Quantitative methodology for stability analysis of nonlinear rotor systems |
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| Authors: | Zheng Hui-ping Xue Yu-sheng Chen Yu-shu |
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| Affiliation: | School of Mechanical and Electronic Engineering, Hebei University of Science and Technology, Shijiazhuang 050054, P.R.China；;Nanjing Automation Research Institute, Nanjing 210003, P.R.China；;School of Mechanical Engineering, Tianjin University, Tianjin 300072, P.R.China |
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| Abstract: | Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modern concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quantitative stability analysis method for rotor systems is presented. At first, ann-dimensional nonlinear non-autonomous rotor system is decoupled inton subsystems after numerical integration. Each of them has only one-degree-of-freedom and contains time-varying parameters to represent all other state variables. In this way,n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare are determined. Contributed by CHEN Yu-shu Project supported by the National Natural Science Foundation of China (No. 19990510) and the National Major Basic Research Special Foundation of China (Nos. G1998020316 and G1998010301) |
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| Keywords: | nonlinear rotor system bifurcation stability margin extended phase plane dynamic central point kinetic energy difference sequence |
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