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National Instruments Order Analysis Toolset, User Manual

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Glossary

LabVIEW Order Analysis Toolset User Manual

G-2

ni.com

F

FFT

Fast Fourier transform.

fundamental component

Portion of a signal whose frequency is at the fundamental frequency.

G

Gabor coefficient

The result of Gabor transform.

Gabor expansion

The inverse Gabor transform used on Gabor coefficients to recover a time 
domain input signal.

Gabor transform

One of the invertible joint time-frequency transforms.

H

harmonic

Frequencies that are integer or fractional multiples of a fundamental 
frequency.

L

LMSE

Least mean square error.

N

Nyquist frequency

Half the sampling frequency. Any analog frequency component above 
the Nyquist frequency will, after sampling, be converted, or aliased, to a 
frequency below the Nyquist frequency. 

See also

 

aliasing

 

and

 

anti-aliasing 

filter

.

O

order

A harmonic related to the rotational speed of a machine.

order analysis

The analysis of harmonics related to rotational speed. The application of 
harmonic analysis to rotating machinery

Summary of Contents for Order Analysis Toolset

Page 1: ...LabVIEW TM Order Analysis Toolset User Manual LabVIEW Order Analysis Toolset User Manual August 2003 Edition Part Number 322879B 01...

Page 2: ...rmany 49 0 89 741 31 30 Greece 30 2 10 42 96 427 India 91 80 51190000 Israel 972 0 3 6393737 Italy 39 02 413091 Japan 81 3 5472 2970 Korea 82 02 3451 3400 Malaysia 603 9131 0918 Mexico 001 800 010 079...

Page 3: ...ccident actions of third parties or other events outside reasonable control Copyright Under the copyright laws this publication may not be reproduced or transmitted in any form electronic or mechanica...

Page 4: ...sis of Rotating Machinery 1 2 System Requirements 1 3 Installation 1 3 Example VIs 1 4 Acquiring Data for Example VIs 1 4 Configuring DAQ Hardware Used with Examples 1 4 Acquire Data Analog Tach VI 1...

Page 5: ...8 Calculating Waveform Magnitude 3 10 Chapter 4 Resampling Based Order Analysis LabVIEW Order Analysis Toolset Resampling Method 4 1 Determining the Time Instance for Resampling 4 2 Resampling Vibrat...

Page 6: ...learn about how to use the LabVIEW Order Analysis Toolset Refer to Chapter 1 Introduction to the LabVIEW Order Analysis Toolset for information about the example VIs If you want to learn more about t...

Page 7: ...ters that you should enter from the keyboard sections of code programming examples and syntax examples This font is also used for the proper names of disk drives paths directories programs subprograms...

Page 8: ...ther time or rotational speed Extraction of the order components from the original noise or vibration signal Measurement of the magnitude and phase of any order component as a function of rotational s...

Page 9: ...s for the Analysis of Rotating Machinery Order analysis is a powerful tool for analyzing rotating machinery when the rotational speed might change over time However to successfully use the LabVIEW Ord...

Page 10: ...isable any automatic virus detection programs before you install After installation check your hard disk for viruses and enable any virus detection programs you disabled Windows 2000 NT XP Complete th...

Page 11: ...have a Boolean control named Data Source The Data Source control has two choices Example and DAQ When you choose Example the VI uses prerecorded data generated during a fan run up as the data source W...

Page 12: ...out the Acquire Data with PXI 4472 and TIO VI Acquire Data Analog Tach VI In analog tachometer examples setting Data Source to DAQ and clicking the Run button opens the Acquire Data Analog Tach VI The...

Page 13: ...Figure 1 2 Figure 1 2 Acquire Data Analog Tach VI Acquisition Tab The Acquisition tab shown in Figure 1 2 allows you to acquire and observe data Click the Acquire button to acquire data Continue to co...

Page 14: ...e the DAQ devices Use one of the counters on a TIO device to receive TTL compatible tachometer pulses Use the controls in the TIO Board Setting Digital Tach Signal section of the Configuration tab to...

Page 15: ...th PXI 4472 and TIO VI Acquisition Tab The Acquisition tab shown in Figure 1 4 allows you to acquire and observe data Click the Acquire button to acquire data Continue to configure the data acquisitio...

Page 16: ...diagnosing heart problems You can use order analysis to study design and monitor rotating machinery By measuring and analyzing sound or vibration signals generated by a system with rotational compone...

