# “Squirrel cage” flexibility in supports of aviation gas turbine engine rotors

## Abstract

Elastic damper supports composed of elastic elements of “the squirrel cage” type are widely applicable in the design of aviation gas turbine engines. They are used for engine frequency detuning from unwanted resonance frequencies and for unloading of hydrodynamic dampers from the rotor weight. “Squirrel cage” elements are designed in different ways but the schemes with straight, compound and curvilinear rods are the most frequently used ones. Total flexibility of the rods that form “the squirrel cage” mainly determines the flexibility of the whole elastic-damper support in general. References [1] and [2] give simple equations to obtain radial stiffness coefficient of the elastic part of “the squirrel cage” with straight rods of the rectangular cross-section. However, “the squirrel cage” transmits not only radial forces but axial ones and moments as well. This fact necessitates consideration of other coefficients of the general flexibility matrix of “the squirrel cage”. The present article presents a methodology of determining the flexibility matrix of an elastic bush of “the squirrel cage”. The given methodology is applicable for bushes with straight rods (finite-element methods should be used for compound and curvilinear rods). Flexibility matrix components are obtained using the methods of strength of materials. The elastic bush of “the squirrel cage” is considered as a set of straight short rods restricted by stiff flanges from the butts. As a result, an analytical equation depending on the bush characteristics was obtained for every matrix component. As a test example, a flexibility matrix for the defined characteristics was obtained. Meanwhile, the time of obtaining the flexibility matrix does not exceed fractions of a second. Similarly, a flexibility matrix was obtained using calculations in the finite-element complex. The difference between the results obtained was less than 1%. The given algorithm and the flexibility matrix obtained with its help may be used for the simulation of support units of aviation gas turbine engines in rotor dynamics tasks.

## About the authors

### S. A. Degtiarev

Scientific and Technical Center of Rotor Dynamics Alfa-Tranzit Co.Ltd

Author for correspondence.
Email: degs@alfatran.com

Function supervisor on the development of simulation tools

Russian Federation

### M. K. Leontiev

Moscow Aviation Institute (National Research University)

Email: lemk@alfatran.com

Doctor of Science (Engineering)

Professor of Department “Construction and Design of Engines”

Russian Federation

### V. V. Popov

Bauman Moscow State Technical University

Email: vvpopov.bmstu@gmail.com

Teaching assistant of the Department PK-5 “Applied Mechanics”

Russian Federation

## References

1. Belousov A.I., Baljakin V.B., Novikov D.K. Teorija i proektirovanie gidro-dinamicheskih dempferov opor rotorov [Theory and design of hydrodynamic rotor support dampers]. Samara: SNTs RAN Publ., 2002. 335 p.
2. Sergeev S.I. Dempfirovanie mehanicheskih kolebanij [Damping of mechanical vibrations]. Moscow: Fizmatgiz Publ., 1959. 408 p.
3. Birger I.A., Shorr B.F. Dinamika aviacionnyh gazoturbinnyh dvigatelej [Dynamics of aircraft gas turbine engines]. Moscow: Mashinostroenie Publ., 1981. 232 p.
4. Baljakin V.B., Barmanov I.S. Design procedure of factor of rigidity flexible elements of support of rotors aviation gas turbine engines // Izvestija Samarskogo nauchnogo tsentra RAN. 2013. V. 15, no. 4-1. P. 205-209. (In Russ.)
5. Feodos'ev V.I. Soprotivlenie materialov [Strength of materials]. Moscow: Bauman Moscow St. Tech. Univ. Publ., 2010. 590 p.

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