New techniques to control the transverse vibration of centrally-clamped rotating disks are presented based on the deep comprehension of the closed-loop system behaviors. Much control efforts in the past are limited to some experimental results without fully understanding the behavior of the closed-loop control system.
The vibration control of rotating disks significantly differs in nature from that of stationary disks in that the dynamic characteristics of a rotating disk vary with the rotational speed and a mode separates into two travelling waves with the different apparent frequencies. It has been well known that the backward travelling waves of low apparent frequencies are important to the disk vibrations rather than the forward travelling waves of high apparent frequencies. Hence the vibration control of rotating disks often aims at suppressing the lower backward travelling waves.
To uncouple the backward and forward travelling wave states in a mode, the wave coordinates are introduced. Reformulating the equations of motion in the wave coordinates for a rotating disk, the classical proportional and derivative control is analytically re-examined and the stability and the roles of control gains and the sensor location are investigated. The results show that the classical proportional and derivative control technique is inadequate for the vibration control of rotating disks.
To concentrate the control force on the lower backward travelling waves of interest, the travelling control techniques are presented based on the finite dimensional subsystem including those waves, which can be constructed in wave coordinates. But, a disk belongs to the distributed parameter systems of infinite dimensional and the stability of the closed-loop system is not guaranteed due to the spillover effect of the ignored residual waves. In flexible systems such as a disk, the instability due to the spillover effect often occurs because they have small dampings.
In travelling wave con...