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# Order tracking

Order tracking method is used to extract the harmonic components related to the rotational frequency of the machine. Order tracking is used in the analysis of vibration signals from rotating machines. There we use order spectrum instead of the frequency spectrum. An order spectrum gives the amplitude and the phase of the signal as a function of the harmonic order of the rotation frequency.

## Order Tracking Analysis Theory

Analysis of vibration signals from rotating machines is often preferred in terms of order spectrum rather than frequency spectrum. An order spectrum gives the amplitude and the phase of the signal as a function of harmonic order of the rotation frequency. This means that a harmonic or subharmonic order component remains in the same analysis line independent of the speed of the machine. The technique is called tracking as the rotation frequency is being tracked and used for analysis.

The order tracking method is used to extract the harmonic components related to the rotational frequency of the machine. The machine vibration pattern is a mixture of excitation frequencies, usually related to rotational speed (such as unbalance, eccentricity, bearing faults and others) and machine response function, which relates to machine natural frequencies based on the structure and mounting of that machine.

With order extraction, we can see a specific harmonic component which relates to a certain machine fault. That is - the first order (harmonic) usually relates to unbalance of the machine, the second harmonic often relates to eccentricity, such as if we have for example 9 rotor blades, the 9th harmonic relates to errors on the blades. Or, if we have for example 31 teeth on a gear, then the 31st harmonic will show the gear mesh frequency.

These are excitations, forces which produce vibration accelerations. The ratio between excitation and system response is defined by the system transfer curve. The final measured vibration of the system is a product of the excitation force and the system transfer curve. Since the transfer curve is fixed, we get different responses for excitations at different rotation speeds. When the excitation passes natural frequency, we get the so-called resonance with increased vibration amplitudes, which could be fatal to the machine. ## What is Order Tracking Analysis

Rotating machines produce repetitive vibrations and acoustic signals related to the rotational speed. These relationships are not always obvious with standard dynamic signal analysis, particularly with variations in the rotational speed. A measurement technique called order analysis is the secret to sorting out all the many signal components that a rotating machine can generate.

Order tracking is a family of signal processing tools aimed at transforming a measured signal from the time domain to angular (or order) domain. These techniques are applied to asynchronously sampled signals (i.e. with a constant sample rate in Hertz) to obtain the same signal sampled at constant angular increments of a reference shaft. In some cases, the outcome of the order tracking is directly the Fourier transform of such angular domain signal, whose frequency counterpart is defined as "order". Each order represents a fraction of the angular velocity of the reference shaft.

Order tracking is based on a velocity measurement, generally obtained by means of a tachometer or encoder, needed to estimate the instantaneous velocity and/or the angular position of the shaft.

Rotating machines under operational conditions require additional analysis such as order tracking. Compared to normal FFT the spectrum is based on orders instead of frequency (time). With this method, you can separate frequency components which are related to engine speed and those that are related to the structure. Dewesoft X software provides a powerful and very easy-to-use order tracking module for fast and efficient results. The data and the RPM information is recorded simultaneously in the time domain and re-sampled in the order tracking module. Therefore, we can show a narrow band FFT, waterfall spectrum, and still keep all other convenient functions in the time domain.

The classical problem of smearing of the frequency components caused by speed variations of the machine is solved by using order analysis. In situations where the frequency components from a normal frequency analysis are smeared together, proper diagnosis is order analysis.

Of particular interest is the analysis of the vibrations during a run-up or a coast-down of a machine in which case the structural resonances are excited by the fundamental or the harmonics of the rotational frequencies of the mechanical system. Determination of the critical speeds, where the normal modes of the rotating shaft are excited, is very important on large machines such as turbines and generators.

