Study on multi-state of meshing-impacting dynamic characteristics of spur gear systems considering friction under localized tooth breakage

\nLocalized tooth breakage is one of the common failures of spur gears, which affects the smooth and safe operation of spur gear transmission systems. The tooth collision cannot be neglected, and it is especially important to reveal the meshing-impacting dynamic characteristics of the gear system under localized tooth breakage to improve the safe and stable operation of the gear system. Based on the gear meshing principle and the dissipative collision contact force model, the drive-side tooth meshing model and back-side tooth impacting model are established with considering the transient nature of tooth back-side contact. The tooth surface meshing model and tooth back collision model under partial breakage are established. According to the contact state and force environment of the gear pair, the multi-state meshing-impacting behaviour under local breakage is classified, and the discrete meshing-impact dynamics model of an involute spur gear system under local breakage is established to explore the influence of local breakage on the meshing stiffness and load distribution. The mechanism of contact force under partial tooth breakage is revealed, and the influence of load coefficient and meshing frequency on the nonlinear dynamics is studied by defining two Poincaré maps. It is found that local tooth breakage affects the contact force of single-and double-tooth meshes and reduces gear load carrying capacity. Larger loads inhibit back-side impact, and smaller loads induce the coexistence behaviour and back-side impact. Larger or smaller meshing frequency induce back-side impact behaviour. The coexistence of chaotic and periodic motions induces back-side impact behaviour, and localized tooth breakage affects the coexistence phenomenon and aggravates the complexity of the dynamic behaviour. The dynamic model of gear system considering energy dissipation and nonlinear vibration under the presence of local tooth breakage of the pinion is explored, and the conditions of back-side impact are studied. This research provides new methods and ideas for nonlinear dynamic modelling and analysis of faulty gear systems.\n