FFT Setup - Revision history

Charles: /* Navigation */

2024-07-02T23:58:27Z

Navigation

← Older revision		Revision as of 23:58, 2 July 2024
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	:[[Plot Tabs]]		:[[Plot Tabs]]

			[[Benchmarking]]

	[[Troubleshooting]]		[[Troubleshooting]]

Charles: /* Aliasing Filters */

2024-06-06T02:19:51Z

Aliasing Filters

← Older revision		Revision as of 02:19, 6 June 2024
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	Always check this before buying a hardware package.		Always check this before buying a hardware package.

			== Navigation ==

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			:[[Setup Tab]]

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			[[Troubleshooting]]

			[[Custom Data Processing]]

			[[FFT Setup]]

Charles: /* Recommend Sample Rate */

2024-06-04T04:57:21Z

Recommend Sample Rate

← Older revision		Revision as of 04:57, 4 June 2024
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	<math>BW=</math>Δ<math>f \times WF=\frac{F_{MAX} \times WF}{LOR}</math>		<math>BW=</math>Δ<math>f \times WF=\frac{F_{MAX} \times WF}{LOR}</math>

	== ~~Recommend Sample Rate~~ ==		== Recommended Settings ==

	The first question to ask yourself is, will I be able to repeat the measurement if I discover later that the sample rate was not high enough? If the answer is no, or "yes but I will have to answer some difficult questions", use a higher sample rate.		The first question to ask yourself is, will I be able to repeat the measurement if I discover later that the sample rate was not high enough? If the answer is no, or "yes but I will have to answer some difficult questions", use a higher sample rate. Second, how well do you understand the potential problems? If you do not already know exactly what you are looking for, start by taking a measurement with a very high sample rate, check for unexpected high frequency content, and then lower the sample rate if that makes it easier to work with the data. These days, laptop memory and processing capacity allows for far higher sample rates and measurement durations, and there are benefits to taking advantage of both.

	These days, memory and processing allowing for both far higher sample rates and measurement durations, and there are advantages to taking advantage of both. We recommend taking at least one initial measurement at the maximum sample rate to check for unexpected high frequency vibration. Note that integrating measured acceleration once to get velocity, and twice to get displacement, will effectively filter out high frequency vibration. So, when you ~~are performing this~~ check, look at acceleration data. ~~Likewise~~, vibration amplitudes (and frequencies) are never steady over time, and the time frame over which they change can be anywhere from seconds to years, depending on the cause of the variation. Typically, you will want to measure for somewhere between several minutes and several hours.		Note that integrating measured acceleration once to get velocity, and twice to get displacement, will effectively filter out high frequency vibration. So, when you check for high frequency vibration, look at acceleration data.

			High frequency vibration may not be real. For example, you may be measuring an internal resonance of the sensor, or the mount resonance. For a magnet mounted accelerometer, the mounted natural frequency will depend on things like paint thickness, surface roughness, magnet strength, accelerometer and magnet weight, cleanliness of the magnet and the care with which it is placed.

			High frequency vibration may not be relevant. At high frequencies, the mode shape has a short spacing between nodes. That is, even apparently rigid structural components will wobble like jelly, so the amplitude can change significantly just by moving the sensor slightly, and that is not even accounting for mounting issues.

			Reasons to measure at very high frequencies including detecting a short tachometer pulse, detecting noise, detecting vibration induced by high speed flow, detecting 'spikes' and using an enveloping function (eg peak-vue) to detect bearing faults.

			Vibration amplitudes (and frequencies) are never steady over time, and the time frame over which they change can be anywhere from seconds to years, depending on the cause of the variation. Typically, you will want to measure for somewhere between several minutes and several hours.

			A very fine frequency resolution will help you distinguish between two separate pure tones, typically caused by two components running at slightly different speeds. This may also be necessary to detect sidebanding. On the other hand, a coarse frequency resolution is better for identifying broadband vibration, or vibration whose frequency is unsteady. This is often the case with flow induced vibration. Note also that frequency resolution affects window length, which affects the extent to which the FFT process averages the amplitude. This is not an issue for steady vibration, but for rapidly changing vibration the amplitude can change significantly depending on your FFT settings. FFT averaging can be used if necessary.

