Beginning Vibration Analysis with Basic Fundamentals

1 Beginning Vibration AnalysiswithBasic FundamentalsBy: Jack PetersJack D. PetersBeginning Vibration2 IntroductionUnderstanding the basics and Fundamentals of Vibration Analysis are very important in forming a solid background to analyze problems on rotating between time and frequency is a common tool used for Analysis . Because the frequency spectrum is derived from the data in the time domain, the relationship between time and frequency is very important. Units of acceleration, velocity, and displacement are typical. Additional terms such as peak-peak, peak, and rms. are often used. Switching units correctly, and keeping terms straight is a must.

2 As much as possible, this training will follow the criteria as established by the Vibration D. PetersMass & Stiffness3 Mass & StiffnessAll machines can be broken down into two specific & StiffnessMassis represented by an object that wants to move or represented by springs or constraints of that D. PetersMass & Stiffness4 Mass & Stiffnessfn= 1/2Пk/mWhere:fn= natural frequency (Hz)k = stiffness (lb/in)m = massmass = weight/gravityweight (lb)gravity ( in/sec2)Jack D. PetersMass & Stiffness5 Concept !fn= 1/2Пk/mIf k increasesThen f increasesIf k decreasesThen f decreasesJack D. PetersMass & Stiffness6 Concept !fn= 1/2Пk/mIf m increasesThen f decreasesIf m decreasesThen f increasesJack D.

3 PetersSpectrum7 What s This ? Hz100 0 Hz 1 Jack D. PetersSpectrum8 FFT, Frequency Spectrum, Power Hz100 0 Hz 1 Jack D. PetersSpectrum9 Scaling X & Hz100 0 Hz 1 XYJack D. PetersSpectrum10 Scaling X & Hz100 0 Hz 1 FREQUENCYAMPLITUDEJack D. PetersSpectrum11 Scaling X & Hz100 0 Hz 1 What is itHow BadI sI tJack D. PetersTime Waveform12 What s That ? 0 s 1 Jack D. PetersTime Waveform13 Time 0 s 1 Jack D. PetersTime Waveform14 Scaling X & 0 s 1 Jack D. PetersTime Waveform15 Scaling X & 0 s 1 Jack D. PetersTime Waveform16 Scaling X & YWhat is itHowBadI sI 0 s 1 Jack D. PetersTime Waveform17 Scaling X & YWhat is itHowBadI sI s1 0 s 1 Jack D.

4 PetersTime & Frequency18 Double 0 s Hz100 0 Hz 1 Jack D. PetersThe X Scale19 The X ScaleJack D. PetersThe X Scale20 Hertz (Hz)One Hertz (Hz) is equal to 1 cycle / secondIt is the most common term used in Vibration Analysis to describe the frequency of a forget the 1 cycle / second relationship !Traditional Vibration Analysis quite often expresses frequency in terms of cycle / minute (cpm). This is because many pieces of process equipment have running speeds related to revolutions / minute (rpm). 60 cpm = 1 cps = 1 Hz Jack D. PetersThe X Scale21 Relationship with TimeThe frequency domain is an expression of amplitude and individual single frequency can be related to (Hz)= 1 / T(s)The inverse of this is also true for a single (s)= 1 / F(Hz)Keep in mind that the time domain is an expression of amplitude and multiple D.

5 PetersThe X Scale22 Concept !If: F = 1/T and T = 1/FThen: FT = 1 Jack D. PetersThe X Scale23 Concept !FT = 1If: F increasesThen: T decreasesIf: T increasesThen: F decreasesJack D. PetersThe X Scale24 Single Frequency1 Vrms0 Magnitude Hz100 0 HzPwr Spec 11V-1 Real sTime 1X:55 mVJack D. PetersThe X Scale25 Multiple Frequencies1 Hz100 0 HzPwr Spec 11 Hz100 0 HzPwr Spec 11 Hz100 0 HzPwr Spec 11 Hz100 0 HzPwr Spec 1X:55 mVX:78 mVX:21 mVX:42 mVJack D. PetersThe X Scale26 Multiple Time1V sTime 78 11V sTime 21 11V sTime 42 11V sTime 55 1 Jack D. PetersThe X Scale27 Real Life Time4V-4 Real sTIME 155 + 78 + 21 + 42 = Trouble !

