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Research Papers

Nonlinear Dynamic Modeling of the Cracked Rotor Ball Bearing System With Emphasis on Damage Detection Capabilities

[+] Author and Article Information
Rajiv Kumar Vashisht

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB R3T 5V6, Canada
e-mails: dr.rajiv1972@gmail.com;
vashisrk@myumanitoba.ca

Qingjin Peng

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB R3T 5V6, Canada
e-mail: qingjin.peng@umanitoba.ca

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 13, 2017; final manuscript received February 7, 2018; published online March 30, 2018. Assoc. Editor: Miao Yu.

J. Vib. Acoust 140(4), 041018 (Mar 30, 2018) (10 pages) Paper No: VIB-17-1415; doi: 10.1115/1.4039404 History: Received September 13, 2017; Revised February 07, 2018

It is confirmed experimentally that in case of a rotor with crack, multiple harmonics are generated when the rotor revolves at a particular frequency. Only few modeling techniques successfully predict this particular behavior of the cracked rotor. It is observed in this research that modeling cracked rotors using conventional finite element methods cannot predict this particular behavior successfully. A nonlinear dynamic model of the flexible rotor with ball bearings is developed using discrete mass spring damper elements combined with an existing model of the crack to truly predict this confirmed experimental behavior. Certain crack detection techniques based on the steady-state response work well on this basic concept of the multiharmonics generation due to nonlinearities caused by cracks in the rotor. The presence of ball bearings, rotor-coupling misalignment, rotor-stator rub, and rotor bow can also cause significant nonlinearities in the overall system. These additional nonlinearities render these crack detection techniques to lose their effectiveness. Our work justifies through simulations that the Jeffcott rotors are the over simplified version of real-life rotor-bearing systems. Hence, these crack detection techniques cannot be efficiently applied for condition monitoring of real-life rotor-bearing systems. The proposed model also helps to understand that the presence of flexible bearing supports affects the dynamics of the system considerably and negatively affects the effectiveness of these crack detection techniques.

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Figures

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Fig. 1

Schematic of the FEM of rotor with end supports

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Fig. 2

Schematic of the FEM of rotor bearing system

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Fig. 3

Ball bearing system

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Fig. 4

Reduced order model of the rotor bearing system

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Fig. 5

Cracked rotor model

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Fig. 6

Vertical response of the system at disk 1 at different rotor spin frequencies with crack function f(Ωt)=(1+cos(Ωt))/2: (a) rotor spin frequency 40 Hz, (b) rotor spin frequency 80 Hz, (c) rotor spin frequency X/3, and (d) rotor spin frequency X/2

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Fig. 7

Vertical response of the system at disk 1 at 27 Hz rotor spin frequency for linear bearing and ball bearing with rigid bearing support: (a) healthy rotor with linear bearing, (b) healthy rotor with ball bearing, (c) 40% cracked rotor with linear bearing, and (d) 40% cracked rotor with ball bearing

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Fig. 8

Vertical response of the system at disk 1 at different rotor spin frequencies of the rotor ball bearing system with flexible bearing support: (a) healthy rotor with ball bearing at 1/2 X rotor spin frequency in subharmonic region, (b) 40% cracked rotor with ball bearing response at 1/2 X rotor spin frequency in subharmonic region, (c) healthy rotor with ball bearing at 25 Hz rotor spin frequency, and (d) 40% cracked rotor with ball bearing at 25 Hz rotor spin frequency

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Fig. 9

Vertical response of the system at disk 1 at 27 Hz rotor spin frequency and 18 Hz auxiliary harmonic excitation frequency (at disk 1) for linear bearing and ball bearing with rigid bearing support: (a) healthy rotor with linear bearing at AHE frequency of 18 Hz, (b) healthy rotor with ball bearing at AHE frequency of 18 Hz, (c) 40% cracked rotor with linear bearing at AHE frequency of 18 Hz, and (d) 40% cracked rotor with ball bearing at AHE frequency of 18 Hz

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Fig. 10

Vertical response of the system at disk 1 with auxiliary harmonic excitation frequency at 18 Hz (at disk 1) for rotor with linear bearing and ball bearing with flexible bearing support (rotor spin frequency 27 Hz): (a) healthy rotor with linear bearing at AHE frequency of 18 Hz, (b) healthy rotor with ball bearing at AHE frequency of 18 Hz, (c) 40% cracked rotor with linear bearing at AHE frequency of 18 Hz, and (d) 40% cracked rotor with ball bearing at AHE frequency of 18 Hz

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Fig. 11

Vertical response of the system at disk 2 with multisine excitation (at disk 1 with odd frequencies) for rotor with linear as well as ball bearing at 3 g unbalanced mass with flexible bearing support (rotor spin frequency 27 Hz): (a) healthy rotor with linear bearing, (b) 40% cracked rotor with linear bearing, (c) healthy rotor with ball bearing, and (d) 40% cracked rotor with ball bearing

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Fig. 12

Vertical response of the system at disk 2 with multisine excitation (even frequencies) frequencies for rotor with linear as well as ball bearing at 3 g unbalanced mass with flexible bearing support (rotor spin frequency 30 Hz): (a) healthy rotor with linear bearing, (b) 40% cracked rotor with linear bearing, (c) healthy rotor with ball bearing, and (d) 40% cracked rotor with ball bearing

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