Reduced-Order Method For Vibration Characteristic And Response Analysis Of Aero-Engine Components

Aero-engine is a kind of complicated mechanical equipment which works under complex load conditions.With the improvement of the performance,the requirement for the prediction accuracy of aero engine structure vibration characteristics is gradually improved.On the other hand,the increasing structural complexity of various engine components,the calculation scale of vibration characteristic analysis is greatly increased.Therefore,it is necessary to study a reasonable and effective model reduction method for the structural components of the engine,so as to ensure the calculation accuracy and improve the efficiency of dynamic analysis.For this purpose,the research of this paper is carried out from the following two aspectsFor the aero-engine compressor bladed disk structure,which has the characteristics of linear vibration and geometrical uncertainty between different blades,the free interface modal synthesis method based on the structural decomposition is used to reduce the order of the whole structure.Due to different grid sizes between blades and the disk,the discretization error of the surface and the geometric mistuned interface,the mesh of different substructure finite element models may not match with others.To solve this problem,the triangle gap element(two-dimensional)and the pyramid gap element(the three-dimensional)are introduced and the conversion relationship of the displacement and the force between different substructures is obtained.Then,with no extra energy imported,the equilibrium equation of traditional modal synthesis method is rewritten to make it suitable for the non-matching mesh.Because only the physical information of the nodes on the interface is used and the original finite element model of the substructure need not be modified,this method can be directly applied to the existing modal synthesis method.After that,the vibration characteristics of two two-dimensional models and a simplified three-dimensional single sector blade structure were analyzed by using the improved modal synthesis method,and the results were compared with those obtained by the finite element method.The results show that for the 2d and 3d structures with nonmatching mesh,the original vibration characteristics of the structure can be reflected by the reduction model obtained by the modified modal synthesis method,regardless of whether there is a gap at the interface of the finite element model of the substructure.In addition,the computational efficiency is improved due to the reduction of model size.The aero-engine case is mainly made up by thin-walled plate and shell structure and it is prone to have geometrically nonlinear deformation,so the geometrically nonlinear reduction model is used.According to the large deformation theory of plates and shells and the reduce-order method of weakly geometrically nonlinear system,additional quadratic and cubic nonlinear stiffness matrices,which describes the influence of geometrically nonlinear deformation,are added to the original linear dynamic vibration equation.For the problems such as the selection of reduction basis and the solution of nonlinear term coefficients,the applied loads procedure method is used.By applying the static load on the structure and solving the corresponding nonlinear deformation,the coupling degree between different modes of the structure is judged,which provides the basis for reduce-order basis and nonlinear coefficients.After that,the nonlinear model reduction method was used to obtain the reduction models of a clamped-clamped beam,flat plate and thin-walled case.The nonlinear response of the structure subjected to random excitation in a specific frequency range is analyzed by the above reduction model,and the results are compared with those of the complete finite element model.The results show that the nonlinear reduction model can be used to analyze the dynamic characteristics of plate,beam and shell structures.For the symmetric flat plate and straight beam models,the influence of quadratic nonlinear terms can be ignored and only cubic terms can be considered when constructing the reduction model.In addition,there is a quantitative relationship between the coefficients of the nonlinear terms in the reduction model,so this relationship can be used to reduce the number of unknown coefficients to be solved and improve the analysis efficiency.