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Research Papers

Order Tracking Analysis Using Generalized Fourier Transform With Nonorthogonal Basis

[+] Author and Article Information
Jaafar Alsalaet

College of Engineering,
University of Basrah,
Qarmat Ali Compound,
Basra 61004, Iraq
e-mail: jaafarkhalaf@gmail.com

Saleh Najim

College of Engineering,
University of Basrah,
Qarmat Ali Compound,
Basra 61004, Iraq
e-mail: saleh.najim52@gmail.com

Abduladhem Ali

College of Engineering,
University of Basrah,
Qarmat Ali Compound,
Basra 61004, Iraq
e-mail: abduladem1@yahoo.com

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 19, 2013; final manuscript received August 7, 2014; published online August 27, 2014. Assoc. Editor: Yukio Ishida.

J. Vib. Acoust 136(6), 061002 (Aug 27, 2014) (9 pages) Paper No: VIB-13-1371; doi: 10.1115/1.4028269 History: Received October 19, 2013; Revised August 07, 2014

The nonorthogonal basis generalized Fourier transform is used as orders extraction technique during machinery speed-up and slow-down tests due to nonstationary nature of vibration signals in these tests. The kernels of this transform have time-dependent frequency which is related to the operating speed of the machine. Since these kernels may belong to different groups or shafts, they are generally nonorthogonal. The actual amplitudes and phases of the orders can be found by solving the system of linear equations resulting from decomposition process which is proposed in this work as an improvement to the time variant discrete Fourier transform (TVDFT) method. The proposed scheme is proved to be efficient and the processing time is very small as compared to other schemes such as the Vold–Kalman order tracking (VKOT) method. The accuracy and efficiency of the proposed scheme are investigated using simulated vibration signal and also actual signals.

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References

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Qian, S., 2003, “Gabor Expansion for Order Tracking,” Sound Vib., 37(6), pp. 18–22, available at: http://www.sandv.com/downloads/0306qian.pdf.
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Herman, R. L., 2013, “An Introduction to Fourier and Complex Analysis With Application to the Spectral Analysis of Signals,” University of North Carolina Wilmington, Wilmington, NC, online publication, http://people.uncw.edu/hermanr/mat367/FCABook/Book2013/FunctionSpaces.pdf
Gridhar, P., and Scheffer, C., 2004, Practical Machinery Vibration Analysis and Predictive Maintenance, Newnes Publications/Elsevier, Oxford, UK.
Tuma, J., 2005, “Setting the Passband Width in the Vold–Kalman Order Tracking Filter,” Twelfth International Conference on Sound and Vibration (ICSV12), Lisbon, Portugal, July 11–14.

Figures

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Fig. 1

Time signal of two close orders: (a) time from 0 to 1 s and (b) time from 1 to 2 s

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Fig. 2

Simulated run-up time signal

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Fig. 3

Simulated vibration signal for run-up test: (a) actual and (b) uncompensated components

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Fig. 4

Extracted orders at 0.25 s interval without window: (a) OCS of Ref. [12] and (b) proposed scheme

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Fig. 9

Extracted orders without constant frequency excitation

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Fig. 10

Extracted orders with constant frequency excitation: (a) 25 Hz, (b) 35 Hz, and (c) 45 Hz

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Fig. 11

FFT spectrum of the response at excitation frequency of 35 Hz

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Fig. 5

Extracted orders at 0.125 s interval with window: (a) OCS of Ref. [12] and (b) proposed scheme

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Fig. 6

Extracted orders at five revolutions interval: (a) OCS of Ref. [12] and (b) proposed scheme

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Fig. 7

Extracted orders (a) VKOT [16] and (b) proposed scheme with 10 revolutions block size

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Fig. 8

Experimental setup for run-up test with constant frequency excitation

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