Page 17: ...ysis for rotating machinery Figure 2 1 shows the relationship between frequency and order spectra Figure 2 1 Order and Frequency Domain Display of a Shaft Rotating at 3 000 rpm The top graph in Figure...

Page 18: ...lts in a spectral peak at the first order Misalignment or bending of the shaft generates a large second order Oil whirl might lead to strong fractional orders Gears belts and blades might enhance high...

Page 19: ...ysis is effective only when the rotational speed remains constant Effect of Rotational Speed on Order Identification The ability to make a reliable identification of individual orders from the convent...

Page 20: ...d on the fast Fourier transform FFT The upper right plot in Figure 2 3 shows the frequency time spectral map computed from the short time Fourier transform STFT with a 1 024 point Hanning window Becau...

Page 21: ...change in the frequency and amplitude of the signal The faster the frequency changes the wider the overall frequency bandwidth becomes as measured from the power spectrum Figure 2 4 illustrates a con...

Page 22: ...e overall frequency bandwidth of the signal whose frequency increases with time in Figure 2 5 is much wider than that of the signal whose frequency is constant in Figure 2 4 When frequency or amplitud...

Page 23: ...onal speed increases both the fundamental frequency bandwidth and the frequency bandwidths of related orders widen causing orders to overlap Whether you can separate nearby orders in a power spectrum...

Page 24: ...annot control the rotational speed of the system well or the system is not allowed to run at the critical rotational speed for a sufficient length of time Order Analysis An important goal of order ana...

Page 25: ...bor expansion you cannot reconstruct the general STFT using an inverse Fourier transform You can compute the Gabor transform by either STFT or windowed Fourier transform However to ensure reconstructi...

Page 26: ...r expansion the reconstructed data is longer than the original data To avoid the reconstructed data being longer than the original data consider the signal as periodic and use wrap padding shown in Fi...

Page 27: ...out the Gabor transform and the Gabor expansion Refer to Chapter 3 Gabor Transform Based Order Tracking for information about how the LabVIEW Order Analysis Toolset uses a method based on the Gabor tr...

Page 28: ...r or a multiplied tachometer signal to trigger the analog to digital conversion which ensures a sampling process spaced equally in the rotation angle The hardware solution requires additional hardware...

Page 29: ...he spectrum of angle samples Figure 2 10 Spectrum of Angle Samples In Figure 2 10 the Angle Samples plot shows the signal sampled at a constant angle interval The Order Spectrum plot shows the order s...

Page 30: ...onents change as the rotational speed changes you can consider the rotational speed and the frequency of order components to remain constant in a relatively short time interval The adaptive filter met...

Page 31: ...ise or vibration signal Reconstruct the desired order components in the time domain Overview of Gabor Order Analysis The Gabor transform can give the power distribution of the original signal as the f...

Page 32: ...hite curves have magnitudes larger than the magnitudes in local neighborhoods off the curves The white curves indicate the order components and are referred to as order curves From the frequency time...

Page 33: ...performing Gabor expansion f Calculate the waveform magnitude and phase Refer to the Important Considerations for the Analysis of Rotating Machinery section of Chapter 1 Introduction to the LabVIEW O...

Page 34: ...some coefficients in the neighborhood You must include the coefficients in the neighborhood when selecting the order component Constant frequency bandwidth and constant order bandwidth are two ways t...

Page 35: ...er curves select a subset of the initial Gabor coefficient array The subset of the initial Gabor coefficient array contains only the coefficients in the neighborhood of the selected order curves You c...

Page 36: ...number of elements set to TRUE determines the bandwidth of the passband Extracting Orders Figure 3 4 illustrates the order extraction and signal reconstruction process Figure 3 4 Gabor Coefficients Fi...

Page 37: ...3 5 Original Signal and Extracted Order Component Unlike the reverse discrete Fourier transform the Gabor expansion in general is not a one to one mapping A Gabor coefficient is the subspace of a two...

Page 38: ...outside the passband the magnitude of the reconstructed signal is no longer zero Instead the magnitude does have some certain value However the value of the magnitude quickly decreases as the frequenc...

Page 39: ...ar to the rpm time function shown in Figure 3 7 b In Figure 3 7 a notice the horizontal white lines The horizontal white lines indicate the large power around the resonance frequencies The physical ch...

