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Harmonic Removal

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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:

  • Correcting “runout” in measurements
  • Isolating harmonics due to a specific rotating component
  • Removing harmonics from operating data for an operational modal analysis
  • Correcting data contaminated with unwanted harmonics
  • And more…

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.

 1b.pngFigure 1: Spectrum with harmonics (red) and without harmonics (green).

k2b.png

 

To do this processing, the rotational speed of the rotating system of interest is needed.

 

Harmonic Removal Background                         

 

Harmonic removal consists of several steps:

  1. Time to Angle: First, the data is transformed from time domain to angle domain.
  2. Cycle Averaging: In the angle domain, averaging is done over a user defined number of cycles/revolutions to create an average. The average will consist of data synchronous/harmonic with the selected tachometer.
  3. Cycle Subtraction: The average is then subtracted from each individual cycle to remove the fundamental frequency and its harmonics.
  4. Angle to Time: The modified angle domain data is transformed back to the time domain.

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).

 2.pngFigure 2: In a four stoke engine, there is one combustion event per two revolutions of the crankshaft. Therefore, a cycle consists of two revolutions.

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.

 

From the main Simcenter Testlab menu, select ‘Tools -> Add-ins’ (Figure 3) and turn on ‘Harmonic Removal’ (15 tokens) and ‘Time Signal Calculator’ (26 tokens).  

 

3.pngFigure 3: Tools -> Add-ins -> Harmonic Removal.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.

 

4.pngFigure 4: Harmonic filter is available in the Time Signal Calculator.

After pressing the OK button, there are several settings to perform harmonic removal as shown in Figure 5.

 

5.pngFigure 5: There are six settings in the Harmonic Filter menu.

The settings are as follows:

  • function1: The data channel from which the harmonics will be removed.
  • tacho: The rpm channel used to convert from the time domain to the angle domain and vice versa. The harmonics related to this channel will be removed.
  • samples_per_rev: The number of data points per revolution in the transformed angle domain data. The maximum order that is removed is half the number of samples per revolution.
  • cycle_definition: Number of revolutions per cycle. For example, in a four stroke motor, there are 2 revolutions for a complete cycle.
  • nr_of_cycles_for_avg: The number of cycles used to calculate one average harmonic. This is a sliding average that is used to calculate the harmonic average. The order resolution is equal to 1/(Number of Cycles for Average). For example, 10 cycles for the average is 0.1 order resolution, assuming there is 1 revolution per cycle.
  • mode: Choose if the output is in the time domain or the angle domain.

 

k2.png

 

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 the time domain, the pulses will not be evenly spaced due to the varying speed
  • In the angle domain, the pulses are evenly spaced as the event occurs in the same location on the shaft, cycle by cycle

In Figure 6, each revolution is colored with alternating blue and orange.

 6.pngFigure 6: Looking at a once per revolution event in the time domain vs the angle domain. The events are not evenly spaced in the time domain but the events are evenly spaced in the angle domain.

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).

 

 7.pngFigure 7: Top: Full signal. Bottom: Zoomed in signal (first 10 cycles) shows a combination of 1st and 2.3 order

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.

 

8.pngFigure 8: Averaging within the sliding window is used to remove harmonics.

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.

 

9.pngFigure 9: A ten cycle frame is slid through the angle time history. The blue and orange bars are the revolutions which are averaged together into a single cycle (indicated by red lines).

The sliding window is moved thru the time history one sample at a time.

 

k3.png

 

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.

 

figure0.pngFigure 10: The data can once again be viewed in the time domain.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.

 
11.pngFigure 11: To measure torsional fluctuations, zebra disc is mounted at end of shaft with laser pointing at it.

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.

 

12.pngFigure 12: A zebra disc mounted off-center on a shaft creates an artificial once per revolution increase (pink oval) and decrease in rpm (green oval).

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).

 

13.pngFigure 13: Off-center rotation of zebra disk causing RPM fluctuation in time domain.

Because the rpm speeds up and slows down once per revolution, runout manifests itself as a first order phenomenon with integer harmonics (Figure 14).

 

14.pngFigure 14: Off center rotation is first order phenomenon. Dominant first order and its harmonics should be filtered out.

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 torsionals.

 

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.

 

15.pngFigure 15: Harmonic removal shows which component is responsible for a given order of vibration. Orders in red are due to hydraulic pump while orders in green are due to the alternator.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.

 

zoom.pngFigure 16: Top – Colormap of signal has 8 Hz and harmonics (vertical lines), Bottom – Same data as top, zoomed into 100 Hz frequency range.

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.

 

key.png

 

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.

 

tsc.pngFigure 17: Time Signal Calculator is used to create a tachometer rpm

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.

 

before_after.pngFigure 18: Top – Colormap of original data with 8 Hz harmonics, Bottom – Colormap of data with harmonics removed.

 A “2D” view of the same data is shown in Figure 19.

 

spectrum.pngFigure 19: Spectrum with and without eight Hertz harmonics.

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.

 

Conclusions

 

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:

  1. Perform pitch correction on runout issues
  2. Identify which rotating subsystem is responsible for a response in the overall system
  3. Removing harmonics from operating data for an operational modal analysis
  4. Correcting data contaminated with unwanted harmonics
  5. And much more!

Questions?

 

Feel free to post a reply, email scott.beebe@siemens.com, or contact Siemens PLM GTAC support.

 

Related Rotating Machinery Links

Related Simcenter Testlab Acquisition Links

Comments
Creator
Creator

Hi Friends!

 

I did a OMA Test in a maritime structure (Catamaran), and I placed six acelerometers on the deck of the structure and a tachometer to recorder the RPM of the main engine in the test (two engines). The RPM value were: 1800 RPM, the RPM of the propulsion shaft were: 718 RPM and the 1rst frequency of the propellers were: 47,4 Hz. Using a EFDD Method to calculate the Singular Value Diagram of the test and I obtained the following:

 

Sin título.jpg

 

And the harmonic components list are shown here too:

 

ee.jpg

 

And those values corresponding to RPM Main engine, propeller and propulsion propeller, and their 0,5X, X1, X2, X3, etc (I show their here too):

 

QQQ.jpgt

 

My question is:

 

It's possible to remove this harmonics components? I used the kurtosis method to do that but can't remove those components. Other solution suggested was to do other tests in differents revolutions of the main engine to the harmonic components change the position and so let me to identificate natural modes hidden.

 

Greetings

Alvaro