Simcenter Testlab Multi-Run Modal is used to correct mode shapes that are distorted due to inconsistencies between FRFs that were acquired in different measurement runs.
When collecting Frequency Response Functions (FRFs) for a modal test, it is sometimes necessary to collect the data in different runs or moves. This happens when there are not enough accelerometers and channels to collect all the desired modal points at the same time in a single measurement.
Take the example in Figure 1. To perform a modal test on a golf club, an impact hammer is used to apply a force at a consistent location, while a triaxial accelerometer is roved between response points.
By using a consistent force reference, it is not a problem to collect the data in different measurement runs. The individual measurement runs can be phased together using the reference.
However, there can be inconsistencies between FRF measurement runs (Figure 2) caused by mass loading due to roving the accelerometer.
These inconsistencies cause shifts in the peak frequencies between different FRF measurements. If these shifts are not considered when analyzing the complete FRF data set, the result is incorrect mode shapes as shown at the top of Figure 3.
The Simcenter Testlab Multi-Run Modal software helps improve mode shapes calculated from inconsistent FRF measurement runs. This is done by analyzing each measurement run separately, which results in partial mode shapes for a given frequency. The partial shapes from different measurement runs are then merged together into a complete mode shape. This merged mode shape is of higher quality and is better suited for CAE correlation (Figure 3 – Bottom).
This article covers the background of how a mode shape can be corrected, and how to do this in Simcenter Testlab Modal Analysis:
1. Multi-Run Modal on a Transmission Housing
2. Multiple Accelerometer Moves
3. Accelerometer Mass Loading: Overview
3.1 Accelerometer Mass Loading: Local versus Global Modes
3.2 Accelerometer Mass Loading: Cantilever Effects
3.3 Accelerometer Mass Loading: Grouping and Spacing
4. Modal Curve Fitting Inconsistent Data Sets
5. Calculating and Merging Partial Shapes
6. Simcenter Testlab Multi-Run
1. Multi-Run Modal on Transmission Housing
To understand how Simcenter Testlab Multi-Run Modal works, an in-depth example using a transmission housing is used in the rest of the article.
Suppose a modal test is being done on a transmission housing as shown in Figure 4.
This modal test requires 60 points to be measured, but only a limited number of accelerometers are available to do the modal test. The accelerometers have to be moved multiple times to different measurement locations to complete the test. Each move is a different measurement run.
2. Multiple Accelerometer Moves
In Figure 5, the pink circles indicate accelerometer locations for three different moves of the accelerometers. After moving the accelerometers between measurement runs, the Frequency Response Functions (FRFs) are acquired. The frequency peaks in the FRFs are different in each measurement run, as indicated by the vertical lines.
These shifting frequencies are confusing to any modal curve fitting algorithm used to analyze the data. Which frequency is the correct frequency? How can the amplitude of the mode shape be determined from the FRFs? Using the peak frequency from one FRF measurement run does not yield the correct amplitude in the other FRF runs.
These shifts are caused by mass loading from the accelerometers. Each time the accelerometers are moved, the mass distribution of the test object is changed. The reasons for this mass change are explained in the next few sections.
3. Accelerometer Mass Loading: Overview
While there are other reasons (temperature changes, boundary conditions changes) that can lead to shifts in frequency peaks between FRF measurement runs, a common reason is accelerometer mass loading.
Intuitively, it might be hard to understand how moving an accelerometer with such a low mass could shift the natural frequencies of a large object. The natural frequency of an object is equal to the square root of stiffness (k) over mass (m) as given in Equation 1 below.
Since the mass of transmission might be close to 200 kilograms, and an accelerometer is around 200 grams (a 1000x ratio), it seems the natural frequency could not change very much. However, it is not as simple as calculating the ratio of the test object mass versus the accelerometer mass to determine the shift in frequency.
3.1 Accelerometer Mass Loading: Local versus Global Modes
An object can have both local and global modes:
Figure 6 shows both a global mode (left) and a local mode (right) of the transmission housing.
There is more mass of the structure participating in the global mode. In the local mode of the transmission rib, only a small amount of mass participates (sometimes referred to as the modal mass). So even if the transmission weighs 200 kilograms, far less mass participates in a local mode of the structure. As a result, the accelerometer’s apparent mass to the test object mass is much larger for a local mode.
3.2 Accelerometer Mass Loading: Cantilever Effects
In Figure 7, the apparent mass of the accelerometer is made larger by its placement at the end of the shifter, due to the cantilevered mode shape.