Use of an FFT analyser in the normal sampling mode with a fixed sampling frequency (non-tracking) and plotting of the spectrum at certain fixed steps in the rotation speed of the machine gives the Campbell diagram (3D waterfall type of a plot, where vibration levels as a function of frequency are plotted against rotation speed (RPM) of the machine (plotted vertically). This means that the harmonic components appear on radial lines through the point (0 Hz, 0 RPM) while structural resonances appear on vertical straight lines (constant frequency lines). The smearing of the components, which appears because the time window used for the individual spectra represents a certain sweep in the speed, is, however, a disadvantage. The power of the components becomes spread over several lines. In particular, high-frequency components in the spectrum, such as tooth mesh frequencies, might be smeared so much that details in sideband structures are lost in the analysis. This is the main reason why order analysis is used instead.  For order tracking, the time record is measured in revolutions and the corresponding FFT spectrum is measured in orders or in frequency. Just like the resolution, delta f [Hz], of the frequency spectrum, equals 1/T, where T [s] is seconds per FFT-record, the resolution of the tracked analysis, delta ord [ORD], equals 1/rev, where rev [REV] is revolutions per FFT-record. For the analysis with one or more revolutions per record, the resolution of the spectrum is equal to or better than 1 ORD. The result of the analysis is a high-resolution order-spectrum, where the individual orders or fractions of orders, relate directly to the various rotating parts of the machinery.

Tracking analysis (with use of an FFT analyser) is an analysis by which the harmonic pattern of the vibration signal from a rotating machine is stabilized in certain lines independent of speed variations. This means that all the power of a certain harmonic is concentrated in one line and the smearing that would result in normal analysis is avoided.

## Why Do We Need Order Tracking Module ?

Before we start explaining all the different options of the setup, let's check at first why we need the order tracking module.

An electrical scooter motor standing on a rubber foam is analysed. The RPM is controlled by DC voltage and measured by an optical probe (reflective sticker on a shaft) and the vibration by an acceleration sensor mounted on top. ## FFT spectrum at 800 rpm

In the first example, the engine is running at a constant speed of 800 rpm. When we look at the vibration spectrum, the lowest frequency of the highest peak is 13,73 Hz (13,73 * 60 = 823 rpm), which is most likely the first order. The next peak could be the 16th order (13,73 * 16 = 219,7 Hz).

When we increase the RPM now, the distance between some of the spectral lines gets bigger. We call the lines moving with RPM harmonics. They can be calculated by multiplying the base frequency with an integer number.

## FFT spectrum at 1950 rpm

Then we run the engine at a constant speed of 1950 rpm. The first order is again the lowest frequency peak at 32,04 Hz (32,04 Hz * 60 = 1922 rpm). Around 518 Hz, is most probably the 16th order. The 1754 Hz more or less stays the same and doesn't seem to be related to rpm (compare with 800 rpm measurement).

So, the spectrum consists of harmonics of the rotation speed and other frequencies.

## FFT spectrum during runup / coastdown

Of course, it would take too much time to make an FFT for each RPM, so we can try to use the FFT during engine runup or coast down. The following experiment shows the FFT while the engine is slowing down from 1700 to about 1400 rpm. When you compare the spectrum with the ones before, you see that there are no sharp lines anymore. The reason is that the rpm is changing while the FFT still needs time for calculation. This effect is called “smearing”.

Furthermore, from its nature, the FFT always has a frequency and an amplitude error.

To demonstrate, we generate a simple 100 Hz sine wave using the Dewesoft X mathematics (sine(100)). When we use a sampling frequency of 2048 Hz and an FFT with 1024 points we get (because of Nyquist criteria) a line resolution of exactly 1 Hz. Amplitude and frequency in the FFT are correct. Now we change the sine wave to 99.5 Hz. The energy of the peak is now distributed to both neighbour lines at 99 and 100 Hz, therefore, the amplitude is also not exact anymore. In real life, it is very unlikely that the input signal will be at a constant frequency directly at the FFT line. Different windowing algorithms are designed for each application (“flat top” for example shows the correct amplitude).

In Dewesoft X, the FFT calculation time window is shown as a yellow frame in the overview instrument in Analyse mode if you click on the FFT. Manual order tracking would mean setting up each constant rpm sequentially, e.g. 600, 700, 800 then manually extracting the peaks from the FFT, and sorting them out to find the orders. You cannot be absolutely sure you will catch the right peaks (some frequency lines are not related to rpm and you can mix them up).

