Order Analysis of Rotating Machines

Course overview

The Order Analysis of Rotating Machines course introduces a critical vibration analysis method tailored for variable-speed systems—order tracking. Unlike traditional FFT, order tracking converts signals into the angular domain, allowing you to monitor vibration content tied to rotational speed rather than time, delivering sharper insights into mechanical faults.

You’ll begin by learning how to configure DewesoftX’s Order Tracking module: define reference sensors such as tachometer or encoder, select resampling parameters, and set FFT-based order extraction options ([turn0search0]). The course carefully explains how to choose relevant orders—such as 1× for unbalance or higher orders for gear/rotor-specific faults—to diagnose system behavior.

Hands-on segments guide you through run-up/coast-down measurement campaigns. Using visualizations like 3D waterfalls (order vs. RPM), polar and Nyquist plots, and Campbell diagrams, you’ll detect resonance speeds, misalignment issues, and gear defects with clarity and accuracy ([turn0search0]). The training also teaches how to extract and export order amplitude data as a function of RPM, enabling diagnostics, trend analysis, and export to downstream tools.

By the end, you’ll be proficient in applying order tracking analysis with DewesoftX—enabling precise fault diagnosis, resonance detection, and mechanical insights in rotating machinery testing setups.

Analysis of vibration signals from rotating machines is often performed using the order spectrum rather than the frequency spectrum. An order spectrum shows the amplitude and phase of the signal as a function of the harmonic order of the rotational frequency. This means that a harmonic or subharmonic order component remains on the same analysis line, independent of the machine’s speed. This technique is called tracking, as the rotational frequency is tracked and used for analysis.

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

With order extraction, we can identify specific harmonic components associated with particular machine faults. For example, the first-order harmonic usually indicates unbalance, while the second-order harmonic often indicates eccentricity. If a rotor has, for instance, 9 blades, the 9th harmonic corresponds to blade errors. Similarly, if a gear has 31 teeth, the 31st harmonic corresponds to the gear mesh frequency.

These excitations are forces that generate vibration accelerations. The ratio between excitation and system response is defined by the system transfer function. The measured vibration of the system is the product of the excitation force and the system transfer function. Since the transfer function is fixed, the system responds differently to excitations at different rotational speeds. When an excitation frequency coincides with a natural frequency, resonance occurs, leading to increased vibration amplitudes, which can potentially damage the machine.

This page provides a rough idea of what 1st, 2nd, and higher orders mean, as well as their possible sources.

1st order = imbalance

The first order corresponds to the shaft frequency. If the first order is the primary cause of high vibration, it is typically related to an unbalanced shaft or blade.

Imagine a blade, shaft, or any rotating part that has more weight on one side. This imbalance will rotate at the same speed as the shaft (1st order), generating a force and, consequently, a vibration frequency that matches the rotational speed, or first order. Therefore, high amplitudes in the first order 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. In this case, the shaft is bent twice per revolution (2nd order), creating a vibration force that is transmitted to the mechanical structure and generates vibration.

Diesel and gasoline engines

In diesel and gasoline engines, we often observe that the 2nd, 3rd, or 6th order vibrations are dominant. Why is this the case?

It depends on the cylinder count of the engine. Let’s assume we have a 4-cylinder, 4-stroke engine. One cylinder fires every 2 revolutions, so a single-cylinder engine would produce 0.5-order vibration.

With a 4-cylinder engine, the firing of the cylinders is distributed over 4 revolutions: 2 rev / 4 = 0.5 rev. This means that one of the four cylinders fires every 0.5 revolutions, which leads to high second-order vibration.

Similarly, a 6-cylinder, 4-stroke engine produces a high 2 rev / 6 = 0.33 rev → 3rd-order vibration.

Rotating machines produce repetitive vibrations and acoustic signals related to their rotational speed. These relationships are not always obvious with standard dynamic signal analysis, especially when the rotational speed varies. A measurement technique called order analysis is the key to separating the many signal components generated by a rotating machine.

