Abstract
In view of the numerical instability and low accuracy of the traditional transfer matrix method in solving the high-order critical speed of the rotor system, a new idea of incorporating the finite element method into the transfer matrix is proposed. Based on the variational principle, the transfer symplectic matrix of gyro rotors suitable for all kinds of boundary conditions and supporting conditions under the Hamilton system is derived by introducing dual variables. To verify the proposed method in rotor critical speed, a numerical analysis is adopted. The simulation experiment results show that, in the calculation of high-order critical speed, especially when exceeding the sixth critical speed, the numerical accuracy of the transfer symplectic matrix method is obviously better than that of the reference method. The relative errors between the numerical solution and the exact solution are 0.0347% and 0.2228%, respectively, at the sixth critical speed. The numerical example indicates the feasibility and superiority of the method, which provides the basis for the optimal design of the rotor system.
Highlights
With the development of modern industrial technology, the application prospect and running speed of rotary machinery have been greatly improved
The numerical analysis methods of rotor dynamics are mainly divided into two categories: transfer matrix method and finite element method. e finite element method combines the variational principle of mathematics with the energy principle of mechanics [3, 4]
We firstly review the classical transfer matrix methods such as Prohl transfer matrix method and Riccati transfer matrix method and introduce the dual-rotor system and its transfer matrix method
Summary
With the development of modern industrial technology, the application prospect and running speed of rotary machinery have been greatly improved. In order to make the rotor work smoothly, avoid resonance and other vibration faults, and ensure high rotation accuracy, the study of the natural frequency and mode of the rotor dynamics system, the critical speed, and the unbalanced response has become an indispensable important content of rotor dynamics. The numerical analysis methods of rotor dynamics are mainly divided into two categories: transfer matrix method and finite element method. With the increase of frequency of trial computation, the accuracy decreases, especially in solving the critical speeds and unbalance response of the rotor structure system, which is of large scale and high speed. Consider the advantages and disadvantages of each method mentioned above, in order to make the rotor work smoothly, avoid resonance, and guarantee its high rotation accuracy; the idea of finite element is incorporated into the transfer matrix in this paper. We mainly introduce the conclusions and innovations
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