Basic theory of helical gear dynamics and calculation of static transmission error after modification

Helical gear system is a complex elastic mechanical system composed of gear pair, transmission shaft, bearing and box. In the helical gear system, the power and motion are transmitted through the continuous interaction of the conjugate tooth surface of the teeth. The primary problem in the dynamic analysis of the helical gear system is to study the basic principle of the dynamic excitation in the meshing process of the helical gear and determine the type and nature of the dynamic excitation. The dynamic excitation of helical gear system includes internal excitation and external excitation. The main difference from general mechanical system is its internal excitation. Even if the external excitation is zero or constant, the helical gear system will produce vibration and noise due to this internal excitation. Moreover, as an important part of the transmission system, during the operation of the helical gear, the vibration and noise of the helical gear is too large due to the dynamic meshing excitation caused by the manufacturing and assembly error of the helical gear, the deformation of the shell, shaft, bearing and itself of the helical gear system; The contact condition of helical gear tooth surface changes, resulting in serious eccentric load, excessive transmission error and unstable transmission. Through the modification of helical gear profile and tooth direction, the eccentric load can be reduced, the gear can still run smoothly after tooth deformation, the meshing in and meshing out impact can be reduced, and the vibration and noise of helical gear system can be reduced.

On the basis of discussing the relevant theories of gear dynamics and tooth modification, the optimal modification amount of helical gear for tooth profile linear modification, tooth profile parabola modification and tooth direction drum modification is determined based on romax software, and the static transmission error curve of helical gear after tooth profile linear modification, tooth profile parabola modification and tooth direction drum modification is calculated, The minimum static transmission error of peak to peak value of helical gear system is obtained.

This paper mainly introduces the basic theory of gear modification and gear dynamics, determines the optimal modification amount of helical gear for linear modification, parabolic modification and drum modification based on romax software, calculates the static transmission error curve after modification by each modification method, and obtains the static transmission error with the minimum peak to peak value of helical gear system. It mainly includes the following aspects:

① This paper introduces various modification methods of gear profile modification and tooth direction modification, as well as the calculation methods of modification amount, modification length and modification curve of different modification methods.

② This paper introduces the basic theories of gear dynamic excitation, transmission error and gear dynamic response characteristics, briefly expounds the dynamic modeling method of gear system, and expounds the establishment of coupling vibration analysis model of helical gear system.

③ Romax software is used to determine the optimal modification amount of helical gear tooth profile linear modification, tooth profile parabola modification and tooth direction drum modification, and the optimal modification amount is calculated. The static transmission error after modification is the smallest peak value of helical gear static transmission error after linear modification.

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