Two closely related dynamic tests performed on aircraft are Ground Vibration Tests (GVT) and Flutter Tests. These tests are used to help define the safe flight “envelope” for a given aircraft configuration:
The GVT is a modal test of the entire airframe, which determines the resonant frequencies, modeshapes, and damping. This is performed on the aircraft before first flight while it is still on the “ground”. GVT modal results are compared with the structural Finite Element Model used for flutter predictions. If the models and test results agree, the aircraft is cleared for the next round of tests, which usually includes ground runs and a flight flutter investigation.
Flutter is an in-flight phenomenon which causes the wings and other key components to vibrate uncontrollably, due to the convergence of multiple modes as the resonance and damping shift due to aero-elastic loading, making flight impossible. Before flying an actual aircraft, flutter performance is predicted, so the flight envelope (altitude and speed) of the aircraft is safely bounded. This is later verified by performing a flutter test with the actual aircraft.
The analytical flutter predictions bring together a structural model and an aerodynamic model. The aerodynamic model is verified by scale model testing in a wind tunnel, while the structural model is verified by GVT testing.
The Importance of Flutter
The flutter envelope of a new airframe needs to be well understood.
Flutter Examples Video
Flutter is a dynamic instability of an elastic structure in a fluid flow, caused by positive feedback between the body's deflection and the force exerted by the fluid flow. The interaction of these different forces are depicted in the Collar diagram in Figure 1.
Figure 1: The interaction of the different forces that are in play for an airplane are depicted in the Collar Diagram. The coalescence of these can result in an unstable condition called flutter.
Flutter needs to be avoided since this can be a catastrophic event, and total loss of the airframe is possible. Model predictions need to be supplemented with ground testing to build up absolute confidence in the predictions.
After verification with analysis, an actual flutter flight test methodically and carefully expands the flight envelope (Figure 2) based on altitude and flight speed, where the airplane is designed to fly.
Figure 2: Expanding the flight envelope is done slowly and methodically at specific “flight data points” during flutter flight testing. Test points are shown in the right side plot.
The FAA will type certify an airframe for its specific flight regime only after the successful GVT and flutter flight test is completed for each structural derivative.
Performing a GVT Test
The duration of the GVT campaign can consume from a few days to a couple of weeks, depending on the size of the airframe, the number of channels, the number of different payload or mission configurations, etc.
High Aspect Ratio Aircraft Solar Impulse Ground Vibration Testing
Pretest planning to ensure testing efficiency is very important so that the down time of the new aircraft is minimized. If the preliminary finite element model is available, it can be used to help in the most efficient configuration of the test, including shaker and accelerometer number and location, and boundary condition verification.
Building up to a full aircraft GVT is given in the product development timeline in Figure 3 as depicted with the famous “V” diagram.
Figure 3: Building up to the GVT is depicted here in the Software Development Life Cycle (SDLC) “V” shaped diagram.
As time moves from left to right, the individual components and subsystems are modeled, and verified with test. Eventually the full aircraft GVT is performed, clearing the way for a safe “Flutter Envelope Clearance” (FEC) through flutter flight testing, and finally FAA type certification allowing the aircraft entry into commercial service.
If it is determined that structural responses can change significantly due to additional payload and fuel configurations, (Figure 4), then a GVT will be performed on that configuration. It is important to test any airplane configuration which can have an effect on flutter performance.
Figure 4: Depending on an aircraft, many different store and fuel configurations may be tested with GVT.
Variants can add significant time to the GVT test program, risking the planned first flight schedule.
GVT Data Acquisition: Excitation and Instrumentation
It is not uncommon for multiple exciters and hundreds of accelerometers to be used in a single GVT test.
Bombardier C-Series GVT Video
Prior to testing, careful consideration of shaker and accelerometer placement is important. Some airplane bodies can be quite large and compliant, and require multiple exciters to obtain high quality modal data. Other aircraft bodies are smaller, but stiffer, so less exciters are required. Two exciters placed laterally and vertically on an aircraft engine are shown in Figure 5.
Figure 5: Lateral exciter (on left side) and vertical exciter (on bottom) for an aircraft engine.
For all cases it is important to provide sufficient excitation energy throughout the entire structure to get good signal-to-noise response. The various excitation signals available for GVT are given in Figure 6.
Figure 6: Different excitation signals are available for GVT. Some are sinusoidal and some are random in nature.
Typical excitation signals are burst random or swept sine, but for the critical modes important for the flutter predictions, other signals which are sinusoidal in nature are used.
Sinusoidal Methods: Stepped Sine and Normal Modes
Special cases of these sinusoidal signals are Stepped Sine and Normal Modes:
Stepped Sine consists of a short dwell at each spectral line, stepping through the entire frequency range several times, based on the number of shakers.
Normal Mode testing strives to tune a particular mode and isolate it as a single-degree-of-freedom response by managing the amplitude and phase of all exciter forces with respect to the acceleration responses at each driving point or response control point.
