Research Papers: Gas Turbines: Structures and Dynamics

A Node-Dependent Kinematic Approach for Rotordynamics Problems

[+] Author and Article Information
Matteo Filippi

Mul2 Team,
Politecnico di Torino,
Corso Duca degli Abruzzi, 24,
Torino TO, 10129, Italy
e-mail: matteo.filippi@polito.it

Enrico Zappino

Mul2 Team,
Politecnico di Torino,
Corso Duca degli Abruzzi, 24,
Torino TO, 10129, Italy
e-mail: enrico.zappino@polito.it

Erasmo Carrera

Mul2 Team,
Politecnico di Torino,
Corso Duca degli Abruzzi, 24,
Torino TO, 10129, Italy
e-mail: erasmo.carrera@polito.it

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 24, 2017; final manuscript received December 7, 2018; published online January 8, 2019. Assoc. Editor: Damian M. Vogt.

J. Eng. Gas Turbines Power 141(6), 062501 (Jan 08, 2019) (12 pages) Paper No: GTP-17-1630; doi: 10.1115/1.4042285 History: Received November 24, 2017; Revised December 07, 2018

This paper presents the dynamic analysis of rotating structures using node-dependent kinematics (NDK) one-dimensional (1D) elements. These elements have the capabilities to assume a different kinematic at each node of a beam element, that is, the kinematic assumptions can be continuously varied along the beam axis. Node-dependent kinematic 1D elements have been extended to the dynamic analysis of rotors where the response of the slender shaft, as well as the responses of disks, has to be evaluated. Node dependent kinematic capabilities have been exploited to impose simple kinematic assumptions along the shaft and refined kinematic models where the in- and out-of-plane deformations appear, that is, on the disks. The governing equations of the rotordynamics problem have been derived in a unified and compact form using the Carrera unified formulation. Refined beam models based on Taylor and Lagrange expansions (LEs) have been considered. Single- and multiple-disk rotors have been investigated. The effects of flexible supports have also been included. The results show that the use of the node-dependent kinematic elements allows the accuracy of the model to be increased only where it is required. This approach leads to a reduction of the computational cost compared to a three-dimensional model while the accuracy of the results is preserved.

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Fig. 3

A two-node beam based on the LE, Ref. [1]

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Fig. 2

A two-node beam based on the Taylor expansion, Ref.[1]

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Fig. 4

A three-node 1D element with NDK

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Fig. 1

Reference system of the beam model

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Fig. 5

Typical geometry of a rotor and its deformations

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Fig. 6

Beam model of a rotor. A variable cross section is considered to include the disk. The kinematic assumptions of classical models lead to a rigid disk, that is, no shell-like deformations can be detected.

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Fig. 7

FE model of a rotor built using one- and two-dimensional elements. The use of the shell elements allows complex deformations to be detected, but inconsistencies in the geometry and kinematic field may arise at the interface.

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Fig. 8

FE model of a rotor built using node-dependent kinematic elements. The nodes of the elements in the disk area use a LE model while the nodes of the elements of the shaft use a TE model.

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Fig. 16

Dynamic bearing forces

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Fig. 17

Mode shapes and frequencies computed with the Model 0 of Table 2

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Fig. 18

Percentage errors versus mode shape numbers with respect to the solution shown in Fig. 17

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Fig. 19

Campbell's diagrams computed using Model 0 (continuous lines) and Model 2 (dashed lines) of Table 2

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Fig. 11

Campbell's diagrams of the overhung rotor

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Fig. 12

Stiffness and damping coefficients of the front and rear bearings

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Fig. 13

5-kN gas turbine model

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Fig. 14

Campbell diagrams of the 5-kN gas turbine system

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Fig. 15

Unbalance responses at specified structural nodes. Bold lines: TE2/TE2, fine lines: TE2/L9.

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Fig. 9

The overhung rotor

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Fig. 10

First mode shapes of the overhung rotor (see Table 1)



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