Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature

The instantaneous flash temperature is an important factor for gears in service. To investigate the effect of the flash temperature of a tooth surface on the dynamics of the spur gear system, a modified nonlinear dynamic model of a gear-rotor-bearing system is established. The factors such as the contact temperature of the tooth surface, time-varying stiffness, tooth surface friction, backlash, the comprehensive transmission error and so on are considered. The flash temperature of a tooth surface of pinion and gear is formulated according to Blok's flash temperature theory. The mathematical expression of the contact temperature of the tooth surface varied with time is derived and the tooth profile deformation caused by the change of the flash temperature of the tooth surface is calculated. The expression of the mesh stiffness varied with the flash temperature of the tooth surface is derived based on Hertz contact theory. The temperature stiffness is proposed and added to the nonlinear dynamic model of the system. The influence of load on the flash temperature of the tooth surface is analyzed in the parameters plane. The variation of the flash temperature of the tooth surface is studied. The numerical results indicate that the calculated method of the flash temperature of the gear tooth surface is effective and it can reflect the rules for the change of gear meshing temperature and sliding of the gear tooth surface. The effects of frequency, backlash, bearing clearance, comprehensive transmission error and time-varying stiffness on the nonlinear dynamics of the system are analyzed according to the bifurcation diagrams, Top Lyapunov Exponent (TLE) spectrums, phase portraits and Poincaré maps. Some nonlinear phenomena such as periodic bifurcation, grazing bifurcation, quasi-periodic bifurcation, chaos and its routes to chaos are investigated and the critical parameters are identified. The results provide an understanding of the system and serve as a useful reference in designing such systems.