# Basic theory of gear transmission dynamics

Most of the vibration and noise of the machine come from the vibration generated by the gear transmission system when it works. Therefore, the research on the nonlinear dynamic characteristics of the gear transmission system plays an important role in the dynamic design of gear teeth. Taking a hybrid electric vehicle power transmission system of a company as an example, according to the structural model of the gear transmission system in the figure below, the nonlinear dynamic model of the gear transmission system is established under the hybrid drive mode, Calculate the dynamic response of gear transmission system under internal excitation, modify the design parameters, improve its dynamic characteristics, and continuously analyze to achieve dynamic optimization design. Therefore, the study of nonlinear dynamic characteristics of gear transmission system has become an important part of gear dynamic design. The basic parameters of each element in the gear transmission system include the number of teeth Z, modulus m, mass m / kg and moment of inertia I / kg M2, base circle radius R / mm, tooth width B / mm, pressure angle α/ ° measured.

The motion of each component in the gear transmission system of hybrid electric vehicle affects and interacts with each other, and the power transmission system is composed of one engine and two motors as the power source, while the hybrid power split system with multiple power sources has a variety of driving modes, which makes the transmission system show more complex vibration characteristics. Therefore, the system is divided into two parts. Fully considering the nonlinear factors in the system, such as time-varying meshing stiffness, tooth side clearance, comprehensive meshing error and so on, the transverse torsional nonlinear dynamic equation of composite planetary gear system is established by using the second kind of Lagrange equation, and then the bending torsional shaft nonlinear dynamic equation of parallel shaft gear transmission is established, The nonlinear dynamic model of the whole system is established by properly simplifying the connecting part between the composite planetary gear train and the parallel shaft gear. Finally, the nonlinear factors such as gear transmission meshing comprehensive stiffness, tooth side clearance and comprehensive meshing error are mathematically described. The establishment of nonlinear dynamic model of hybrid electric vehicle gear transmission system lays a theoretical foundation for the subsequent analysis and research of dynamic characteristics of the system by using dynamic theory.

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