Microsoft Word - SQ_Oct06_Env_Cepstrum(J).doc
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1 Hermitage Road, Richmond October Envelope Analysis BPFOball passing frequency outer racebpfiball passing frequency inner race BFFball fault frequencyftffundamental train frequency
2 rpm 102.4kHz(1)2(a) s2(b)948Hzf c carrier frequency 105Hz 2(c)105.45Hz= 1 / Hz - 2 -
3 2. (a) (b) (c) - 3 -
4 3. (a) 6 (b) (c) 2 2FFT MCSA MCSA 3 (a) 6-4 -
5 33.5 Hz MCSA(3)(4) 3.2 Hz 3. Hilbert transform x(t)x(ω) 1, ω Xˆ isgn X sgn(ω) = 0, ω -1, ωfft X(ω) x(t) xˆ t Xˆ xˆ t 1 F Xˆ 1 F isgn X MicrosoftExcel Excelx(t) td n Excelx(t) IMREAL(ω)IMAGINARY(ω) R(ω)I(ω) R(ω)1 Î 1D n /2 Î Rˆ COMPLEX( Rˆ, Î I(ω) Rˆ 1D n /20 ) rˆ t î t xˆ t 2 rˆ t 2 iˆ t 2 xˆ t 2 85Excel D n = 4096 f max 10 khzf max = 10kHzt = 1/(2.56f max ) = sf = 1/(tD n ) = 6.25 Hz - 5 -
6 f1hz t Et Et 1 xˆ t Et 1 τ6 τ500μs Excel 8 8 t s8 = sd n 4096 / 8 = 512 f max = 1 / (2.56t) = 1250 Hzf = 1 / (D n t) = 6.25 Hz D n 4096f = 1 / ( ) = Hz Hz 7 f max 1250Hz7 500Hz78.1Hz
7 4. Cepstrum Analysis spectrum 1 x[n] 1 j jn complex cepstrum: Ccplx logx e e d j jn real cepstrum: Creal log X e e d * jn power cepstrum: C power logxx e d 1. Spectral analysis Cepstral analysis spectrum cesptrum Hzfrequency squefrency harmonic rahmonic filter lifter 1 2 FFT 8-7 -
8 9 (a) 2 (b) (c) 83 9(a) Hz(600rpm) Hz270Hz29(b)2 2 9(c)9(b) - 8 -
9 9(c) AB2 A0.0037s0.0074s0.0111s0.0148s0.0185s0.0222s0.0259s 270HzB s s s s s180Hz A2 B AB0.0111s0.0222s (a)A 10(b) 270Hz 180Hz369 10(a) A (b) - 9 -
10 11B 270Hz 11 (a) B (b) 12 (a) A (b)
11 13 (a) B (b) A270Hz 10(a)180Hz 12 B13 270Hz 5. Process of Cepstrum Analysis x(t) x t x1 t x2t xn t xnt N n1 x(t) x t x t x t x t * 1 2 N X N n 1 X X X N X 1 2 n X(ω) = F[x(t)]X n (ω) = F[x n (t)]
12 log X x t log X1 log X 2 log X N log X n F N 1 log X F log 1 c X n n1 N n1 MicrosoftExcel Excelx(t) td n Excelx(t) IMREAL(ω)IMAGINARY(ω) R(ω)I(ω) 2 2 P 2 R I P(ω) 2 10Log(P(ω) 2 )R(ω)I(ω) 0 COMPLEX(R(ω),I(ω)) (s) s 20m s0.4s s s (Hz) (s)
13 Hz0.0128s s (s) [1] Spectra Quest Tech Note, Some Observations of the Detection of Rolling Element Bearing Outer Race Fault, September [2] Spectra Quest Tech Note, Analyzing Gearbox Degradation Using Time-Frequency Signature Analysis, March [3] Spectra Quest Tech Note, Diagnostics of Induction Motor with Broken Bars Using Motor Current Signature Analysis (MCSA), January [4] W. T. Thomson, A Review of On-Line Condition Monitoring Techniques for Three-Phase Squirrel- Cage Induction Motors Past Present and Future Note: all the references are available in pdf file format at
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