Using FFT during runup / coast down would result in unprecise measurement because of smearing and other FFT disadvantages.

With the Order tracking module of Dewesoft X, the order analysis is very easy to setup and easy to use.

## Dewesoft X Order Tracking Analysis Module

The Dewesoft X order tracking module is used for e.g. vibration analysis on engines or other rotating machinery, both in development and optimization. With the small, handy form factor of the Dewesoft instruments (DEWE-43, SIRIUSi), it is also a smart portable solution for service engineers coping with failure detection.

The order tracking module is included in the DSA package (along with other modules like torsional vibration, frequency response function, …).

How does it work? - Usually a run up or coast down of the engine is done. The measured vibration sensor data is calculated according to the angle sensor data, split up into orders, which can then be analysed across the whole rpm range. With order tracking the frequencies can be separated into those related to the RPM and spurious ones. The powerful visualisation and mathematic options lead to a clear picture of the situation.

Furthermore, calculations can also be done offline (after the measurement), like with most of the other modules, e.g. if a very high sampling rate is required or the CPU of the used computer simply is too weak.

If the powerful integrated post-processing features of Dewesoft X are not enough, you can even export the data to several different file formats.

## System overview

Depending on what to analyze, e.g. acceleration sensors, microphones or pressure sensors are used to the analog input to measure sound/vibration. If they are e.g. voltage or ICP type, they are connected to the SIRIUS ACC amplifier or DEWE-43 with MSI-ACC adapter.

For the angle sensor, you have various possibilities: you can use either an Encoder with individual pulse count, CDM- 360/-720 or a simple tacho probe with 1 pulse/revolution (TTL or analog output) or 60-2, 36-2 tooth wheel sensor. If the RPM is changing slowly and the phase information is not of interest, the RPM can also be derived from any kind of signal (e.g. 0...20mA, which equals 0...6000rpm) or data channel, e.g. the CAN bus of a car. ## General setup

In the first step we add one module in the Dewesoft X -> Add -> Order tracking button: The input mask of the order tracking module is split into following sections: • input channels define the input channels to perform the analysis on (e.g. acceleration sensor)
• output channels: switch the output channels with arrow buttons and see preview values
• frequency channel setup defines the type of angle sensor (e.g. Enc-512, Tacho)
• calculation criteria sets the RPM limits, delta RPM, runup/coastdown/both
• order FFT setup specify maximum orders and the resolution (e.g. 1/16th order), order FFT vs. time, order FFT vs. RPM and order domain harmonics
• Time FFT setup defines the change calculation method from resampled data to FFT, time domain harmonics and update rate on RPM change
• common properties defines the harmonic list, FFT window, update criteria and how to average data

In most of the cases, the analysis will be done with a vibration sensor. Just enable the desired channel in the list on the left upper side of the module setup. Basically, any analog input can be used, here are some examples:

• acceleration sensor
• microphone
• pressure sensor
• output of the rotational vibration / torsional vibration module

## Frequency channel setup

For determining the engine speed (rpm), an RPM sensor is needed. A lot of different sensors are supported: • Tacho probe (1 pulse/revolution; connect to analog or digital input)
• Encoder (e.g. 1800 pulses/revolution or CDM-360 / CDM-720 or 60-2; connect to Counter input)
• any RPM channel (e.g. analog voltage or RPM from CAN bus; but then the phase of the harmonics cannot be extracted, because there is no zero-angle information)

## Counters

Select “Counters” if you connect an Encoder to the Dewesoft instrument Counter input (usually 7pin Lemo connector).

An encoder (e.g. 1800 pulses/revolution) or CDM (CDM-360, CDM-720) or Tacho (digital = TTL levels) or tooth wheel sensor (60-2) can be used. The counter setup in the background is then controlled (locked) by the Order tracking module, the counters will not be accessible (greyed out), to prevent double-usage.

In Counter mode, you can optionally set the filter, to suppress glitches/spikes shorter than the shown value (100ns...5μs). The optimal setting is derived from the following equation: The biggest error is caused by improper mounting of an encoder. There are different mounting errors using a coupling, such as parallel, skewed, angled. The error will appear as periodic angle/frequency deviation during constant engine speed.

