EDM Users Guide - Crystal Instruments India Private Limited
Contents
1. 300 Orn irm 300 Or Tus D m B00 Or 300 m 1 2 Figure 4 Time Domain Waveform in CoCo A very common reading will show a spectrum peak at 100Hz with a peak value reading 1 0208 in in s Peak COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 7 CRYSTAL instruments h1 ipeckrumfi 300 0r 0 00 100 00 Hz div Figure 5 FFT Spectrum in CoCo in s Peak If somebody is interested in the RMS value of this frequency component he can change the spectrum type to RMS then the display value will be changed to 0 7218 RPM 101 ch 1 300 0rn r J A li p E 150 0rm 0 00 100 00 Hz Jdiw Figure 6 FFT Spectrum in CoCo in s RMS Similarly the user can look at Peak to Peak vDB SI and vDB US of the spectral peak Now let s introduce the concept of dB Most often spectra are shown in the logarithmic unit decibels dB Using this unit of measure It is easy to view wide dynamic ranges that is it is easy to see small signal components in the presence of large ones The decibel is a unit of ratio and is computed as follows dB 10logi0 Power Pref where Power is the measured power and Pret is the reference power COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 8 CRYSTAL instruments Use the following equation to compute the ratio in decibels from amplitude values dB 20log10 Ampl Aret where Ampl is the measured amplitude and Ar2. PAGE 30 CRYSTAL instruments Figure 30 Connecting Channel 1 to Accelerometer Case 2 Tri axis Vibration Measurement You can use either one tri axis accelerometer to measure the 3D vibration Simply connect chi ch2 and ch3 of CoCo to the X Y and Z axis of the tri axis sensor The sensor will generate signals for three channels simultaneously Figure 31 Connecting Tri axis Accelerometer Case 3 Single Channel Vibration Measurement Tacho Connect chi of CoCo to the analog output of tachometer connect ch2 of CoCo to the sensor COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 31 CRYSTAL instruments Figure 32 Connecting Tachometer and Accelerometer Case 4 Tri axis Vibration Measurement Tacho Connect ch1 of CoCo to the analog output of the tachometer Connect ch2 ch3 and ch4 of CoCo to the X Y and Z axis of the tri axis sensor Figure 33 Connecting Tachometer and Tri axis Accelerometer COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 32
3. first is when the whole time capture is long enough to cover the complete duration of the signals This can occur with short transient signals For example in a hammer test if the time capture is long enough it may extend to the point where the signal decays to zero In this case a data window is not needed The second case is when a periodic signal is sampled at such a sampling rate that is perfectly synchronized with the signal period so that with a block of capture an integer number of cycles of the signal are always acquired For example if a sine wave has a frequency of 1000Hz and the sampling rate is set to 8000Hz Each sine cycle would have 8 integer points If 1024 data points are acquired then 128 complete cycles of the signal are captured In this case with no window applied you still can get a leakage free spectrum Figure 8 shows a sine signal at 1000 Hz with no leakage resulting in a sharp spike Figure 9 shows the spectrum of a 1010 Hz signal with significant leakage resulting in a wide peak The spectrum has significant energy outside the narrow 1010 Hz frequency It is said that the energy leaks out into the surrounding frequencies COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 10 CRYSTAL instruments Figure 8 Sine spectrum with no leakage Figure 9 Sine spectrum with significant leakage Uniform window rectangular w k 1 0 Uniform is the same as no window function Hann window 21
4. in the exponential average is given by yln y n 1 1 a x n a where y n is the nth average and x n is the nth new record is the weighting coefficient Usually is defined as 1 Number of Averaging For example in the instrument if the Number of Averaging is set to 3 and the averaging type is selected as exponential averaging then a 1 3 The advantage of this averaging method is that it can be used indefinitely That is the average will not converge to some value and stay there as is the case with linear averaging The average will dynamically respond to the influence of new records and gradually ignore the effects of old records Exponential averaging simulates the analog filter smoothing process It will not reset when a specified averaging number is reached The drawback of the exponential averaging is that a large value may embed too much memory into the average result If there is a transient large value as input it may take a long time for y n to decay On the contrary the contribution of small input value of x n will have little impact to the averaged output Therefore exponential average fits a stable signal better than a signal with large fluctuations Peak Hold This method technically speaking does not involve averaging in the strict sense of the word Instead the average produced by the peak hold method produces a record that at any point represents the maximum envelope among all the component
