Introduction

Abstract

The term “gyroscope” is defined here as a high-speed rotor with moments of inertia that can not be neglected so that the rotor is subject to gyroscopic forces. High-speed rotors are of increasing technical interest. They are used in turbines, grinding-machines, centrifuges and gyroscopic devices of various constructions. The design of these rotors requires knowledge and control of their dynamic behavior and motion. The critical speeds characterize an essential part of the dynamic behavior. They denote the speeds for which the flexural vibrations reach dangerous values and lead to a critical state. Many of the questions arising thereby have already been treated in numerous publications. The investigations of SMITH [1] and the works of BIEZENO-GRAMMEL [2] shall be mentioned in particular. The increasing technical requirements and the now available theoretical and experimental means demand and permit more extensive investigations, particularly with regard to the optimum of the rotor design that is aimed at in the final analysis.