with various degrees of freedom are observed and a number of design curves, suggesting the best zones of operation for the simulated spindle under radial/ axial loading are also presented. The gyroscopic contribution of an ideal precision spindle was found to be insignificant. The model was further expanded to study the response characteristics of the spindle under lubricated contact conditions. A regression formula is used to model the non-linear spring/ damper arrangement,corresponding to the contact elastohydrodynamic oil film thickness. It is noted that the presence of the oil film along the line of contacts do not significantly alter the position of the major modes of the system. However; its contribution in damping the amplitude of oscillation are found to be significant. Various graphs indicating the overall system response, subjected to varying oil film viscosity, number of balls and the spindle màss are also presented. Furthermore, experimental investigations are conducted to validate the employed methodology. Good agreement is observed between the results of the simulation and the experimental spectra for the fundamental modes of response. Although manufacturing anamalies are not simulated,the formulated models incorporate sufficient versatility to forsee various spindle/bearing configurations, different loading arrangement as well as various geometrical features of a system to be modelled.