Parametrically Excited Vibration with External Constant Load and Damping

Abstract

The vibrations of gears can be expressed by differential equations of parametrically excited vibrations. In this paper, the stabilities of parametrically excited vibrations of the MeiBner and Mathieu types (the former expresses the torsional vibrations of spur gears and the latter expresses those of helical gears) and their vibrational characteristics in the stable region are theoretically investigated. Through this investigation, the effects of the helix angle and the damping factor on the vibrations of gears are made clear. The vibrations of helical gears are smaller than those of spur gears. And the vibrations of helical gears with a large helix angle are smaller than those with a small helix angle. When the damping factor ζ increases, the unstable region decreases, and the peak levels of vibrations decrease remarkably, although the amplitude at the other region does not decrease. When we drive a pair of gears at a speed whose meshing frequency is two times faster than the natural frequency of the gearing system, the gears with a small damping have a very large vibration, but the gears with a large damping rotate smoothly.