6 Jack D. PetersThe X Scale28 Frequency Spectrum4V-4 Real sTIME 11 Vrms Hz100 0 HzFREQUENCY 1X:78 mVX:55 mVX:42 mVX:21 mVJack D. PetersThe X Scale29 The Most Copied Slide in the History of Vibration Analysis !AmplitudeInputTimeFrequencyTime WaveformSpectrumJack D. PetersThe X Scale30 Lines of Hz100 0 Hz 1 The FFT always has a defined number of lines of resolution. 100, 200, 400, 800, 1600, and 3200 lines are common spectrum has 800 lines, or the X scale is broken down into 800 D. PetersThe X Scale31 Filter Windows Window filters are applied to the time waveform data to simulate data that starts and stops at zero. They will cause errors in the time waveform and frequency spectrum.

7 We still like window filters !Jack D. PetersThe X Scale32 Window ComparisonsJack D. PetersThe X Scale33 Filter Windows Hanning (Frequency) Flat Top (Amplitude) Uniform (No Window) Force Exponential Force/Expo Set-up(Frequency Response)Hanning 16% Amplitude ErrorFlat Top 1% Amplitude ErrorWindow functions courtesy of Agilent The Fundamentals of Signal Analysis Application Note #AN 243 Jack D. PetersThe X Scale34 Filter Windows Use the Hanning Window for normal Vibration monitoring (Frequency) Use the Flat Top Window for calibration and accuracy (Amplitude) Use the Uniform Window for bump testing and resonance checks (No Window)Jack D. PetersThe X Scale35 Minimum Derived HzThe minimum derived frequency is determined by:Frequency Span / Number of Analyzer Lines (data points)The frequency span is calculated as the ending frequency minus the starting number of analyzer lines depends on the analyzer and how the operator has set it : 0 - 400 Hz using 800 linesAnswer = (400 - 0) / 800 = Hz / LineJack D.

8 PetersThe X Scale36 BandwidthThe Bandwidth can be defined by:(Frequency Span / Analyzer Lines) Window FunctionUniform Window Function = Window Function = Top Window Function = : 0 - 400 Hz using 800 Lines & Hanning WindowAnswer = (400 / 800) = Hz / LineNote: More discussion later on window functions for the analyzer !Jack D. PetersThe X Scale37 ResolutionThe frequency resolution is defined in the following manner:2 (Frequency Span / Analyzer Lines) Window FunctionorResolution = 2 (Bandwidth)Example: 0 - 400 Hz using 800 Lines & Hanning WindowAnswer = 2 (400 / 800) = Hz / LineJack D. PetersThe X Scale38 Using ResolutionThe student wishes to measure two frequency disturbances that are very close #1 = #2 = 30 instructor suggests a hanning window and 800 frequency span is required to accurately measure these two frequency disturbances ?

9 Jack D. PetersThe X Scale39 Using ResolutionResolution = 30 - = Hz / LineResolution = 2 (Bandwidth)BW = (Frequency Span / Analyzer Lines) Window FunctionResolution = 2 (Frequency Span / 800) = 2 (Frequency Span / 800) = 3 (Frequency Span) / 800400 = 3 (Frequency Span)133 Hz = Frequency SpanJack D. PetersThe X Scale40 Data Sampling TimeData sampling time is the amount of time required to take one record or sample of data. It is dependent on the frequency span and the number of analyzer lines being Nlines / FspanUsing 400 lines with a 800 Hz frequency span will require:400 / 800 = secondsJack D. PetersThe X Scale41 Average & Overlap Average - On Overlap Percent - 50%TR#1TR#2TR#3 FFT#1 FFT#2 FFT#3TR#1TR#2TR#3 FFT#1 FFT#2 FFT#30% Overlap50% OverlapHow long will it take for 10 averages at 75% overlap using a 800 line analyzer and a 200 Hz frequency span?

10 Jack D. PetersThe X Scale4275% Overlap ? 10 Averages 75% Overlap 800 Lines 200 HzAverage #1 = 800 / 200 Average #1 = 4 secondsAverage #2 - #10 = (4 x )Average #2 - #10 = 1 second eachTotal time = 4 + (1 x 9)Total time = 13 secondsJack D. PetersThe Y Scale43 The Y ScaleJack D. PetersThe Y Scale44 AmplitudeThe Y scale provides the amplitude value for each signal or units for the Y scale are volts is an EngineeringUnit (EU).RMSis one of three suffixes meant to confuse you !The other two are:(Peak) and (Peak - Peak) Jack D. PetersThe Y Scale45Pk-Pk (Peak - Peak)1V-1 Real sTime 12 VPk-Pk0 Magnitude Hz100 0 HzPwr Spec 1 mVX:55 VThe Peak - Peak value is expressed from the peak to peak spectrum value uses the suffix Pk-Pk to denote D.