# Vibration characteristics of two stage helical gear transmission excited by time varying meshing stiffness

After solving the differential equations, the vibration acceleration of two teeth in each direction is synthesized into “the relative vibration acceleration in the direction of end meshing line” AI (I = 1,2)

In order to analyze the vibration characteristics of two-stage high-speed helical gear drive and compare its vibration characteristics with that of single-stage helical gear drive, the differential equations of the formula are solved and synthesized according to the formula. The input speeds of the reducer are 3000rpm, 6000rpm and 15000rpm The vibration responses of the input and output gear pairs of the two-stage helical gear transmission at three different speeds under the independent excitation of time-varying meshing stiffness are shown in Fig. 1-fig. 6. In the figure, FZ1 represents the tooth frequency of the input tooth pair and FZ2 represents the tooth frequency of the output tooth pair.

It can be seen from (b) and (d) in Fig. 1 to Fig. 6 that under the excitation of time-varying meshing stiffness, the phase diagram of the two-stage helical gear transmission is a series of intertwined and crossed curves, and the Poincare section diagram is a series of discrete points which can form a closed curve, so the vibration response shows obvious quasi periodic characteristics. In other words, the periodicity of the system at each adjacent time is different, but its periodicity is a complex large period reciprocating cycle. Because its vibration characteristics are between periodicity and aperiodicity, it is called quasi periodic response. The quasi periodic vibration seems to be chaotic, but in fact, there are extremely complex changing rules in it. Compared with the single-stage helical gear transmission, the non periodic vibration response of the two-stage helical gear transmission is obviously enhanced.

This phenomenon shows that the vibration response frequency of two pairs of gears in two-stage helical gear transmission affects each other, which makes the vibration of the system more complex. This is because the secondary helical gear system can be regarded as a multi frequency excitation system. For example, in addition to the excitation frequency generated by the time-varying meshing stiffness of the output end teeth pair, the vibration generated by the meshing of the input end tooth pair can also stimulate the output tooth pair. Therefore, in addition to its own body, the vibration response frequency of the system also has the form of superposition of frequency doubling of two teeth to tooth frequency. Since the input tooth pair is the power source of the output end tooth pair, the influence of the input end tooth pair vibration on the output end tooth pair is more obvious. This phenomenon is a significant difference between single-stage helical gear drive and two-stage helical gear drive. Because of this phenomenon, the vibration response of the system becomes more complex and non periodic.

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