Rotor Dynamics

Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 198)

Abstract

The aim of this chapter is to elucidate a number of physical phenomena (some of them counter intuitive) which are typical of rotor dynamics: gyroscopic effects, dependency of the natural frequencies on the spin velocity, destabilizing effect of the damping at supercritical speeds, etc. Each of these issues is discussed with a model of minimum complexity. The chapter begins with the model of the Jeffcott rotor; the complex coordinates are introduced; the effect of stationary and rotating damping is analyzed and the stability condition is derived. Next, the gyroscopic effects are analyzed by expressing the kinetic energy of a wobbling rigid disk; the forward whirl and the backward whirl are easily introduced by using the complex coordinates. The gyroscopic effects are responsible for a dependency of the natural frequencies on the spin velocity, which is represented by the Campbell diagram. The critical speed is the spin velocity when the imbalance excitation is exactly tuned on the natural frequency of the forward whirl. This chapter also analyzes a rigid rotor on elastic supports, the effect of anisotropic supports and anisotropic shaft. The chapter concludes with the analysis of a vibrating angular rate sensor and a set of problems.

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Active Structures LaboratoryUniversité Libre de BruxellesBrusselsBelgium

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