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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.


2.1 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



      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.


      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.


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