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Calculate a VECTOR SUM to make understanding vibration data easy!

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

triax.png

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 rpmA 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:

 

equation1.png

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

equation2.png

However, when using 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:

 

equation3.png

 

Calculating a VECTOR SUM in LMS Test.Lab Signature

 

In LMS Test.Lab, 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 LMS Test.Lab 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 SUMIn 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" menuChoose 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 functionChannel names can be used in the VECTOR_SUM function

 

Channel numbers can be used in the VECTOR_SUM functionChannel 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 linesTwo lines - Black and Blue - take the place of six lines

LMS Test.Lab Processing Tips:

 

LMS Test.Lab Acquisition Tips:

 

LMS Test.Lab Display Tips:

Comments
Enthusiast
Enthusiast

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

Many thanks!

Smiley Very Happy

Jeongsoo

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