Research On Finite Element Modeling And Dynamic Behaviors Of Complex Multi-rotor Coupled Systems

The transfer matrix method and the finite element method are commonly applied in engineering analysis of rotor dynamics. The transfer matrix method is deeply investigated and extensively used in China, though the finite element method for rotor dynamics is insufficiently studied and immaturely developed in the domestic research. However, a finite element model of rotor-bearing systems is more powerful and advantageous, which can include the effects of gyroscopic moments, rotary inertia, transverse shear deformation and gravity, and the model features concise formula and straight forward physical meaning. This computational model can easily be coupled with the ambient structures and forces, which makes it particularly suitable for dealing with complex multi-rotor coupled systems. On the other hand, for simple rotor-bearing systems, the numerical computing is now developed maturely within the framework of linear theory, so both domestic and international scholars begin to focus their study on the influence of various nonlinear factors, which always besed on the Jeffcott rotor model. Meanwhile, for complex multi-rotor coupled systems, it is necessarily to achieve more development, modification and optimization for their computational modelings.Gears are widely used in the mechanical field. The multi-parallel axis gear rotor system is one kind of important and special rotor system, but the existence of gear pair makes the dynamics research complicated. The dynamic characteristics of parallel axis rotor mutual coupling system are different from those of non-coupling single axis rotor system, and therefore the separate design and calculation of each parallel axis rotor cannot meet the requirement of high-precision calculation. Dual rotor system has been applied in aviation engines. The counter-rotating of the inner and external rotor can offset some gyroscopic torque, and improve aircraft maneuverability. For these reasons, this paper took the finite element method as the theoretical theory, focused on multi-parallel shaft gear rotor system and dual rotor system modeling method, and analyzed the dynamic characteristics of these two systems by numerical calculation. Specific works were carried out as follows:1) For the common single rotor bearing system, the finite element method combined with Rayleigh beam theory and Timoshenko beam theory was used to deduce the differential equations of motion in detail; The system eigenvalue problem and the solving method for unbalance response and transient response were theoretically analyzed based on the above; A Program written on MATLAB realized the calculation of rotor system critical speed, unbalance response and transient. 2) In the rotor dynamics analysis of a radial turbine in design stage, the commercial software ANSYS and the program developed in this paper were respectively used to carry on calculation of static deflection, critical speed, mode of vibration and unbalance response. The consistent results obtained from two ways verified that the program was correct and effective. At the same time, the analysis results were helpful to determine the radial turbine rotor structure and the selection of bearing parameters.3) This study originated from the Key Industrial Projects founded by Zhejiang Province Science and Technology Department:"Investigation and Application of the Key Technologies for Large Marine gearboxes"(2009C11062). The research analyzed the inherent characteristics of a three parallel axis gearbox meshing rotor transmission system for marine ships, inspected each transmission level’s meshing frequency and the system’s frequency, and distinguished between the flexural and torsional vibrations through the inspection of each level inherent frequencies varied by the gear meshing stiffness. In the research of multi parallel axis gear meshing rotor system modeling methods, this paper derived the differential equations of motion for gear meshing unit in the line pressure coordinate firstly, which could obtain the differential equations of motion in the global coordinate by coordinate transformation; Then, this paper found a way to integrate the stiffness matrix of gear meshing unit into the whole rotor stiffness, and obtained the meshing rotor motion equation finally.4) In the research on modeling method for rotor system, this paper derived the transfer of medium bearing force and the coupling process of internal and external rotor, provided the dynamic model of dual rotor system, and developed the transfer matrix method of dual rotor structure. In the numerical case, the critical speed of the dual rotor structure with normal and reverse rotation calculated by the finite element method dynamics model and the transfer matrix method model was agreed. This paper inspected the effects of the intermediate bearing’s rigidity and speed ratio to the system’s vibration characteristics; Combined with the direct integral method, the numerical simulations were carried on the system’s start and stop transient response. The model established in this paper provided the relatively complete basis for the prediction of dual rotor system’s dynamic behavior, and the results of this research have important theoretical significance and engineering application value for improving the dynamic performance of aero engine’s rotor system and guiding the design of dual rotor system.