Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases

Hector Laos

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotordynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this chapter is to show examples of how the linear vs. nonlinear formulations differ. This chapter also shows how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.

Original languageEnglish
Title of host publicationSpecial Topics in Structural Dynamics and Experimental Techniques, Volume 5 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021
EditorsDavid S. Epp
PublisherSpringer
Pages39-54
Number of pages16
ISBN (Print)9783030759131
DOIs
StatePublished - 2022
Event39th IMAC, A Conference and Exposition on Structural Dynamics, 2021 - Virtual, Online
Duration: Feb 8 2021Feb 11 2021

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Conference

Conference39th IMAC, A Conference and Exposition on Structural Dynamics, 2021
CityVirtual, Online
Period02/8/2102/11/21

Funding

This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http:// energy.gov/downloads/doe-public-access-plan).

FundersFunder number
U.S. Department of Energy

    Keywords

    • Equations of motion
    • Generalized forces
    • Nonlinear
    • Rigid body
    • Rotordynamics

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