On the Critical Speed Regions of an Asymmetric Rotating Shaft Supported by Asymmetrically Elastic Pedestals : 2nd Report, On the Forced Vibrations

Abstract

In the 1st report, the authors studied the unstable regions of a system in which a disk is mounted at the center of an asymmetrical elastic shaft, and is supported at both ends by asymmetrically elastic pedestals. However, in an actual rotating system, as inevitable errors in the qualities of materials and the machining processes are present in the shaft and disk, the forces of unbalance caused by them, effects of gravity in supporting horizontally, and others, must be taken into consideration. Hence, for the vibrational characteristics of the system, analysis of the unstable regions only is not sufficient. Analysis of forced vibrations is also required. To elucidate the vibrational characteristics of the system ranging from the first critical speed to the fourth critical speed, the authors have made analyses by using the asymptotic method in the same way as in 1st report, to know what are dynamic characteristics of such a system in relation to the relationship among the spring constant, the internal and external dampings, the magnitude of eccentricity in the shaft and disk, the angle of unbalance, gravity, and others. The vibrational phenomena in the neighbourhood of the first and second critical speeds at comparatively low speed regions have been experimentally confirmed.