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

Order tracking relies on a velocity measurement, generally obtained using a tachometer or encoder, to estimate the instantaneous velocity and/or angular position of the shaft.

Rotating machines operating under real conditions often require additional analysis, such as order tracking. Unlike a standard FFT, order spectra are based on orders (periods per revolution) rather than frequency (periods per unit time). This approach allows you to separate the frequency components related to the engine speed from those related to the machine structure.

DewesoftX software provides a powerful and easy-to-use order tracking module for fast and efficient results. The data and RPM information are recorded simultaneously in the time domain and then re-sampled in the order tracking module. This allows for displaying a narrow-band FFT or waterfall spectrum while still retaining all other convenient time-domain functions.

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

Of particular interest is the analysis of vibrations during a run-up or coast-down of a machine, during which structural resonances are excited by the fundamental or harmonic frequencies of the rotating system. Determining the critical speeds, where the normal modes of the rotating shaft are excited, is especially important for large machines such as turbines and generators.

Using an FFT analyzer in normal sampling mode with a fixed sampling frequency (non-tracking) and plotting the spectrum at certain fixed steps of the machine's rotation speed produces the Campbell diagram. This is a 3D waterfall plot where vibration levels as a function of frequency are plotted against the rotation speed (RPM) of the machine. In this plot, harmonic components appear on radial lines passing through the point (0 Hz, 0 RPM), while structural resonances appear on vertical lines (constant frequency lines).

However, smearing of components occurs because the time window used for the individual spectra represents a certain sweep in speed. As a result, the power of the components is spread over several lines. High-frequency components, such as gear tooth mesh frequencies, may be smeared to the point that sideband details are lost in the analysis. This limitation is the main reason why order analysis is preferred.

For order tracking, the time record is measured in revolutions, and the corresponding FFT spectrum is measured in orders. Just as the resolution, Δf [Hz], of the frequency spectrum equals 1/T, where T [s] is the duration of the FFT record, the resolution of the tracked analysis, Δord [ORD], equals 1/rev, where rev [REV] is the number of revolutions per FFT record. For analyses with one or more revolutions per record, the spectrum resolution is equal to or better than 1 ORD. The result is a high-resolution order spectrum, in which individual orders—or fractions of orders—correspond directly to specific rotating parts of the machinery.

Tracking analysis (using an FFT analyzer) is a method by which the harmonic pattern of a vibration signal from a rotating machine is stabilized along specific lines, independent of speed variations. This ensures that the entire power of a given harmonic is concentrated in a single line, avoiding the smearing that would occur in conventional frequency analysis.

Before we begin explaining all the different setup options, let's first examine why the order tracking module is needed.

An electric scooter motor, mounted on a rubber foam base, is being analyzed. The RPM is controlled by a DC voltage and measured with an optical probe (using a reflective sticker on the shaft), while the vibration is measured by an accelerometer mounted on top.

FFT spectrum at 800 rpm

In the first example, the engine runs 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 correspond to the 16th order (13.73 × 16 ≈ 219.7 Hz).

When we increase the RPM, the distance between some of the spectral lines becomes larger. We refer to the lines that move with RPM as harmonics. These harmonics can be calculated by multiplying the base frequency by an integer.

FFT spectrum at 1950 rpm

Next, 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 × 60 ≈ 1922 rpm). Around 518 Hz, we most likely observe the 16th order. The peak at 1754 Hz remains more or less constant and does not appear to be related to the RPM (compare with the measurement at 800 rpm).

Thus, the spectrum consists of harmonics of the rotational speed as well as other unrelated frequencies.

Of course, it would take too much time to perform an FFT for each RPM, so we can instead use the FFT during the engine run-up or coast-down. The following experiment shows the FFT while the engine slows down from 1700 to approximately 1400 rpm.

When you compare this spectrum with the previous ones, you can see that there are no sharp lines anymore. This is because the RPM is changing while the FFT still requires time for calculation. This effect is called smearing.