5. 1 0 033 Time seconds Figure 12 A 1 kHz sine wave sampled at 8 kHz top and also sampled at 5 12 kHz bottom It is clear that the higher the sampling frequency the closer this digitized signal is to the true analog waveform When the sampling rate is low the digital integration will have significant calculation error For example the 5 12 kHz sampled signal is not symmetric about O volts so the integration will drift and a double integration may grow with accumulated error very fast In general you should use a sampling rate at least 10 times higher than the frequency content that is of interest in the signal when you apply numerical integration For example a motor at 3600 RPM is driving a machine through a gear box which has a 3 1 reduction gear with 36 12 gear teeth To detect the gear mesh frequency the motor speed of 60 Hz is multiplied by the number of teeth to get the gear mesh frequency of 2160 Hz To detect problems in the gearbox it is necessary to sample at 2 16 kHz or higher Think of trying to draw a single sine wave using points on a graph It will be much more clear with 10 points or more than with only two DC offset is the second type of digital integration error and can be more severe It is caused by any measurement error before integration and may result in huge amplitude errors after the integration The illustration below shows how a small measurement error in acceleration will create a constant DC offset in the acce
6. CRYSTAL instruments Vibration Data Collector Signal Analysis James Zhuge Ph D President Crystal Instruments Corporation 4633 Old lronsides Drive Suite 304 Santa Clara CA 95054 USA WWW gO ci com Part of VDC User s Manual 3 16 2009 COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 1 CRYSTAL instruments Dynamic Signal Analysis in Vibration Data Collector The CoCo 80 90 provides two different user interfaces for Dynamic Signal Analyzer and Vibration Data Collector The style and settings are different to meet industrial conventions The user has the choice to enter one of the interfaces when system is powered on The VDC user interface is specifically designed for fast data collection operation and ease of use A professional user focused on research and development can open and use the DSA functions instead of that of VDC This section explains in detail about how the signals are processed when CoCo runs in the VDC mode CoCo uses various different technologies of digital signal processing Among them the most fundamental and popular technology is based on the Fast Fourier Transform FFT The FFT transforms time domain signals into the frequency domain To perform FFT based measurements however it helps to understand the fundamental issues and computations involved This Appendix describes some of the basic signal analysis computations discusses anti aliasing and acquisition front end for F
7. FT based signal analysis explains how to use windowing functions correctly explains some spectrum computations and shows you how to use FFT based functions for some typical measurements Users should be aware of the subtle differences between a traditional dynamic signal analyzer and a vibration data collector even though they all employ the same signal processing theory General Theory of Spectral Analysis Time Domain Waveform A typical time waveform signal in analog form from the sensor such as an accelerometer velocity meter or displacement probe could take an appearance like that shown in the following picture COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 2 CRYSTAL instruments m 03 11 2009 02 51 49 Entry2 3600 RPM MATAITAI in s TRY 0 461 0 554 0 646 0 739 0 834 0 924 Time Seconds Figure 1 Time Domain Waveform In a digital instrument much the same thing is seen However it is necessary in a digital instrument to specify several parameters in order to accurately represent what is truly happening in the analog world It is important to tell the instrument what sample rate to use and how many samples to take In doing this the following are specified p Spectral Lines FBG o Figure 2 Parameter Setup in CoCo Measurement Quantity This field is required to determine what measurement quantity is to be displayed Even if the sensor is an accelerometer the CoCo device can int
8. The filter cutoff frequency is specified at 3dB attenuation To remove unwanted signals at or near DC please set up the cutoff frequency of the digital high pass filter as high as possible as long as it won t chop off useful frequency content of your interest To give an example if you are not interested in any frequency less than 20Hz then you can set the cutoff frequency to approximately 10Hz With this setting the amplitude attenuation at 20Hz will be less than 1dB Typically the lowest frequency of interest on rotating machinery will be one half the running speed of the machine If the high pass filter is set to one third the running speed the half order vibration will still be detectable COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 18 CRYSTAL instruments Readings in a Vibration Data Collector Readings Readings are overall values that represent the characteristics of the measured signals They are either calculated from time waveform or frequency spectrum In CoCo these readings can be displayed individually or together with the waveform or spectrum g overall mns ch 1 infs peak inis true ms ret mi eH m 1i C RPM 100 0 ch 1 brunt Figure 15 Onsite Measurement Display Peak and Peak Peak Peak and Peak Peak values are calculated from the time waveform Peak value is the largest signal level seen in a waveform over a period of time For sine signals the peak val
9. ctor AmpCorr is calculated based on the data window shape Step 4 Apply one of the averaging techniques to the power spectrum Sxx see below for averaging techniques Step 5 Finally take the square root of the averaged power spectrum to get final spectrum result COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 6 CRYSTAL instruments Spectrum Type Display Preference b Acceleration Spectrum Type b Acceleration Engineering Unit p Velocity Engineering Unit p Displacement Spectrum Type PRED k Displacement Engineering Unit Current Spectrum Type Peak Peak amp Current Engineering Unit dB SII P Spectrum Y Axis Type vdB U5 k Spectrum s Axis Type Figure 3 Display Preference Setup Now we come to a confusing part about the spectrum of a signal With the same time domain signal the spectrum can actually be displayed in different values This is controlled by a parameter spectrum type set in the Display Preference on the CoCo The motivation of doing so is that people may want to look at different aspect of the spectrum and give different physical interpretation to the original time signals For example from the spectrum the user may wants to know the frequency component at 1X rotating speed represented in its Peak Peak to Peak or RMS To give a practical example a 100Hz sine wave with roughly 1 0 peak in s is fed into the CoCo system The time waveform is shown below h1
