Analysis of Vibration of Bevel Gears

Equation of motion for free vibrations of a pair of gears is derived in a general form. A vibration system of two-degrees of freedom which represents the fundamental characteristics of bevel gears is constructed mathematically. It is found from the analysis of the system that the fundamental characteristics of vibrations which distinguish bevel gears from spur and helical gears are caused by a change in the direction of the tooth-normal in tooth-meshing. the influences of parameters such as the contact ratio, stiffness of gear-carrying shafts and damping ratios on the band width of unstable regions of the vibration are also shown.