The easiest way is using a tacho probe with digital output. It can be directly connected to the Dewesoft instrument's counter input and is easy to mount. For example, the optical tacho probe only requires a reflective sticker on the rotating part, see picture below. ## Analog pulses

If you have a tacho probe (1 pulse/rev, optic, magnetic or any other type) with analog output signal, you can just connect it to an analog input (e.g. SIRIUS-ACC module) and use the “analog” setting of the frequency section.

Here example signals of a magnetic and an optic probe are shown.  Beyond that, also 60-2 and 36-2 analog signals from the crank sensor (inside nearly every vehicle) are supported.

Click the “...” button to adjust the correct trigger level. You can also use the “Find” algorithm, which will automatically determine the best possible value. Please take care when using a magnetic probe, that also the induced voltage will change depending on the RPM, resulting in a different trigger level. Therefore perform some test runs across the interesting RPM range to find the best trigger level.

Below, an example of 60-2 analog sensor is shown. HINT: If machines with highly dynamic rpm, or with a high rotational vibration are analysed (big rpm deviations during one revolution), and also high orders should be extracted, an encoder or a tacho probe with more than one pulse/rev. (180p/rev or higher) is recommended, to get higher accuracy.

Reason: The order tracking algorithm resamples the time domain data into the angle domain. If we get more information from the RPM probe, we have more pulses per revolution and the resampling to the angle domain will be much more accurate!

## RPM channel

You can also use any signal or channel as input, which directly represents the RPM (e.g. 0...10V equals 0...5000 rpm).

The disadvantage, however, is, that there is no zero-angle information, and therefore extraction of the phase angles of the single orders is not possible.

Following example shows an RPM signal from CAN bus inside a vehicle (red line). Note that the sampling points are asynchronous. The blue line is the output signal of an acceleration sensor. ## Calculation criteria - time and frequency limit

To cover the whole frequency spectrum, a run-up or a coast-down of the engine has to be performed.

Select the RPM limits (upper and lower RPM limit), and whether you want to calculate the waterfall spectrum and order extraction while run-up, while coastdown or both. Upper and lower RPM limit define the range for calculation and are used to correctly set up the resampling algorithm, depending on the max orders extracted.

Delta RPM will define when a new update of the waterfall spectrum and also the extracted order domain harmonics are calculated. In case, the RPM is not changing only channels from Time FFT setup can be calculated according to the maximum time limit setting.

Output channel calculation rate

• Order data (Order domain harmonics, Order waterfall vs. RPM, Overall RMS) are updated on delta RPM
• Order FFT vs. time is updated on each FFT calculation (when you acquire enough samples needed)
• Time data (Time domain harmonics, FFT waterfall vs. RPM) are updated on delta RPM or on update time limit or both.

## Common properties To extract the orders simply enter the wanted number in the Harmonics list field. Separate multiple entries with the semicolon (;). In the example below the 1st, 2nd and 3rd, 4th and 5thorders are selected. If the extracted order falls between discrete order resolution steps, the closest fitting resolution will be taken, so if the resolution is 1st order and 1.8 is extracted, 2ndorder will be used.

Data can be averaged in two ways:

• None (Center of the class is taken. For example, if the class is defined from 125 RPM to 175 RPM (delta RPM is 50), the calculations will be done only at the lines (number of lines is calculated from maximum order and order resolution) around 150 RPM.)
• Average between classes (it takes consecutive FFTs through the class and averages them.) Update criteria is applied to array channels (Order domain harmonics, Order waterfall vs. RPM, FFT waterfall vs. RPM). It defines if the waterfall should be updated:

• Always: (if you have more run-up or coast-downs, the new value will be written in an element of an array)
• Only: first time (if you have more run-up or coast-downs, only the first run will be used)
• Average: (if you have more run-up or coast-downs, the element of an array will be calculated as an average between the old and new samples.) With the Order FFT setup channels, the update is done if the RPM changes bigger than the Delta RPM or if the maximum time limit is reached.