10. d 10V 10V user selectable This tacho channel accepts either the tacho sensor with regular voltage output or a tacho sensor with IEPE ICP interface Typical tacho measurement specification using a PLT200 tachometer from Monarch Instrument is RPM Range 5 200 000 RPM Accuracy 0 01 of reading COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 29 CRYSTAL instruments Resolution 0 001 to 10 RPM Operating Range 2 inches to 25 feet Figure 29 Monarch PLT200 Tachometer Pocket Laser Tachometer 200 Kit includes Tachometer Remote Contact Assembly RCA Carrying Case Factory Calibration Certificate and 5 ft roll of T 5 reflective tape PLT200 has a TTL compatible Pulse Output that can be connected to the channel 1 of CoCo Typical Connections of CoCo with Accelerometers and Tachometer Several typical connections are recommended below using a four channel CoCo device If you are doing the route data collection make the same parameter setup in EDM upload the route to the CoCo and conduct the test This setup cannot be changed on CoCo If you are conducting onsite measurement set the input channels accordingly in the Input Channel and Sensor setup on CoCo Case 1 Single Channel Vibration Measurement This is the simplest measurement Connect chi of CoCo to the sensor ss COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED
11. ducer and a second engineering unit after the integration For example first the instrument must provide a means to set the sensitivity of the sensor say 100mV g in acceleration After the double integration the instrument must have the means to set the engineering unit to a unit that is compatible with the integration such as mm of displacement The CoCo instrument handles these three issues effectively so you can get reliable velocity or displacement signals from the acceleration measurement or displacement signals from the velocity measurement The CoCo hardware has a unique design to provide 130dB dynamic range in its front end measurement The signals with high dynamic range will create better results after digital integration Since such built in integration is conducted in the time domain before any other data conditioning or spectral analysis the time streams generated after the digital integration can be treated in the same way as other time streams They can be analyzed or recorded COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 15 CRYSTAL instruments CoCo also provides differentiation and double differentiation to calculate the acceleration or velocity from velocity or displacement transducers Differentiation is not as commonly used as integration It must be noticed that the displacement value derived after double integration of the acceleration s
12. e performed at the analog hardware level or at the digital level The CoCo provides a means to digitally integrate or double integrate the incoming signals The integration module fits into the very first stage after data is digitized as shown below Anag A D Spona Data Spectral Signal High Pass Filter ee Z B Converter m Conditioning m Analysis Conditioning and Integration CoCo Figure 11 Signal Processing Sequence in CoCo There are several issues to address in such implementation 1 The integration and double integration algorithm has to be accurate enough and it must find a way to reduce the effects of a DC offset A tiny initial value offset in the measurement or temperature drift before the integration may result in a huge value after single or double integration This DC effect can be removed using a high pass filter 2 The initial digital signal must have a high signal to noise ration and high dynamic range The integration process in essence will reduce the high frequency energy and elevate the low frequency components f the original signals do not have good signal to noise ratio and dynamic range the signals after integration and double integration will have too much noise to use The noise will corrupt the integrated signal 3 The instrument must be able to set two different engineering units one engineering unit for the input trans
13. ectrum in frequency domain between Fmin and Fmax f max gt Power f f min TrueRms BW Where BW noise power bandwidth of window Fmax maximum frequency of interest Fmin minimum frequency of interest Fmax and Fmin are set in the Analysis Parameters in CoCo They control the maximum and minimum frequency of interest as shown below gt Measurement Quantity b Fmin Hz Figure 17 CoCo Display Setting Fmax Obviously the true RMS will be no greater than the Overall RMS Demodulation Spectrum A useful technique for measuring and analyzing data is a process called Demodulation The demodulation process is effective for detection of high frequency low amplitude repetitive patterns that lie embedded within the time waveform These are characteristic of certain types of mechanical faults particularly rolling element bearing faults such as inner or outer race cracks and spalls that make a clicking or ringing tone as the rolling elements pass over the fault Demodulation is useful as an early warning device as it detects bearing tones before they are visible in a normal spectrum As the fault progresses towards failure the frequencies will spread out and appear more as an increase in the noise floor of the FFT spectrum as the amplitude increases The process works by extracting the low amplitude high frequency impact signals and then tracing an envelope around these signals to identify t
