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Research Papers

Nonlinear Analysis of Mineral Wool Fiberization Process

[+] Author and Article Information
Benjamin Bizjan

Abelium d.o.o,
Kajuhova 90,
Ljubljana 1000, Slovenia
e-mail: benjamin.bizjan@abelium.eu

Brane Širok

Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia
e-mail: brane.sirok@fs.uni-lj.si

Edvard Govekar

Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia
e-mail: edvard.govekar@fs.uni-lj.si

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received September 24, 2013; final manuscript received February 11, 2014; published online January 12, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 10(2), 021005 (Mar 01, 2015) (8 pages) Paper No: CND-13-1226; doi: 10.1115/1.4026842 History: Received September 24, 2013; Revised February 11, 2014; Online January 12, 2015

In this paper, the mineral wool fiberization process on a spinner wheel was studied by means of the nonlinear time series analysis. Melt film velocity time series was calculated using computer-aided visualization of the process images recorded with a high speed camera. The time series was used to reconstruct the state space of the process and was tested for stationarity, determinism, chaos, and recurrent properties. Mineral wool fiberization was determined to be a low-dimensional and nonstationary process. The 0–1 chaos test results suggest that the process is chaotic, while the determinism test indicates weak determinism.

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References

Figures

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Fig. 1

Simplified presentation of a spinner wheel and initial fiber formation

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Fig. 2

Four-wheel industrial spinner for mineral wool production [9]

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Fig. 3

Experimental setup for visualization of the fiberization process

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Fig. 4

Left: window of interest (yellow rectangle) for velocity calculation. Center: chosen coordinate system. Right: region of interest shown for a sequence of four consecutive frames, 400% magnification.

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Fig. 5

Time series of vy before (upper panel) and after the application of the low pass filter at 2 kHz cutoff frequency (lower panel)

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Fig. 6

Power spectrum of the filtered time series

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Fig. 7

Autocorrelation function and mutual information for the filtered time series of vy

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Fig. 8

Fraction of false nearest neighbors (fnn) with respect to the embedding dimension m, for τ = 19

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Fig. 9

Cross prediction errors for the filtered time series

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Fig. 10

Determinism test. The left panel features the reconstructed phase space using τ = 19 and m = 4, while the right panel shows the pertaining approximated directional vector field. Determinism factor of the phase space is κ = 0.66.

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Fig. 11

Recurrence plot of the filtered time series

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Fig. 12

Recurrence quantification analysis plots

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