			For screening for resonances on variable speed equipment, use the peak hold function while slowly changing the machine speed. If a problem is found, take more time to find the worst case speed and run the machine at that speed until you are confident that you have found the steady state amplitude.

			Disclaimer: none of this should be taken as a recommendation or advice on your particular circumstance. Vibration problems can be very difficult to find, diagnose and rectify, so always seek advice from an experienced vibration engineer.

	== Aliasing Filters ==		== Aliasing Filters ==

Charles at 04:31, 4 June 2024

2024-06-04T04:31:49Z

← Older revision		Revision as of 04:31, 4 June 2024
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	There are two common approaches to setting the sample rate and FFT parameters.		There are two common approaches to setting the sample rate and other FFT parameters.

	When digital data loggers first came out, they were pushing the limits of the available memory and processing power. In order to use the absolute minimum sample rate and logging duration, the user was prompted to enter in the maximum frequency of interest, as well as the required frequency resolution. This approach has remained the industry standard for routine condition monitoring ("route based") data acquisition systems. It has the advantage of allowing the user to focus on the critical ~~diagnostics~~ requirements of a spectrum. It is the approach that is taught in ISO 18436 (VCAT) training courses. These courses leave out some fundamental relationships that can lead to confusion when practitioners then come across the alternative approach, which is to set the sample rate directly and either log indefinitely (until the stop button is pressed) or for a specified period of time. To address this potential confusion, this page attempts to bridge to the gap between the two approaches.		First, a little background. When digital data loggers first came out, they were pushing the limits of the available memory and processing power. In order to use the absolute minimum sample rate and logging duration, the user was prompted to enter in the maximum frequency of interest, as well as the required frequency resolution. This approach has remained the industry standard for routine condition monitoring ("route based") data acquisition systems. It has the advantage of allowing the user to focus on the critical diagnostic requirements of a spectrum, but reduces flexibility in analysis. It is the approach that is taught in ISO 18436 (VCAT) training courses. These courses leave out some fundamental relationships that can lead to confusion when practitioners then come across the modern alternative approach, which is to set the sample rate directly and either log indefinitely (until the stop button is pressed) or for a specified period of time, and then change the window length as required during analysis. To address this potential confusion, this page attempts to bridge to the gap between the two approaches.

	The sample rate in Hertz (Hz) is the number of samples taken per second. The maximum frequency in an FFT is equal to half the sample rate. This is referred to as the Nyquist frequency. However, anti aliasing filters reduce the amplitude of data in the FFT at frequencies close to the Nyquist frequency. In addition, they allow some aliasing. That is, they allow signals that are slightly higher than the Nyquist frequency to appear in the FFT at slightly lower than the Nyquist frequency. For this reason, the highest frequencies in the FFT should be ignored, discarded or treated with great caution. Condition monitoring software typically divides the sample rate by 2.56 instead of 2 to account for this. This gives an "Fmax" that is somewhat lower than the Nyquist frequency. Note that this number (2.56) is somewhat arbitrary. It depends on the properties of the anti aliasing filter used and the tradeoff between amplitude accuracy, permitting aliased signals in, and how much wasted data you can tolerate in terms of oversampling.		The sample rate in Hertz (Hz) is the number of samples taken per second. The maximum frequency in an FFT is equal to half the sample rate. This is referred to as the Nyquist frequency. However, anti aliasing filters reduce the amplitude of data in the FFT at frequencies close to the Nyquist frequency. In addition, they allow some aliasing. That is, they allow signals that are slightly higher than the Nyquist frequency to appear in the FFT at slightly lower than the Nyquist frequency. For this reason, the highest frequencies in the FFT should be ignored, discarded or treated with great caution. Condition monitoring software typically divides the sample rate by 2.56 instead of 2 to account for this. This gives an "Fmax" that is somewhat lower than the Nyquist frequency. Note that this number (2.56) is somewhat arbitrary. It depends on the properties of the anti aliasing filter used and the tradeoff between amplitude accuracy, permitting aliased signals in, and how much wasted data you can tolerate in terms of oversampling.
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	To complicate matters further, the spectrum in a condition monitoring program is not defined by Fmax and frequency resolution, but by Fmax and lines of resolution, which is the number of bins (data points in the FFT) up to Fmax.		To complicate matters further, the spectrum in a condition monitoring program is not defined by Fmax and frequency resolution, but by Fmax and lines of resolution, which is the number of bins (data points in the FFT) up to Fmax.