14. ef is the reference amplitude As shown in the preceding equations for power and amplitude you must supply a reference for a measurement in decibels This reference then corresponds to the O dB level Different conventions are used for different types of signals The vibration velocity level in dB is abbreviated VdB and is defined as p Vra f Va B 2 log y Mab 20log 10 m sec The Systeme Internationale or Sl is the modern replacement for the metric system The reference or 0 dB level of 10 9 meter per sec is sufficiently small that all our measurements on machines will result in positive dB numbers This standardized reference level uses the Sl or metric system units but it is not recognized as a standard in the US and other English speaking countries The US Navy and many American industries use a zero dB reference of 10 8 m sec making their readings higher than SI readings by 20 dB The VdB is a logarithmic scaling of vibration magnitude and it allows relative measurements to be easily made Any increase in level of 6 dB represents a doubling of amplitude regardless of the initial level In like manner any change of 20 dB represents a change in level by a factor of ten Thus any constant ratio of levels is seen as a certain distance on the scale regardless of the absolute levels of the measurements This makes it very easy to evaluate trended vibration spectral data 6 dB increases always indicate doubling o
15. egrate it digitally into velocity or displacement Fmax This field defines the maximum frequency of interest for analysis The sampling rate of the analog digital A D digitizer will be determined based on this parameter Fmin This is the low frequency cut off filter that will be applied in the frequency domain for spectral analysis Block Size Spectral Lines The block size is usually defined in blocks of two binary to the power of 10 or more Block size of 2 is 1024 2 is 2048 2 is 4096 etc The block size and Fmax will determine the total time period of each sampling block for frequency analysis A larger block size for the same frequency band will increase the accuracy of the measurement Immediately after the signal is digitized it will also go through e Low pass filters to eliminate any high frequencies that are not wanted COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 3 CRYSTAL instruments e High pass filters to eliminate DC and low frequency noise that are not wanted Additionally the integration of the signal provides velocity or displacement from an accelerometer or a displacement from a velocity pickup Traditional signal analyzers have a drawback of dynamic range in the digital domain and some argue that the analog integration is superior to that of digital The situation is greatly improved due to the very high dynamic range technology in the CoCo With more than 130dB dynamic range i
16. er must pay attention to the sensitivity of the sensor when they source it Select an accelerometer by matching its output for expected acceleration levels Don t crowd the full scale specifications Allow a margin for unexpectedly large accelerations Using only the lower 2096 of an accelerometer s response range will ensure ample margins for unpredicted COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 28 CRYSTAL instruments overloads After you select an accelerometer that can survive predicted worst case shock limits compute the sensor s output voltage At a sensitivity of 10 mV g for example an accelerometer that encounters a 100 g shock will produce a 1 V peak signal This is well wthin the 10V range of CoCo input channels However it must be noted that this definition is accounted in the acceleration domain To transform the specification from the velocity domain the frequency factor has to be accounted Integral Electronics Piezoelectric IEPE Sensor IEPE accelerometers operate from a low cost constant current power source over a two wire circuit with signal power carried over one wire and the other wire serving as ground The cable can be ordinary coaxial or ribbon wire Low noise cable is not required Constant current to operate the accelerometer comes from a separate power unit or it may be incorporated inside a readout instrument such as an FFI analyzer or Data Collector Integrated electronic acceler
17. f the magnitudes Data Window Selection Leakage Effect Windowing of a simple signal like a sine wave may cause its Fourier transform to have non zero values commonly called leakage at frequencies other than the frequency of this sine This leakage effect tends to be worst highest near sine frequency and least at frequencies farthest from sine frequency The effect of leakage can easily be depicted in the time domain when a signal is truncated As shown in the picture after data windowing truncation has distorted the time signal significantly hence causing a distortion in its frequency domain COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 9 CRYSTAL instruments Actual Input l Windowed Input Nor Periodic Assumed Inout h ra l i l Figure 7 Illustration of a non periodic signal resulting from sampling If there are two sinusoids with different frequencies leakage can interfere with the ability to distinguish them spectrally If their frequencies are dissimilar then the leakage interferes when one sinusoid is much smaller in amplitude than the other That is its spectral component can be hidden or masked by the leakage from the larger component But when the frequencies are near each other the leakage can be sufficient to interfere even when the sinusoids are equal strength that is they become undetectable There are two possible scenarios in which leakage does not occur The
