Dynamic response of geared shaft systems with time-dependent boundary conditions subjected to static transmission error

A rotating gear pair experiences high vibration and noise mainly due to tooth profile error, mounting error, tooth wear, friction backlash and periodic change of meshing stiffness. The combined effect of the manufacturing error, mounting error and elastic tooth deformation is considered as the static transmission error that introduces internal displacement excitation within the gear pair. Such internal excitation generates torsional vibration through the driving and driven shafts even in absence of external excitations. Thus the vibration problem of a geared system involves homogeneous equations of motion with time dependent boundary conditions. The present research is to investigate the torsional vibrations of a geared system by developing a continuous model that converts the homogeneous equations with non-homogeneous boundary conditions into non-homogeneous equations with homogeneous boundary conditions. The influence of friction, tooth wear, backlash and other nonlinear variables have been ignored in the formulation.;The experimental investigations are carried out by measuring free torsional vibrations with strain gauge and frequency analysis by a spectrum analyzer.;The free vibration results of the proposed model are validated by developing the classical Rayleigh-Ritz model with Bhat's boundary characteristic orthogonal polynomial functions. The results are also validated by performing experiments in the laboratory for a simple geared system. Torsional vibration responses are determined in both time and frequency domains. In addition to the proposed continuous model the discrete model is simulated to determine torsional vibrations and dynamic torque generated due to static tooth error.