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After acquiring dynamic data on rotating machinery, it is sometimes desired to separate harmonic components from the rest of the data.
Harmonic separation has a number of applications including:
Harmonics are discrete frequencies which are caused by a rotating component. The “Harmonic Removal” software module of Simcenter Testlab (formerly called LMS Test.Lab) can be used to remove or extract a fundamental frequency of a rotating system and its harmonics from test data as shown in Figure 1.
To do this processing, the rotational speed of the rotating system of interest is needed.
Harmonic Removal Background
Harmonic removal consists of several steps:
In the examples that follow, the terms “cycle” and “revolution” will be used interchangeably. In practice, they may be the same or different. In some rotating machinery applications, like a four stroke engine, two revolutions equal one complete cycle of the engine (see Figure 2).
This is defined by the “cycle_definition” field in Simcenter Testlab (Figure 5).
Harmonic Removal in Simcenter Testlab
To remove the harmonics in Simcenter Testlab, use the Time Signal Calculator with the HARMONIC_FILTER function.
The ‘Harmonic Removal’ tool takes time histories as input and can create either time or angle domain histories as output.
In the ‘Time Data Selection’ worksheet, the ‘Harmonic Filter’ command can be accessed by pressing on the ‘f(x)’ button as shown in Figure 4.
After pressing the OK button, there are several settings to perform harmonic removal as shown in Figure 5.
The settings are as follows:
Below is an example with a signal containing 1st order and 2.3 order. The following steps are all performed by a single HARMONIC_FILTER operation:
1. Time to Angle
In the first step of harmonic removal, time domain data is transformed to the angle domain using the specified rpm trace.
Using the angle domain is very practical when analyzing systems with rotating components. In the angle domain, data is plotted versus cycle rather than versus time.
The angle domain is especially useful when the RPM trace is non-constant.
In this example, the RPM is increasing. Once per revolution, a piece of reflective tape passes an optical probe producing a tacho pulse (Figure 6).
In Figure 6, each revolution is colored with alternating blue and orange.
By transforming the data into the angle domain, the revolutions are distributed evenly along the angle axis. This allows averaging to be done easily on a ‘per cycle’ basis.
The angle domain data will be used for the next two steps.
2. Cycle Averaging in Angle Domain
In the next step, an average cycle is calculated in the angle domain via a sliding window throughout the duration of the signal. This average will be removed from the original data in the next step. The number of cycles in the sliding time window is defined by the ‘nr_of_cycles_for_avg’ parameter (Figure 5).
Anything that rotates “in sync” (i.e., an order that is an integer multiple of the rotation) with the shaft is a harmonic that will be included in the average.
Anything that rotates “out of sync” with the first order shaft will be averaged out.
The 2.3 order content does not rotate “in sync” with the first order shaft and is therefore averaged out. This is shown in Figure 8.
Only the first order component (and multiples of first order if there were any) remain in the average.
3. Cycle Subtraction
To remove the harmonic content and isolate the 2.3 order content, the average from the sliding window is subtracted cycle by cycle from the original signal as shown in Figure 9.
The sliding window is moved thru the time history one sample at a time.
4. Angle to time
The resultant data is then transformed back to the time domain. Only the 2.3 order remains as shown in Figure 10.
These are the basic steps to harmonic removal. Some example applications are highlighted next.
Application Example #1: Removing Harmonics Caused by Runout
Harmonic removal can be used to correct rpm estimations from a zebra disc. A zebra disc can be used at the end of a pulley to measure torsional fluctuations in the rpm of a rotating shaft as shown in Figure 11.
If not carefully mounted, the zebra disc could be off of the center of the shaft as shown in Figure 12. This causes a one per revolution modulation in the rpm estimation. The zebra disc appears to speed up and slow down once per revolution.
In Figure 12, the red dots indicate laser points which indicate how the tachometer pulses are spaced. The dots circled in pink indicate where the rpm artificially increases as the stripes are closer together, the dots circled in green indicate where the rpm artificially slows down.
This causes the rpm to be inaccurate. This type of error is apparent in the time domain signal (red) as shown in Figure 13. Using the harmonic removal function of Simcenter Testlab, the runout error can be removed (green).
Because the rpm speeds up and slows down once per revolution, runout manifests itself as a first order phenomenon with integer harmonics (Figure 14).
Using the harmonic removal function of Simcenter Testlab, the artificial first order and its multiples can be removed from the tachometer signal. With the artificial harmonics removed, the signal can be analyzed for torsional vibration.
Application Example #2: Determining Orders Created by Different Rotating Components
Many rotating machinery systems have multiple spinning components which create harmonic orders. Harmonic removal can be used to determine which components are responsible for overall vibration in the system as shown in Figure 15.
Order content in green is related to the rotation of the alternator, and order content in red is related to the hydraulic pump.
For this separation of orders to work, the rpm relationship of the alternator and pump could not be integer multiples. For example, if the pump's rpm was exactly twice (x2) the rpm of the alternator, they could not be separated. The rpm relationship would need to be a non integer number. A rpm ratio of 2.3 or 1.4 or 4.6, etc would allow the separation to occur.
Application Example #3: Removing 8 Hz Harmonics
Sometimes data can be contaminated by harmonics from external sources. In Figure 16, a colormap of a contaminated signal is shown. This signal is contaminated harmonics of 8 Hz.
The eight Hertz harmonics show as vertical lines in the colormaps. The colormaps consist of amplitude (color), frequency (X-axis), and time (Y-axis).
Can these harmonics be removed? Rather than reacquire the data, the harmonic removal tool can be used to remove these unwanted harmonics. The harmonic removal tool needs a rpm information, like a tachometer to do so, and in this case, no tachometer exists.
Because the harmonics are constant frequency, an artificial tachometer rpm can be created for the harmonic removal.
The Time Signal Calculator can be used to create the tachometer rpm information as shown in Figure 17.
An 8 Hertz square wave is generated in the first step, and the converted to a RPM in the second step. This allows the HARMONIC_FILTER command to be performed on the data as shown in Figure 18.
A “2D” view of the same data is shown in Figure 19.
It is also common for data to be contaminated by electric power harmonics. In the United States, this is often 60 Hertz and its multiples. In Europe, this is 50 Hz.
Harmonic removal is a powerful tool that can be used to better understand signals with unwanted harmonic content.
It can be used in a number of ways:
Related Rotating Machinery Links
Related Simcenter Testlab Acquisition Links