In this research, an analytical solution of the dynamic excitation of elastic system depending on parametric changes in the stiffness of teeth during engagement is presented. It is shown that the main source of excitation in a differential gear is the central internal gear, and the intensity of the excitation depends on the manufacturing accuracy of the tooth profile. With increase of the flank size on the addendum of the sun gear more than a particular value, vibration levels in the gear increases. Introduction of optimal value of pitch variation in gear wheel reduces vibration to minimum.

Analytical research was carried out with the aim of finding the cause of dynamic processes of vibrationexcitation 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 passingfrom one tooth mesh to double pair meshing and vice versa. The dynamics of an elastic system can be controlledby using the contact ratio e in the gear mesh which does not depend on the transmitted power. The size of instabilityzones 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 frequenciesexcept those equal to doubled first frequencies. All zones of instability and resonances are located in thezones of phase vibration changes, with maximum efforts taking place in the areas of one tooth mesh before passingthe 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.

No abstract