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frequencies of vibration of rotating blades, US Patent 5,974,882, 1999. [5] Jousselin O. Russhard P. A method for establishing the uncertainty levels for aero-engine blade tip amplitudes extracted from blade tip timing data, 10th International Conference on Vibrations in Rotating Machinery - IMECHE, London, 2012. [6] Kaźmierczak K., Przysowa R. Standard Sine Fitting Algorithms Applied to Blade Tip Timing Data, Journal of Konbin, 2/2014. [7] Kucher O.G. Kharton V.V. Laine J.P. Thouverez F. Criteria of Discrete Phase Control of Blade Working Condition, Aerospace Engineering

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.

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Instrumentation and Measurement , 57 (11), 2647-2653. [4] Ramos, P.M., Cruz Serra, A. (2008). A new sine-fitting algorithm for accurate amplitude and phase measurements in two channel acquisition systems. Measurement , 41 (2), 135-143. [5] Vucijak, N.M., Saranovac, L.V. (2010). A simple algorithm for the estimation of phase difference between two sinusoidal voltages. IEEE Transactions on Instrumentation and Measurement , 59 (12), 3152-3158. [6] Shen, T.A., Tu, Y.Q., Zhang, H.T. (2014). A novel time varying signal processing method for Coriolis mass flowmeter. Review of

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

timing and tip clearance problems in turbomachinery, Lecture Series, von Karman Institute for Fluid Dynamics, VKI-LS-2007. [9] 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). [10] R. Tomassini, JF Brouckaert, G. Rossi Contactless magnetoresistive sensor for tip timing and tip clearance measurement systems STO-MP-AVT-229-14 (2015). [11] M. Witos, R. Szczepanik “Turbine Engine Health/Maintenance Status Monitoring with Use of Phase-Discrete Method of Blade Vibration

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discrete phase delay detection. Chinese Journal of Scientific Instrument , 34 (5), 994-1000. [16] Balázs, R, István, K, Tamás, D. (2016). Efficient implementation of least squares sine fitting algorithms. IEEE Transactions on Instrumentation and Measurement , 65 (12), 2717-2724. [17] Händel, P. (2010). Amplitude estimation using IEEESTD-1057 three-parameter sine wave fit: Statistical distribution, bias and variance. Measurement , 43 (6), 766-770. [18] Bilau, T.Z., Megyeri, T., Sárhegyi, A., Márkus, J., Kollár, I. (2004). Four-parameter fitting of sine wave testing

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