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 mass 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 anamolies 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.