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LMS Test.Lab Modal Analysis: Modification Prediction

Siemens Genius Siemens Genius
Siemens Genius


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LMS Test.Lab Modal Analysis: Modification Prediction

 

Think design modifications can only be made on Finite Element models? Think again…!

After performing an experimental modal analysis and calculating a set of modes, each mode has a mass and stiffness matrix that can be modified. 

 

LMS Test.Lab Modal Analysis Modification Prediction can be used to:

 

  • Add or subtract mass at a node or point
  • Increase or decrease stiffness between two nodes or points
  • Create tuned absorbers targeted to a frequency

After creating a group of modifications, a new set of mode shapes and modal frequencies is calculated that incorporates the changes.

 

Spring-Damper and Mass Modification Background

 

Consider a single degree of freedom system, consisting of:

  • M – Mass
  • K – Stiffness
  • C – Damping

The natural frequency (wn) is equal to the square root of the stiffness over the mass as shown in Figure 1.

Figure 1: Single Degree of Freedom Mass-Spring-Damper systemFigure 1: Single Degree of Freedom Mass-Spring-Damper system

A modal frequency can be increased by:

 

  • decreasing mass
  • increasing stiffness

This holds true for all structures, even more complicated ones.

 

A ‘Spring-damper’ modification can be used to alter the stiffness between two points as shown in Figure 2.

 

 

Figure 2: Modified mass-spring system with increased stiffenerFigure 2: Modified mass-spring system with increased stiffener

By increasing the stiffness of the spring, the modal frequency will shift higher as shown in Figure 3.

Figure 3: Frequency Response Function of original system and system with increased stiffnessFigure 3: Frequency Response Function of original system and system with increased stiffness

How would increasing stiffness address vibration issues? For example, if vibration from driving on rough road ranged from 1 to 20 Hz, increasing the first body modes beyond 20 Hz would reduce vibration experienced by the driver.

 

 In addition to the stiffness, the damping can also be changed.

 

Tuned Absorber Background

 

A tuned absorber is a secondary mass-spring system that is added to an existing mode as shown in Figure 4.

 

 

Figure 4: Tuned absorber (M2, K2) applied to mass-spring system (M1, K1)Figure 4: Tuned absorber (M2, K2) applied to mass-spring system (M1, K1)

A tuned absorber takes the original frequency of the original system and divides it into two modes.  The frequency of the first mode is lower than the original system.  The frequency of the second mode is higher than the original system as shown in Figure 5.

Figure 5: Original System versus Tuned Absorber systemFigure 5: Original System versus Tuned Absorber system

The mode shape of the lower frequency would have both the original system mass (M1) and the tuned absorber mass (M2) move back and forth in phase. The two masses would move back and forth out of phase in the higher frequency mode. This is illustrated in Figure 6. If the tuned absorber mass and stiffness is carefully selected, the motion on the original system can be forced to zero by the absorber.

 

 

Figure 6: Original System versus Tuned Absorber systemFigure 6: Original System versus Tuned Absorber system

How can a tuned absorber be used to abate a noise and vibration issue?  Consider a vehicle where the combustion frequency of engine idle excites a bending mode of the steering wheel column. A tuned absorber could be placed on the end of the steering wheel.  This would place one mode of vibration at a frequency lower than the idle which would never be excited.  The higher mode could be placed at an engine combustion frequency that the vehicle does not commonly operate at, like 30 mph.

 

Additional Considerations

 

When using experimental modes for modification prediction, the following should be considered:

 

  1. Calibration – It is important that the proper calibration was used during data acquisition. This includes both the input and response transducers.  If the accelerometer calibration was off by a factor of 100, a 2 kilogram modification could act like a 200 kilogram modification.
  2. Dimensions - Proper dimensions should be used when creating the geometry. The dimensions can affect the modification prediction results.
  3. Out-of-Band Modes – To have accurate modal predictions, it is advisable to have at least one mode below and one mode above the frequency of interest for the modification. It is even better if several modes above and below the frequency of interest is included. When using a modal model for a limited frequency band it is possible that important structural modifications would generate modes with a natural frequency outside the range of this frequency band. Since the original modal models are not valid at these frequencies, the predicted results will not be very reliable.
  4. Proper Frequency Shift - If adding mass, modes should shift down. If they shift up instead, there is a high probability that there is a sign direction convention problem.  For example, on the input point, the +Z direction may have been substituted for the –Z direction. Check the directions again.

Getting Started with LMS Test.Lab Modification Prediction

 

Under “Tools -> Add-in” from the main menu, select “Modification Prediction”.  If using LMS Test.Lab tokens, it requires 23 tokens total (Figure 7).

 

 

Figure 7: Tools -> Add-ins -> Modification PredictionFigure 7: Tools -> Add-ins -> Modification Prediction

A new worksheet called ‘Modification Prediction’ appears at the bottom as shown in Figure 8.

Figure 8: Tools -> Modification Prediction on worksheetFigure 8: Tools -> Modification Prediction on worksheet

There are two minor worksheets at the top of the ‘Modification Prediction’ worksheet:

 

  • List Modifications – Create the set of modifications to be applied
  • Predict Modes – Calculate and view new mode set with modifications

Select a set of modes for modification in the upper left corner of the ‘Modification Prediction’ worksheet. Drag and drop modal frequencies over the geometry to view the shape as shown in Figure 9

 

 

Figure 9: Select mode set in upper right, drag and drop to geometryFigure 9: Select mode set in upper right, drag and drop to geometry

Viewing the mode shape aids in deciding appropriate modifications to alter the modal frequency.

