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Research Papers

Extended Angular-Velocity Vold–Kalman Order Tracking

[+] Author and Article Information
Min-Chun Pan

Department of Mechanical Engineering, Graduate Institute of Biomedical Engineering, National Central University, No. 300, Jhongda Road, Jhongli City, Taoyuan County 320, Taiwanpan_minc@cc.ncu.edu.tw

Cheng-Xue Wu

Department of Mechanical Engineering, Graduate Institute of Biomedical Engineering, National Central University, No. 300, Jhongda Road, Jhongli City, Taoyuan County 320, Taiwan

J. Dyn. Sys., Meas., Control 132(3), 031001 (Apr 14, 2010) (11 pages) doi:10.1115/1.4001326 History: Received September 28, 2006; Revised February 10, 2010; Published April 14, 2010; Online April 14, 2010

Dynamic signals acquired from rotary machines can be characterized by the order tracking (OT) techniques. The extracted order components correspond to the operation of specific machine elements and reflect their current healthy or faulty states. The study extends the angular-velocity Vold–Kalman OT scheme to simultaneously extract multiple order components. Theoretical derivation is illustrated with simulation of processing three synthetic signals to show its merit. Additionally, as an example to validate its effectiveness, the improved OT scheme is used to process pass-by noise emitted from an electric scooter with a planetary-gear-set transmission system. The gear-meshing orders are effectively decoupled from structure-borne resonances.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(Synthetic signal 1) Illustration of (a) rpm-frequency spectrum and (b) order spectrum, where two close orders (4 and 4.2) are characterized

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Figure 2

(Synthetic signal 1) Waveforms of orders 4 and 4.2 tracked by using (a) angular-velocity and (b) extended angular-velocity VKF_OT, respectively

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Figure 3

(Synthetic signal 1) Amplitudes of orders 4 and 4.2 tracked by using (a) angular-velocity and (b) extended angular-velocity VKF_OT, respectively

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Figure 4

(Synthetic signal 2) Spectrogram of two sets of order components

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Figure 5

(Synthetic signal 2) Estimation of order components tracked by extended angular-velocity VKF_OT scheme, waveform of (a) order 9, (b) order 4, and (c) order 1

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Figure 6

(Synthetic signal 2) Amplitudes of orders 1, 4, and 9 tracked by (a) angular-velocity VKF_OT and (b) extended angular-velocity VKF_OT

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Figure 7

(Synthetic signal 3) Illustration of (a) rpm-frequency spectrum and (b) order spectrum

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Figure 8

(Synthetic signal 3) Waveform extraction by using the extended angular-velocity VKF_OT (a) varying order, (b) order 1, and (c) order 4

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Figure 9

(Synthetic signal 3) Amplitude estimation by using the extended angular-velocity VKF_OT

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Figure 10

Schematic of the transmission system of test electrical scooter (the number of gear tooth: G51–64t, G41–53t, G32–40t, G31–54t, G22–23t, G21–77t, G11–39t, and the planetary-gear set with sun-53t, planet-16t, and ring-85t)

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Figure 11

Computed rpm-spectrogram of riding noise emitted from the test electric scooter

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Figure 12

Riding-noise waveforms of different components tracked by using extended angular-displacement VKF_OT. (a) Order-86 component before two resonances filtered out (without decoupling), (b) order-86 component after two resonances filtered out (with decoupling), (c) 600 Hz resonance, (d) 1020 Hz resonance.

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Figure 13

Riding-noise waveforms of different components tracked by using extended angular-displacement VKF_OT. (a) Order-64 component before two resonances filtered out (without decoupling), (b) order-64 component after two resonances filtered out (with decoupling), (c) 600 Hz resonance.

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Figure 14

SPL of order/spectral components versus revolution speed. (a) Order-86 component before two resonances filtered out (without decoupling), (b) order-86 component after two resonances filtered out (with decoupling), (c) resonance at 600 Hz, and (d) resonance at 1020 Hz.

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Figure 15

SPL of order/spectral components versus revolution speed. (a) Order-64 component before two resonances filtered out (without decoupling), (b) order-64 component after two resonances filtered out (with decoupling), and (c) resonance at 600 Hz.

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