Furthermore, due to its inherent nature, the FFT always has some frequency and amplitude error.

To demonstrate this, we generate a simple 100 Hz sine wave using the DewesoftX mathematics function sine(100). Using a sampling frequency of 2048 Hz and an FFT with 1024 points, we obtain a line resolution of exactly 1 Hz (according to the Nyquist criterion). In this case, both the amplitude and frequency in the FFT are correct.

Now, if we change the sine wave to 99.5 Hz, the energy of the peak is distributed across the neighboring lines at 99 Hz and 100 Hz. Consequently, the amplitude is no longer exact.

In real life, it is very unlikely that the input signal will match a constant frequency exactly at an FFT line. Different windowing algorithms are designed for specific applications; for example, a flat-top window provides a more accurate amplitude measurement.

Manual order tracking would require setting up each constant RPM sequentially—for example, 600, 700, 800—and then manually extracting the peaks from the FFT to identify the orders. You cannot be absolutely certain that you will capture the correct peaks, as some frequency lines may not be related to RPM and could be mistaken.

Using FFT during a run-up or coast-down can result in imprecise measurements due to smearing and other inherent FFT limitations.

With the Order Tracking module in DewesoftX, performing order analysis becomes straightforward and user-friendly.

The Dewesoft X Order Tracking module is used for vibration analysis on engines or other rotating machinery, both in development and optimization. With the compact and handy form factor of Dewesoft instruments (DEWE-43, SIRIUSi), it also provides a portable solution for service engineers handling failure detection.

The Order Tracking module is included in the DSA package, along with other modules such as torsional vibration analysis, frequency response function, and more.

How does it work? Typically, a run-up or coast-down of the engine is performed. The measured vibration sensor data is calculated according to the angle sensor data, then separated into orders, which can be analyzed across the entire RPM range. Using order tracking, frequencies related to RPM can be distinguished from spurious ones. The powerful visualization and mathematical options provide a clear understanding of the system’s behavior.

Additionally, calculations can be performed offline after measurement, as with most other modules. This is useful if a very high sampling rate is required or if the CPU of the computer used is insufficient for real-time processing.

If the integrated post-processing features of Dewesoft X are not enough, the data can also be exported in several different file formats.

System overview

Depending on the type of analysis, acceleration sensors, microphones, or pressure sensors can be used with the analog input to measure sound or vibration. Voltage-type or ICP sensors, for example, are connected to the SIRIUS ACC amplifier or DEWE-43 with the MSI-ACC adapter.

For the angle sensor, various options are available. You can use an encoder with individual pulse count, CDM-360/-720, or a simple tacho probe with 1 pulse per revolution (TTL or analog output), or a 60-2 / 36-2 tooth wheel sensor. If RPM changes slowly and phase information is not critical, RPM can also be derived from any suitable signal (e.g., 0–20 mA, which equals 0–6000 RPM) or from a data channel, such as the CAN bus of a car.

To add the Order Tracking module in DewesoftX, go to Measure mode, open Channel Setup, and click on More…. Then, search for Order Tracking and select it.

The input mask of the Order Tracking module is divided into the following sections:

In most cases, the analysis is performed using a vibration sensor. Simply enable the desired channel(s) in the list at the upper-left side of the module setup. Essentially, 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

To determine the engine speed (RPM), an RPM sensor is required. A variety of sensors are supported.

In the Frequency Source drop-down menu, you can choose between Counters, Analog Pulses, or RPM Channel. The Sensor menu allows you to select the sensor you have previously created and saved in the Counter Sensor Editor. From the Frequency Channel, you can select the channel connected to your sensor.

Acceptable Sensors for Order Tracking

Digital

• Tacho Probe – 1 pulse per revolution; connect to analog or digital input.

• Encoder – e.g., 1800 pulses per revolution, CDM-360 / CDM-720, or 60-2; connect to Counter input.

Analog

• Geartooth Sensors – e.g., 36-2 or 60-2 sensor; connect to an analog input.

