Vibration measurements2

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Information about Vibration measurements2

Published on December 12, 2016

Author: MagedMostafa10

Source: slideshare.net

1. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Vibration of Structures

2. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Vibration Measurements

3. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Course Contents SDOF M-DOF Cables/String  Bars  Shafts  Vibration Attenuation  Beams  Membranes & Thin Plates o Vibration Testing and Measurements

4. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Objectives • Vibration Measurements Hardware • Introduction to signal Processing • Vibration Measurements Terminology

5. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Objectives • Vibration Measurements Hardware • Introduction to signal Processing • Vibration Measurements Terminology

6. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Measurements Hardware

7. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Measurements Hardware Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network, Smart Mater. Struct. 16 (2007) 1208–1217

8. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Measurements Hardware • Transducers • Exciters • Signal Conditioning • Analyzer

9. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Measurements HW: Transducers • Load cell: a piezoceramic device configured to produce a voltage proportional to force • Accelerometer: (piezoceramic) produce a signal proportional to acceleration at the point of attachment • Proximity probes: magnetic device gives a signal proportional to local displacement

10. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com • Laser vibrometers: give a signal proportional to local velocity (or scanned to give velocity field) • Strain gauges: (local strain or strain rate) Measurements HW: Transducers

11. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com • Electromagnetic shakers: which may apply a force through a range of frequencies (harmonic or random inputs) • Instrumented hammers: which simulate an impact Measurements HW: Exciters

12. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com • The direct out put of a transducer not usually well suited for input into an analyzer: Impedance miss matched, voltage or current levels too low • SC is a charge or voltage amp designed to take an accelerometer signal and match it to the input requirements of the analyzer Measurements HW: SC

13. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com • Electronic boxes (dedicated computers) gathers signals and manipulate them mathematically • Modern analyzers have evolved almost in to chip sized devices • Main source of manipulation is Digital Fourier Transforms for manipulating the vibration data in the frequency domain Measurements HW: Analyzer

14. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Objectives • Vibration Measurements Hardware • Introduction to Signal Processing • Vibration Measurements Terminology

15. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Fourier Series: Physical Meaning

16. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Fourier Series of F(t) of period T   ,....3,2,1 )sin()( 2 ,)cos()( 2 )( 2 2 )sin()cos( 2 )( 00 0 0 1 0           n dttntF T bdttntF T a dttF T a T tnbtna a tF T Tn T Tn T T n TnTn    

17. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Fourier Series: Physical Meaning

18. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Fourier Series: Physical Meaning

19. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Fourier Series: Physical Meaning

20. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Digital Signal Processing The analyzer takes signals form the transducer and puts the signal into a form that can be mathematically `manipulated

21. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Analog-to-Digital Converter Analog signal x(t) is sampled at many equally spaced time intervals to produce the digital record: {x(t1), x(t2), ….x(tN)} where x(tk) is the discrete value of x(t) at time tk and N is the number of samples taken

22. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Analog-to-Digital Converter What happens if Sampling rate is too large? sec1 ) 4 7 sin( ) 4 sin( 2 1    T tx tx  

23. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Analog-to-Digital Converter What happens if Sampling rate is too large?

24. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Analog-to-Digital Converter • Aliasing: When sampling rate is too large, the digital record does not catch the details of the analog signal • What is the optimum Sampling rate? • Min. 2 Samples / Cycle • Experience: 2.5 Samples / Cycle Shannon’s sampling theorem

25. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Analog-to-Digital Converter • Antialiasing Filter: low-pass Filter(only allows low frequencies through). • The filter cuts off frequencies higher than about half the maximum frequency of interest: (ωmax , Nyquist frequency). • Most modern digital analyzers provide built-in antialiasing filters.

26. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Digital Fourier Transform ,....3,2,1 2 sin 1 , 2 cos 1 1 2 sin 2 cos 2 )( 11 1 0 2/ 1 0                                         n t T n x N bt T n x N a x N a t T n bt T n a a txx N k kkn N k kkn N k k N n knknkk   N is fixed by hardware (a power of 2)

27. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Digital Fourier Transform Above becomes the matrix equation x=Ca Where: C: contains the sin and cos terms x: is the vector of samples and a: is the vector of Fourier Coefficients • Analyzer computes the coefficients in the DFT formula: a=C-1x

28. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Digital Fourier Transform What happens if Samples do not match the periods?

29. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Digital Fourier Transform Leakage: If the signal is not periodic in N samples (signal cut off mid period) the DFT will produce extra frequencies

30. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Digital Fourier Transform Windowing: multiply signal by a function which is zero at the end points

31. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Radom Signals • Autocorrelation: Tells how fast x(t) is changing    T T kxx dtxtx T tR 0 )()( 1 lim)(          dexRS j xxxx )( 2 1 )( • Power Spectral Density (PSD): Frequency domain of Autocorrelation [ FT(Rxx) ]

32. Periodic Structure Maged Mostafa #WikiCourses http://WikiCourses.WikiSpaces.com Radom Signals • Crosscorrelation: Tells how fast x(t) is changing w.r.t. f(x)    T T kxf dtftx T tR 0 )()( 1 lim)(          dexRS j xfxf )( 2 1 )( • Cross Spectral Density (PSD): Frequency domain of Autocorrelation FT(Rxf)

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