Parametric instability of the dynamics of gear wheels

Analytical research was carried out with the aim of finding the cause of dynamic processes of vibration excitation of gear wheels. This paper presents an elastic model of gearing without regard for compliance of supports. It is shown that parametric oscillations are caused by a periodic change of mesh force gearing in passing from one tooth mesh to double pair meshing and vice versa. The dynamics of an elastic system can be controlled by using the contact ratio e in the gear mesh which does not depend on the transmitted power. The size of instability zones depends both on the gear wheel rotation frequency and on the degree of overlap in teeth mesh. There are several zones of instability and stable operation of elastic systems at all gear wheel rotation frequencies except those equal to doubled first frequencies. All zones of instability and resonances are located in the zones of phase vibration changes, with maximum efforts taking place in the areas of one tooth mesh before passing the zone of instability or resonance, while after passing these zones the maximum mesh force, on the contrary, will take place in the areas of double pair meshing.