Any RPM Channel

• Math channel, analog voltage, or RPM from CAN bus. Note: when using an RPM channel, the phase of the harmonics cannot be extracted relative to the rotational angle because there is no zero-angle information. Instead, the phase can be determined relative to the 1st order absolute phase.

Counters

Select Counters if you connect an Encoder to the Dewesoft instrument’s Counter input (usually a 7-pin Lemo connector).

An encoder (e.g., 1800 pulses per revolution), CDM (CDM-360, CDM-720), Tacho (digital = TTL levels), or tooth wheel sensor (60-2) can be used.

The counter setup in the background is 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 a filter to suppress glitches or spikes shorter than the specified value (100 ns–5 μs). The optimal setting is derived from the following equation:

\(RPM_{max}... max \space revolutions \space per \space minute \space [min^{-1}]\)

\(PulsesPerRev... pulses \space per \space revolution \space of \space encoder\)

The biggest errors are usually caused by improper mounting of an encoder. Mounting errors can occur in various ways when using a coupling, such as parallel, skewed, or angled misalignment. These errors appear as periodic angle or frequency deviations during constant engine speed.

The easiest solution is to use a tacho probe with a digital output. It can be connected directly to the Dewesoft instrument’s Counter input and is easy to mount. For example, an optical tacho probe only requires a reflective sticker on the rotating part (see Image 8).

Analog pulses

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

The following are example signals from a magnetic probe and an optical probe.

In addition, 60-2 and 36-2 analog signals from the crank sensor (found in nearly every vehicle) are also supported.

Click the … button to adjust the correct trigger level. You can also use the Find algorithm button, which automatically determines the optimal value. When using a magnetic probe, keep in mind that the induced voltage changes with RPM, which affects the trigger level. Therefore, perform several test runs across the relevant RPM range to determine the best trigger level.

Below is an example of a 60-2 analog sensor.

RPM channel

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

The disadvantage, however, is that there is no zero-angle information; therefore, it is not possible to extract the phase angles of individual orders.

The following example shows an RPM signal from the CAN bus inside a vehicle (red line). Note that the sampling points are asynchronous. The blue line represents the output signal of an acceleration sensor.

Speed ratio

With speed ratio settings, it is possible to account for gearing ratios between a rotation source and the rotation of another component where the frequency channel sensor might be located. For example, for practical reasons, it may be necessary to perform the frequency channel measurement on a machine component different from the main crankshaft. By using the speed ratio settings, the frequency channel can be converted to represent the speed of another component, such as the crankshaft.

If the measured frequency channel is taken from the output shaft of a system and the order tracking should relate to the input shaft, the speed ratio should be set as input/output.

The reference channel is used as an additional axis or dimension, linked to related order results. For example, a reference channel can represent the measured RPM or temperature, with order results found at each bin—creating 3D waterfall spectrograms and extracted harmonics versus the reference.

To capture all vibration characteristics, a run-up or coast-down of the engine must be performed.

Image 21 shows a recording of RPM over time. All terms that you will encounter during the setup of Order Tracking are visually presented. In this illustrated example, the reference channel is set to RPM, but it could also be set to another measured channel representing a different physical quantity.

Reference signal - binning

Select the Upper and Lower Limits to define the range of the Reference Channel used for calculations, and choose whether to calculate the waterfall spectrum and order extractions during a run-up, coast-down, both, or based on the First Direction.

Delta defines the bin width of the Reference (REF) axis in waterfall spectra and in the extracted order-domain harmonics.

Hysteresis is used to determine when measured data is assigned to a different bin. It is expressed as a percentage of the Delta bin width. Data will only be reassigned to another bin if the reference value crosses the bin edge by more than the specified hysteresis percentage.