For this shifter mode, it is the inertia (I) that acts like the mass. By the equation I=mr^{2}, the inertia of the transmission shifter is increased by the mass (m) multiplied the radius (r) squared. The radius (r) is the distance from the base to the end of the shifter.
3.3 Accelerometer Mass Loading: Spacing
Multiple accelerometers are used in a modal test. If they are all placed in the same area of the structure (Figure 8), then the mass effect is larger.
Keeping the accelerometers spaced out over the object is a good practice. Another good practice when taking multiple separate FRF measurements on a structure is to place dummy masses at all potential accelerometer locations. This helps minimize the shifting in frequencies.
4. Modal Curve Fitting Inconsistent Data Sets
How does the shifting of frequency peaks in the FRFs impact calculating mode shapes?
In Figure 9, notice that multiple columns of letters occur at each natural frequency peak in the modal curvefitting stabilization diagram. One possible cause is that there are multiple modes at each frequency peak. This can happen in symmetric structures. In this case, the structure was not symmetric and the FRFs were gathered in multiple runs. This can also cause multiple columns of letters (i.e., possible modes) to appear where there should only be one.
One way to tell is to analyze a single measurement run instead of all the runs. In Figure 10, there is just one column of letters for each peak, unlike Figure 9. This means the multiple columns of letters at each peak were due to accelerometers being moved between runs.
If an inconsistent set of data from multiple measurement runs is analyzed, the resulting mode shape is not correct. In the case of the transmission housing, notice that the modal vectors (i.e., shape) are not exactly in and out of phase, like the top graph in Figure 11.
Ideally, the mode should look like the bottom display of Figure 11. In a normal mode shape, all points are exactly in and out of phase. In a complex shape, this is not the case. When using simulation code to calculate mode shapes, like Nastran Solution 103, the mode shapes are all normal.
Looking at the mode shapes in Figure 11, one could argue they are similar. However, if calculating a Modal Assurance Criterion between these mode shapes and the same mode in simulation, the MAC percentage would be 20% lower (out of a hundred) for the distorted mode than the merged mode. For example, instead of a correlation percentage of 100%, it would be 80%. This is because the simulation mode would not have complex motion.
To get the correct mode shape, each measurement run will have to be analyzed separately, and then merge the results.
5. Calculating and Merging Partial Shapes
To get the proper mode shape, the following is done:
This process is illustrated in Figure 12.
The partial mode shapes are calculated for each FRF measurement run separately and then merged to create a full mode shape.
6. Simcenter Testlab Multi-Run Modal
Simcenter Testlab Multi-Run Modal Analysis is part of the Modal Analysis add-in as shown in Figure 13.
The Modal Analysis add-in uses 77 tokens, if using token licensing. Go to the worksheet called “MultiRun Modal” (Figure 14).
To take advantage of Multi-Run Modal Analysis, multiple sets of partial modes must have already been calculated using a Modal Curvefitter.
For example, in Figure 15, FRF data was acquired in 6 different sets: Setup1, Setup2, Setup3, Setup4, Setup5, and Setup6. Each set of FRFs was only measured on a subset of the measurement points. Each set was analyzed, and an analysis called Modes_Setup1, Modes_Setup2, Modes_Setup3, etc was created from each FRF set.
One of the partial mode sets needs to be selected and set as the target modes (Figure 15). Selecting the target modes determines the frequencies of the final merged mode set. Be sure to select a mode set that represents all the important modal frequencies.
Select one of the mode sets and press the “Add” button under “Add Target Modes”.
Next a different set of modes is selected, and the “Add” button is pressed under “Add Processing to be Merged” as shown in Figure 16.
This will be done for all the remaining mode sets as shown in Figure 17. Mode sets are selected in the upper left of the Multi-Run Modal worksheet. After selecting a partial mode set, it gets added for merging by pressing the “Add” button in the lower left.
Each mode in the added set is aligned with a target mode based on its proximity in frequency. This works well if the structure has modes well separated in frequency. Be careful when working with symmetric structures which have distinct and separate modes with very similar frequencies.
After selecting all the mode sets for merging, press the “Merge Modes” minor worksheet at the top of the Multi-Run Modal worksheet as shown in Figure 18.
Once in the Merge Modes minor worksheet, enter a name in the Processing area for the name of the merged mode set as shown in Figure 19. All the partial mode sets will be merged into a single mode set by this name.
Press the “Merge” button. The complete mode set is now created!
Questions? Contact Siemens GTAC support or email peter.schaldenbrand@siemens.com
Modal Data Acquisition
Modal Analysis and Operational Deflection Shapes