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Gas Turbines: Structures and Dynamics

Controlled Deflection Approach for Rotor Crack Detection

[+] Author and Article Information
Zbigniew Kulesza

Faculty of Mechanical Engineering,  Bialystok University of Technology, Bialystok, Polandz.kulesza@pb.edu.pl

Jerzy T. Sawicki

Center for Rotating Machinery Dynamics and Control, (RoMaDyC), Fenn College of Engineering,  Cleveland State University, Cleveland, OH 44115-2214,j.sawicki@csuohio.edu

J. Eng. Gas Turbines Power 134(9), 092502 (Jul 23, 2012) (13 pages) doi:10.1115/1.4006990 History: Received June 19, 2012; Revised June 20, 2012; Published July 23, 2012; Online July 23, 2012

A transverse shaft crack is a serious malfunction that can occur due to cyclic loading, creep, stress corrosion, and other mechanisms to which rotating machines are subjected. Though studied for many years, the problems of early crack detection and warning are still in the limelight of many researchers. This is due to the fact that the crack has subtle influence on the dynamic response of the machine and still there are no widely accepted, reliable methods of its early detection. This paper presents a new approach to these problems. The method utilizes the coupling mechanism between the bending and torsional vibrations of the cracked, nonrotating shaft. By applying an external lateral force of constant amplitude, a small shaft deflection is induced. Simultaneously, a harmonic torque is applied to the shaft inducing its torsional vibrations. By changing the angular position of the lateral force application, the position of the deflection also changes opening or closing of the crack. This changes the way the bending and torsional vibrations are being coupled. By studying the coupled lateral vibration response for each angular position of the lateral force one can assess the possible presence of the crack. The approach is demonstrated with a numerical model of a rotor. The model is based on the rigid finite element method (RFE), which has previously been successfully applied for the dynamic analysis of many complicated, mechanical structures. The RFE method is extended and adopted for the modeling of the cracked shafts. An original concept of crack modeling utilizing the RFE method is presented. The crack is modeled as a set of spring-damping elements (SDEs) of variable stiffness connecting two sections of the shaft. By calculating the axial deformations of the SDEs, the opening/closing mechanism of the crack is introduced. The results of numerical analysis demonstrate the potential of the suggested approach for effective shaft crack detection.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagrams of the method for different angular positions of the external force: (a) ϑ=0 deg, fully closed crack; (b) ϑ=120 deg, partially open crack; (c) ϑ=180 deg, fully open crack; and (d) arrangement of the measuring probes

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Figure 2

Rigid finite element model of the rotor: (a) original division into 50 spring-damping elements, (b) secondary division into 51 rigid finite elements, and (c) local coordinate systems of RFEs (xr,1, xr,2, xr,3) and SDEs (yk,1, yk,2, yk,3)

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Figure 3

Model of the crack: (a) possible location of the crack, (b) two RFEs and several SDEs at the location of the crack, and (c) shaft cross section at the location of the crack

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Figure 4

Possible deformations of the small SDE: (a) compression and (b) tension

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Figure 5

Frequency transfer function of the free-free rotor (continuous line) and its RFE model (dashed line)

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Figure 6

Torsional response for different angles ϑ; uncracked shaft; fQ=60 Hz

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Figure 7

Bending response for different angles ϑ; uncracked shaft; fQ=60 Hz

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Figure 8

Torsional response for different angles ϑ; 25% crack; fQ=60 Hz

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Figure 9

Bending response for different angles ϑ; 25% crack; fQ=60 Hz

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Figure 10

Bending response for different angles ϑ; 25% crack; fQ=80 Hz

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Figure 11

Torsional response for different angles ϑ; 40% crack; fQ=60 Hz

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Figure 12

Bending response for different angles ϑ; 40% crack; fQ=60 Hz

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Figure 13

Bending response for different angles ϑ; 40% crack; fQ=80 Hz

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Figure 14

Crack breathing at subsequent phases of the exciting torque; 25% crack; fQ=60 Hz; ϑ=90 deg

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Figure 15

Crack breathing at subsequent phases of the exciting torque; 40% crack; fQ=80 Hz; ϑ=0 deg

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Figure 16

Crack breathing at subsequent phases of the exciting torque; 40% crack; fQ=80 Hz; ϑ=90 deg

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Figure 17

Crack breathing at subsequent phases of the exciting torque; 40% crack; fQ=80 Hz; ϑ=180 deg

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