Sometimes it is also necessary that the order tracking calculation is done in a fixed time interval, independent of the rpm, e.g. when a car is driving a defined track or a machine is operated and observed during a working cycle. If this is needed, update on must be checked, so the calculation will be updated independently from the rpm every 0.5 sec (overwrites frequency limits – delta RPM setting). This applies only to the Time FFT setup channels.

## Order FFT setup

In the Order FFT setup, we can define the maximum number of orders to be extracted, and the order resolution (the number of lines between two orders). Depending on the Upper RPM limit and the Maximum order used, the OT module will output a warning if the used sample rate is too low. In this example, we have set Upper RPM limit = 6000 and Maximum order = 64, so the minimum required sample rate is calculated like this:

First order at max speed: 6000 rpm / 60 = 100 Hz; so the highest order would be 100Hz * 64 = 6400 Hz Because for FFT analysis minimum the double sampling frequency has to be used (Nyquist criteria): 2 * 6400 = 12800 Hz.

In an FFT, if the line resolution is 0.5 Hz, the required data window must be 2s. The same is true for the ordered resolution: If the resolution is set to 0,25 orders, 4 revolutions are required for one data block.

The higher the required order resolution, the more slowly the rpm must change.

## Order domain harmonics are complex channels displayed on 2D graph. In the harmonic list section, we define which harmonics we want to extract. ## Order waterfall vs. RPM Order waterfall vs. RPM monitors current values of orders. We define the order resolution and the maximum order that will be shown on a 3D graph. ## Order waterfall vs. time Order waterfall vs. time monitors orders through time and not only the current values. The channel is updated when every new FFT is being calculated. ## Output extracted harmonics as channels

This will extract specific orders from the order waterfall plot to be used as channels. So it is possible to draw a specific order over time, or over engine speed.

To extract the orders simply enter the wanted number in the Harmonics list field. Separate multiple entries with the semicolon (;). In the example below the 1st, 2nd and 3rd, 4th and 5th orders are selected. If the extracted order falls between discrete order resolution steps, the closest fitting resolution will be taken. Time domain and order domain harmonics are both complex channels. To get the amplitude from the complex number, use the ABS function in math. To get the phase angles from complex numbers use the ANGLE function in math (only available when using RPM sensor with zero-angle information). To get the real and imaginary part as separate channels out of the complex number, use two math formulas:

• real = real('acc/Time domain')
• imag = imag('acc/Time domain')

In the example above, the index  will show 1st harmonic, index  will show 2nd, and  the 3rd harmonic.

## Extracting the interharmonics

In order tracking module there is an option to extract interharmonics (half-orders). Enter the number in the harmonic list section. Order domain harmonics and interharmonics are complex channels displayed on the 2D graph. WARNING: Only the amplitude will be calculated for the interharmonics (0.5, 1,5, ...) and not the phase. The phase can only be calculated for the whole harmonics (1st, 2nd, ...). The phase is turning on the interharmonics because they are not integer multipliers of first order and phase gets to be calculated in different places in each period (with normal harmonics this calculation is always on the same spot).

## Time FFT setup

The order tracking module creates a waterfall plot out of the rpm change. So every time the rpm changes for the defined delta rpm, an FFT is calculated for that data block and shown in the Time FFT diagram.

The FFT resolution and data block length is per default automatically calculated out of sampling rate, order resolution and maximum order.

This data block is fed into a special mathematic algorithm, which resamples the data so that we get exactly 2x values during one revolution. Out of that, we can get the order and phase spectrum without any leakage of FFT values. So FFT lines (=orders) will have the exact amplitude (no smearing) and phase, almost no matter how fast we change the engine speed. If Time FFT lines are checked, the Time FFT waterfall diagram will have a user defined number of lines for one rpm shot. So we manually change the FFT resolution in the FFT waterfall diagram with this setting.

The resolution of the FFT waterfall vs. RPM can be defined by the number of lines (delta frequency is also shown). It can be also set to Auto - the resolution is calculated from the max. order, sample rate and order FFT size. Below you see the difference (left: Df = 24 Hz; right: Df = 6 Hz): The second picture shows much sharper lines, and separates much clearer into single frequencies.

