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Dynamic modelling strategy of a shaft-disk-blade coupling system integrating beam and shell theories

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Abstract

Despite the remarkable success achieved in modelling the rotor-disk-blade coupling system, the existing research does not adequately consider both the structural flexibility and the rotating effects in the shaft, disk, and blade components. To bridge this gap, a dynamic modelling strategy has been developed for the shaft-disk-blade coupling system using an in-house code that integrates the Timoshenko beam and Mindlin-Reissner shell elements. In addition, two critical issues concerning the couplings of the shaft-disk and disk-blade are successfully addressed by using the penalty method in conjunction with the compatibility equation of deformation. Subsequently, the improved modelling strategies for the shaft-disk coupling system, with and without blade components, are verified by comparing their static/dynamic frequencies and modal shapes with those obtained from experiments and solid models in ANSYS. The results indicate that the beam-shell hybrid model exhibits good accuracy and high efficiency in simulating the dynamic characteristics of the shaft-disk coupling system with and without blades. The modal characteristics of the entire rotor system have a series of flexible vibration modes, including bending/torsion/axial mode for the shaft, pitch diameter/umbrella-type mode for the disk, and bending mode for the blade.

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The datasets used and/or analysed in the current study can be obtained from the corresponding author upon reasonable request.

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Acknowledgements

This project is financially supported by the National Natural Science Foundation (Grant nos. 12202368, 12172307, 12172311), the Natural Science Foundation of Sichuan Province (Grant Nos. 22NSFSC0576, 22NSFSC0666, 2023NSFSC0068), the Opening Project of Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province (No. SZZZKT-202206), the Key Laboratory of Vibration and Control of Aero-Propulsion System, Ministry of Education, Northeastern University of China (No. VCAME202205, VCAME202103), and the Fundamental Research Funds for the Central Universities (Grant nos. 2682021CX081, 2682021ZTPY036).

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Authors and Affiliations

  1. School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Jin Zeng, Yang Yang, Yiren Yang & Chenguang Fan

  2. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, Liaoning, People’s Republic of China

    Hui Ma

  3. Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Jin Zeng

  4. Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang, 110819, Liaoning, People’s Republic of China

    Jin Zeng & Yang Yang

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  1. Jin Zeng
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Appendix A: Shaft-related matrices

Appendix A: Shaft-related matrices

The mass matrix \({\mathbf{M}}_{{{\text{beam}}}}^{{\text{e}}}\) is defined as follows:

(24)

The structural stiffness matrix \({\mathbf{K}}_{{\text{beam,0}}}^{{\text{e}}}\) is defined as follows:

(25)

The expressions of the shape functions in Eqs. (24) and (25) are shown as follows:

$$\left\{ \begin{gathered} N_{u,1} = 1 - \xi ,N_{u,2} = \xi ,N_{\theta x,1} = 1 - \xi ,N_{\theta x,2} = \xi \hfill \\ N_{v,1} = \overline{\Phi }_{z} \left( {1 - 3\xi^{2} + 2\xi^{3} + \left( {1 - \xi } \right)\Phi_{z} } \right) \hfill \\ N_{v,2} = l_{k} \overline{\Phi }_{z} \left( {\xi - 2\xi^{2} + \xi^{3} + 0.5\left( {\xi - \xi^{2} } \right)\Phi_{z} } \right) \hfill \\ N_{v,3} = \overline{\Phi }_{z} \left( {3\xi^{2} - 2\xi^{3}_{z} + \xi \Phi } \right) \hfill \\ N_{v,4} = l_{k} \overline{\Phi }_{z} \left( { - \xi^{2} + \xi^{3} + 0.5\left( { - \xi + \xi^{2} } \right)\Phi_{z} } \right) \hfill \\ N_{w,1} = \overline{\Phi }_{y} \left( {1 - 3\xi^{2} + 2\xi^{3} + \left( {1 - \xi } \right)\Phi_{y} } \right) \hfill \\ N_{w,2} = l_{k} \overline{\Phi }_{y} \left( { - \xi + 2\xi^{2} - \xi^{3} + 0.5\left( { - \xi + \xi^{2} } \right)\Phi_{y} } \right) \hfill \\ N_{w,3} = \overline{\Phi }_{y} \left( {3\xi^{2} - 2\xi^{3} + \xi \Phi_{y} } \right) \hfill \\ N_{w,4} = l_{k} \overline{\Phi }_{y} \left( {\xi^{2} - \xi^{3} + 0.5\left( {\xi - \xi^{2} } \right)\Phi_{y} } \right) \hfill \\ \end{gathered} \right.$$
(26)

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Zeng, J., Yang, Y., Ma, H. et al. Dynamic modelling strategy of a shaft-disk-blade coupling system integrating beam and shell theories. Int J Mech Mater Des 20, 107–127 (2024). https://doi.org/10.1007/s10999-023-09664-7

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