Gear Vibrations in Supercritical Mesh-Frequency Range Caused by Teeth Impacts

摘要

After gear teeth impact, natural free vibrations arise, attenuating in a short period of time. Teeth impacts repeat with the frequency of teeth entering the mesh, vibrations become restorable, and restore with teeth mesh frequency. In the range of sub-critical teeth mesh frequency range these natural free vibrations are covered by forced vibrations caused by the fluctuation of teeth deformations. In the supercritical mesh frequency range, restorable free vibrations dominate in the frequency spectrum of gear system vibrations. These restorable free vibrations effectuate the increase of total vibration level with the speed of rotation increase. Also, in this frequency range the modal structure (natural frequency) of the gear system is not stable and effectuates super-critical resonances arising. Gear vibration measurements and frequency analysis (FFT-Analysis) are performed in very high speeds of gear rotations as high as 40,000 rpm. A mathematical model for experimental results synthesis is established. For this purpose, the theory of singular systems is used. Gear teeth mesh is treated as a singular system, with a continual process of load transmission with singularities caused by teeth impacts. Damping coefficients and energy attenuation is determined using the developed mathematical model.