			The terms spectrum and FFT are used interchangeably here.

	== Equations ==		== Equations ==
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	<math>N</math> the number of samples taken, or the number of samples used to produce the FFT.		<math>N</math> the number of samples taken, or the number of samples used to produce the FFT.

	<math>LOR</math> is the number of lines of resolution, or number of bins (data points) in an FFT.		<math>LOR</math> is the number of lines of resolution, or number of bins (data points) in an FFT scaled to <math>f_{MAX}</math>.

	<math>WF</math> is the window factor, (1.5 for a hanning window)~~, which~~ captures the extent to which a pure tone will be 'spread' between bins.		<math>WF</math> is the window factor (1.5 for a hanning window). This number captures the extent to which a pure tone will be 'spread' between bins.

	<math>SF</math> is the separation frequency, which is the minimum frequency offset to distinguish two separate FFT peaks in ideal conditions (pure tones with steady frequency). This is the 'bare minimum' requirement.		<math>SF</math> is the separation frequency, which is the minimum frequency offset to distinguish two separate FFT peaks in ideal conditions (pure tones with steady frequency). This is the 'bare minimum' requirement.

Charles: Charles moved page Sample Rate to FFT Setup without leaving a redirect: Better name

2024-06-04T04:18:06Z

Charles moved page Sample Rate to FFT Setup without leaving a redirect: Better name

← Older revision	Revision as of 04:18, 4 June 2024
(No difference)

Charles: /* Recommend Sample Rate */

2024-06-03T23:00:12Z

Recommend Sample Rate

← Older revision		Revision as of 23:00, 3 June 2024
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	== Recommend Sample Rate ==		== Recommend Sample Rate ==

			The first question to ask yourself is, will I be able to repeat the measurement if I discover later that the sample rate was not high enough? If the answer is no, or "yes but I will have to answer some difficult questions", use a higher sample rate.

			These days, memory and processing allowing for both far higher sample rates and measurement durations, and there are advantages to taking advantage of both. We recommend taking at least one initial measurement at the maximum sample rate to check for unexpected high frequency vibration. Note that integrating measured acceleration once to get velocity, and twice to get displacement, will effectively filter out high frequency vibration. So, when you are performing this check, look at acceleration data. Likewise, vibration amplitudes (and frequencies) are never steady over time, and the time frame over which they change can be anywhere from seconds to years, depending on the cause of the variation. Typically, you will want to measure for somewhere between several minutes and several hours.

	== Aliasing Filters ==		== Aliasing Filters ==

Charles at 22:58, 3 June 2024

2024-06-03T22:58:39Z

← Older revision		Revision as of 22:58, 3 June 2024
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	To complicate matters further, the spectrum in a condition monitoring program is not defined by Fmax and frequency resolution, but by Fmax and lines of resolution, which is the number of bins (data points in the FFT) up to Fmax.		To complicate matters further, the spectrum in a condition monitoring program is not defined by Fmax and frequency resolution, but by Fmax and lines of resolution, which is the number of bins (data points in the FFT) up to Fmax.

