# Nonlinear dynamics theory of straight bevel gear

In the process of gear tooth transmission, there will be elastic deformation between gears, and the logarithm of straight bevel gears in meshing state changes periodically with time, so the meshing stiffness of straight bevel gears is time-varying. In addition, due to the existence of factors such as tooth lubrication, manufacturing error, assembly error and tooth surface wear, there will be different degrees of clearance in the components of gear system such as straight bevel gear teeth and bearings. If the straight bevel gear system works under heavy load, the meshing surface of the straight bevel gear will always contact, and there will be no tooth side clearance or small tooth side clearance between the teeth, which will not affect the dynamic performance of the straight bevel gear system. If the straight bevel gear system works under the working conditions of light load, high speed or frequent start and braking, there will be large tooth side clearance between the teeth, resulting in abnormal meshing of the teeth, resulting in contact, separation and re contact of the teeth, which will affect the transmission performance and dynamic performance of the straight bevel gear system.

Therefore, it is very necessary to study the nonlinear factors such as tooth side clearance and meshing stiffness of straight bevel gear system. The nonlinear dynamic analysis of tooth clearance includes the analysis of single pair of gear pairs and the whole straight bevel gear system. The single pair gear pair is studied, the vibration impact model considering tooth side clearance is established, and the method of solving this kind of model is studied. The dynamic behavior of straight bevel gear system is analyzed by solving vibration differential equation, which is helpful to study the influence of tooth side clearance of straight bevel gear system on gear transmission efficiency. The whole straight bevel gear system is studied, including establishing the analysis model, determining the nonlinear parameters in the model, selecting effective solution methods, analyzing the dynamic performance and vibration characteristics of the system, etc.

According to the different nonlinear factors involved in the model, the nonlinear dynamic mathematical model of straight bevel gear system can be divided into the analysis model containing only tooth clearance; At the same time, it includes the analysis model of meshing stiffness and tooth clearance; An analytical model including multiple pairs of gears, shafts, bearings and other clearances; At the same time, the analysis model includes time-varying meshing stiffness and tooth clearance.

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