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Blade wave finite element
Davydov D. P., Ermakov A. I.
Samara State Aerospace University, 34, Moskovskoye shosse, Samara, 443086, Russia
Abstract: This paper considers the construction of an effective beam finite element for the blade as a the component of cyclic symmetric system. The resulting equations of the element are implemented as a computer program in Fortran. The comparison of the blades natural frequencies obtained by calculation and experimentally showed a good agreement.
Keywords: gas turbine engine, blade, finite element, modal analysis, efficiency.
The task of ensuring the vibration reliability concerning the rotor systems of turbomachines and their elements is accompanied by the implementation of a large amount of computational studies for the set of design models. There is a theoretical base and modern computational techniques that allow one to predict accurately the dynamic characteristics of complex structures. In this case the three-dimensional large-scale models are usually used. They consist of the universal high-order finite elements. However, the performance of blade wheel optimization work using such models is time consuming and the rotor system optimization for such models is an almost impossible task.
The reduction of time and expenses to ensure the reliability of rotor systems and their components, due to the development of the computer programs that have high rates of speed and accuracy, is an important scientific and applied problem.
Currently, Samara State Aerospace University develops a specialized software for the turbomachinery rotor system dynamics study. The increase of computing performance with the due accuracy provision is achieved due to the mathematical apparatus, which is based on the deep theoretical concepts about the dynamic phenomena accompanying the gas turbine engine operation, in particular the properties of the cyclic symmetric system spectrum. Besides the use of two-level finite element models reduces the operation time. The first level models allow without too much geometric detailing to transform it into a variant close to an optimal one. The using of the second level models allows to perform the some final optimizing calculations. The final optimization stage, which should be performed at full design detailing, demands the attraction of sofware calculation packages (ANSYS, NASTRAN, ABACUS, and others.) which are widely used in various fields of science and technology [1-8].
The purpose of this paper is to develop an effective finite element of a blade (first level model) for the developed software package to study the turbomachinery rotor system dynamics.
2. MATHEMATICAL MODEL OF BLADE WAVE FINITE ELEMENT
2.1 Substantiation of blade beam model selection
2.2 Initial equations of an infinitely small blade element
2.3 Accounting for the cyclic symmetry properties and the transition to the row of blades
2.4 System of differential equations
2.5 Development of blade wave finite element
3. EVALUATION OF ACCURACY AND SPEED FOR BLADE WAVE FINITE ELEMENT
The study results demonstrate the development of a blade wave finite element which has high speed and accuracy values. The calculated values of the natural frequencies are in good agreement with the experimental data and the analysis results in ANSYS. The difference makes less than 5%. At that, the calculation time gain is a multiple one, compared with ANSYS.The blade wave finite element is primarily targeted at solving the problems of the blade dynamics as the part of an impeller, rotor and other parts of the engine. In this case due to its flexibility it may be successfully used for the dynamic analysis of a single blade. Now the Samara State Aerospace University develops in the same way the wave finite elements for discs, shells, shroud shelf and other components of a gas turbine engine. The application of wave finite elements will significantly reduce the time and cost to solve the optimization problems for the development of a rotary engine system dynamic image.
About the authors
First Author Danila P. Davydov, Dipl.-Eng., researcher of the laboratory "Vibration resistance and reliability of aircraft products." The author’s major is dynamics and strength of mechanical systems.
Second Author Alexander I. Ermakov, Dr.-Eng., chief of the laboratory "Vibration resistance and reliability of aircraft products", Professor of Samara State Aerospace University. The author’s major is dynamics and strength of mechanical systems.
CONFLICT OF INTEREST
The author confirms that this article content has no conflict of interest.
This work was supported by the Ministry of Education and Science of the Russian Federation.
 Falaleev, S., Vinogradov, A., Bondarchuk, P. Influence research of extreme operate conditions on the face gas dynamic seal characteristics (2006) Technische Akademie Esslingen International Tribology Colloquium Proceedings, 15, p. 208.
 Ulanov, A.M., Ponomarev, Yu.K. Finite element analysis of elastic-hysteretic systems with regard to damping (2009) Russian Aeronautics, 52 (3), pp. 264-270.
