Research Papers

On Centrifugal Softening in Finite Element Method Rotordynamics

[+] Author and Article Information
Giancarlo Genta

e-mail: giancarlo.genta@polito.it

Mario Silvagni

Department of Mechanical and Aerospace
Engineering and Mechatronics Lab,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10039, Italy

Manuscript received July 20, 2012; final manuscript received March 12, 2013; published online August 22, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(1), 011001 (Aug 22, 2013) (10 pages) Paper No: JAM-12-1335; doi: 10.1115/1.4024073 History: Received July 20, 2012; Revised March 12, 2013

The centrifugal softening effect is an alleged and elusive reduction of the natural frequencies of a rotating system with increasing speed which is sometimes found in finite element rotordynamics. This reduction may, in some instances, be large enough to cause some of the natural frequencies to vanish, leading to a sort of elastic instability. Some doubts can, however, be cast on the phenomenon itself and on the mathematical models causing it to appear. The aim of the present work is to shed some light on centrifugal softening and to discuss the assumptions that are at the basis of three-dimensional FEM modeling in rotordynamics. One and two degrees of freedom models, such as the ones introduced by Rankine and Jeffcott, are first studied and then the classical rotating beam, ring, disk, and membrane are addressed. Some numerical models, built using the FEM, are then solved using both dedicated and general purpose codes. In all cases no strong centrifugal softening is found.

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Fig. 1

Inertial frame xyz and rotating frame ξηz for the dynamic study of a rotor

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Fig. 2

System made of a point mass constrained to move radially in a rotating reference frame

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Fig. 3

Rotating beam: reference frames and geometry of the system

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Fig. 4

Rotating ring: reference frames and geometry of the system

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Fig. 5

(a) Ring meshed using 80 20-node isoparametric elements. (b) Campbell diagram including rigid-body (R.B.), in-plane backward (I.P. Bw), in-plane forward (I.P. Fw) and out-of-plane (O.P.) modes. The numerical solution obtained using the 3-D FEM is compared with the analytical solution (see Eq. (27)); the solution obtained from a commercial 3-D FEM code (ANSYS) and the solution obtained from Eq. (3), by using the same stiffness and mass matrices as for the FEM computation.

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Fig. 6

Same as Fig. 5(b), but with an extended speed range. Additionally, the analytical extensional solution is reported (the small softening effect is not obtained from Eq. (27) and following due to mode uncoupling).

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Fig. 7

Simplified twin-spool turbine rotor: (a) sketch with the main dimensions (in mm), and (b) the FEM model for the DYNROT 1 1/2–dimensional code

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Fig. 8

Campbell diagram of the rotor sketched in Fig. 7. The solutions obtained using the DYNROT and ANSYS FEM codes (1-D, 112-D, and 3-D models) are reported together with the solution obtained from Eq. (3) in Ref. [1] and Eq. (5) in Ref. [8].




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