If Harmonics from FFT is checked, the extracted orders are calculated out of the FFT spectrum and not out of the resampled data. The lines for amplitude (+/-) will define how many FFT lines below/above the center line (=order) are averaged. So sidelobes are calculated back to the central line, and this is done to prevent leakage.

Therefore, a smeared FFT with the right band around the center frequency will also give reliable results.

## Overall RMS vs. RPM This channel show the overall RMS amplitude over the range of RPMs. ## Time domain harmonics This is a complex output channel showing the amplitude of harmonics in a time domain. In the harmonics list section, we define the harmonics that we want to extract. ## Extract specific order

Order domain harmonics are extracted in "orders over RPM", shown on a 2D graph. The graph above shows a vibration spectrum of an electrical scooter motor, standing on rubber foam. The three major orders are marked (1st, 16th and 32th). It is also possible to extract them and see the amplitudes and phases over rpm.

This is the old way but still applies, especially if you want to monitor the behaviour of extracted order over the whole time interval (Order domain harmonic values get overwritten, when we hit RPM value that was already used).

Please use the XY recorder for displaying the extracted data: First pick the OT_Frequency channel from the channel list (x-axis) on the right side, then assign the abs('signal/Time domain') channel (y-axis). ## Measurement and visualization

As the order tracking is done during a run up or coast down, the visualisation instruments show the vibration spectrum (and the orders) over RPM and frequency. Single order lines can additionally be extracted.

## Automatic display mode

With the order tracking module enabled, when you start the measurement, Dewesoft X will automatically generate a display setup showing the major signals for a quick start. The tooth wheel symbol on the display icon indicates that this display is being generated.

In the picture below, the automatic display configuration is shown. The selected visual control is an XY recorder, which can plot e.g. a channel against RPM. The handling of all visuals follows the same concept. For the selected visuals, the properties are shown on the left side. The channel selector for this visual is shown on the right side. Only channel types suitable for the selected visual are shown. E.g. you can't select statistic channels of a visual holding angle based data. Already selected are shown in bold.

We can use the channel filter for quickly finding the wanted channels on top of the channel list. Once you modify the display in the design mode (e.g. adding an addition visual) the tooth wheel on the icon will disappear indicating the automatic mode is disabled.

## Customizing display

Dewesoft X allows a completely flexible arrangement of the displays. The major displays for order tracking measurement are described below.

## Time FFT waterfall

The most important instrument for order tracking is the 3D graph. When you pick it in design mode, assign the signal/TimeFFT from the channel list to it. The waterfall plot shows a number of FFTs plotted across the RPM range (y axis), where the vibration amplitude is shown as color (up-direction in 3D mode).

With this instrument, you can separate the spectrum into frequencies related to RPM (= orders) and other frequencies (e.g. resonances of the mechanical structure, noise from the electrical grid, ...).

The 3D FFT instrument is updated in real-time during measurement, it will grow during runup / coast down, already showing the end result. ## Order FFT waterfall Also with the 3D graph instrument, the order FFT can be shown.

Orders are plot versus rpm. Again, the color shows the vibration amplitude.

The straight lines parallel to the y axis are the orders. This is very helpful, because the frequencies of the orders change with rpm, and sometimes it is difficult to trace them.

Example: frequency change of the first order with rpm:

• 1st order at 600 rpm → 600/60 = 10 Hz
• 1st order at 4600 rpm → 4600/60 = 76,7 Hz

Below you see the comparison: Time FFT (left) and Order FFT (right). The straight 100 Hz noise line in the Time FFT appears as a curve in the Order FFT; marked with a red dotted line in the two graphs. ## Polar diagram / Nyquist plot

For this functionality, you have to enable the “Time domain harmonics” checkbox in the order tracking setup. It is also possible to draw Polar diagram with Order domain harmonics.

