On the Vibration of a Power-Transmission System Having Angular Clearances, Part 1 : Harmonic, Subharmonic, and Ultraharmonic Vibration of a System of Single Degree of Freedom Retarded by Linear Damping

Abstract

The author deals with a one-dimensional power-transmission system having an angular clearance excited by a static torque and a cosine torque simultaneously. Although the system has symmetrically combined linear elasticities, the mean torque puts the characteristic asymmetric, therefore the system vibrates either "unilaterally" or "bilaterally", besides symmetrically. The author solves rigorously the harmonic or subharmonic vibration of the system without damping and discusses stability discrimination, then solves approximately the maximum amplitude state of the system under velocity-proportional damping, and as a result he is convinced that the latter approximation not only is easy to calculate, but also serves as stability discriminant. This approximation method gave practically coincident solution compared with the ones computed by Y. Yoshikawa with an analogue computer. Finally the author approximates the maximum amplitude state of the unilateral ultraharmonic vibration of the above system, and he verifies that velocity-proportional damping retards the vibration of the higher order the less effective contrary to the subharmonic mode, and the retardation characteristic resembles the one of the subharmonic mode of the order 1/2.