Fast Analysis Methods For Mistuned Bladed Disks Using The Mode Family-based Reduced Order Models And Surrogate Methods

Bladed disk is one of the key components of aero-engine,and its quality directly affects the performance and reliability of the engine.There are inevitable mistuning between sectors due to machining errors,uneven wear in service,dispersion of materials and detuning introduced for flutter suppression.Mistuning could lead to severe vibration localization which is one of the main causes of blade high cycle fatigue failure.Therefore,it is crucial to investigate dynamic characteristics of mistuned bladed disks.In this paper,frequency mistuning is simulated by changing blade stiffness in lumped parameter model and Young's modulus in finite element model.Modal and response characteristics of bladed disk are investigated using mode family-based reduced order method and surrogate technology,and the industrial titanium alloy compressor bladed disk and lumped parameter model are used as examples to show the effectiveness of the proposed methods.Firstly,frequency mistuning is introduced to construct stiffness randomly mistuned 2-dof lumped parameter model and material randomly mistuned finite element APDL parameter design model.Secondly,mistuning mechanism is discussed,and vibration mode localization and amplification factor are detailed studied.Then,modal and response characteristics of tuned and mistuned bladed disk are investigated based on concepts of nodal diameter spectrum and mode family.To raise analysis efficiency of dynamic characteristics,a reduced order method based on tuned modal information is proposed to get vibration mode and response of mistuned bladed disk.The number and integrity of mode family are studied then.Compared with full model,reduced order model improves the analysis efficiency by more than 80%.Through this reduced order model,the modal localization factor and amplification factor of 100 samples under different mistuning intensities were studied.The results show that the vibration modes in blade mode family and frequency veering region are more sensitive to blade mistuning,and the amplification factor has a "threshold" effect under different mistuned intensities.Meanwhile,in order to suppress random mistuning,two types of intentional mistuning are studied,and the effect of vibration suppression is explored then.Because mistuning is uncertain,in order to study the statistical properties of mistuned bladed disk,a large number of samples should be extracted.When the sample size is too large,reduced order model is still time-consuming.Therefore,surrogate models are proposed to replace the costly finite element and reduction analysis.The lumped parameter model with single-sector and multi-sector mistuning is presented to calculate amplification factor.Results show that amplification factor is strongly nonlinear,and the prediction accuracy of EI-Kriging model is higher than quadratic response surface model,thus EI-Kriging model is more suitable to solve strong nonlinear problems.Finally,the maximum Expected Improvement criterion is improved to promote computational efficiency of EI-Kriging model.A multi-point sampling EI criterion is proposed to select more than one new sample which is space-independent in each iteration.This sampling strategy improves the computing efficiency by 28%.