On the Vibration of a Power-Transmission System Having Angular Clearances, Part 4 : Vibration Excited by Irregularities of Gear Teeth, Analysis of an Equivalent One-Mass Two-Stiffness System Reduced from a System with Two Degrees of Freedom

Abstract

Displacement excitation by errors of gear shape or by eccentricities of gear axes gives a one-dimentional shaft system substancially the same behaviour as torque excitation does, but in approximate solutions it is necessary to change the expression of excitation term. As stiffness fluctuation of gear teeth also excites vibration, the author solves the vibration of unilateral, symmetrical mode without damping, supposing the fluctuation as rectangular. The solution appears different from the one in the former cases, difficult to calculate, and is not yet numerically treated. The author thinks that this excitation gives rather high frequency, then the damping would act more effectively and this mode probably disappears. The author presents an approximation method to solve by hand a two-dimensional system at its higher resonance state solving rigorously an equivalent one-dimensional system and approximating the damped maximum amplitude state. Though the solution from this approximation method does not sufficiently agree with the one derived by Y. Yoshikawa with an analogue computer because of inadequate data, the method gives a new solution of the equivalent system, which is a limit case of clearance systems.