 

Making a Modification: Spring-Damper

 

Choose a modification of interest.  For example, this vehicle body has a torsion mode as shown in Figure 10. Adding additional stiffness around the windshield can make the torsion mode frequency higher.

Figure 10: Vehicle body torsion modeFigure 10: Vehicle body torsion mode

To add a stiffener, select ‘Add Spring-Damper’ at the bottom of the screen as shown in Figure 11.

Figure 11: ‘Add Spring-Damper’ buttonFigure 11: ‘Add Spring-Damper’ button

In the ‘Add Spring Damper’ menu, define two connection points and a spring constant value. By default, the XX stiffness is added axially between the two points as shown in Figure 12. Damping can also be added.

Figure 12: Select mode set in upper rightFigure 12: Select mode set in upper right

It is not necessary to type the node names into the ‘Attachment point’ menu fields.  You can simply click on the node in the geometry and it will fill into the ‘Attachment point’ automatically, as shown in Figure 13. Press the ‘Apply’ button when finished.

Figure 13: Select mode set in upper rightFigure 13: Select mode set in upper right

Multiple modifications can be made.  In this case, two ‘Spring-damper’ elements were added to increase the torsion mode of the vehicle as shown in Figure 14.

 

 

Figure 14: Multiple ‘Spring-Damper’ modificationsFigure 14: Multiple ‘Spring-Damper’ modifications

Click on the ‘Predict Modes’ tab at the top of the ‘Modification Prediction’ worksheet as shown in Figure 15. Press the ‘Calculate’ button to create a new set of modes, with the modifications applied.

Figure 15: Press ‘Predict Modes’ button then the ‘Calculate’ button to calculate a new set of predicted modesFigure 15: Press ‘Predict Modes’ button then the ‘Calculate’ button to calculate a new set of predicted modes

The Frequency Response Functions (FRFs) of on the points of interest are displayed.  Green is from the modified mode set, while red is from the original mode set.

 

Making a Modification: Tuned-Absorber

 

At 27.39 Hz, there is a roof pumping mode as shown in Figure 16. A tuned absorber can be applied to this mode.

 

 

Figure 16: Roof pumping modeFigure 16: Roof pumping mode

Click on the ‘List Modifications’ minor worksheet. If desired, eliminate any previous modifications by highlighting the entire row and pressing the ‘Delete’ button as shown in Figure 17.

 

 

Figure 17: Highlight complete row and press ‘Delete’ button to remove a modificationFigure 17: Highlight complete row and press ‘Delete’ button to remove a modification

Click on the ‘Add Tuned Absorber’ button.

 

In the tuned absorber menu (Figure 18):

 

  • Select an attachment point (can be done by clicking on node in geometry display)
  • Enter a tuned absorber mass
  • Enter a frequency to target with the absorber
  • Then press ‘Tune’ button to calculate a stiffness and damping value
  • Press ‘Apply’ when finished

 

Figure 18: ‘Modify Tuned Absorber Modification’ menuFigure 18: ‘Modify Tuned Absorber Modification’ menu

Press ‘Predict Modes’ tab to create a new set of modified modes.  Just above the ‘Calculate’ button, on the middle left, enter text in the ‘Processing data’ field to name the new data set. Press the ‘Calculate’ button to apply the tuned absorber as shown in Figure 19.

Figure 19: ‘Predict modes’ and ‘Calculate’Figure 19: ‘Predict modes’ and ‘Calculate’

The new modes and their frequencies are listed in the lower left of the screen.  The FRF with the red line is based on the original set of modes.  The FRF with the green line includes the tuned absorber modification.

 

Tuned Absorber Trivia

 

From a dynamics point of view, skyscrapers are equivalent to long metal beams coming out of the ground.  They have low frequency modes of vibration excited by the wind.  The top of a skyscraper can move many feet.  Many have tuned absorbers to help reduce the movement/vibration.

 

The Taipei 101 skyscraper contains the world's largest and heaviest tuned mass dampers, at 660 metric tons (730 short tons) as shown in Figure 20.

 Figure 20: Tapei 101 (left) and tuned absorber (right)Figure 20: Tapei 101 (left) and tuned absorber (right)

The tuned absorber is viewable by the public on an indoor observation deck at the top of the skyscraper.  It cost an estimated $4 million to build.

 

Conclusion

 

Use LMS Test.Lab Modal Analysis Modification Prediction to simulate product design modifications on experimental modal analysis results.  The following modifications can be done:

 

  • Add or subtract mass at a node or point
  • Increase or decrease stiffness between two nodes or points
  • Create tuned absorbers targeted to a frequency

After creating a new mode set, it is interesting to use the Modal Assurance Criterion (MAC) to compare the original set of modes to the modified modes as shown in Figure 21.

 

 

Figure 21: Modal assurance criterion analysis of original versus modified mode setFigure 21: Modal assurance criterion analysis of original versus modified mode set

Using the MAC analysis, it is possible to see the effects of modifications on modal frequencies and mode shapes. In the MAC table of Figure 21, red indicates modes that are 100% alike.

 

  • For these modes with a MAC of 100%, the frequencies were changed by the modifications, but the mode shape was not.
  • The orange color indicates modes that are 80% alike. In this case, we can see that the second mode of the original structure at 27.4 Hz was shifted upward to 30.6 Hz, and the shape was significantly changed.

 

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