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The objective of closed loop random vibration control testing is simple: recreate a broadband random vibration on a shaker table to find any durability related flaws in the product.
A typical vibration control system is shown in Figure 1. A Power Spectral Density function (PSD), determined to represent the real life vibration exposure, is used as the target vibration at the control accelerometer location.
The control accelerometer is positioned directly on the shaker table, where it is continuously measured and compared to a target reference control PSD spectrum. If there are any deviations from the target PSD, the drive output to the shaker is adjusted to reduce the error between the control and reference.
Seems like control should be easy, right? Not so fast! The control is being done on an averaged PSD of random data. As a result, there is variation in the measured vibration, as shown in Figure 2.
In Figure 2, the average measured vibration (blue) does not perfectly match the target vibration (green) due to the variation in the average.
The amount of variation depends on how much averaging is done in the control loop. Given enough averaging time, the target and measured vibration at the control PSD can be identical.
However, using a long amount of averaging time means the control is less responsive to changes. If the output to the shaker cannot be adjusted quickly enough, there might be difficulty matching the target vibration profile.
This article details the settings that affect the amplitude variation and control loop time in a vibration control test.
The settings are described in the following sections:
1. Inner and Outer Control Loop
The control logic used in a random control test of Simcenter Testlab is shown in Figure 3. There are two loops: an inner and an outer control loop.
The control PSD is measured and compared against the target PSD (T). The voltage drive (V) to the shaker is updated to minimize the difference between current control PSD and target according to Equation 1 below:
Equation 1 consists of the following frequency based functions:
For speed considerations, the inner control loop is executed continuously on the Simcenter SCADAS data acquisition hardware. It constantly computes a linear average PSD on all the accelerometer channels, including the control accelerometer.
The outer control loop is performed on the host PC. It does the following:
There are specific settings that govern the behavior of these control loops which are covered in the next sections.
2. Inner Control Loop: Averages Per Loop
In the inner control loop (Figure 4), an averaged Power Spectral Density (PSD) is calculated for each channel. The setting called Averages per Loop determines how many individual PSDs are acquired before an average is calculated.
The average PSD for each channel is calculated according to Equation 2:
The average being performed in Equation 1 is known as a stable average. A stable average yields the same result as a linear average:
The averages per loop (M) are set under the “Advanced…” button of Random Control setup as shown in Figure 5.
By default, the averages per loop is 5 for the inner loop. The averages per loop can be increased to reduce the amount of variation in the target PSD as shown in Figure 6.
However, increasing the averages also increases the control loop time, making the test less responsive to changes and shifts in the test structure and shaker system that occur during the test.
This inner loop is executed in the memory of the SCADAS hardware as to make it as fast as possible. The PSD calculated by the inner loop is not displayed in the software interface.
3. Loop Time: Frequency Resolution
The control loop time is equal to the averages per loop (M) multiplied by the acquisition time (T) for each average as shown in Equation 3. The acquisition time for each average is the inverse of the frequency resolution used in calculating the PSD. It is the minimal amount of time needed, as there is overhead for other operations, etc.
The frequency resolution is the spacing between data points in the frequency domain. For example, the frequency resolution might be 2 Hz, meaning there is data points in the PSD spectrum at 0 Hz, 2 Hz, 4 Hz, 6 Hz, etc.
For more information on the inverse relationship between frequency resolution and acquisition time, see the Knowledge Base Article Digital Signal Processing: Spectral Lines, Frequency Resolutions, etc.
The frequency resolution in Simcenter Testlab Random Control is set in upper right of the Setup worksheet as shown in Figure 7.
The software will show all PSD measurements with the resolution entered in the control panel. However, a finer frequency resolution might be employed in the inner control loop. To keep the control loop speed as short as possible, it is done within the firmware of the Simcenter SCADAS hardware, not in the software of the host PC. The firmware has a fixed number of frequency resolutions that can be used. The control loop time is based on the SCADAS front end hardware, regardless of the resolution specified in the software interface.
The actual hardware-based frequency resolution can be viewed by turning on the “Use FE resolution” option under the “Advanced…” button (Figure 8). The initials FE are short for Front End, which refers to the SCADAS hardware.
After turning on the “Use FE resolution” checkbox, the resolutions shown in the software interface change to the frequency resolution that is actually used for the measurements in the hardware.
The control loop time is shown in the field “Min Control Loop Time” under the “Advanced…” button as shown in Figure 9.
The minimum control loop time field is a calculated (based on averages per loop and frequency resolution) and is not directly settable in the user interface.
How quickly the control PSD measurement is updated is determined by the control loop. The speed at which the output drive is corrected is based in part on the weighting factor, which is covered in the next section.
4. Outer Control Loop: Weighting
The average Power Spectral Density (PSD) calculated in the inner control loop is transferred to the outer control loop after all the averages are taken (see Figure 10).
