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Study of Synchronous Full Annular Rub of Jeffcott Rotor and Its Dynamic Stability

Wen Zhang

Open publisher page 4 citations

Abstract

The synchronous full annular rub motion of a Jeffcott rotor and its dynamic stability behaviour are studied analytically in detail.The linear spring model is adopted to model the local impact-deformation phenomenon.The formula for evaluating the equivalent stiffness of the spring is obtained.The eccentricity of the disk is considered in the Jeffcott rotor.The exact full annular rub solutions are obtained mathematically.It is found that the full annular rub motions exist in a wide spinning region of the rotor.The dynamic stability of the full annular rub motions is also studied seriously by linear perturbation method and by the Routh-Hurwitz criterion.An accurate formula for the stability criterion is deduced.An approximate formula of the stability criterion is also obtained.The approximate formula is simple and explicit for engineers.

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What this paper is about

The synchronous full annular rub motion of a Jeffcott rotor and its dynamic stability behaviour are studied analytically in detail.The linear spring model is adopted to model the local impact-deformation phenomenon.The formula for evaluating the equivalent stiffness of the spring is obtained.The eccentricity of the disk is considered in the Jeffcott rotor.The exact full annular rub solutions are obtained mathematically.It is found that the full annular rub motions exist in a wide spinning region of the rotor.The dynamic stability of the full annular rub motions is also studied seriously by linear perturbation method and by the Routh-Hurwitz criterion.An accurate formula for the stability criterion is deduced.An approximate formula of the stability criterion is also obtained.The approximate formula is simple and explicit for engineers.

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Available abstract

The synchronous full annular rub motion of a Jeffcott rotor and its dynamic stability behaviour are studied analytically in detail.The linear spring model is adopted to model the local impact-deformation phenomenon.The formula for evaluating the equivalent stiffness of the spring is obtained.The eccentricity of the disk is considered in the Jeffcott rotor.The exact full annular rub solutions are obtained mathematically.It is found that the full annular rub motions exist in a wide spinning region of the rotor.The dynamic stability of the full annular rub motions is also studied seriously by linear perturbation method and by the Routh-Hurwitz criterion.An accurate formula for the stability criterion is deduced.An approximate formula of the stability criterion is also obtained.The approximate formula is simple and explicit for engineers.

Key concepts: Eccentricity (behavior), Rotor (electric), Spinning, Stability (learning theory), Spring (device), Stiffness, Classical mechanics, Equations of motion

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