Order Tracking Analysis Object (Order Tracking Option – deprecated and removed from Gallery in FlexPro 2021)
Note: In FlexPro 2021, order tracking was changed to a completely new procedure. This analysis object was replaced in the process, but it is still available in FlexPro so that your existing evaluations will work without any changes. The deprecated order tracking analysis objects which were removed from the gallery with FlexPro 2021 can still be viewed in the Gallery via File > Options > System Settings. Activate this option if you want to continue using the deprecated analysis objects in new projects (not recommended).
This analysis object performs an order tracking analysis for speed-dependent vibrations. Vibrations measured at rotating machines show a spectrum in which the maxima occur for frequencies that correspond to multiples of the speed of the machine. There are two different causes for the appearance of these maxima. On the one hand, you can view the machine as a non-linear transmission system that is activated by a harmonic vibration corresponding to the speed. The non-linearity generates harmonic components of this fundamental vibration that lead to the corresponding maxima. On the other hand, this type of machine may contain components whose speed is not equal to the base speed, but always corresponds to a fixed multiple of this speed. Different axles have different speeds in a transmission, for instance. But also the teeth of a gearwheel or the balls in a ball bearing create vibrations that are permanently related to the speed. If you recognize this relationship described as the order from the fundamental frequency of a component to the fundamental frequency of the machine, then individual maxima in a spectrum can be assigned to one or a few components of the machine. With this, the cause of resonances, for instance, can be isolated.
For order tracking analysis, the vibration signals measured at a certain speed are subjected to a Fourier transform (FFT). Individual spectral lines whose frequencies correspond to a multiple (order) of the fundamental frequency determined by the speed are then taken from the spectrum.
Essentially, two measuring methods are used for the order tracking analysis. For a ramp-up, the vibration and instantaneous speed are synchronously measured while the machine is slowly brought up from its lowest to its highest speed. A search is performed in the speed signal for the speeds to be analyzed, and a Fourier transform is calculated for the corresponding locations in the vibration signal. The frequencies corresponding to the orders are then extracted from the spectrum. For a result with optimum precision, an angle-based sampling is to be preferred over a time-based sampling. In this case, the number of samples per revolution for each speed is equal in size and thus the spectral resolution of FFT is independent of the instantaneous speed. In addition, it is important to note that for this process, the speed of the machine should not vary too quickly. For each desired speed position, a time segment for the FFT must be taken for which the speed is assumed as constant. If the speed in such a time segment varies, then the peaks in the spectrum blur, i.e. they become flatter and wider.
In a second method, the machine is first brought up to a certain speed and then a measurement of the vibration for this speed is taken. This process is repeated for all desired speeds. If the speed of the machine cannot be maintained exactly at the particular specified value, then this speed can be synchronously measured and provided for the order tracking. The order tracking then determines the mean value of the measured speed and assigns this to the respective vibration signal.
The result of the order tracking is a signal series with a Z component. The two-dimensional Y component always contains the spectral amplitude values. The X and Z components contain the speed or frequencies and the order.
Note Make sure that the sampling rates are high enough. For the highest frequency to be evaluated (= highest speed * highest order / 60), at least two samples per period must be present, according to the Nyquist theorem.
Data Tab
Sampling
The analysis object can process time and angle signals. A time signal is present if you have measured with a constant time-related sampling rate. If you are working with time signals, the time axis of the vibrations often has a different physical unit than the reciprocal of the speed. For instance, the speed is often specified using the unit 1/min or RPM, while the unit of time is 1s. For this reason, you can specify a correction divisor by which the speed is to be divided to calculate the frequency. An angle signal is present if the sampling rate is speed-dependent, i.e. a certain number of samplings per revolution has been made. Select the option Angle signal with angle in radians in the X component if your data already contains the correct angle in radians. If this is not the case, then select the option Angle-based data with fixed number of samples per revolution. In this case, an X component does not need to be present. Instead, specify the number of samples per revolution as the fixed value.
The instantaneous speed is often measured using an pulse sensor that records a certain number of pulses per revolution. You can specify the pulse signal resulting from this directly as the speed signal. For this, select the Speed is an pulse signal and specify the Number of pulses per revolution. If the measured data are present as time signals, then this pulse signal must be specified as a time signal as well. If angle-based data are present with a fixed number of samples per revolution, then it suffices to specify a data series with the measured pulses because the angle information can be calculated.
Data
The analysis object can process three different data structures. You can specify a signal series. The Y component will then contain several oscillations that were measured at different speeds. Each column of the Y data matrix contains the vibration signal for a certain speed. The X component contains either the sampling points or the angle in radians, which are ignored if the number of samples per revolution was specified. The Z component contains the speeds for which the individual oscillations were measured.
As a second alternative, you can specify several signals and their assigned speeds. The signals can be angle or time signals and can vary in length. If angle-based data are present with a fixed number of samples per revolution, you can omit the X components here as well and specify a data series. For every signal, you specify a speed or corresponding pulse data. You can specify a scalar value, data series or signal for the speed. A scalar value is interpreted directly as the corresponding speed. Otherwise, if applicable, the speed is calculated first as specified above from the pulse data. The speed series is then averaged to obtain a scalar value.
