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Stability Analysis of a Rotating Stepped Shaft via Lyapunov Criterion

[+] Author Affiliations
Jafar Abbaszadeh Chekan, Kaveh Merat, Hassan Zohoor

Sharif University of Technology, Tehran, Iran

Paper No. IMECE2012-89565, pp. 701-706; 6 pages
doi:10.1115/IMECE2012-89565
From:
  • ASME 2012 International Mechanical Engineering Congress and Exposition
  • Volume 4: Dynamics, Control and Uncertainty, Parts A and B
  • Houston, Texas, USA, November 9–15, 2012
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4520-2
  • Copyright © 2012 by ASME

abstract

In this investigation, the stability analysis of a rotating elastic stepped shaft is studied and the sufficient condition for system stability in the sense of Lyapunov is derived. The model consists of an elastic stepped shaft which is clamped rigidly to a rotary device. From the model’s point of view, the entire length of shaft is partitioned into uniform segments with different characteristics. The Lyapunov direct method is applied in this survey where the Hamilton function has been chosen as the candidate Lyapunov function. Since the dynamical mode shapes of the shaft are required for the stability analysis, the shaft has been modeled by the Euler–Bernoulli beam theory and the corresponding mode shapes have been derived based on the boundary conditions and the continuity conditions between adjacent segments. In this study, the shaft is considered to have two segments with different properties. It is notable that this model can be an appropriate model for the spindle in tool machines. Our aim in this research study is determining the area of stability for the system considering the shaft characteristics. The effects of bending stiffness and mass distribution parameters of each segment are investigated on the stability margins of the system.

Copyright © 2012 by ASME
Topics: Stability

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