 Polyakov, K.A., Klebanov, Ya.M., Remnev, V.V., Bogomolov, R.M., Erisov, A.E. Modeling of loads on cutting elements of drill bits (2008) Chemical and Petroleum Engineering, 44 (9-10), pp. 499-502.
 Klebanov, I.M., Davydov, A.N., Kirdina, L.N., Polyakov, K.A. Transformation of the results of the finite-element analysis of optical-surface displacements for use in optical-analysis packages (2014) Journal of Optical Technology (A Translation of Opticheskii Zhurnal), 81 (7), pp. 388-391.
 Igolkin, A., Koh, A., Kryuchkov, A., Safin, A., Shakhmatov, E. Pressure reducing valve noise reduction (2012) 19th International Congress on Sound and Vibration 2012, ICSV 2012, 3, pp. 2458-2464.
 Vinogradov, A.S. Seal design features for systems and units of aviation engines (2014) Life Science Journal, 11 (8), pp. 575-580.
 Tikhonov, V., Davydov, D., Gelfgat, M., Alikin, R. Comparative strength analysis of aluminum drill pipes with steel connectors assembled by different methods (2011) Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, 4, pp. 87-93.
 Nemov, A., Modestov, V., Buslakov, I., Loginov, I.N., Ivashov, I.V., Lukin, A., Borovkov, A.I., Kochergin, M.M., Mukhin, E.E., Litvinov, A.E., Koval, A.N., Tolstyakov, S.Y., Andrew, P. Development of ITER divertor Thomson scattering support structure design on the basis of engineering analyses (2014) Fusion Engineering and Design, 89 (7-8), pp. 1241-1245.
 Vorobyov Yu.S., Shorr B.F., Pretwisted beams theory. Naukova Dumka, Kiev, 1983. [in Russian]
 Vorobyov Yu.S., Bekh M.V., Korsunski M.L. The features of system free oscillations with a finite and a small order of rotational symmetry, Proceedings of CIAM: Aeroelastic of Turbomachine Blade 1266 (1989) 64–71. [in Rissain]
 B.O. Al-Bedoor, A.A. Al-Qaisia, Stability analysis of rotating blade bending vibration due to torsional excitation, Journal of Sound and Vibration 282 (2005) 1065–1083.
 Ha Seong Lima, Jintai Chungb, Hong Hee Yoo, Modal analysis of a rotating multi-packet blade system, Journal of Sound and Vibration 325 (2009) 513–531.
 S.K. Sinha, Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end, International Journal of Non-linear Mechanics 40 (2005) 113–149.
 Avramov K.V., Pierre C., Shyriaieva N. Flexural-flexural-torsional Nonlinear Vibrations of Pre-twisted Rotating Beams with Asymmetric Cross-sections, Journal of Vibration and Control 13 no.4 (2008).
 Temis J.M., Karaban V.V., Geometrically nonlinear finite element model of a pretwisted beam for static and dynamic assessment of blades, Proceedings of CIAM 1319 (2001) 10-20. [in Russian]
 M. H. Yao, W. Zhang, Y. P. Chen, Analysis on nonlinear oscillations and resonant responses of a compressor blade, Acta Mechanica 225 (2014).
 V.V. Volovoi, D.H. Hodges, C.E.S. Cesnik, B. Popescu, Assessment of beam modeling methods for rotor blade applications, Mathematical and Computer Modelling, Volume 33, Issues 10–11, 2001, Pages 1099-1112
 David J. Malcolm1, Daniel L. Laird, Extraction of equivalent beam properties from blade models, Wind Energy, Volume 10, Issue 2, pages 135–157, 2007.
 Lin Wang, Xiongwei Liu, Lianggang Guo, Nathalie Renevier, Matthew Stables, A mathematical model for calculating cross-sectional properties of modern wind turbine composite blades, Renewable Energy, 2014, 64, 52.
 Ivanov V.P. Vibration of blade wheels. Moscow: Mashinostroenie (Mechanical engineering), 1983. [in Russian]
 Ermakov, A.I., Ivanov, V.P., Frolov, V.A. Computation of the natural vibration frequencies of impellers in gas turbine engines on the basis of the method of dynamic wave stiffnesses and flexibilities (1988) Strength of Materials, 20 (6), pp. 804-810.
 Norrie D.H., de Vries G., An Introduction to Finite Element Analysis. New York: Academic Press, 1978.