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# Calculate a VECTOR SUM to make understanding vibration data easy!

Siemens Experimenter

### Measuring vibration with a triaxial accelerometer?

Use a VECTOR SUM to simplify your data analysis!

Products and humans experience vibration in 3 dimensions/directions.  Whether a particular vibration is in the lateral direction or in the vertical direction, it can still fatigue a part or lead to operator discomfort.

A VECTOR SUM can be applied to the three directions of a triaxial accelerometer to calculate the overall magnitude of vibration, independent of the direction.

A VECTOR SUM (in black) reflects both the high amplitude vibration in the X and Y directions from 500 to 700 rpm

The formula for a VECTOR SUM of a triaxial vibration measurement consisting of X, Y and Z is as follows:

So for a vibration levels where X=5g, Y=7g and Z=12g, the VECTOR SUM would be equal to: 14.76g as follows:

However, when using Simcenter Testlab (formerly LMS Test.Lab), complex quantities (with both a real and imaginary portion) are often measured.  For example, spectrums can include phase. In reality, the VECTOR SUM equation is a bit more complicated, as follows:

Calculating a VECTOR SUM in Simcenter Testlab Signature

In Simcenter Testlab Signature, one can calculate a VECTOR SUM either:

• during a measurement with real time viewing OR
• after a measurement has already been performed in throughput processing

To calculate a VECTOR SUM, set it up in either:

• During Measurement: In “Online Processing worksheet” of Simcenter Testlab Signature, choose “Derived” tab in upper right OR
• Offline Processing: In “Time Data Processing” worksheet, click on the “Change Settings” button from the “Channel Processing” area and select the “Derived FS” tab (Note: "Time Data Processing" can be turned by selecting "Tools -> Add-ins -> Signature Throughput processing" from the main menu)

In the “Derived” tab, highlight the first cell in the “Formula” column and press the “F(x)” button above.

In the "Derived" tab, highlight the formula cell and select the "F(x)" button to define a VECTOR SUM

Scroll to the bottom of the “Select Function” menu and choose the VECTOR_SUM function. You may need to click the “New function” button once to make three entries possible in the menu.

Choose the VECTOR_SUM function from the "Select Function" menu

In the VECTOR_SUM dialog, enter either the Channel reference (CH1, CH2, CH3, etc) or the PointID (left_mnt_act:+X, left_mnt_act:+Y, etc). If you do not know the Channel reference, it is available in the drop down menu in the upper right of the 'Channel Processing Settings' menu.

Channel names can be used in the VECTOR_SUM function

Channel numbers can be used in the VECTOR_SUM function

Either method (the name or number) can be used to refer to a channel.  Press OK when finished.

Now a VECTOR_SUM will be calculated on any and all frequency-based data functions: spectrums, autopowers, orders, frequency sections, etc.

Conclusion

Once a VECTOR SUM calculation is setup and created, it is much easier to interpret vibration data.  Instead of having to look at three individual graphs for each vibration measurement location, only one graph needs to be viewed to ascertain the overall vibration.

Two lines - Black and Blue - take the place of six lines

Simcenter Testlab Acquisition Tips

Simcenter Testlab Processing Tips

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Enthusiast

It is quite useful method for me to assess vibration severity.

Many thanks!

Jeongsoo

Experimenter

So what is the calculation process? Is it VectorSum (Time Data) --> FFT  OR is it FFT --> VectorSum(FFT). Which one does LMS use?

Siemens Phenom

Hello, since the VECTORSUM command is a Derived Channel on Online Processing in Signature Acquisition or Channel Processing in Time Data Processing \ Signature Throughput Processing it would be done on the frequency domain data.  The screen shows it as a Frequency spectrum so it is being calculated from the spectrums.

I would personally not every try a vector sum on the time domain data.  So, to answer your question, it is FFT --> VectorSum(FFT).

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