18. hem as repetitions of the same fault COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 21 CRYSTAL instruments The resulting spectrum with the low frequency data removed will now clearly show the high frequency impact signals and harmonics The high frequency signals that demodulation aims to extract are do not travel well through large structures therefore extra care must be taken to ensure the accelerometer is setup correctly Ensure that e The accelerometer is mounted close to the fault source with the shortest direct path through the structure to the accelerometer e The accelerometer is well coupled using either stud mounting or a very strong magnet on bare metal A handheld probe or stinger is not recommended e The accelerometer mounting is consistent between visits If not a trend plot of overall RMS values will be meaningless The demodulation process can be graphically described in the following flow chart Acceleration Signal High pass filter Envelope Low pass amp decimation FFT Analysis Figure 18 Demodulation Process Flow Chart Below is a depiction of an acceleration time waveform with a repetitive high frequency component Because of the large difference in amplitude and frequency a very low amplitude high frequency signal could be overlooked during routine vibration analysis Figure 19 Acceleration Time Waveform with Fault The high pass filter removes the low frequency componen
19. ignal is not the same as that directly measured by a proximity probe A proximity probe measures the relative displacement between a moving object such as a rotor shaft to the fixed coordinates seated by the probe mounted to the case The accelerometer and its integration value can only measure the movement of the moving object against the gravity field Sensor Considerations Accelerometer signals that are non dynamic non vibratory static or quasi static in nature low acceleration of an automobile or flight path of a rocket are typically integrated in the digital domain downstream of the signal conditioner Piezoelectric and IEPE accelerometers are commonly used to measure dynamic acceleration and therefore dynamic velocity and displacement They should not be used to measure static or quasi static accelerations velocities or displacements because the IEPE includes analog high pass filtering in the sensor conditioning that cuts out any low frequency signal At low frequencies approaching O Hz piezoelectric and IEPE accelerometers cannot with the accuracy required for integration represent the low frequency accelerations of a test article When this slight inaccuracy is integrated in order to determine velocity and displacement it becomes quite large As a result the velocity and displacement data are grossly inaccurate A piezoresistive or variable capacitance accelerometer is a better choice for low frequency signals and for integrat
20. ion These types of sensors measure acceleration accurately at frequencies approaching O Hz Therefore the integration calculation of velocity and position can be used to produce accurate results Calculation Errors in Digital Integration Two types of calculation errors can be introduced by parameters chosen for digital integration low sampling rate and DC offset The sampling rate of a signal must be high enough so that the digital signal can accurately depict the analog signal shape According to the Nyquist sampling theorem as long as the sampling speed is more than twice of the frequency content of the signals before the integration the integration results should be acceptable This is not true Satisfying the Nyquist frequency only ensures an accurate estimate of the highest detectable frequency of a measurement It will not provide an accurate representation of the signal shape Integration error can still occur of a signal is sampled at more than twice the signal frequency The figure below shows a 1kHz sine wave sampled at 8kHz and 5 12kHz COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 16 CRYSTAL instruments 8 SI60013 BLOCK ch1 0 024 0 025 0 026 0 027 0 028 0 029 0 030 0 031 0 032 0 033 Time seconds Signals SIG0014 BLOCK ch1 4bx e u BM b Begin 0 0240 End 0 0330 amp SIG0014 BLOCK ch1 1 000 0 500 0 0004 0 500 1 000 0 024 0 026 0 028 0 029 0 03
21. k w k 0 5 0 5 cos N 1 Flattop window aur COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 11 CRYSTAL instruments 21k 4r k 67k w k 1 1 93 COS 1 29 cosy 0 388 cosa fork 0 N 1 0 032 Mi cos The term Hanning window is sometimes used to refer to the Hann window but is ambiguous as it is easily confused with Hamming window If a measurement can be made so that no leakage effect will occur then do not apply any window in the software select Uniform As discussed before this only occurs when the time capture is long enough to cover the whole transient range or when the signal is exactly periodic in the time frame If the goal of the analysis is to discriminate two or multiple sine waves in the frequency domain spectral resolution is very critical For such application choose a data window with very narrow main slope Hanning is a good choice In general we recommend Hanning window in VDC applications When you are extremely sensitive to the accuracy of peak estimation at certain frequency choose Flattop window It will give you the best estimation for the frequency components measured at a rotating machine or reciprocating machine Averaging Techniques Averaging is widely used in spectral measurements It improves the measurement and analysis of signals that are purely random or mixed ra
