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Research Papers: Gas Turbines: Structures and Dynamics

Solid Element Rotordynamic Modeling of a Rotor on a Flexible Support Structure Utilizing Multiple-Input and Multiple-Output Support Transfer Functions

[+] Author and Article Information
Lingnan Hu

Department of Mechanical Engineering,
Texas A&M University,
3123 TAMU,
College Station, TX 77843
e-mail: lingnan@tamu.edu

Alan Palazzolo

TEES Professor
Fellow ASME
Department of Mechanical Engineering,
Texas A&M University,
3123 TAMU,
College Station, TX 77843
e-mail: a-palazzolo@tamu.edu

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 17, 2016; final manuscript received June 24, 2016; published online August 16, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(1), 012503 (Aug 16, 2016) (11 pages) Paper No: GTP-16-1226; doi: 10.1115/1.4034207 History: Received June 17, 2016; Revised June 24, 2016

The authors present an improved modeling approach to analyze the coupled rotor-support dynamics by modeling the rotor with solid finite elements (FEs) and utilizing multiple-input and multiple-output transfer functions (TFs) to represent the flexible support. A state-space model is then employed to perform general rotordynamic analyses. Transfer functions are used to simulate dynamic characteristics of the support structure, including cross-coupling between degrees-of-freedom. These TFs are derived by curve-fitting the frequency response functions of the support model at bearing locations. The impact of the polynomial degree of the TF on the response analysis is discussed, and a general rule is proposed to select an adequate polynomial degree. To validate the proposed approach, a comprehensive comparison between the complete solid FE rotor-support model (CSRSM) and the reduced state-space model (RSSM) is presented. Comparisons are made between natural frequencies, critical speeds, unbalance response, logarithmic decrement, and computation time. The results show that the RSSM provides a dynamically accurate approximation of the solid FE model in terms of rotordynamic analyses. Moreover, the computation time for the RSSM is reduced to less than 20% of the time required for the CSRSM. In addition, the modes up to 100,000 cpm are compared among the super-element, beam element, and RSSM. The results show that the RSSM is more accurate in predicting high-frequency modes than the other two approaches. Further, the proposed RSSM is useful for applications in vibration control and active magnetic bearing systems.

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References

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Figures

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Fig. 1

Axisymmetric solid FE model of a hollow rotor

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Fig. 2

Solid tetrahedron element mesh model of the support structure with two fictitious nodes

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Fig. 3

Cross section (top) and 3D solid (bottom) FE mesh models of the rotor supported by two tilting-pad bearings

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Fig. 4

Stiffness coefficients of the bearing

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Fig. 5

Damping coefficients of the bearing

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Fig. 6

Solid FE mesh model of the rotor-support system

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Fig. 7

Grid sensitivity test for the third mode of the CSRSM at the rotational speed of 5000 rpm

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Fig. 8

Transfer function GZ2Z2 with the second/third and fifth/sixth polynomials

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Fig. 9

Critical speeds for the first and second modes

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Fig. 10

Critical speeds for the third and fourth modes

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Fig. 11

Mode shapes for the first (top), second (middle), and third (bottom) critical speeds of the rotor-support system

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Fig. 12

Mode shape (top: orthographic projection, middle: front view, bottom: top view) for the fourth critical speed of the rotor-support system

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Fig. 13

Horizontal magnitude of the unbalance response at the center of the middle disk

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Fig. 14

Vertical magnitude of the unbalance response at the center of the middle disk

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Fig. 15

Horizontal magnitude of the unbalance response at the left bearing location

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Fig. 16

Vertical magnitude of the unbalance response at the left bearing location

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Fig. 17

Horizontal magnitude of the unbalance response at the right bearing location

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Fig. 18

Vertical magnitude of the unbalance response at the right bearing location

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Fig. 19

Stability analysis of the rotor-support system

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Fig. 20

Mode shapes of the solid FE rotor-support model corresponding to modes 7 (top) and 16 (bottom) in Table 2

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Fig. 21

Mode shape of the solid FE rotor-support model corresponding to mode 12 in Table 2

Tables

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