Page 40: ...ral map and the order rpm spectral map you can clearly and efficiently observe all the order components in the entire time and rpm ranges Calculating Waveform Magnitude The reconstructed time waveform...

Page 41: ...to complete the following tasks Resample even time space samples to even angle spaced samples Obtain magnitude and phase information for each order Figure 4 1 illustrates the resampling based order a...

Page 42: ...r magnitudes and phases if necessary Refer to the Important Considerations for the Analysis of Rotating Machinery section of Chapter 1 Introduction to the LabVIEW Order Analysis Toolset for informatio...

Page 43: ...me sequence for a smaller angle The transfer function of the CIC filter is given by the following equation where L is the interpolation factor and n is the order The CIC filter has the advantage of on...

Page 44: ...le spaced samples you must be able to calculate the value of the vibration signal at any time instance According to the Nyquist sampling theorem you can exactly reconstruct the signal for all time ins...

Page 45: ...s lower that the previous sampling rate The LabVIEW Order Analysis Toolset uses a digital adaptive interpolation filter to complete the entire resample process The bandwidth of the adaptive interpolat...

Page 46: ...nsated signal Figure 4 4 Slow Roll Compensation The LabVIEW Order Analysis Toolset can perform the vector based slow roll compensation on order magnitudes and phases The toolset performs slow roll com...

Page 47: ...al speed as a function of time during the data acquisition process The LabVIEW Order Analysis Toolset uses a digital differentiator to calculate the rotational speed The tachometer processing VIs buff...

Page 48: ...wing equation you can present rotational speed as the first derivative of k While the time interval between pulses varies with the rotational speed the cumulative angle increment remains constant Calc...

Page 49: ...ate the rotational speed also increases The LabVIEW Order Analysis Toolset can automatically adjust the order of the differentiator according to the number of pulses in the buffer Automatically adjust...

Page 50: ...In Figure 5 2 the dotted line represents the results of calculating the rotational speed with no averaging The solid line in Figure 5 2 represents the results of calculating the rotational speed avera...

Page 51: ...mplementation was an open research topic until Bastiaans discovered the relationship between the Gabor expansion and the short time Fourier transform STFT in the early 1980s Over the years many differ...

Page 52: ...ansform in Equation A 2 contains redundancy from a mathematical point of view However the redundancy in Equation A 2 provides freedom for the selection of better window functions h k and k Notice that...

Page 53: ...or LMSE For the LMSE solution the Euclidean distance between the dual functions is minimum as given by the following equation where denotes the matrix form of Equation A 4 When the error is small and...

Page 54: ...t exist For example the following equation represents a modified two dimensional function where m n denotes a binary mask function whose elements are either 0 or 1 Applying the Gabor expansion to the...

Page 55: ...the Gabor expansion from Equation A 1 and the Gabor transform from Equation A 2 in matrix form as shown in the following equations where H denotes the analysis matrix and G denotes the synthesis matri...

Page 56: ...est in terms of the LMSE to the masked Gabor coefficients C The masked Gabor coefficients are the desirable Gabor coefficients The case of k h k usually implies considerable over sampling which result...

Page 57: ...er Order Tracking Methods SAE Noise and Vibration Conference and Exposition Traverse City MI April 30 through May 3 2001 Gade S H Herlufsen H Konstantin Hansen and H Vold Characteristics of the Vold K...

Page 58: ...ted Support Options Contact NI engineers and other measurement and automation professionals by visiting ni com support Our online system helps you define your question and connects you to the experts...

Page 59: ...ency less than half the sampling frequency See also anti aliasing filter and Nyquist frequency anti aliasing filter Analog lowpass filters used before analog to digital conversion to filter out the fr...

Page 60: ...int time frequency transforms H harmonic Frequencies that are integer or fractional multiples of a fundamental frequency L LMSE Least mean square error N Nyquist frequency Half the sampling frequency...

Page 61: ...k over sampling Occurs in a Gabor transform when the window length is greater than the window shift step In over sampling the number of Gabor coefficients cm n is more than the number of original dat...

Page 62: ...1 4 guidelines for 1 4 diagnostic resources C 1 displaying spectral maps 3 8 documentation conventions used in the manual vii getting started vii how to use this manual vii online library C 1 related...

Page 63: ...Up Kit 1 1 Order Analysis Toolset using in analysis of rotating machinery 1 2 orders definition of 2 2 over sampling definition of A 2 P phone technical support C 1 processing tachometer signals 5 1 c...

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