Common properties

To extract orders, simply enter the desired numbers in the Harmonics list field. Separate multiple entries with a semicolon (;). In the example above, the 0.5 sub-order and the 1st, 2nd, 3rd, and 36th orders are selected. If an extracted order falls between discrete order resolution steps, the closest fitting resolution will be used. For example, if the resolution is 1st order and 1.8 is extracted, the 2nd order will be applied.

FFT Window & Amplitude define the time-weighting function and the amplitude scaling of your measured spectral data. You can learn more about FFT windowing in theFFT course.

Data collection can be performed in two ways:

Bin Update determines how the collected data will be processed. It specifies whether all results related to the reference channel (versus reference results) should be updated:

The output results affected by the Bin Update setting are:

• Order domain harmonics

• Order waterfall vs. reference

• FFT waterfall vs. reference

• Overall RMS vs. reference

Spectral Weighting is supported in the Order Analysis module and provides the following functions:

• Acoustic Weighting – A- and C-weighting are used for sound pressure signals. When analyzing sound and noise signals, acoustic weighting filters can be applied to account for human auditory perception.

  Integration/Differentiation – Integration and differentiation functions are primarily used for vibration signals to convert between physical quantities. A common scenario is transforming data from the acceleration domain to the displacement domain. The table below illustrates how integration and differentiation functions can be used to convert vibration-related physical quantities:

Skip missing bins

Empty bins typically occur when the Delta bin width is too narrow to capture the number of cyclic revolutions required to generate a spectrum. The number of revolutions needed for each spectrum is the reciprocal of the order resolution—higher resolution requires angle data from more revolutions.

If “Skip missing bins” is enabled, all REF bins that lack sufficient revolutions to produce a spectrum will remain empty.

If “Skip missing bins” is disabled, REF bins that lack sufficient revolutions will use overlapping data from previous REF bins to compensate for the missing revolutions required to generate a spectrum.

 In the Order FFT setup, you can enable or disable various options to customize the acquisition according to your needs.

For example, set the Upper RPM to 6000 and the Maximum Order to 64. The minimum required sample rate is calculated as follows:

• First-order at maximum speed: 6000 rpm ÷ 60 = 100 Hz

• Therefore, the highest order is 100 Hz × 64 = 6400 Hz

• Because of the order FFT analysis, the sampling frequency must be doubled to satisfy the Nyquist criterion: 2 × 6400 = 12,800 Hz

Order domain harmonics

Order-domain harmonics are complex channels displayed on a 2D graph. In the Harmonic List section, you specify which harmonics you want to extract

Order waterfall vs. reference

Order waterfall vs. reference monitors the current values of orders. You specify the order resolution and the maximum order to be displayed on the 3D graph.

Order waterfall vs. time

Order waterfall vs. time monitors orders over time, not just the current values. The channel is updated each time a new order FFT is calculated.

This will extract specific orders from the order waterfall plot to create channels, allowing you to plot a specific order over time or as a function of engine speed.

To extract orders, simply enter the desired numbers in the Harmonics list field. Separate multiple entries with a semicolon (“;”). For example, to extract the 1st, 2nd, 3rd, 4th, and 5th orders, enter 1;2;3;4;5 and press Enter. If an extracted order falls between discrete order resolution steps, the closest matching resolution will be used.

Time-domain and order-domain harmonics are both complex channels. To obtain the amplitude from a complex number, use the ABS function in the Math module.

1abs('AI 1/Order H1')

1angle('AI 1/Order H1')

1Real = real('acc/Time domain'[0])

1Imaginary = imag('acc/Time domain'[0])

In the example above, the index [0] will show 1st harmonic, index [1] will show 2nd, and [2] the 3rd harmonic.

Extracting interharmonics

In the Order Tracking module, there is an option to extract fractional order components, also known as interharmonics. Enter the numbers in the Harmonic List section, using a period (.) as the decimal separator. For example: 0.5; 1.2; 3.87, etc.

Order-domain harmonics and interharmonics are complex channels displayed on the 2D graph.

In this section, you define the frequency-domain spectral properties and the parameters for harmonic extraction in the time domain.

