回転角速度が変動する扁平軸の不安定振動 : 第2報, 回転体が並進運動をする場合の不安定振動の近似解析

抄録

This paper deals with an approximate solution and instability for lateral vibrations of an asymmetrical shaft. When a rotating speed of the shaft fluctuates periodically with N times in a revolution, unstable vibrations occur at angular velocities near the major critical speed ω_c and near 2ω_c/|2±N|. In the cases that N=1, 3/2, 2 and 3, the approximation of the higher order than the first report is carried out for various values of an asymmetry of shaft stiffness Δ and an angular velocity fluctuation ε, and the effect of these parameters Δ, ε on the position and width of instability regions is made more clear. Then, the equations of motion are directly integrated, and loci of the shaft whirling are described in the x, y plane in order to know a dynamic behavior of a rotating shaft in instability regions. Furthermore, it is shown that very narrow instability regions occur at the angular velocities ω≒ω_c/N and 2ω_c/N.