Calculate a Vector Sum to Make Understanding Vibration Data Easy

Measuring vibration with a triaxial accelerometer? Use a VECTOR SUM to simplify your data analysis!

Products and humans experience vibration in three 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 (in purple) reflects both the high amplitude vibration in the X direction (green) around 2800 rpm and Z direction (red) above 3000 rpm
 

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.

The vector sum is often used in the calculation of Human Body Vibration.

This article has the following contents:
   1. Vector Sum Background
   2. Vector Sum in Simcenter Testlab Signature
   3. Vector Sum in Simcenter Testlab Neo
   4. Conclusion

1. Vector Sum Background

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:

2. Vector Sum in Simcenter Testlab Signature

Direct YouTube link: https://youtu.be/tBm2ZJvliGQ


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.

3. Vector Sum in Simcenter Testlab Neo

Vector sum can be calculated in Simcenter Testlab Neo Process Designer using the Block Calculate method. An example process is shown below:

Process to calculate vector sum of an order in Simcenter Testlab Neo.

For example, if 18th order was calculated in the "Order Sections" method, the block calculate method could be configured as follows:

Block Calculate method for vector sum

In the method above, the 18th order in the X, Y, and Z directions were R1, R2, and R3 respectively.  The F1 formula is defined as "vectorsum(R1;R2;R3)".

More information on the block calculator method in the knowledge article: Simcenter Testlab Neo: Combined, Block Calculator, and Signal Generation Methods.
 

4. 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

Enjoy! Questions?  Email charles.rice@siemens.com or contact Siemens Support Center.

Simcenter Testlab Acquisition Tips

• Index of Testing Knowledge Articles
• Simcenter Testlab Signature
• Simcenter Testlab Audio Replay and Filtering
• Hands-free acquisition (almost)
• Capturing Transient Events in Simcenter Testlab
• Cool Channel Setup tricks for Triaxial Accelerometers
• Data Acquisition Based on GPS Location
• How to calculate a VECTOR SUM
• Tips and tricks for acquiring torsional orders
• CAN Bus Measurements
• No more tach! Use OBDII to get engine and vehicle speed...
• Record Raw CAN Bus Data and Decode Offline!
• Single Plane Balancing in Simcenter Testlab
• Correcting a bad calibration factor
• Simcenter Testlab Calibration

Simcenter Testlab Processing Tips

• Simcenter Testlab Throughput Processing Tips
• Human Body Vibration
• RPM Extraction in Simcenter Testlab
• Run Comparison in Simcenter Testlab
• Order Sections: Setting Parameters
• Time Signal Calculator Tips
• Simcenter Testlab: Calculating Statistics from Time Histories
• Simcenter Testlab: Appending Time Histories
• Simcenter Testlab: Create a new recording from a segment cut
• Simcenter Testlab Sound Diagnosis
• Can I view data in Google Earth?
• Analyzing PWM Signals in Simcenter Testlab
• Simcenter Testlab YouTube Playlist