In the Time FFT Setup section, the following data results can be selected as output channels:

Time-domain harmonics – Complex output values providing magnitude and phase information of the defined harmonics over a time axis. In the Harmonics List, you specify which harmonics you want to extract.

FFT waterfall vs. reference – Frequency spectra over the defined range of the Reference Channel.

Overall RMS vs. reference – Overall RMS values over the defined range of the Reference Channel.

The FFT resolution and data block length are, by default, automatically set based on the sampling rate, Order resolution, and Maximum order.

Time-domain harmonics

This is a complex output channel showing the amplitude of harmonics over time. In the Harmonics List section, you define the harmonics to extract.

The parameters Update on Reference Change (Delta) and Update on are used to define when new harmonic values are extracted along the time axis.

FFT waterfall vs. reference

If FFT Waterfall vs. Reference is enabled, the Time FFT Waterfall Spectrogram will display a defined number of lines for each REF bin. The resolution is calculated based on the Maximum Order, sample rate, and Order FFT block size. For better understanding, the delta frequency is also shown.

By default, the resolution is set to Auto. You can manually adjust the FFT resolution in the FFT Waterfall diagram by selecting a value from the FFT Lines drop-down menu.

Example of the difference between calculated and displayed data:

The second picture shows much sharper lines and separates the frequencies much more clearly.

Overall RMS vs. RPM

This channel displays the overall RMS amplitude across the defined range of the reference channel.

Order domain harmonics are extracted as "orders over reference bin values" and displayed on a 2D graph.

The graph above shows the vibration spectrum of an electric scooter motor mounted on rubber foam. The three major orders are marked (1st, 16th, and 32nd). It is also possible to extract them and observe their amplitudes and phases over RPM.

This is the traditional method but still applies, especially if you want to monitor the behavior of extracted orders over the entire time interval. (Order domain harmonic values are updated whenever reference values that have already been used are reached.)

Please use the XY recorder to display the extracted data:

First, select the OT_Frequency channel from the channel list (x-axis) on the right side, then assign the abs('signal/Time domain'[0]) channel to the y-axis.

As order tracking is performed during a run-up or coast-down, the visualization instruments display the vibration spectrum (and the orders) over RPM or another selected reference channel, as well as frequency. Individual order lines can also be extracted.

Automatic display mode

When the order tracking module is enabled and you start the measurement, DewesoftX will automatically generate a predefined display setup showing the major signals for a quick start.

In the picture below, the automatic display configuration is shown. The visual controls in the bottom left of the screen are 2D graphs that display the selected channels in various complex presentations. In this example, you can see the magnitude of the overall RMS alongside the 1st and 2nd extracted harmonics..

The handling of all visuals follows the same concept. For the selected visual, the properties are displayed on the left side, while the channel selector for that visual is shown on the right side. Only channel types suitable for the selected visual are available. For example, you cannot select statistical channels for a visual that displays angle-based data. Channels that are already selected are shown in bold.

You can use Search at the top of the channel list to quickly find the desired channels.

Customizing display

DewesoftX allows a completely flexible arrangement of displays. The main displays used for order tracking measurements are described below.

The most important instrument for order tracking is the 3D graph.

FFT waterfall vs. reference

When you add it in Design mode and assign the channel/FFT waterfall from the channel list, you will obtain the FFT waterfall versus reference.

The waterfall plot displays multiple FFTs across the defined reference RPM range (y-axis), with vibration amplitude represented by color (upward direction in 3D mode).

This instrument allows you to separate the spectrum into frequencies related to RPM (orders) and other frequencies, such as mechanical resonances or electrical grid noise.

The 3D FFT instrument updates in real-time during measurement, growing dynamically during run-up or coast-down while already showing the end result.

Order waterfall vs. reference

With the 3D graph instrument, the order FFT can also be displayed.

Orders are plotted versus RPM or another selected reference channel quantity, with color representing vibration amplitude.

