Simcenter Testing Solutions Vibration Control: Multi-Point Response Averaging

Figure 1: Shaker Test System configured for vertical excitation.
 

The shaker is configured with a head expander as shown in Figure 2. The expander table has a resonance that occurs just above the common test frequency range of 2000Hz. The mode shape of the resonance is also shown in the same figure and will have a major influence in our example. 
 

Figure 2: Shaker Head Expander and Resonant Mode Shape at ~2kHz.
 

In closed-loop vibration control testing, the goal is to replicate the responses, and expose the test article in a controlled laboratory condition to what it will experience in real-life operational conditions. Most of the time this is a very difficult challenge since the boundary conditions cannot be reproduced in a lab exactly as they would be in the real world. If the boundary conditions are different, then the dynamic responses will be different as well. In some circumstances this can very easily lead to over-testing or under-testing the device being tested.

2. Effects of Fixture Resonance

There can also be situations where the fixture used to hold the test article has resonances that can amplify the structural responses beyond the normal conditions. This can happen without the test operator being aware of these dangers, and parts can end up breaking. It is critical that the shaker system and fixture resonances be completely understood, and actions taken to avoid, or at least mitigate this situation.

There are different strategies that can be used to deal with this, and sometimes compromises must be made. One strategy that is available in Simcenter Testlab is called Multi-Point Control Response Averaging. The rest of the article will discuss using this strategy as a compromise for a control test setup.

The example given in the Figure 3 shows a schematic for a control test setup. It has a simulated test article with a Center of Gravity (CG) located somewhere above the table, and approximately in the center of the table. 
 

Figure 3: Case #1 - Single-point control setup (control point highlighted in red).
 

In practice, the center of gravity (CG) should be located as close to the center as possible to avoid moments of inertia. Shakers have limits to these “Overturning Moments” as given in the shaker manuals. For smaller structures it is usually not much of a problem, but for large structures it can be, and moment limiting must be used with an elaborate force measurement device system. (We will keep it simple for this example).

Keeping the CG in the center of the table can also avoid “rocking” dynamics of the test system, which also adds to the control challenge. The CG is attached to the mount points 1-4, and for our example we will consider the connections to be rigid. However, in a real test this will probably not be the case, and the resonance of the fixture, along with the mass and stiffness of the structure it holds, must be considered also. 

Let’s compare two different cases with this setup: a single point control and a multi-point control.

2.1 Case 1: Single Point Control Case

The first case will use the control Pt1 as a single control sensor located at the center of the head expander directly below the CG of the structure, and away from the attachment points, where the resonance response at about 2000Hz is most profound. A controlled sine sweep from 20 – 2kHz is applied. The control profile has an increasing response level from 20 to 100Hz, then continuous amplitude at 1g until 2kHz. The results from the sweep are shown in Figure 4. 
 

Figure 4: Results of a controlled Sine Sweep with a Single Control Point in the center of the head expander. In this example, all CG connection points deviate significantly from the target throughout the sweep.  At 2000 Hz, the difference between the control and individual points (Example Pt3 in magenta) grows even greater, meaning the CG will be over-tested.
 

In reviewing the results, it’s important to remember that all structural components in the setup will contribute to the mass and stiffness of the “System” response, and hence contribute to the overall structural responses throughout the test frequency range. As can be seen, there are deviations in response at the attachment points compared to the control point, due in part from the dynamics of the test structure. As the excitation frequency approaches the head expander resonance close to 2kHz the responses start to grow quite a bit more, and the connection points will drive a large response of the CG.

The problem with this test setup is obviously due to the transmission of energy from these attachment points up to the CG of the structure. So even though the test operator may be happy that they successfully completed the test with a perfectly maintained control, with a 77% amplification of response in the structure, it could be completely broken apart from over-testing! After that there will be a lot of finger pointing between the test lab and their customer, who owns the design of the structure being tested. In this case the test operator has a good point, since they were just running the test as instructed, but it behooves everyone involved to get a good handle on understanding all the dynamics in the complete test setup.

2.2 Case 2: Multi-point Control Case

So, what could have been done about this? Let’s explore this in the next part. 

After studying the structural dynamics of the test system by conducting a Modal Analysis or Operational Deflection Shape (ODS) survey of the entire setup, the best strategy here would be to use the multi-point average responses in the control averaging. This would average the response at each attachment point.

An alternative to the test survey would be to have the analysts conduct a finite element analysis (FEA) of the test setup to provide the structural modes and frequencies. This actually may be required since the FEA is the only way to include the entire system, including the simulated test structure. With this kind of information about the test system provided from test or analysis, then people involved in the test can make much better engineering judgements in the test setup, and to understand the compromises required for a successful test.

