Dynamic Model of Spur Gear with Friction and Crack in Tooth Root

A mathematical model developed to support investigation of pairs of gears is presented. It includes the effects of actuation, the loads, the changing tooth stiffness, and the changing friction between tooth flanks during engagement. Friction between the tooth flanks generates an alternating non-symmetrical periodic function and the behaviour during the contact. The system actuation is modelled for different sources and the tooth stiffness. The mathematical model of the mechanical system of gear has the form of a system of two non-homogeneous nonlinear second-order differential equations.