Periodicity

Prepare by Ji Kim, Bokman Kim

FFT spectrum

FFT Spectrum Analyzers, such as the SR760, SR770, SR780and SR785, take a time varying input signal, like you wouldsee on an oscilloscope trace, and compute its frequency

spectrum.

Fourier's theorem states that any waveform in the time domain

can be represented by the weighted sum of sins and cosines.

The FFT spectrum analyzer samples the input signal,computes the magnitude of its sine and cosine components,and displays the spectrum of these measured frequencycomponents.

Electronic Test Instrument

Function generator

FFT (Fast Fourier Function) Spectrum

Oscilloscope

SPC Gauge

Formula and Data

F=C/λ F= Frequency C=Line speed λ=Wave length Wave length is given

by customer (Defect Spacing)

λ 65FPM

100FPM

200FPM

0.543ft

1.995HZ

3.07HZ

6.14HZ

0.456ft

2.375HZ

3.655HZ

7.31HZ

0.255ft

4.25HZ

6.54HZ

13.07HZ

0.243ft

4.45HZ

6.86HZ

13.71HZ

RFS Provided Data March (2009)

Applied Formula

Defect spacing are given by customer.

Line speed=300FPM

Example F=(300/60)/(6.516/12) =9.208HZ

T=1/(9.21)=0.108S

Defect Spacing

HZ T(sec)

6.516Inch

9.21HZ

0.108S

3.06Inch

19.61HZ

0.051S

0.267Inch

224.72HZ

0.004S

Justify of the FFT Analyzer 1

6.14HZ Test with 24.41HZ span

Justify of the FFT Analyzer 2

13.07 HZ Test with 48.82Hz span

Justify of the FFT Analyzer 3

149.81HZ Test with 781.25HZ span

How to Avoid the Frequency band?

V=2pR/T V=2pRF V=DF D=V/F

Change Rolling Mill and Bearing.

Bearing

Rolling Mill

Conclusion

Line speed and Wave Length to determine the affects on periodicity.

Ready to set up with FFT to Gamma Gauge.

FFT analyzer is functionally correct, Ready to test at Rolling Mill.