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5. Literatura [1] B. Hayes (chair) “ANSI/ISA-107.1-2013 Industry Standard File Format for Revolution-Based, Tip Timing Data”, www.isa.org [2] R. Przysowa Analysis of synchronous blade vibration with the use of linear sine fitting, Journal of KONBiN, 2(30), pp. 5-20, De Gruyter Open (2014). [3] R. Przysowa “Inductive Sensors for Blade Tip-Timing in Gas Turbines”, Test Cell and Controls Instrumentation and EHM Technologies for Military Air, Land and Sea Turbine Engines, MP-AVT-229-10, Rzeszów (2015) [4] R. Przysowa, P. Gazda “Direct sampling and phase detection of

References [1] Grant K. Experimental Testing Of Some Tip-Timing Techniques, 1 st Evi-GTI Conference, Barcelona, 2004. [2] Heath S. Imregun M. An improved single-parameter tip-timing method for turbo-machinery blade vibration measurements using optical laser probes, International Journal of Mechanical Sciences, Vol. 38, №10, 1996, 1047–1058. [3] Heath S. A new technique for identifying synchronous resonances using tip-timing. ASME Journal of Engineering for Gas Turbines and Power. Vol. 122, No. 2. April 2000, 219-225. [4] Heath S. Identification of resonant

improved single-parameter tip-timing method for turbomachinery blade vibration measurements using optical laser probes, International Journal of Mechanical Sciences, Vol. 38, No. 10, 1996. 6. Heinemann T, Becker S.: Axial fan blade vibration assessment under inlet cross-flow conditions using laser scanning vibrometry. Appl Sci. 7(8), 2017, DOI: 10.3390/app7080862. 7. IEEE Standard for Digitizing Waveform Recorders, IEEE Std 1057TM-2007. IEEE 2007. 8. Kaźmierczak K., Przysowa R.: Standard sine fitting algorithms applied to blade tip timing data. Journal of Konbin, Vol. 30

. AITECH (Artificial Intelligence Laboratory). Katowice 2006. 8. Rokicki E., Turbine blade condition assesment with the lateral-magnetic-field sensors. Air Force Institute of Technology, Warsaw 2011. 9. Rokicki E., et al., Induction sensor to measure vibrations of a turbo-machine rotor blade US Patent 8,240,212. 10. Rokicki E., et al., Measuring vibrations of a turbo-machine rotor blade with the help of an induction sensor in high temperature US Patent 8,125,215. 11. Szczepanik R., et al., Application of Blade-Tip Sensors to Blade-Vibration Monitoring in Gas Turbines, in

vibration measurement. Proceedings of lecture series on Tip Timing an Tip Clearnce Problems in Turbomachines Von Karman Instytute Belgium 2007 [17] Szabatin J.: Podstawy teorii sygnałów [The basics of the theory of signals] , WKŁ Warszawa 2000, [18] Szczepanik R., Przysowa R.: Wykonanie badań i pomiarów drgań łopatek metodą bezstykową w odwirowni ALSTOM Power w Elblągu. [Studies and measurements of blade vibrations with a non-contact method in the ALSTOM rotor balancing facility in Elbląg] Sprawozdanie ITWL nr 36/3/2004 Warszawa 2004 [19] Washburn R. S.: A State of The

14. References [1] http://www.piwg.org/sensor/sensor_btdeflection.html [2] A European Lab Gap Matrix. European Virtual Institute for Gas Turbine Instrumentation [3] J. S. Wilson. “Sensor Technology Handbook”, Newnes, ISBN-13: 978-0750677295 (2004). [4] E. Rokicki, R. Przysowa, J. Spychała, R. Szczepanik, M. Perz. “Electronic system of current inductive sensor, especially for measurement of flow blades vibrations of rotor machines”, Polish patent PAT.209634 (2007). [5] R. Szczepanik, R. Przysowa, J. Spychała, E. Rokicki, K Kaźmierczak., P. Majewski “Application

Abstract

Blade Tip Timing (BTT) is a non-intrusive method to measure blade vibration in turbomachinery. Time of Arrival (TOA) is recorded when a blade is passing a stationary sensor. The measurement data, in form of undersampled (aliased) tip-deflection signal, are difficult to analyze with standard signal processing methods like digital filters or Fourier Transform. Several indirect methods are applied to process TOA sequences, such as reconstruction of aliased spectrum and Least-Squares Fitting to harmonic oscillator model. We used standard sine fitting algorithms provided by IEEE-STD-1057 to estimate blade vibration parameters. Blade-tip displacement was simulated in time domain using SDOF model, sampled by stationary sensors and then processed by the sinefit.m toolkit. We evaluated several configurations of different sensor placement, noise level and number of data. Results of the linear sine fitting, performed with the frequency known a priori, were compared with the non-linear ones. Some of non-linear iterations were not convergent. The algorithms and testing results are aimed to be used in analysis of asynchronous blade vibration.

. Mechanical Systems and Signal Processing , 85, 912-926. [7] Lin, J., Hu, Z., Chen, Z.-S. (2016). Sparse reconstruction of blade tip-timing signals for multimode blade vibration monitoring. Mechanical Systems and Signal Processing , 81, 250-258. [8] Guo, H., Duan, F., Zhang, J. (2016). Blade resonance parameter identification based on tip-timing method without the once-per revolution sensor. Mechanical Systems and Signal Processing , 66-67, 625-639. [9] dos Santos, F.L.M., Peeters, B., van der Auweraer, H. (2016). Vibration-based damage detection for a composite

Experimental and Numerical Crack Initiation Analysis of the Compressor Blades Working in Resonance Conditions

This paper presents the results of a complex experimental and numerical crack initiation analysis of the helicopter turbo-engine compressor blades subjected to vibrations. A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects as well as those with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. The obtained results were next used as an input data into crack initiation (ε-N) analyses performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis, the different methods such as: Neuber elastic-plastic strain correction, linear damage summation and Palmgreen-Miner rule were utilized. As a result of ε-N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material were calculated using the Baumel-Seeger and Muralidharan methods. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of the work, the finite element results were compared with the results of experimental vibration HCF tests performed for the compressor blades.

Abstract

Turbocharger turbine blades suffer from periodic vibration and flow induced excitation. The blade vibration signal is a typical non-stationary and sometimes nonlinear signal that is often encountered in turbomachinery research and development. An example of such signal is the pulsating pressure and strain signals measured during engine ramp to find the maximum resonance strain or during engine transient mode in applications. As the pulsation signals can come from different disturbance sources, detecting the weak useful signals under a noise background can be difficult. For this type of signals, a novel method based on optimal parameters of Ensemble Empirical Mode Decomposition (EEMD) and Teager Energy Operator (TEO) is proposed. First, an optimization method was designed for adaptive determining appropriate EEMD parameters for the measured vibration signal, so that the significant feature components can be extracted from the pulsating signals. Then Correlation Kurtosis (CK) is employed to select the sensitive Intrinsic Mode Functions (IMFs). In the end, TEO algorithm is applied to the selected sensitive IMF to identify the characteristic frequencies. A case of measured sound signal and strain signal from a turbocharger turbine blade was studied to demonstrate the capabilities of the proposed method.