In the outer control loop, the inner control loop PSD is exponentially averaged and monitored for potential abort situations. This is the actual control PSD which is shown in the software interface.
The drive to the shaker is also evaluated and updated based on this PSD. This is done by calculating an Inverse Transfer Function (ITF) between the drive and control accelerometer. The ITF is a Frequency Response Function (FRF) in units of volts (from the drive output) per g (acceleration at the target). The drive is altered based on the measured ITF, which tries to reduce the error between the outer loop control measurement and the target spectrum.
The control PSD is averaged as shown in Equation 4.
The weighting factor is set in the “Advanced Control Setup” menu as shown in Figure 11.
The weighting factor (W) determines how much the previous averages influence the current average:
For a random control test, this means that a lower weighting factor shows more variation in the control PSD as shown in Figure 12.
The weighting factor (W) influences how quickly the outer loop average PSD varies with a sudden change in system behavior.
For example, if the control accelerometer was disabled during the middle of a test, the average control PSD will not change as much when computed with a high weighting factor as shown in Figure 13.
In both cases, the tests aborted in the same amount of time (there is a separate open threshold check also active on all the channels). However, the control PSDs (blue versus brown curves in Figure 13) are quite different.
With a weighting factor of 90 (brown curve), the control PSD is close to the average. With a weighting factor of 5 (blue curve), the control PSD deviates more from the average. The PSD with the lower weighting factor changed more rapidly in response to the accelerometer than the PSD computer with the higher weighting.
High weighting helps reduce the amount of variation in the control PSD. The total amount of expected variation based on the test settings is reflected in the Degrees of Freedom parameter, which is discussed in the next section.
5. Degrees of Freedom (DOFs)
The Degrees of Freedom (DOFs) is a function of the averages per loop and the weighting factor as shown in Equation 5:
The Degrees of Freedom is used in random control test specifications as a check on the expected variation of the spectral data. The higher the Degrees of Freedom, the lower the expected variation around the average control PSD.
A random control test uses a gaussian random when generating the drive signals. The table below (Figure 14) shows the relationship between the number of degrees of freedom and the confidence levels of a signal with a gaussian random distribution.
Using the table, it can be determined if test tolerances can be met in theory, before actual testing occurs. From statistics, a confidence level can be calculated on the gaussian signal distribution. For 126 Degrees of Freedom, 99% of the averaged amplitude values in the spectrum will lie between +1.32 dB and -1.52 dB of the target.
For more about dB values and how they work, see the Knowledge Base article What is a Decibel?;
After setting the weighting and averages per loop, the Degrees of Freedom are calculated and displayed in the Simcenter Testlab Random Setup worksheet (Figure 15).
In random profile specifications, a minimal number of Degree of Freedoms is often specified. For example, in MIL-STD 810, the Environmental Engineering Guidelines of the Department of Defense, a minimum of 120 Degrees of Freedom (Figure 16) are recommended for a random vibration control test.
This predicts that the 99% of the amplitude signal values will lie about +/- 1.5 dB from the average amplitude.
If the predicted variation is less than the alarm and abort limits, the test should be able to run without issues. The actual variation is monitored during the test as described in the next section.
6. Tolerance Alarms and Aborts
Variation within the control PSD is monitored two different ways while the test is in progress (Figure 17): tolerance alarms and aborts.
The monitoring works as follows:
In practice, a small number of frequency lines that exceed the alarm and abort limits can be tolerated. In the Random setup worksheet, on the right side, the maximum alarm and abort lines that are allowed outside of the limits is specified (Figure 18).
This allows a few lines in the control spectrum to be outside the limits when proceeding to a new test level. The number of allowed lines is usually defined in the test specification.
When switching test levels, the average on the control PSD can be also be reset. This is discussed in the next section.
7. Reset Average at Level Switch
In the runup to the full level of a random vibration control test, there are several intermediate levels. The average can be reset every time there is a change in level by changing “Reset exp. avg. on level switch” check box to ON in the Advanced Control setup dialog (Figure 19).
When changing levels, it is quite possible that the input/output relationship between the drive (voltage to shaker) and the output (control accelerometer response) changes. If the test object and shaker system are linear, this relationship will remain fixed. If the test object is non-linear, then the relationship can vary widely.
What exactly constitutes non-linear behavior between level changes? Let’s say for a given frequency, that one volt of drive produces two g’s of vibration. The relationship is 2 g per volt, or 2 g/V. When the drive level is increased from one volt to two volts, if the structure and shaker system are linear, then four g’s of vibration should be produced. Double the drive voltage, double the acceleration response. If the system is non-linear, then perhaps five g’s of vibration are produced when the drive level is set to two volts. The relationship is non-linear and harder to predict.
By starting the average “fresh” with a change in level, non-linear behavior can be detected and accounted for in the drive output in a timelier fashion.
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