22. lap means 25 of the old data will be used for each spectral processing 0 overlap means that no old data will be reused Overlap processing can improve the accuracy of spectral estimation This is because when a data window is applied some useful information is attenuated by the data window on two ends of each block However it is not true that the higher the overlap ratio the higher the spectral estimation accuracy For Hanning window when the overlap ratio is more than 50 the estimation accuracy of the spectra will not be improved Another advantage to apply overlap processing is that it helps to update the display more quickly Built in Digital Integration And Filtering Introduction to Digital Integration Ideally a measurement is made using a sensor that directly measures the desired quantity For example an accelerometer should be used to measure acceleration a laser velocimeter or velocity pickup should be used to measure velocity and a linear voltage displacement transducer LVDT should be used to measure position However since position velocity and acceleration are related by the time derivatives it is possible to measure an acceleration signal and then compute the velocity and position by mathematical integration Alternatively COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 14 CRYSTAL instruments you can measure position and compute velocity and acceleration by differentiating The integration can b
23. leration integrated to compute velocity and result in a drift and eventually an infinitely large magnitude of displacement after double integration COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 17 CRYSTAL instruments Displacement Velocity a Y Acceleration Figure 13 A small error in acceleration results in a DC offset in velocity and a huge drift in displacement Of course the computed velocity and displacement signals are unrealistic They are artifacts of the integration errors In order to remove such a problem caused by inaccurate measurement and digital integration a high pass filter can be applied before or after the integration It should be noted that the high pass filter will distort the waveform shape to some extent because it alters the low frequency content of the signal However this effect must be tolerated if numerical integration is used Digital High Pass Filter The most effective way to remove the DC drift effect as described above is to apply a high pass digital filter to the continuous time streams In CoCo a unique algorithm is realized so that even the data is sampled at high rate the high pass filter can still achieve very low cutoff frequency The high pass filter parameter can be entered in the channel table Input Channel amp Sensor Setup che Sensor Input Mode Hi PassFltr accel 612 mwito J Ere JC Single i Figure 14 CoCo Input Channel Setup Table
24. n the front end digital integration can achieve excellent accurate results The Fourier Transform CoCo fully utilizes FFT frequency analysis methods and various real time digital filters to analyze measurement signals The Fourier Transform is used to convert quantities amplitude vs time in the time domain time waveform to amplitude vs frequency in the frequency domain FFT spectrum usually derived from the Fourier integral of a periodic function when the period grows without limit often expressed as a Fourier transform pair In the classical sense a Fourier transform takes the form of X f f secet dt Where x t continuous time waveform f frequency variable j complex number X f Fourier transform of x t As the theory of Jean Baptiste Fourier states All waveforms no matter how complex can be expressed as the sum of sine waves of varying amplitudes phase and frequencies In the case of rotating machinery vibration this is most certainly true A machine s time waveform is predominantly the sum of many sine waves of differing amplitudes and frequencies The challenge is to break down the complex time waveform into the components from which it is made Mathematically the Fourier Transform is defined for all frequencies from negative to positive infinity However the spectrum is usually symmetric and it is common to only consider the single sided spectrum which is the spectrum from zero to positive infinity For discrete
25. ndom and periodic Averaged measurements can yield either higher signal to noise ratios or improved statistical accuracy Typically three types of averaging methods are available in DSA products They are Linear Averaging Exponential Averaging and Peak Hold Linear Averaging In linear averaging each set of data a record contributes equally to the average The value at any point in the linear average in given by the equation Sum of Records A d verage N N is the total number of the records The advantage of this averaging method is that it is faster to compute and the result is un biased However this method is suitable only for analyzing short signal records or stationary signals since the average tends to stabilize The contribution of new records eventually will cease to change the value of the average Usually a target average number is defined The algorithm is made so that before the target average number reaches the process can be stopped and the averaged result can still be used COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 12 CRYSTAL instruments When the specified target averaging number is reached the instrument usually will stop the acquisition and wait for the instruction for another collection of data acquisition Exponential Averaging In exponential averaging records do not contribute equally to the average A new record is weighted more heavily than old ones The value at any point
