New Analytical Model of Spur Gears with 5 DOF Shafts and its Comparison with Other DOF Models

Abstract

This study relates to the research on improving analytical models of gears. A new analytical model of gear shaft with 5 DOF was proposed. Equations of vibration were derived without small-angle approximation and were presented in a form that could be implemented in Simulink. In order to determine the effect of the additional DOF, four popular models having 2 DOF, 4 DOF, 6 DOF and 8 DOF were investigated, too. The proposed model has 12 DOF in total. This number of DOF could be increased; this, however, would result in a greater difference between the considered models, thus making it more difficult to evaluate the impact of the additional DOF of shafts. As a benchmark, the dynamic meshing force in the considered analytical models was calculated. Simulations were carried out with and without friction. Additionally, for the 12 DOF model, the effects of the position of the centre of gear and the centre of mass were investigated.

Influence of the movement of involute profile gears along the off-line of action on the gear tooth position along the line of action direction

“…Detailed information about tooth stiffness, Coulomb friction and other details concerning the analytical model can be found in [10,11]. The reaction force in Fig.…”