The straight lines parallel to the y-axis indicate the orders. This is particularly helpful because the frequencies of the orders change with RPM, making them sometimes difficult to trace.

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 is the comparison: Frequency FFT (left) and Order FFT (right). The fixed straight 100 Hz noise line in the Frequency FFT appears as a curve in the Order FFT, marked with a red dotted line in both graphs.

For this functionality, you need to enable the Time domain harmonics checkbox in the Order Tracking setup. It is also possible to create a Polar diagram using Order domain harmonics.

In the scooter motor example, the strongest orders are relatively high, so we selected 1; 16; 32 in the Harmonics list.

The complex output (Re + i * Im) must be split into real and imaginary parts using the Math module. To do this, create a new formula and add one starting with real() and imag() applied to the signal/Time domain channel. This can also be done offline on the data file after the measurement. Go to Recalculate and review the Math preview again.

1real('acc/Time domain')

An array will be created, which essentially combines the four channels re1, re16, re32, and re48 into a single multidimensional channel. To access the components, simply add [i], where i is the index {0,1,2,3}, representing the orders {1,16,32,48} in this example. For instance, real('signal/Time domain'[0]) will give the real part of the 1st order.

1
2real('acc/Time domain'[0])

Next, do the same for the imaginary part using imag('signal/Time domain'[0]).

1-
2imag('acc/Time domain'[0])

Then, take the XY recorder and first assign the Real1 channel, followed by the Imag1 channel.

The x-axis and y-axis should be manually scaled to the same minimum and maximum values to display the angle proportions correctly.

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

Take another look at a waterfall spectrogram, similar to the FFT waterfall vs. reference. As discussed earlier, it consists of many frequency spectra (one for each delta REF). It may be useful to extract a single spectrum for a user-defined REF bin.

While measuring or in post-processing Analyze mode, right-click on the 3D graph widget and select Add markers. To extract spectral data from a single REF bin, select Y cut (in the example below, Y cut (RPM) is used since the reference tag axis is RPM).

In addition to being displayed on the graph widget, each added marker will also create a derived channel that can be used in other widgets and math modules. To visualize it, add a 2D graph from the instrument toolbar:

Assign the channel signal/TimeFFT/X cut or signal/TimeFFT/Y cut to the graph. The 2D widget will now display the derived marker cut channel.

Another commonly used analysis result (for worst-case scenarios) is the run-up of the machine, with a calculation of the maximum amplitude values across the entire FFT spectrum.

Add an FFT math from the Math module.

Then select the input channel—for example, choose an acceleration sensor. Set the following parameters:

• Output spectra to Amplitude

• Averaging - Mode to Overall

• Averaging - Type to Maximum

Add a 2D graph from the Widgets menu and assign the Channel/AmplFFT.

In the recorder, you can select a specific section of the data file that covers a certain REF range. The selected section will be used to calculate the spectral results.

You can also display frequency spectra and order spectra on a Campbell plot.

Click the Widgets button and add a Campbell plot by clicking on the icon shown below.

A comparison between the 3D graph and the Campbell plot is shown below:

Options

The Campbell plot offers multiple options to customize its design.n.

• Cutoff

• Levels

• High-value size

• Low-value size

• Palette

• Circle style

• Projections

• Interaction

    Cutoff

The cutoff is given in percent [%]. It determines the portion of the value range that will be excluded from the display. The diagram's scale indicates which values are hidden by masking the scale's color map.

The example below shows no cutoff (0%) on the left and a 30% cutoff on the right. The scale’s color maps are adjusted accordingly.

High and low amplitude values correspond to the diameters of circles, ranging from largest to smallest. Diameters of circles for intermediate levels increase linearly from the smallest to the largest, depending on the number of levels. Each level has its own diameter.

Levels

The minimal and maximal values on the diagram's scale (located on the left side of the Campbell plot visual control) define the range of values that will be segmented into levels. Values greater than the maximal value are assigned to the highest level, while values smaller than the minimal value fall into the lowest level.