In the example with the scooter motor the strongest orders are relatively high, so we selected 1; 16; 32. The Complex output (Re + jIm) has to be split up into real and imaginary part using Math. Create a new formula and add one the beginning “real()” and “imag()” to the signal/Complex channel. This can also be done “offline” on the data file, after the measurement. Go to Recalculate and take a look at the Math preview again. An array will be created, which is basically the four channels re1, re16, re32 and re48 combined into one multidimensional channel. If we want to access the components, we simply add “[i]”, where i is the index {0,1,2,3} representing the order {1,16,32,48} in our example. So real('signal/Complex') will give the Real part of the 1st order. Then do the same for the imaginary part imag('signal/Complex') : Then take the XY recorder and assign first Real1, then Imag1 to it. The x and y axis were manually scaled to the same min/max value to show the angle proportion correctly.

On the left side, in the properties you can select if you want to display all data, only the current data, or over a specified window with the Pre time limit option.

## 3D FFT cut

Take a look at the Time FFT waterfall again. As discussed before, it consists of a lot of FFT's (one for each delta RPM) and it might be interesting to extract a single FFT for a user-defined RPM. Open a data file, go to design mode and right-click on the 3D FFT instrument, select “Info channels”.

Enable the channels X cut and Y cut. Then add a 2D graph from the instrument toolbar. Unassign all other channels, only assign the channel signal/TimeFFT/X cut to it. Exit the design mode. Then click on the 3D FFT instrument on the interesting point, where you want to cut the FFT. When you see a marker, e.g. “1”, move the mouse over the 2D graph on the right and it will be updated. ## FFT peak calculation

One of the standard measurements to do for example, is the run up of the machine and then calculate the max amplitude over the FFT.

Add a Fourier transform math from the math section. Then select the input channel, in this example, an acceleration sensor. Set the output to Amplitude, calculation type to Overall, and averaging type peak. This example was done “offline”, on a data file after the measurement. You can also do it during the measurement.

Then a 2D graph was added (see instrument bar, red box) and the AmplFFT math channel assigned.

In 2D graph display options, type of Y-axis can be set to logarithmic. In the recorder you can select only one section of data file, to perform the PeakFFT over a specific RPM range.

After that the calculated math data can be exported.

## Campbell plot

You can also display TimeFFT or Order FFT on Campbell plot.

Click on Design button and add Campbell plot with clicking on the icon shown below. On the upper picture an ordinary 3D graph is shown and the lower one is Campbell plot. Also, the order FFT can be displayed. Campbell plot presents multiple options to manipulate its design.

Minimal and maximal value on the diagram’s scale (on the left side of Campbell plot visual control) represents the range of values which will be segmented into levels. Values, bigger than maximal value, belong to the highest level and values, smaller than minimal values fall into the lowest level. On the picture below we can see an example, how value’s range is segmented into levels, where number of levels is set to 5. Number of levels can be changed within Levels edit field on the Options tab. Cutoff is given in percent. It determines size of portion that will be cut out from the range of shown values. Diagram’s scale shows which values will not be shown by hiding scale’s color map. Next picture shows example with no cutoff (0%) on left side and on the right side cutoff was equal to 30%. Scale’s color maps are changed accordingly. NOTE: By clicking on the diagram and hovering over the scale with your mouse, you can easily define your Cutoff by scrolling up and down.

High and low value amplitudes correspond to the diameters of circles from largest to smallest. Diameters of circles from levels in between increase linearly from lowest to highest diameter with respect to number of levels. Each level has its own diameter.

Scale’s colour map can be generated from different palettes (Palette drop-down). Below you can se examples of all of them; Rainbow (warm), Rainbow, Grayscale and single colour, which is colour from the channel on the diagram. There are two possible circle styles; outline (by default) and fill. On the left "filled" circle style is shown and on the right only "outlined" circle style is displayed. Campbell plot lets you choose between XY and YX projections. XY has x axis horizontal and y axis vertical, YX projection has it the other way around; x vertical and y horizontal. Positions of x and y axes are set as on the selected icon. Left we have XY projection and YX on the right. Selection marker (selected on the image below), shows you the value of the area where your mouse cursor is currently positioned on the diagram. Value is shown in upper left corner of visual control. Free marker (not selected above), allows you to mark the position with one left click of the mouse on the wanted area. You cannot click on the area where there are no values (cut out levels). Little cross will be drawn, to show marker’s position with its index written on the side. If Show marker values is checked, value on the marker will be shown instead of its index. On the picture there is also a marker table, which has all marker values collected. Only for demonstration reasons on the picture below, line connects markers and their values in the table. ## Orbit graph

