Research Papers: Gas Turbines: Structures and Dynamics

Rotordynamic Energy Expressions for General Anisotropic Finite Element Systems

[+] Author and Article Information
Manoj Settipalli

Honeywell Technology Solutions Lab Pvt. Ltd.,
Mechanical COE,
Bangalore 560103, India
e-mail: saikrishnamanoj@gmail.com

Venkatarao Ganji

Honeywell Technology Solutions Lab Pvt. Ltd.,
Mechanical COE,
Bangalore 560103, India
e-mail: venkatarao.ganji@honeywell.com

Theodore Brockett

Honeywell Aerospace,
Mechanical Systems, Structures, and Dynamics,
111 S. 34th Street,
Phoenix, AZ 85034
e-mail: theodore.brockett@honeywell.com

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 6, 2017; final manuscript received July 17, 2017; published online October 4, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(2), 022502 (Oct 04, 2017) (10 pages) Paper No: GTP-17-1307; doi: 10.1115/1.4037722 History: Received July 06, 2017; Revised July 17, 2017

It is often desirable to identify the critical components that are active in a particular mode shape or an operational deflected shape (ODS) in a complex rotordynamic system with multiple rotating groups and bearings. The energy distributions can help identify the critical components of a rotor bearing system that may be modified to match the design requirements. Although the energy expressions have been studied by researchers in the past under specific limited conditions, these expressions require computing the displacements and velocities of all degrees-of-freedom (DOFs) over one full cycle. They do not address the overall time dependency of the energies and energy distributions, and their effect on the interpretation of a mode shape or an ODS. Moreover, a detailed finite element formulation of these energy expressions including the effects of anisotropy, skew-symmetric stiffness, viscous and structural damping have not been identified by the authors in the open literature. In this article, a detailed account of orbit characteristics and planarity for isotropic and anisotropic systems is presented. The effect of orbit characteristics on the energy expressions is then discussed. An elegant approach to obtaining time-dependent kinetic and strain energies of a mode shape or an ODS directly from the structural matrices and complex eigenvectors/displacement vectors is presented. The expressions for energy contributed per cycle by various types of damping and the destabilizing skew-symmetric stiffness that can be obtained in a similar way are also shown. The conditions under which the energies and energy distributions are time-invariant are discussed. An alternative set of energy expressions for isotropic systems with the DOFs reduced by half is also presented.

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Fig. 1

Coordinate system and degrees-of-freedom

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Fig. 2

Rotordynamic system schematic

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Fig. 3

Fifth critical speed mode shape of generally anisotropic system

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Fig. 4

Time-dependent strain (a) and kinetic (b) energies of supports and disks

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Fig. 5

Fourth critical speed mode shape of specially anisotropic system

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Fig. 6

Mode shape of fourth critical speed specially anisotropic system with rotated coordinate system

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Fig. 7

Time-dependent strain (a) and kinetic (b) energies of bearings and disks

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Fig. 8

Peak rotor shaft and bearing strain energy percentage distribution

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Fig. 9

%PKE and %GKE of lumped disc D1

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Fig. 10

Logarithmic decrement map of first four modes

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Fig. 11

Energy contribution from skew-symmetric stiffness and viscous damping



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