On the Torsional Vibrations of the Shafts System Having a Periodically Variable Moment of Inertia : Specially the Bad Effect of the Finite Length of the Connecting Rod on the Ranges of the Unstable Vibration

Abstract

This paper presents the effects of the finite length of the connecting rod on the ranges of unstable vibrations for the torsional vibrations of the shafts systems having a periodically variable moment of inertia and viscous damping force. In studying this problem, we established a differential equation containing a parameter λ, which is the ratio of the crank radius to the length of connecting rod, and a damping parameter δ. We solved this equation by the method of successive approximation, and as the results we obtained the following two remarkable points. First, in the case of no damping, there arise the unstable vibrations in the vicinities of the number of revolutions of shaft 2N_er, 2/3N_er and 1/2N_er in addition to the vicinity of N_er, which corresponds to the ordinary critical speed for torsional vibrations of shaft. Secondly, we pointed out by considering δ that the unstable ranges were reduced and there exists the "ranges of taking along by (Mitnahmebereich⁽⁶⁾)" over the unstable ranges, though it is not too much to say that there is no literature considering the damping parameter δ.