The Figure 5 shows the new setup schematic.
 

Figure 5: Case #2 - Multi-point average control setup with four attachment points (Control points Pt2, Pt3, Pt4, Pt5 marked in red).
 

The outcome of the control is to take the average response of the 4 attachment points. If the shaker system moves somewhat rigidly, which it will never do completely, then the response at the CG will be somewhere in the middle of the 4 attachment points. This can only be anticipated if the dynamics of test structure are understood fully.  For this second case, we can see the individual and averaged responses in a small segment of the time history close to the table resonant frequency in Figure 6.
 

Figure 6: Time domain response of each connection point (green, blue, magenta, yellow) and the 4-point average response (dashed brown) at the center of gravity (CG) around the table resonance of 2 kHz. 
 

The data shows that the center of gravity (CG) has a controlled response at the required 1g amplitude. Even with some dynamics in the system due to the expander and connections from the expander to the CG, the average response is exactly where it should be. The response on the center of the table, (Case #1 control point) is 40% less. As was shown in the first case, if the control accelerometer is placed at the table center, the response of the CG would have been much greater. The spectral responses for Case #2 are shown in Figure 7.
 

Figure 7: Frequency responses of all control points, showing the large difference in response of Pt1 (red) at the center of the table compared to the center of gravity (CG) response (green).
 

The data shows that taking the average of the 4 attachment points and using that as the control response in the control loop, the intended response at the CG is much closer to the desired response of 1g throughout the entire test frequency range. This shows the benefit of Multi-point control response averaging when a compromise is needed in the test setup due to inherent resonant frequencies.

3. Resonance as an Advantage

Up to this point in the article, multi-point control was used as a strategy to mitigate the effects of the structural resonances. These resonances are not all bad, and they can be used to an advantage. The amplification of the responses due to resonance has the effect of reducing the required drive voltage from the controller to obtain the required control response.

This is shown in Figure 8 by comparing the drive output from Case 1 compared to Case 2.
 

Figure 8: Frequency responses of all control points, showing the large difference in response of Pt1 (red) at the center of the table compared to the center of gravity (CG) response (green).
 

In Case 2, the required response is achieved at the CG, while at the same time reducing the amount of drive voltage to obtain the response. This can also have side benefits in the control by reducing the amount of dynamic range of the drive voltage out of the data acquisition system, which will reduce the chance of overloads. 

The results show that the voltage in Case 1 is 50% greater than for the desirable Case 2.

4. Simcenter Testlab for Multi-point Control Averaging

Setting the parameters for the scenario described above is very straight forward in Simcenter Testlab. After the control points have been established, and the accelerometers have been defined for those points, then the “Channel Setup” worksheet is used to enter this information.

There is a pull-down menu to establish which channels represent the control sensors. All sensor information is also added in the table. Figure 9 shows the parameter “Channel/GroupID” used to define the control channels.
 

Once the channel information is filled out, then in the “Sine Setup” worksheet, the “Control Strategy” parameter is established, as shown in Figure 10.
 

Figure 10: Control Strategy parameter set to “Average”
 

In this example the “Average” strategy is chosen, however a “Maximal” and “Minimal” strategy can also be selected if desired or warranted by the mode shape of the fixture resonance.

Questions? Email william.flynn@siemens.com or contact the Siemens Support Center.
 

Related Links on Vibration Control

• Index of Testing Knowledge Articles
• What is Vibration Control Testing?
• Vibration Control FAQs
• Vibration Control: Understanding Selfcheck
• Getting Started with Random Control
• Random Control: Averages per Loop, Frequency Resolution, Weighting, and DOFs
• Random Control: Measurement Channels
• Combined Modes: Sine on Random (SoR), Random on Random (RoR), Sine on Random on Random (SoRoR)
• Kurtosis
• Power Spectral Density
• Simcenter Testlab: Breakpoint Generator
• Shock Response Spectrum (SRS)
• How to Calculate a Shock Response Spectrum with Testlab?
• Shock Response Analysis and Synthesis
• Sine Control: Estimation Methods
• Sine Control: Closed Loop Control Parameters
• Sine Data Reduction
• Sine Control: Notching
• Simcenter Testlab: Tracked Sine Dwell
• Single Axis Waveform Replication (SAWR)
• Vibration Control: Test Sequencing
• Direct Field Acoustic Noise Testing
• What is Total Harmonic Distortion (THD)?
• "Excessive DC Level" message
• Inverse Transfer Function (ITF) in Random Vibration Control
• Vibration Control YouTube Playlist