26. ometers are available under several different trademark names such as ICPe PCB Piezotronics Isotrone Endevco Delta Trone B amp K and Piezotrone Kistler to mention a few CoCo IEPE input mode provides 4 7mA constant current for each channel The main advantage of low impedance operation is the capability of IEPE accelerometers to operate continuously in adverse environments through long ordinary coaxial cables without increase in noise or loss of resolution Cost per channel is less since low noise cable and charge amplifiers are not required The main limitation involves operation at elevated temperatures above 325 F The signal conditioning circuitry in the instrument box usually has high pass and low pass filter When IEPE is selected in the CoCo the high pass filter cutoff frequency is set fixed at 0 3 Hz 3dB and 0 7 Hz 0 1dB IEPE sensor will not be able to measure the DC or quasi constant acceleration signal This is usually not a problem to the acceleration measurement because in our world no objects can keep moving at constant acceleration Tachometer Tachometer is used to measure the rotating speed of the rotating machines There are many kinds of tachometers that can be chosen for CoCo In general as long as the tachometer claims that it output analog pulse signal it will be able to interface to the CoCo input channel The first analog input channel can be configured as a tachometer measurement Threshol
27. ought of as a smoothing function This smoothing can be represented by an effective filter shape of the window i e energy at a frequency in the original data will appear at other frequencies as given by the filter shape Since time domain windows can be represented as a filter in the frequency domain the time domain windowing can be accomplished directly in the frequency domain Because creating a data window attenuates a portion of the original data a certain amount of correction has to be made in order to get an un biased estimation of the spectra In linear spectral analysis an Amplitude Correction is applied COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 5 CRYSTAL instruments Spectrum A spectrum in CoCo in VDC mode is calculated based on a few steps including data window FFT amplitude scaling and averaging You can extract the harmonic amplitude by reading the amplitude values at those harmonic frequencies in a spectrum To compute the spectrum the instrument will follow these steps Step 1 A window is applied to the time waveform x k w k x k Where x k is the original data and x k is the data used for a Fourier transform Step 2 The FFT is applied to x k to compute Sx N 1 Sx 2 x k e sere n 0 Next the periodogram method is used to compute the spectra with amplitude correction using Sx step 3 Calculate the Power Spectrum Sxx Sx Sx AmpCorr The fa
28. records The equation for a peak hold is y n MAX x n JD Peak hold is useful for maintaining a record of the highest value attained at each point throughout the sequence of ensembles Peak Hold is not a linear math operation therefore it should be used carefully It is acceptable to use Peak Hold in auto power spectrum measurement but you would not get meaningful results for FRF or Coherence measurement using Peak Hold Peak hold averaging will reset after a specified averaging number is reached COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 13 CRYSTAL instruments Overlap Processing To increase the speed of spectral calculation overlap processing can be used to reduce the measurement time The diagram below shows how the overlap is realized Signal Captured in the Time Domain 2 a Acquired Signal Data Transformed into FFT Frames No Overlap Processing Acquired Signal Post Processed with Overlap FFTs 1024 Samples 1024 Samples 1024 Samples 1024 Samples FFTs Overlap Samples Overlap Interval Samples 1024 Samples Figure 10 Illustration of overlap processing As shown in this picture when a frame of new data is acquired after passing the Acquisition Mode control only a portion of the new data will be used Overlap calculation will speed up the calculation with the same target average number The percentage of overlap is called overlap ratio 25 over
29. sampled signals this can be expressed as N 1 X k 2 x k g Jane n 0 COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 4 CRYSTAL instruments Where x k samples of time waveform n running sample index N total number of samples or frame size k finite analysis frequency corresponding to FFT bin centers X k discrete Fourier transform of x k In CoCo a Radix 2 DIF FFT algorithm is used which requires that the total number of samples must be a power of 2 total number of samples in FFT 2 where m is an integer The Fourier Transform assumes that the time signal is periodic and infinite in duration When only a portion of a record is analyzed the record must be truncated by a data window to preserve the frequency characteristics A window can be expressed in either the time domain or in the frequency domain although the former is more common To reduce the edge effects which cause leakage a window is often given a shape or weighting function For example a window can be defined as w t g t T 2 lt t lt T 2 0 elsewhere where g t is the window weighting function and T is the window duration The data analyzed x t are then given by x t w t x t where x t is the original data and x t is the data used for spectral analysis A window in the time domain is represented by a multiplication and hence is a convolution in the frequency domain A convolution can be th
30. t of the signal below COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 22 CRYSTAL instruments Figure 20 Acceleration Time Waveform after High Pass Filter The next step in the process is enveloping which lowers the frequency of the signal to that of the repetitive element MII IISA A Figure 21 Signal after Enveloping The final step is to process the resulting time waveform signal into a frequency spectrum Since the signal has been altered by removal of low frequencies and enveloping it is referred to as the Demodulated Spectrum COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 23 CRYSTAL instruments liu Figure 22 Demodulated Spectrum A Bearing Detection Example of Demodulation The following examples show CoCo screens in VDC mode being used to analyze a rolling element bearing with a slight defect RBM 100 0 200 0 ZU nm ERE Y 0 00 100 0rn 00 m 300 Or 400 r ormichi Wr awe aM APM 100 ED m Em LL UBI C Masc anl i 100m 0 00 700 00 Meldi Figure 23 CH1 Time Waveform and FFT with slight bearing defect Spectrum The following is the same signal with the demodulation spectrum on the lower trace COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 24 CRYSTAL instruments ormichij W awe omm 0 30 Sidiv ENT PM 100 0 mee edm eu m 16 0m 12 0m aim lanl Puh Loh di k Ju or TT UN
