Reduced-order Modelling Methodology And Dynamic Characteristics Analysis Of Mistuned Bladed Disk System

Because of the existence of mistuning, the cyclic symmetry of bladed disk system is destroyed. To predict the dynamic properties of an actual bladed disk in gas-turbine engine accurately, high fidelity large-scale finite element models of a full bladed disk must be used. However, mistuning is also an uncertainty problem. Monte-Carlo simulation is always needed to predict the statistics properties of the mistuned forced response, making the computation resource consumption reach an intolerable degree. In this paper, a new reduced-order modelling and dynamic response prediction methodology for mistuned bladed disks is developed. Taking full advantage of cyclic symmetry of tuned bladed disk, a sector model is used to provide primary information about dynamic properties in the local coordinate systems. Just doing modal analysis on a small amount of nodes utilizing the concept of “active nodes”, the dimensions of operation matrices are reduced enormously but the model properties of the mistuned structure are preserved very high accuracy. In the process of dynamic response prediction, the response properties on the natural frequencies, can be used for choice of the narrow frequency ranges, the dangerous blades and nodes which need to calculate response. The main advantages are its efficiency and accuracy, which allow the high precision maximum forced responses. The results show that, compared with traditional FE method, the inverse matrices in this method are reduced from 1.5 million to 384, but the errors of first 50 natural frequencies are limited in 0.005%. In addition, the computational complexity of maximum response calculation is lowered more than 99%, which just produces-0.35% deviations.Moreover, a compressor bladed disk was considered in a set of engine order excitation case studies to demonstrate the random mistuning effects on forced responses using statistical analysis with effective reduced-order models. It is found that the normalized forced response rapidly increases with increasing mistuning up to a certain value, but a further increase in mistuning decreases the response and towards stability. Considering mistuning as design parameters, this paper also discussed the response properties of bladed disks with common intentional mistuning patterns, which shows some intentional mistuning design bladed disks have lower forced response levels and good robustness to additional random mistuning.It is well known that the excitation forced in gas-turbine engines can have a very high and dense frequency spectrum. In order to enhance the practicability of the research, a problem of analysis for bladed disks excited in high-mode frequency ranges is considered. The existence of high amplification levels for the high modes mistuning vibrations has been discovered including cased when such amplitudes are higher than the Whitehead limit. In addition, a new method to fast calculate the stresses and strains for a mistuned structure is presented, which allows take advantages of cyclic symmetry properties.In the end, some formula to get the first and second order sensitivities of maximum displacement with respect to blade frequency mistuning are proposed.