In the past 30 years, scholars at home and abroad have used the finite element method to analyze the rotor dynamics of various rotor systems, and solved many practical problems.
Kahraman et al. Established a finite element model of gear rotor system supported by flexible bearing, in which the moment of inertia axial load and the stiffness and damping of gear mesh were considered. Later, Rao et al. Applied Nelson’s generalized Timoshenko beam theory to solve the model, and investigated the transverse vibration of gear system under torsional excitation.
Mohammad and peiman studied the stability of spindle tool washing fixture system of high speed iron bed by finite element method. They adopted Timoshenko beam theory and took gyroscopic effect into account. Their research results show that the existence of gyroscopic effect will reduce the stability region of the system. Later, gagnol and bouzgarrou took the rolling bearing support into account when they did this research.
Chen and Cheng established a dual rotor finite element model for the rotor system of induction motor, and developed a set of finite element program to solve the rotor dynamic characteristics of the system, including the natural frequency and vibration mode of the rotor system under rigid or flexible support. The calculation results are close to the test results. The program can be extended to the dynamic analysis of other rotating machinery It can be used in medical analysis.
According to the structural characteristics of the main shaft of a large turbo expander, based on the finite element method, Li Zuhui developed a special software for calculating its rotor dynamics with MATLAB software. The software considers the gyroscopic moment and moment of inertia as well as the stiffness and damping of bearing support, and is suitable for both rigid support and elastic support. After verification, the calculation results of the software are very close to the theoretical calculation results.
Huanglong used the finite element plug-in of SolidWorks to do dynamic analysis on the rotor group of a large domestic two-stage double suction compressor. It was found that the resonance phenomenon of the rotor could be avoided by modifying the shaft diameter and the weight of the impeller, which provided a theoretical basis for how to avoid the resonance phenomenon and design criteria for the rotor group.
Zhou Yawu used the finite element software ANSYS to carry out the modal analysis of the steam turbine rotor system, obtained the first 15 natural frequencies and vibration modes of the rotor, calculated the critical speed of the rotor, and put forward a method of over critical speed. Finally, he analyzed the transient response of the rotor under different accelerations, which provided a reasonable method for the optimization design of the steam turbine rotor.
Zhang Wei established the dynamic model of large hydro generator unit with ANSYS. Through the calculation of an example, the lateral dynamic characteristics of the shaft system of the hydro generator unit and the dynamic response under the action of unbalanced force were deeply studied. The stability of the unit was analyzed and the most unfavorable reaction position was determined, which provided a theoretical basis for the design and stability analysis of the hydro generator unit.
He Peng studied the dynamic characteristics of distributed tie rod rotor with finite element method, and obtained the variation law of rotor critical speed with tie rod tension force. According to the rough surface contact model, the equivalent bending stiffness expression of the contact between the disk and wheel of the pull rod rotor is established. Then, according to the characteristics of the pull rod rotor, the rotor dynamics finite element method is improved to make it suitable for the dynamic analysis of the pull rod rotor. The theoretical calculation results are consistent with the measured results.
With the development of science and technology, numerical method is the most widely used rotor dynamics analysis method, which includes transfer matrix method and finite element method. Horizontal centrifugal casting machine can be regarded as a rotor system consisting of a hollow shaft (mold) supported by two groups of rollers, but no one has carried out dynamic modeling analysis for this kind of rotating machinery at present.