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Dynamic analysis of a multi-disk rod fastening rotor system with rub-impact based on multiple parameters

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Abstract

A dynamic modeling method for multi-disk rod fastening rotor system with rub-impact is proposed based on the structural characteristics of gas turbine and the rub-impact fault features. The comprehensive interaction of multiple parameters on the multi-disk rod fastening rotor system is disclosed in the dynamic model, where multiple parameters include oil-film support, stator stiffness, static clearance, eccentricity, radial clearance of sliding bearing and contact effect between disks. Dynamic responses of the multi-disk rod fastening rotor system with rub-impact are derived by numerical simulation. The influence trend of system parameters on the nonlinear behaviors of the rotor system is analyzed according to time-domain, frequency spectra, whirl orbit, Poincaré map and bifurcation diagram under different system parameters. The results show that system parameters have significant influences on the nonlinear behaviors and dynamic characteristics of multi-disk rod fastening rotor system. Diversified nonlinear phenomena are presented in the rod fastening rotor system under different system parameters, such as P1 motion, P2 motion, P3 motion and quasi-periodic motion. Each nonlinear behavior of the rotor system shows regular diversities with the change of system parameters. The modeling method and numerical results contribute to the identification of dynamic characteristics and the fault diagnosis of the rotor system in gas turbine.

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The data sets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This research work is funded by the National Natural Science Foundation of China (No. 52075170).

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Authors and Affiliations

  1. Department of Mechanical Engineering, North China Electric Power University, Baoding, 071003, Hebei Province, China

    Yue Zhang, Suixian Liu, Ling Xiang & Aijun Hu

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  1. Yue Zhang
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  2. Suixian Liu
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Correspondence to Ling Xiang.

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Appendix A

Appendix A

$$ {\mathbf{\ddot{q}}} = [\begin{array}{*{20}c} {\ddot{x}_{1} } & {\ddot{y}_{1} } & {\ddot{x}_{2} } & {\ddot{y}_{2} } & {\ddot{x}_{3} } & {\ddot{y}_{3} } & {\ddot{x}_{4} } & {\ddot{y}_{4} } & {\ddot{x}_{5} } & {\ddot{y}_{5} } & {\ddot{x}_{6} } & {\ddot{y}_{6} } \\ \end{array} ] $$
$$ {\dot{\mathbf{q}}} = [\begin{array}{*{20}c} {\dot{x}_{1} } & {\dot{y}_{1} } & {\dot{x}_{2} } & {\dot{y}_{2} } & {\dot{x}_{3} } & {\dot{y}_{3} } & {\dot{x}_{4} } & {\dot{y}_{4} } & {\dot{x}_{5} } & {\dot{y}_{5} } & {\dot{x}_{6} } & {\dot{y}_{6} } \\ \end{array} ] $$
$$ {\mathbf{q}} = [\begin{array}{*{20}c} {x_{1} } & {y_{1} } & {x_{2} } & {y_{2} } & {x_{3} } & {y_{3} } & {x_{4} } & {y_{4} } & {x_{5} } & {y_{5} } & {x_{6} } & {y_{6} } \\ \end{array} ] $$
$$ {\mathbf{\ddot{Q}}} = [\begin{array}{*{20}c} {\ddot{X}_{1} } & {\ddot{Y}_{1} } & {\ddot{X}_{2} } & {\ddot{Y}_{2} } & {\ddot{X}_{3} } & {\ddot{Y}_{3} } & {\ddot{X}_{4} } & {\ddot{Y}_{4} } & {\ddot{X}_{5} } & {\ddot{Y}_{5} } & {\ddot{X}_{6} } & {\ddot{Y}_{6} } \\ \end{array} ] $$
$$ {\dot{\mathbf{Q}}} = [\begin{array}{*{20}c} {\dot{X}_{1} } & {\dot{Y}_{1} } & {\dot{X}_{2} } & {\dot{Y}_{2} } & {\dot{X}_{3} } & {\dot{Y}_{3} } & {\dot{X}_{4} } & {\dot{Y}_{4} } & {\dot{X}_{5} } & {\dot{Y}_{5} } & {\dot{X}_{6} } & {\dot{Y}_{6} } \\ \end{array} ] $$
$$ {\mathbf{Q}} = [\begin{array}{*{20}c} {X_{1} } & {Y_{1} } & {X_{2} } & {Y_{2} } & {X_{3} } & {Y_{3} } & {X_{4} } & {Y_{4} } & {X_{5} } & {Y_{5} } & {X_{6} } & {Y_{6} } \\ \end{array} ] $$
$$ {\mathbf{M}} = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {m_{1} } & {} & {} \\ {} & {m_{1} } & {} \\ {} & {} & {m_{2} } \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {m_{2} } & {} & {} \\ {} & {m_{3} } & {} \\ {} & {} & {m_{3} } \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {m_{4} } & {} & {} \\ {} & {m_{4} } & {} \\ {} & {} & {m_{5} } \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {m_{5} } & {} & {} \\ {} & {m_{6} } & {} \\ {} & {} & {m_{6} } \\ \end{array} } \\ \end{array} } \right] $$
$$ {\mathbf{C}} = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {c_{1} } & {} & {} \\ {} & {c_{1} } & {} \\ {} & {} & {c_{2} + c_{3} } \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & { - c_{3} } & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & { - c_{3} } \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {c_{2} + c_{3} } & {} & { - c_{3} } \\ {} & {c_{2} + c_{3} } & {} \\ { - c_{3} } & {} & {c_{2} + c_{3} } \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {c_{2} + c_{3} } & {} & { - c_{3} } \\ {} & {c_{2} + c_{3} } & {} \\ { - c_{3} } & {} & {c_{2} + c_{3} } \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ { - c_{3} } & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & { - c_{3} } & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {c_{2} + c_{3} } & {} & {} \\ {} & {c_{1} } & {} \\ {} & {} & {c_{1} } \\ \end{array} } \\ \end{array} } \right] $$
$$ {\mathbf{K}} = k\left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} 1 & {} & { - 1} \\ {} & 1 & {} \\ { - 1} & {} & 2 \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ { - 1} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ { - 1} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & { - 1} & {} \\ { - 1} & {} & {} \\ {} & { - 1} & {} \\ \end{array} } & {\begin{array}{*{20}c} 2 & {} & {} \\ {} & 2 & {} \\ {} & {} & 2 \\ \end{array} } & {\begin{array}{*{20}c} {} & { - 1} & {} \\ { - 1} & {} & {} \\ {} & { - 1} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & { - 1} & {} \\ {} & {} & { - 1} \\ {} & { - 1} & {} \\ \end{array} } & {\begin{array}{*{20}c} 2 & {} & {} \\ {} & 2 & {} \\ {} & {} & 2 \\ \end{array} } & {\begin{array}{*{20}c} {} & { - 1} & {} \\ {} & {} & { - 1} \\ {} & { - 1} & {} \\ \end{array} } \\ {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & { - 1} \\ {} & {} & {} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} {} & {} & {} \\ {} & {} & { - 1} \\ {} & {} & {} \\ \end{array} } & {\begin{array}{*{20}c} 2 & {} & { - 1} \\ {} & 1 & {} \\ { - 1} & {} & 1 \\ \end{array} } \\ \end{array} } \right] $$

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Zhang, Y., Liu, S., Xiang, L. et al. Dynamic analysis of a multi-disk rod fastening rotor system with rub-impact based on multiple parameters. Nonlinear Dyn 107, 2133–2152 (2022). https://doi.org/10.1007/s11071-021-07122-7

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