
TL;DR
This paper analyzes the spectral stability of gyroscopic systems with dissipative and non-conservative forces, revealing how damping can induce instabilities leading to self-excited vibrations in rotating structures like disc brakes.
Contribution
It provides an analytical description of the instability mechanism caused by damping and non-conservative forces in gyroscopic systems, explaining phenomena like squealing disc brakes.
Findings
Dissipative forces cause eigenvalue splitting and instability bubbles.
Full damping can hide potential instabilities.
The theory explains self-excited vibrations in frictional rotating systems.
Abstract
We consider a gyroscopic system under the action of small dissipative and non-conservative positional forces, which has its origin in the models of rotating bodies of revolution being in frictional contact. The spectrum of the unperturbed gyroscopic system forms a "spectral mesh" in the plane "frequency -gyroscopic parameter" with double semi-simple purely imaginary eigenvalues at zero value of the gyroscopic parameter. It is shown that dissipative forces lead to the splitting of the semi-simple eigenvalue with the creation of the so-called "bubble of instability" - a ring in the three-dimensional space of the gyroscopic parameter and real and imaginary parts of eigenvalues, which corresponds to complex eigenvalues. In case of full dissipation with a positive-definite damping matrix the eigenvalues of the ring have negative real parts making the bubble a latent source of instability…
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Taxonomy
TopicsBrake Systems and Friction Analysis · Railway Engineering and Dynamics · Vibration and Dynamic Analysis
