0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Rao, J. S., 2011, History of Rotating Machinery Dynamics, Springer, New York.
Genta, G., 2009, Vibration Dynamics and Control, Springer, New York.
Genta, G., 2005, Dynamics of Rotating Systems, Springer, New York.
Campbell, W., 1924, “Protection of Steam Turbine Disk Wheels From Axial Vibration,” Trans. ASME, 46, pp. 31–160.
Genta, G., and Tonoli, A., 1996, “A Harmonic Finite Element for the Analysis of Flexural, Torsional and Axial Rotordynamic Behavior of Discs,” J. Sound Vib., 196(1), pp. 19–43. [CrossRef]
Genta, G., and Tonoli, A., 1997, “A Harmonic Finite Element for the Analysis of Flexural, Torsional and Axial Rotordynamic Behavior of Bladed Arrays,” J. Sound Vib., 207(5) pp. 693–720. [CrossRef]
Genta, G., Feng, C., and Tonoli, A., 2010, “Dynamics Behavior of Rotating Bladed Discs: A Finite Element Formulation for the Study of Second and Higher Order Harmonics,” J. Sound Vib., 239(25), pp. 5289–5306. [CrossRef]
Cao, Y., and Altintas, Y., 2004, “A General Method for the Modeling of Spindle-Bearing Systems,” ASME J. Mech. Des., 126, pp. 1089–1104. [CrossRef]
Cao, Y., and Altintas, Y., 2007, “Modeling of Spindle Bearing and Machine Tool Systems for Virtual Simulation of Milling Operations,” Int. J. Mach. Tools Manuf., 47, pp. 1342–1350. [CrossRef]
Rantatalo, M., Aidanpää, J.-O., Göransson, B., and Norman, P., 2006, “Milling Machine Spindle Analysis Using FEM and Non-Contact Spindle Excitation and Response Measurement,” Int. J. Mach. Tools Manuf., 47(7–8), pp. 1034–1045. [CrossRef]
Rankine, W., 1869, “Centrifugal Whirling of Shafts,” Engineer (London), Apr. 9.
Genta, G., and Silvagni, M., “Three-Dimensional FEM Rotordynamics and the So-Called Centrifugal Softening of Rotors,” Atti dell'Accademia delle Scienze di Torino (to be published).
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
Zohar, A., and Aboudi, J., 1973, “The Free Vibration of a Thin Circular Finite Rotating Cylinder,” Int. J. Mech. Sci., 15, pp. 269–278. [CrossRef]
Endo, M., Hatmura, K., Sakata, M., and Taniguchi, O., “Flexural Vibration of a Thin Rotating Ring,” J. Sound Vib., 92(2), pp. 261–272. [CrossRef]
Bickford, W. B., and Reddy, E. S., 1985, “On the In-Plane Vibration of Rotating Ring,” J. Sound Vib., 101(1), pp. 13–22. [CrossRef]
Chen, Y., Zhao, H. B., Shen, Z. P., Grieger, I., and Kröplin, B. H., 1993, “Vibrations of High Speed Rotating Shells With Calculations for Cylindrical Shells,” J. Sound Vib., 160(1), pp. 137–160. [CrossRef]
Hoppe, R., 1871, “The Bending Vibration of a Circular Ring,” Crelle J. Math., 73, p. 158. [CrossRef]
Bryan, G. H., 1890, “On the Beats in the Vibrations of a Revolving Cylinder of Shell,” Proc. Cambridge Philos. Soc., 7, pp. 101–111.
Lin, J. L., and Soedel, W., 1988, “On General In-Plane Vibrations of Rotating Thick and Thin Rings,” J. Sound Vib., 122(3), pp. 547–570. [CrossRef]
Lamb, H., and Southwell, R., 1921, “The Vibrations of a Spinning Disk,” Proc. R. Soc. London, 99, pp. 272–280. [CrossRef]
Rao, J. S., 2002, “Rotor Dynamics Comes of Age,” Proceedings Sixth IFToMM International Conference Rotor Dynamics, Sydney, September 30–October 3, p. 15.
Gerardin, M., and Kill, N., 1984, “A New Approach to Finite Element Modelling of Flexible Rotors,” Eng. Comput., 1, pp. 52–64. [CrossRef]
Genta, G., and Silvagni, M., 2005, “Some Considerations on Cyclic Symmetry in Rotordynamics,” ISCORMA-3, Cleveland, OH, September 19–23.
Silvagni, M., Genta, G., and Tonoli, A., 2003, “Non-Axisymmetrical 3D Element for FEM Rotordynamics,” ISCORMA-2, Gdańsk, Poland, August 4–8.
Rajan, M., Nelson, H. D., and Chen, W. J., 1986, “The Dynamics of Rotor Bearing Systems Using Finite Elements,” ASME J. Vib., Acoust., 108, p. 197. [CrossRef]
Genta, G., Bassani, D., and Delprete, C., 1996, “DYNROT: A Finite Element Code for Rotordynamic Analysis Based on Complex Co-Ordinates,” Eng. Comput., 13(6), pp. 86–109. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Rotating beam: reference frames and geometry of the system

Grahic Jump Location
Fig. 4

Rotating ring: reference frames and geometry of the system

Grahic Jump Location
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.

Grahic Jump Location
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).

Grahic Jump Location
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

Grahic Jump Location
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].

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In