As a third alternative, one signal with ramp-up can be analyzed. For this, the signal must cover all the speeds to be analyzed. The rising instantaneous speed must be made available as a second data set. This does not necessarily have to be measured synchronously with the ramp-up. If both data sets are present as time signals, they are synchronized via the X values. The speed can also be calculated from pulse data. The speeds for which order tracking is to be carried out are searched for in the speed data set. From the relevant position, a segment of the specified length is extracted from the signal. Each of these segments is then subjected to an order tracking. Specify the speeds either as a linear series via the parameters From, To and Increment or select a data set that contains the desired speeds as the data series.
As a fourth alternative, one signal with variable speed can be analyzed. In this case, the instantaneous speed does not have to be ascending, because the order tracking analysis is not carried out for given speeds but for given times. For the times for which an order tracking analysis is to be performed, a segment of the specified length is extracted from the signal. Each of these segments is then subjected to order tracking. Specify the times either as a linear series via the parameters From, To and Increment or select a data set that contains the desired times as a data series.
In general, the speed is assumed to be constant within the time segment assigned to a speed, i.e. the segment should be as large as possible, but only so large that the speed can be assumed to be constant. Otherwise, the spectral lines in the FFT become blurred because the frequencies change in the time window under consideration. The adjustment of the segment length is relatively critical as it influences the resolution of the FFT. For testing, a time-frequency spectrum of the signal should be made with the Time-Frequency Spectral Analysis Object with exactly the desired segment length. Then you should vary the segment length so that the frequencies to be searched for are well resolved.
Options Tab
Spectrum Type
The frequency domain information can be output in a variety of formats. In the following table, δF is the frequency spacing of the FFT, Re is the real component of a given segment's real (single sided) FFT at a given frequency, Im is the imaginary component, and n is the data segment size.
Spectrum Type |
Formula/Description |
|---|---|
Amplitude |
sqrt(Re² + Im²) / n |
RMS Amplitude |
sqrt((Re² + Im²) / 2) / n |
PSD - Power Spectral Density |
(Re² + Im²) / n² / δF / 2 |
MSA - Mean Amplitude² |
(Re² + Im²) / n² / 2 |
Amplitude² |
(Re² + Im²) / n² |
Complex Amplitude |
complex(Re, Im) / n |
Real component |
Re / n |
Imaginary component |
Im / n |
Phase |
arctan(Im / Re) |
FFT Length and FFT Segment Spacing
An FFT is calculated for each vibration signal or, for signals with ramp-up, for each data segment. If you select the option longest in the FFT Length field, then the FFT stretches over the entire data length, or more precisely, over the next smaller power of two. If you select As specified and specify a window length, then a mean FFT is calculated. An FFT window of the specified length wanders across the data segment and an FFT is calculated for each position. The individual spectra obtained in this manner are then averaged to form the result. If you select Seamless under FFT segment spacing, then the individual FFT segments are arranged one after another with no gaps in between. Select As specified and enter a segment spacing to make the segments overlap. For example, an FFT length of 1024 and a segment distance of 512 result in a 50% overlap. The mean spectrum is a periodogram and shows a reduced variance of spectral amplitude for simultaneously reduced spectral resolution compared to an individual FFT.
Windows
To reduce the spectral leakage of the Fourier transform, you can evaluate the oscillations before the transform using a window function. This evaluation leads to a stronger representation of the spectral lines in the result. The amplitudes of the spectrum, however, will also be reduced. If you select Amplitude normalization, this normalizes to the gain of the used window function, i.e. the sum of all values is divided by their number. This compensates for the amplitude attenuation resulting from the window evaluation of the data.
Orders and Band Width
Specify the Orders directly or specify a data set containing these orders. When extracting the frequencies corresponding to the orders, the analysis object examines a frequency band around these frequencies and takes the spectral line with the highest absolute value. Specify the Band width for this process as a percentage of the speed corresponding to the order (order * speed).
Result
The Result of the order tracking can be output in various formats. It is always a signal series whose Y component contains the spectral lines extracted as orders. If you are working with individual signals, these are automatically sorted in the result according to increasing speed.
Depending on the desired result format, the X component either contains the orders of a certain speed, the speeds of a certain order, or the frequency, i.e. the product of speed and order, or data that are taken from an external data set. When displaying across the product of speed and order, resonance points are easily visible because they lie above one other. If you analyze a signal with variable speed, then the times for which an order tracking analysis was performed are transferred to the result instead of the speeds.
Examples
In the project database C:\Users\Public\Documents\Weisang\FlexPro\2021\Examples\OrderT racking Analysis.fpd or C:>Users>Public>Public Documents>Weisang>FlexPro>2021\Examples\Order Tracking Analysis.fpd you can find examples of the different data structures for which order tracking can be performed.