Nonlinear Dynamic Modeling Of Gear System With Tooth Contact Surface Temperature And Analysis

One of the important parts of motion transmission systems is gear, the vibration and noiseof most machinery equipment are caused by gear systems. The majority of research on thegear systems was concentrated on the time-varying mesh stiffness, backlash andcomprehensive error, and few researches are on gear tooth contact temperature and friction. Inthis dissertation, two models named respectively the model of single-stage spur gear systemwith gear tooth contact temperature and friction and the model of two-stage spur gear systemwith gear tooth contact temperature are established. Based on the nonlinear vibration theory,the changes of gear tooth temperature, the sensitivity of kinetic parameters, the couplingrelationship of kinetic parameters and the stability of local and global dynamics areresearched by calculating the cloud of maximum amplitude of the response,the maximumflash temperature of the tooth surface, displacement-time image, bifurcation diagram, phasediagram, Poincarémapping and basin of attraction.Based on the Hertz contact theory, the expression of the time-varying mesh stiffnesscaused by the change of tooth contact temperature is derived. The model of single-stage spurgear system with friction, lubrication conditions, tooth contact temperature, backlash,comprehensive error and time-varying mesh stiffness is established, and the dimensionlessmotion equations of the system are obtained.The local and global dynamics of the single-stage spur gear system is analyzed when thefrequency changed. The phenomenon of the coexistence of multiple steady-state solution ofthe system and the rule of the basin of attraction’s evolution are studied through thecell-to-cell mapping, and the result is that doubling bifurcation and boundary crisis of chaoticattractor have less influence on the topology of basin of attraction, but the saddle-nodebifurcation has much influence on it. The attractors’ competition phenomenon leading toglobal instability of the system is founded when multiple attractors coexist. The phenomenonof the coexistence of multiple solutions will be reduced by friction. The torsion vibrationcharacteristics of the system are analyzed when the gear body temperature is coupled withtime-varying mesh stiffness, comprehensive error and backlash.Finally,the nonlinear dynamics model of two-stage spur gear system with gear toothcontact temperature, backlash, time-varying mesh stiffness and comprehensive error isestablished. The dimensionless motion equations of the system are obtained. The torsionalvibration characteristics of the system is analysed when the gear body temperature is cuopledwith time-varying mesh stiffness, comprehensive error and backlash.The chaos andbifurcation characteristics of the system is analysised.With the same initial condition, thesituition that two pairs of gear have different periodic motion state is founded. The phenomenon of the coexistence of multiple periodic solutions is not founded in the two-stagespur gear system without the tooth contact temperature.