A new bladed assembly simulator and an improved two-parameter plot method for blade tip-timing numerical simulations

Abstract

The blade tip-timing measurement technique is presently the most promising technique for monitoring the blades of axial turbines and aircraft engines in operating conditions. Due to the high cost of experimental simulations of blade tip-timing–based condition monitoring methods, a numerical simulator for the vibrational behavior of bladed assemblies can be helpful for researchers interested in this field. So far, in most of the numerical simulators, the centrifugal effect of rotational speed on the natural frequencies is neglected. In this study, a new bladed assembly considering the centrifugal effect of the rotational speed for blade tip-timing numerical simulations is proposed. Moreover, an improvement in the engine order estimation algorithm in a two-parameter plot method is accomplished. In the assembly, blades are assumed to be cantilevered Euler–Bernoulli beams coupled together using linear springs. The finite element method is used to extract mass and stiffness matrices from differential equations of the system. By using the two-parameter plot method, the engine order of the excitation is detected. To examine the performance of the algorithm, Monte–Carlo simulation is implemented. The new simulator fulfills both cyclic symmetry and increase in the natural frequencies with increase in rotational speed. Engine order estimation with the new formulation in the two-parameter plot method is accurate. Hence, the new simulator and formulation for two-parameter plot method are reliable for numerical simulations.

Keywords

Vibrations finite element tip-timing bladed assembly Monte-Carlo simulation

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References

Heath

Imregun

. A survey of blade tip-timing measurement techniques for turbomachinery vibration. J Eng Gas Turbines Power 1998; 120(4): 784–791.

Zablotsky

Korostelev

. Measurement of resonance vibrations of turbine blades with the ELURA device. Energomashinostroneniye (USSR) 1970; 2: 30–39.

Heath

. A new technique for identifying synchronous resonances using tip-timing. J Eng Gas Turbines Power 2000; 122(2): 219–225.

Carrington

Wright

Cooper

et al. A comparison of blade tip timing data analysis methods. Proc Inst Mech Eng G J Aerosp Eng 2001; 215(5): 301–312.

Dimitriadis

Carrington

Wright

et al. Blade-tip timing measurement of synchronous vibrations of rotating bladed assemblies. Mech Syst Sig Process 2002; 16(4): 599–622.

Garrido

Dimitriadis

Wright

. A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances—Part I: theoretical development. Int J Rotating Mach 2007; 2007: 02747.

Chen

Yang

Xie

et al. Non-contact crack detection of high-speed blades based on principal component analysis and Euclidian angles using optical-fiber sensors. Sens Actuators A 2013; 201: 66–72.

Guo

Duan

Zhang

. Blade resonance parameter identification based on tip-timing method without the once-per revolution sensor. Mech Syst Sig Process 2016; 66: 625–639.

Battiato

Firrone

Berruti

. Forced response of rotating bladed disks: Blade Tip-Timing measurements. Mech Syst Sig Process 2017; 85: 912–926.

10.

Bastami

Safarpour

Mikaeily

et al. Identification of asynchronous blade vibration parameters by linear regression of blade tip timing data. J Eng Gas Turbines Power 2018; 140(7): 072506.

11.

Hajnayeb

Nikpour

Moradi

et al. A new reference tip-timing test bench and simulator for blade synchronous and asynchronous vibrations. Meas Sci Technol 2018; 29(2): 025203.

12.

Chen

Wang

Zhang

et al. New step to improve the accuracy of blade tip timing method without once per revolution. Mech Syst Sig Process 2019; 134: 106321.

13.

Weimin

Zhang

Dongfang

et al. A novel none once per revolution blade tip timing based blade vibration parameters identification method. Chin J Aeronaut 2020; 33(7): 1953–1968.

14.

Bornassi

Firrone

Berruti

. Vibration parameters estimation by blade tip-timing in mistuned bladed disks in presence of close resonances. Appl Sci 2020; 10(17): 5930.

15.

Chung

Yoo

. Dynamic analysis of a rotating cantilever beam by using the finite element method. J Sound Vib 2002; 249(1): 147–164.

16.

Petyt

. Introduction to the Finite Element. Introduction To Finite Element Vibration Analysis. 2nd ed. Cambridge: Cambridge University Press, 2010, pp. 72–76.

17.

Fitzgibbon

Pilu

Fisher

. Direct least square fitting of ellipses. IEEE Trans Pattern Anal Mach Intell 1999; 21(5): 476–480.

18.

Rigosi

Battiato

Berruti

. Synchronous vibration parameters identification by tip timing measurements. Mech Res Commun 2017; 79: 7–14.

19.

Yoo

Shin

. Vibration analysis of rotating cantilever beams. J Sound Vib 1998; 212(5): 807–828.

20.

Wildheim

. Excitation of rotationally periodic structures. J Appl Mech 1979; 46(4): 878–882.

21.

Chapra

Canale

. Numerical Methods for Engineers. 6th ed. New York: McGraw Hill Higher Education, 2010, p. 447.