Sparse Reconstruction Of Multi-frequency Blade Vibration Spectrum By Blade Tip Timing Measurement

The major cause of high cycle fatigue failures of the aero-engine blade is the vibration.The accurate monitoring of blade vibration under operating conditions is essential in turbo-machinery testing.Blade tip timing(BTT)is a promising non-contact technique for the measurement of blade vibrations.However,the BTT sampling data are inherently under-sampled because the number of BTT probes is often strictly limited by engine constraint.In addition,some studies have been proposed to investigate blades responses from tip-timing data where each blade responds at a single frequency.Thus,how to recover multi-frequency spectra of blade vibrations though processing those under-sampled signals is a bottleneck problem.Recovery of multi-mode vibration frequency spectra by the theory of sparse representation is introduced in this paper.By analyzing the dynamic characteristics of blade blades,the spectral characteristics of blade vibration response signals are summarized at first.Secondly,sparse representation model is built by exploiting that the blade vibration signals are sparse in frequency spectra.Then the improved frequency spectra recovery method is adapted to the case of biased BTT data.Simulation and experimental results are presented to evaluate the feasibility of proposed methods.The main contents are organized as follows:1,The non-linear dynamic model of the blade is established in the form of Duffing equation,and the frequency characteristics of tip vibration responses under various excitation conditions are analyzed.The results show that considering the nonlinear dynamic characteristics of blades,the frequency spectra of the blades present a combination of multiple frequency components.To reconstruct the blade frequency spectrum accurately,the proposed reconstructing algorithm must have the ability of blind reconstruction of multi-frequency components in the entire frequency range.2,It is a bottle-neck problem to extract all the frequency components of the blade vibration from the under-sampled BTT signals.Thus,a sparse characterization model of the blade tip timing signal is established and the reconstruction of the tip vibration signal spectrum under the under-sampling condition is carried out by using the basic pursuit algorithm.The results show that if the sparse model satisfied the reconstruction conditions,the proposed sparse reconstruction model could achieve the multi-frequency signal frequency spectrum within few probes.Multiple harmonic frequencies can be extracted from under-sampled BTT data collected by few probes.3,In order to solve the problem that the reconstructed spectrum is not accurate when BTT data are biased,a quantitative relationship between the measurement uncertainty and the displacement of the blade tip vibration is established.The simulation results prove that the improved BTT signal reconstruction method proposed in this paper improves the reconstruction accuracy of the tip vibration spectrum.4,The vibration table was used to complete the single-blade vibration test,and the blade tip vibration test was realized by using a small rotary blade disc.The experimental data verified the non-linear spectral response characteristics of blade.The BTT measurement experimental results show that the spectral reconstruction method is feasible and the uncertainty reduction algorithm is effective.