In this example, we want to visualize the movement of a rotating disc. To have a high angular resolution we use an encoder with 1024 pulses per revolution. A 2-axis acceleration sensor is mounted on the metal frame holding the motor. The axis orientation is shown as below. The output of the sensor is an acceleration in m/s². If we use double integration on it, we can calculate the displacement in μm. This can be done using an IIR filter in Dewesoft X mathematics. The filter order and low-pass frequency have to be chosen carefully in order, not to create an unwanted and unstable output signal. To determine the filter frequency, make an FFT spectrum on the acceleration sensor and look for the lowest dominant frequency. 4th order 4 Hz is a good starting point (signals below 4Hz * 60 = 240 rpm will be cut). If you use lower frequencies / higher orders the filter can start slowly bouncing due to integral math DC output. The visual instrument for that operation is the “Orbit graph”.

Assign first x, then y displacement output. Both axes are scaled with same min/max values automatically. The orientation of the sensors can be modified on the left side, and also the displayed time can be selected. ## Analyse and export

In the Analyse mode, Dewesoft X provides data review, modifying or adding Math-Modules and printing the complete screen for generating your report as well. Similar to the Measurement mode you can modify or add new Visuals or Displays. All these modifications can be stored in the data file with Store Settings and Events. This display layout and formulas can also be loaded on other data files with Load Display & Math Setup or with the multi-file operation Apply action.

## Export of complex data

Go to the Export section, on top you see the “Complex export” box, check e.g. Real and Imag.

Then select the signal/Complex channel. If you additionally select other channels, they will not be affected. This setting is only applied to the Complex dataset. For each order, we selected for calculation in the order tracking setup (1st, 16th, 32nd, 48th) two columns (real, imag) are exported. ## 3D FFT cut export Select the 2D instrument, the data can be copied by using the “Copy data to a clipboard” function from the “Edit” menu on the right upper section in Dewesoft X. The clipboard data is then easily pasted into other programs, for exampe Excel. The copy data to clipboard function is also available on the standard FFT instrument.

After we have shown how to extract orders and visualize them in Dewesoft X, this page should give a rough idea what 1st, 2nd … order means and what might be their possible source.

## 1st order = imbalance

The first order is the shaft frequency, so if the first order is the main reason for high vibration, this is related to an unbalanced shaft or blade. Imagine a blade or shaft or any rotating part that has a higher weight at one side. This weight will rotate with exactly the rotational speed (1st order), create a force and, therefore, a vibration frequency which is exactly the rotation speed or first order. So high amplitudes of first orders indicate an unbalanced system.

## 1st and 2nd order = misalignment If a high second order is observed in the vibration spectrum of a machine, it often indicates a misalignment of two coupled engines. So, two times per revolution (2nd order) the shaft is bent and causes a vibration force, which is transmitted to the mechanical structure and creates a vibration.

## Diesel and gasoline engines

In a diesel and gasoline engines, we can observe that 2nd, 3rd or 6th order are almost all the time dominant, why?

 It depends on the cylinder count of the engine. Let's assume we have a 4 cylinder 4 stroke engine. One cylinder is fired every 2 revolutions, so we would get 0.5 order vibration if we would have a 1 cylinder engine.With a 4 cylinder engine the firing of the 4 cylinders is distributed over 4 revolutions, 2 rev/4 = 0,5 rev so one of the 4 cylinders will fire every 0,5 revolutions. This will lead to high second order vibration.A 6 cylinder 4 stroke engine will produce high 2 rev/6 = 0.33rev → 3rd order. ## Order Tracking Analysis Webinar

Order tracking method is a perfect tool to determine the operating condition of the rotating machines (resonances, stable operation points, determining a cause of vibrations). In this webinar, you will learn how to connect the sensors, configure the setup, perform the measurement and analyze the results.