Study on calculation method of friction excitation and stiffness excitation of helical gear

As an important part of the transmission system, helical gear generates dynamic meshing excitation during operation due to the change of its contact tooth pair, load deformation, manufacturing and assembly errors, resulting in helical gear vibration and noise. The transmission error can be reduced to a certain extent by improving the manufacturing accuracy and shape modification. Under the condition of high torque and low speed, the static transmission error is very small, and the vibration and noise level of helical gear system is still very high. It is necessary to consider other excitation sources. The research shows that friction excitation is also one of the main causes of helical gear vibration and noise, and it is also one of the important excitation sources that can not be ignored. The tooth surface friction of helical gear is formed due to the relative sliding between the meshing contact teeth and the contact tooth surface. The magnitude and direction of the excitation force change periodically with the operation of helical gear. Tooth surface friction will not only cause tooth surface wear, temperature rise and energy loss; Moreover, the tooth surface friction is also one of the internal excitation, which causes the vibration of the helical gear system perpendicular to the meshing line, and is coupled with nonlinear factors such as time-varying stiffness excitation and micro characteristics of the tooth surface, which makes the dynamic characteristics of the helical gear system more complex. The time-varying of contact line is one of the important characteristics of helical gear transmission. The change of the number of contact lines will cause the change of stiffness and tooth surface friction. Therefore, friction excitation is one of the important factors affecting the dynamic response characteristics of helical gear system. It is particularly important to study the influence of helical gear modification and tooth surface friction on the dynamic response characteristics of helical gear, especially for helical gear system.

Assuming that the load is evenly distributed along the length of the contact line, based on the calculation method of time-varying contact line, time-varying friction and time-varying friction considering time-varying meshing force, the time-varying contact line, time-varying friction and time-varying friction torque of helical gear system are calculated, and the effects of different helix angle and different contact tooth width on the time-varying contact line The influence law of time-varying friction and time-varying friction torque. Based on the calculation method of helical gear meshing stiffness per unit contact line length of tooth profile end face, the meshing stiffness before and after helical gear modification is calculated.

Based on the idea that the load is evenly distributed along the length of the contact line during helical gear meshing, the time-varying contact line length, time-varying friction force and time-varying friction torque of Helical Gear Considering time-varying meshing force are calculated, and the effects of different friction coefficient, different helix angle and different contact tooth width on the contact line length, friction force and friction torque of helical gear are analyzed. Through the unit length meshing stiffness of helical gear end face and the relationship between rolling angle and contact line, the single pair meshing stiffness of helical gear is calculated, and the comprehensive meshing stiffness of helical gear is obtained by superposition. The main conclusions are as follows:

① With the increase of helix angle, the variation range of contact line length of helical gear contact teeth increases; With the increase of contact tooth width, the overall amplitude of contact line length of helical gear contact teeth increases, and the variation range of amplitude also increases.

② The friction force and friction torque of the driving and driven gears of helical gears decrease with the increase of helix angle and contact tooth width; The overall amplitude of friction torque of total meshing teeth increases with the increase of helix angle and contact tooth width.

③ Based on the calculation method of helical gear meshing stiffness per unit contact line length of tooth profile end face, the meshing stiffness before and after helical gear modification is calculated.

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