This project addresses three fundamental problems in machine dynamics whose solutions are important in the design of high productivity machines in the material processing and computer industries. The three research topics are (1) supercritical speed rotating plates, (2) vibration of damped, asymmetric, high speed, rotating circular plates subjected to a stationary slider bearing system, and (3) vibration and stability of high speed bands (tapes, fibers, belts, and saws). The first topic's impact will be in computer disk drives and circular sawing machines. Current systems use subcritical speed to avoid resonance of vibration waves by low frequency excitations. Supercritical speed plates are subject to aeroelastic flutter and thereby limited in their use. Supercritical speed plates would imply gains in productivity, and this research seeks to determine the maximum operating speed of a rotating plate. The second problem addresses a class of systems which includes computer disk drives, circular sawing rigs, and disk brake rotors. The plate/slider system can be unstable at subcritical and supercritical speed. This research develops a complete understanding of the stability of axisymmetric plate/slider systems. The third research problem addresses the class of systems which includes digital memory tapes, drive belts, band saws, tramway cables, textiles, paper rolls, and newsprint. Enhanced productivity is possible with higher transport speed, but higher speed also leads to transverse vibration which can lead to reduced accuracy and even system failure. This research provides for higher speeds by developing linear vibration control of distributed axially moving materials through the use of transverse force actuators and of tension control.