The Lissajous display is used to plot the Force vs Acceleration at a driving point location to verify the phases have a 90deg separation, which is an indication of a resonant condition. A driving point location is where both a force is applied and a corresponding acceleration response is measured. In the case of a resonance, the lissajous graph will form a circle, as shown in Figure 7.
Figure 7: A Lissajous graph forms a circle at resonance (top, green), and is a diagonal line when not at resonance (bottom, red).
There are usually multiple exciters used, and the phase of the responses for each must be taken into account simultaneously. Since there are coupled responses between the exciters and responses, a matrix evaluation of the excitation phasing is required in Normal Modes.
In the “old days”, this was done at a console by a highly skilled test operator who would look at multiple Lissajous displays, but nowadays the software programs automatically perform the tuning. An example of an online display for Normal Modes is shown in Figure 8. This can provide a lot of information simultaneously to verify the resonant conditions.
Figure 8: Normal Modes Screenshot with Lissajous displays (bottom)
Due to the time-consuming nature of these tests, normally only 2 or 3 modes may be chosen which are critical for flutter analysis. Varying the amplitudes of excitation allows an assessment of the linear range. Correctly identifying the modal parameters in the linear range, especially the damping, is essential for an accurate flutter prediction.
Normal Mode Testing and Damping
Note that with Normal Mode tuning, Frequency Response Functions (FRFs) are not acquired. Instead mode shapes are calculated directly from the responses, and modal parameter estimation is not necessary. The modal damping is not contained in the Normal Mode results and must be obtained with an extra damping test as shown in Figure 9.
Figure 9: Damping calculation from Exponential decay
There are several techniques available in Test.Lab to determine the modal damping, including:
Log-decrement from an exponential decay using a Hilbert Transform
Complex Power
Force Quadrature
SDOF Circle Fit
Pseudo-Random and Multi-Sines
A compromise between the accuracy obtained with sinusoidal tuning and dwelling, and the speed of the random type of signals is a hybrid approach in the class of “Multi-sines”. A technique that is getting more popular is the Pseudo-random, but with a couple of twists to the classical version. With classical pseudo-random the randomized phases can have a constructive and destructive effect on the amplitudes, possibly causing overloads. If the phases are managed better with the so-called Schroeder sines, then the sinusoidal interactions can produce the best SNR like the sinusoidal signals, and still be comparable to the speed of the random testing.
GVT Data Processing: Modal Analysis
Using FRFs collected by either broadband random, sine approaches, or Stepped Sine FRF data, the general modal model is calculated using a "curve-fitting" parameter estimator. A “curve-fitter” estimates resonant frequencies, modes, and damping from the FRF data. An example of an extracted mode shape is shown in Figure 10.
Figure 10: Mode shape of an F-16 calculated from FRFs collected during GVT test
As mentioned, the modal data for the Normal Modes method is a direct outcome from the mode tuning.
The modal parameters from the test modes are first evaluated at the test site by comparing with the expected results from computer based Finite Element Analysis (FEA) predictions. This post-test assessment is done to make sure there are not any blatant differences before the test is disassembled. FRF's and mode shapes are compared between FEA and Test. These can be directly overlaid in displays by importing the NASTRAN or ANSYS FE Model results directly into Simcenter Testlab. For more information on this please see the community article Viewing Nastran results in Simcenter Testlab.
In addition, a Modal Assurance Criteria (MAC) Matrix can be calculated to quantify the amount of correlation between the set of test and analysis mode shapes. An example of a MAC Matrix is shown in Figure 11. Note the important first several modes show good correlation. A value of 1 along the diagonal means there is perfect correlation of the modeshapes being compared.
Figure 11: MAC Matrix which is used to visualize the amount of correlation between two sets of mode shapes. In this case it is the Test modes versus the Analytical modes.
As mentioned, the purpose of the Modal test is to obtain a modal model that can be compared with the FE model, and update the FE model appropriately. Ideally the test model should be a “Real” mode, meaning the modal model represents a structure with proportional damping throughout, which is a compromise with the FE model since damping can only be estimated. To impose this constraint on the test modal model, an extension to the Test.Lab modal analysis is available called MLMM. This method will iterate on the calculated modal parameters to optimize the modal model with the intent towards the Real modes, and also driving towards a better fit of the synthesized FRF’s.
If there are discrepancies in the results from test compared with analysis, then the FE model goes through an iteration process to update the model and bring it in line with the test results. Of course the test must be a good representation of the configuration of the analysis model in terms of mass properties and boundary conditions. The rigid body modes should not interfere with the flexible structural modes, and this is usually checked as part of the test procedure. Once a validated FE model is obtained then it can be used for analysis which continues with flutter predictions.
A nice way to view the mode shapes is with the CAD model to expand the mode shapes for a better understanding of the modes through Modeshape Expansion.
Conclusion
Together, Ground Vibration Tests and Wind Tunnel Tests are used for verification of the structural and aerodynamic models, which when combined will result in more accurate flutter predictions. The flutter predictions are still only computer model simulations, while flight flutter testing is the final verification that the flight envelope is clear of unwanted flutter dynamics.