The example below shows how the value range is segmented into levels, with the number of levels set to 5.

Palette

The scale's color map can be generated from different palettes (using the Palette drop-down menu on the left). Below are examples of the available options:

• Rainbow (warm)

• Rainbow

• Grayscale

• Single color (color taken from the channel on the diagram)

Circle style

There are two possible circle styles: Outline (default) and Fill. In the example below, the filled circle style is shown on the left, while the outlined circle style is displayed on the right.

Projections

The Campbell plot allows you to choose between XY and YX projections. In the XY projection, the x-axis is horizontal and the y-axis is vertical. In the YX projection, it is reversed: the x-axis is vertical, and the y-axis is horizontal.

Interaction

Selection Marker shows the value of the area where your mouse cursor is currently positioned on the diagram. The value is displayed in the upper-left corner of the visual control.

Free Marker allows you to mark a position with a single left-click of the mouse on the desired area. You cannot click on areas where there are no values (cut-out levels). A small cross will be drawn to indicate the marker's position, with its index shown alongside.

Show Marker Table—when selected, a table with the collected marker values will appear. It displays the values of free markers and also allows you to remove any of them.

Show Marker Values—if checked, the value of the marker will be displayed instead of its index.

In this example, the movement of a rotating disc will be visualized. To achieve high angular resolution, an encoder with 1024 pulses per revolution is typically used. A 2-axis acceleration sensor is mounted on the metal frame supporting the motor. The axis orientation is shown below.

The sensor output is acceleration measured in m/s². By applying double integration, you can calculate the displacement in μm. This can be done directly in the Order Tracking module under Spectral Weighting, or by using Time Integration/Derivation in the DewesoftX Math module.

You must carefully choose the Order and Low-Pass Frequency to avoid creating an unwanted or unstable output signal. To determine the filter frequency, generate an FFT spectrum from the acceleration sensor and identify the lowest dominant frequency. A 4th-order filter at 4 Hz is a good starting point (signals below 4 Hz × 60 = 240 rpm will be cut). Using lower frequencies or higher orders may cause the filter to oscillate slowly due to the DC offset from integral calculations.

The Widget that displays the shaft’s movement is Orbit, located under Machinery Diagnostics.

First, assign the X displacement channel, then the Y displacement channel. Both axes are automatically scaled with the same minimum and maximum values.

The orientation of the sensors can be modified on the left side, and the displayed time can also be selected. Under Angle, define the angle of your First Channel (“X” sensor) position and the Second Channel (“Y” sensor) angle.

In Analyse Mode, DewesoftX allows data review, modification or addition of Math Modules, and printing the complete screen to generate your report. Similar to Measurement Mode, you can modify or add new Visuals or Displays. All these modifications can be stored in the data file using Store Settings and Events. This display layout and formulas can also be loaded into other data files using Load Display & Math Setup or applied to multiple files with the Apply Action feature.

Export of complex data

Go to the Export section to access different export options. Select File Export, and under Data Presentation, you will see the Real, Imag, Ampl, and Phase options. Select Real and Imag.

Select Yes in the Exported column next to the Complex Data Type channel you want to export.

For each order selected for calculation in the Order Tracking setup (1st, 16th, 32nd, and 48th), two columns (Real and Imag) are exported.

Exporting marker cuts from graphs

The data cut from graph widgets can also be exported. To do this, first perform the normal cut procedure as described in the 3D Graphs – Spectrum and Harmonic Marker Cuts section.

Select the 2D Graph widget and open the Edit menu in the upper-right section of DewesoftX. Then navigate to Copy to Clipboard → Widget Data.

The clipboard data can then be easily pasted into other programs, such as Excel.

The Copy Data to Clipboard function is also available on the standard FFT instrument.

The Order Tracking method is an excellent tool for determining the operating conditions of rotating machines, such as identifying resonances, stable operating points, and the causes of vibrations. In this webinar, you will learn how to connect the sensors, configure the setup, perform measurements, and analyze the results.