	These days, memory and processing allowing for both far higher sample rates and measurement durations, and there are advantages to taking advantage of both. We recommend taking at least one initial measurement at the maximum sample rate to check for unexpected high frequency vibration. Note that integrating measured acceleration once to get velocity, and twice to get displacement, will effectively filter out high frequency vibration. So, when you are performing this check, look at acceleration data. Likewise, vibration amplitudes (and frequencies) are never steady over time, and the time frame over which they change can be anywhere from seconds to years, depending on the cause of the variation. Typically, you will want to measure for somewhere between several minutes and several hours.

	In post processing, spectra can be plotted up to the nyquist frequency, with reliable data up to Fmax. Provided you logged continuous data for a long enough period (even if it is split over multiple files), you can obtain a spectrum with any frequency resolution.

	== Equations ==		== Equations ==

Charles: /* Equations */

2024-06-03T21:11:28Z

Equations

@@ Line 21: / Line 21: @@
 <math>f_N</math> is the Nyquist frequency
-<math>f_{MAX}</math>is the maximum frequency shown on a spectrum in a conventional condition monitoring package, or the highest frequency that should be trusted.
+<math>f_{MAX}</math> is the maximum frequency shown on a spectrum in a conventional condition monitoring package, or the highest frequency that should be trusted.
 <math>T</math> is the sample time, or length of data used to produce the FFT.
@@ Line 31: / Line 33: @@
 <math>LOR</math> is the number of lines of resolution, or number of bins (data points) in an FFT.
-The following equations are typically presented in a VCAT course. They are consistent with the above equations:
+<math>WF</math> is the window factor, (1.5 for a hanning window), which captures the extent to which a pure tone will be 'spread' between bins.
 <math>T=T_s \times N=\frac{N}{f_s}=\frac{N}{2.56 \times f_{MAX}}=\frac{LOR}{F_{MAX}}</math>
 == Recommend Sample Rate ==

Charles: /* Equations */

2024-06-03T08:07:50Z

Equations

← Older revision		Revision as of 08:07, 3 June 2024
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	The following equations are typically presented in a VCAT course. They are consistent with the above equations:		The following equations are typically presented in a VCAT course. They are consistent with the above equations:

	<math>T=T_s~~</math>&~~times~~;<math>~~N=\frac{N}{f_s}=N=\frac{N}{2.56 f_{MAX}}</math>		<math>T=T_s \times N=\frac{N}{f_s}=\frac{N}{2.56 \times f_{MAX}}=\frac{LOR}{F_{MAX}}</math>

	== Recommend Sample Rate ==		== Recommend Sample Rate ==

Charles: /* Equations */

2024-06-03T08:01:00Z

Equations

← Older revision		Revision as of 08:01, 3 June 2024
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	== Equations ==		== Equations ==

	The relationships discussed are presented here in equation form:		The relationships discussed are presented here in equation form. The definitions vary slightly between approaches. The condition monitoring definitions typically assume that all of the data obtained is used to produce a single FFT (even though this is not always the case), while for modern systems an indefinite amount of data is obtained and any section of that data can be selected for an FFT.

	<math>f</math> is the sampling rate		<math>f</math><sub>s</sub> is the sampling rate

	<math>f</math~~><sub>N</sub~~> is the Nyquist frequency		<math>f_N</math> is the Nyquist frequency

	<math>f</math~~><sub>MAX</sub~~> is the maximum frequency shown on a spectrum in a conventional condition monitoring package		<math>f_{MAX}</math>is the maximum frequency shown on a spectrum in a conventional condition monitoring package, or the highest frequency that should be trusted.

			<math>T</math> is the sample time, or length of data used to produce the FFT.

			<math>T_s</math> is the time between individual samples.

			<math>N</math> the number of samples taken, or the number of samples used to produce the FFT.

			<math>LOR</math> is the number of lines of resolution, or number of bins (data points) in an FFT.

			The following equations are typically presented in a VCAT course. They are consistent with the above equations:

			<math>T=T_s</math>×<math>N=\frac{N}{f_s}=N=\frac{N}{2.56 f_{MAX}}</math>

	== Recommend Sample Rate ==		== Recommend Sample Rate ==