31. the sensor and the machine surface the more accurate your high frequency response will be High frequency response is based on the sensor specified as well as the method of attachment together with a system Stud mounted sensors are often able to utilize the entire frequency range that the sensor specified Conversely a probe tip mounted sensor has very little surface area contact with the machine surface and offers very little high frequency accuracy above 500Hz 30 000CPM The picture below shows the frequency response of a typical accelerometer It might be Surprising to you that how inaccurate the measurement can be at different frequency range COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 27 CRYSTAL instruments 1 30 f lower frequency limit f calibration frequency 440 f resonance frequency 1 05 1 00 0 95 0 90 0 71 f 2f 3f f 0 2f 0 5f f f 0 3f Figure 27 Frequency Response of a Typical Accelerometer The following chart offers a general guideline for the range of mounting techniques available and the corresponding high frequency response expectations Curved Surface Quick Flat Magnet with Magnet Disconnect with Target Adhesive Mount Stud Mount E Tip ad eme H H NEM CN ACT M Pn 30 000 RPM 120 000 CPM 390 000 CPM 600 000 CPM _ 500 000 CPM Lada Figure 28 Accelerometer Mounting vs Maximum Frequency Response Choose the Sensitivity The us
32. ue is always 1 414 times the RMS value of the signal level For non sine signals this formula will not apply The Peak Peak value is the difference between the maximum and minimum signal levels over a period of time For a pure sine wave the Peak Peak level is two times the peak signal level and 2 828 times the RMS value of the signal level For a non sine signal this formula will not apply COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 19 CRYSTAL instruments peak Figure 16 Illustration of Time Domain Peak Peak Peak If accelerometer is used and the Peak or Peak Peak reading is displayed for velocity or displacement the digital integration will be applied to the time waveform continuously before the Peak or Peak Peak detection Overall RMS In CoCo the overall RMS is calculated based on the spectrum in frequency domain across all of the effective frequency range i e from DC to maximum analysis frequency range f5 0 45 gt Power f BW overallrms Where BW noise power bandwidth of window Fa analysis frequency band Fs sampling frequency band 0 45 the ratio of Fa According to Parseval s theorem such overall RMS is equivalent to that calculated in the time domain COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 20 CRYSTAL instruments True RMS In CoCo the true RMS is calculated based on the sp
33. ustrial Applications Accelerometers are widely used in the vibration data collection By using the feature of CoCo s very high dynamic range 130dB the acceleration signals can also be accurately integrated into velocity and displacement signals There are a wide range of accelerometers to choose in the market Many of them are IEPE mode In most of applications we recommend using IEPE accelerometers There are three types of accelerometers in the market 1 accelerometers used for cost sensitive market such as PDAs electronic toys automotive airbags or laptop computers These are MEMS based sensors that cost a few dollars each They do not fall into our categories 2 The accelerometers used for testing and measurement purpose The US manufacturers like PCB Endevco and Dytran all focus on such applications 3 The accelerometers used for machine vibration or called industrial applications US manufacturers include Wilcoxon CTC and so on Most often the vibration data collector asks for the sensors from the last category These sensors are relatively large in size rugged less accurate and less expensive than those from the category 2 Mounting Accelerometers Care must be taken to insure the appropriate accuracy across the whole frequency range The accuracy of your high frequency response is directly affected by the mounting technique that you select for the sensor In general the greater the mounted surface area contact between
34. y Peet 4 irm 25 00 Hzldiw Figure 24 CH1 Time Waveform and Demodulation Spectrum with slight bearing defect chij Spectrum As the bearing deteriorates the defect typically becomes larger and generates a wider range of frequencies as the rolling elements pass over it The following is the demodulation spectrum with slightly deteriorated bearing 120 0m 3n m EU rn 30 0rn 0 00 30 m 0 r 30 m ormich1 VW awe 30 Stdiw fA 100 0 175m b m 12 5m REY Om chij Spectrum j Ut f og hae A ld Jus ks Mal ova T LL lan t ul 2 A Zo 00 Hz Ji nv Figure 25 CH1 Time Waveform and Demodulation Spectrum with slightly deteriorated bearing As can be seen in the screen below the standard FFT spectrum shows the relatively high first order amplitude but only shows an elevated noise floor in the higher frequencies v s COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 25 CRYSTAL instruments RPM 100 0 300 0rn 50 m 0 00 150 0m 300 Orr 450 m chi arm i i WW awe 0 10 Sidi SPI 100 0 P JU Urn 50m 60 0rm 45 r 300m ERU Em Nm ipeckrum c 100 00 e FER T Figure 26 CH1 Time Waveform and FFT Spectrum with deteriorated bearing COPYRIGHT 2009 CRYSTAL INSTRUMENTS ALL RIGHTS RESERVED PAGE 26 CRYSTAL instruments Using Accelerometers and Tachometer Accelerometers for Ind
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