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Flutter Analysis CH-601XL-B

Reliability Engineering PROF. DR.- ING. U. WELTIN

Flutter Analysis CH-601XL-B

Prof. Dr.-Ing Uwe Weltin and M.Sc. Joseph Gross Institute of Reliability Engineering

University of Technology Hamburg

Figure 1: CH-601XL-B in the Ground Vibration Test

Contents 1. Description ............................................................................................................................................................ 2 2. Ground Vibration Test ......................................................................................................................................... 2 3. Rigid Body Modes of Control Surfaces .............................................................................................................. 7 4. Calculation of Modal Values for the Rigid Body Modes of the Control Surfaces of the CH-601XL-B........ 8 5. Computational Model......................................................................................................................................... 16 5. Flutter Calculation .............................................................................................................................................. 18 6. Normal Modes of the CH-601XL-B ................................................................................................................. 19 7. CH-601XL-B with Minimum Loading ............................................................................................................. 32 8. Flutter Calculation Results for the CH-601XL-B with Maximum Loading................................................... 36 9. Flutter Calculation for Control Surfaces with Maximum Mass ...................................................................... 41 10. Summary and Recommendations .................................................................................................................... 42

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Reliability Engineering

PROF. DR.- ING. U. WELTIN

1.Description The objective of this study is to document up to which velocity and under which conditions the CH-601XL-B is safe from flutter as required in § 23.629, Flutter (including divergence, and control reversal) of part 23 of the Federal Aviation Regulations. Furthermore the Advisory Circular AC No: 23.629-1B dated 9/28/2004 is taken into account. Previously conducted GVT tests of the CH-601XLby this laboratory in June 2009 evaluated the Zodiac CH601XL built to Zenair’s 4

th Edition technical drawings (2008); this new analysis

(December 2011) is based on testing of the now upgraded Zodiac aircraft known as the CH-601XL-B (Ed.4 drawings + Upgrade Drawings 6-ZU-1/4 + LAA MOD/162B/004). Modal parameters such as normal mode shapes, frequencies, generalized masses and damping coefficients are determined for a production model in a ground vibration test. The respective time series analysis that determines the modal parameters is conducted using the commercial software, SDT, by the company SDTools (www.sdtools.com). Due to bearing friction and free play in the flight control system, the modal masses for the rigid body rotations of the ailerons, the rudder and the elevator could not be calculated from the time series analysis like those of the higher order structural modes. For the case of the rigid body motions of the control surfaces, the data from the ground vibration test were used to determine the resonant frequencies only. In order to obtain realistic modal mass values, it was found to be necessary to develop an FE model of the CH-601XL-B’s control system from which the modal parameters for the flutter calculation can be ascertained. Additionally, control surface hinge stiffness measurements were performed to cross check the modal parameters of the rigid body motions of the control surfaces. After all necessary parameters have been attained; flutter calculations are performed using the commercial aeroelastic analysis package, ZAERO (www.zonatech.com). These calculations are conducted for configurations having fixed and free controls with minimal and maximal loadings up to a speed of 500 km/h in order to reveal possible aeroelastic instabilities. In the calculations, the vibrating structure of the CH-601XL-B is represented by the modal data determined from the ground vibration test and from the analytical model of the control system. Additional calculations are performed in order to determine the flutter speed if the expected tolerances of the control surface mass ensure safety from flutter.

2.Ground Vibration Test To obtain the representative modal data with the ground vibration tests, the CH-601XL-B has to be suspended with linear elastic springs without damping as shown in Figure 1. The vertical resonant frequency of the aircraft moving as a rigid body supported in the linear elastic steel springs is approximately 1 Hz. Since the resonant frequencies of the rigid body lie well below the first resonant frequency of the structure (> 10 Hz), the measurement of the higher frequency structural properties is not affected. In order to obtain the modal parameters, 14 tests listed in Table 1 are carried out using two actuators for each test. The list of devices used in the ground vibration test is found in Table 2.

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Table 1: Test Protocol

Configuration List CH-601XL-B� Vertical Suspension Frequency: 0.98 Hz�

Config. No.� Actuators� Driving� Points� Excitation� Controls� Mass (kg)�

� � Node 1� Node 2� Type� � �

1� 2� 2z� 16z� wings-z� constrained� 395�

2� 2� 3z� 17z� wings-z� constrained� 395�

3� 2� 4z� 18z� aileron-z� constrained� 395�

4� 2� 2x� 16x� wings-x� constrained� 395�

5� 2� 22z� 8z� flaps-z� constrained� 395�

6� 2� 25z� 11z� flaps-z� constrained� 395�

7� 2� 30z� 41z� hfin-z� constrained� 395�

8� 2� 30x� 41x� hfin-x� constrained� 395�

9� 2� 32z� 43z� elevator-z� constrained� 395�

10� 2� 51y� 66y� vfin-y� constrained� 395�

11� 2� 55y� 67y� rudder-y� constrained� 395�

12� 2� 55y� 67y� rudder-y� unconstr.� 395�

13� 2� 4z� 18z� aileron-z� unconstr.� 395�

14� 2� 32z� 43z� elevator-z� unconstr.� 395�

Table 2: Test Device Information

Oversampling Filter: x16

Analog Range: ±10 V

Total Data Channels: 16x5 = 80

Synchronization: Trigger started and digitally synchronized

Sampling Rates: 1 kHz (inputs), 8 kHz (outputs)

Shakers (x2):� � �

Max. Force: 75 N Stiffness: 1 kN/m

Max. Current: 5.5 A Max. Velocity: 1.5 m/s

Frequency Range: 0.5 Hz - 7 kHz Max Displacement: 10 mm

Max. Acceleration: 60g Internal Mass: 0.125 kg

Amplifiers (x2):� � �

Signal to Noise Ratio: >80 dB Input Voltage Range: ±5 V

Max. Output Voltage: 20 V Max. Power (protective shut-down): 120 W

Max. Output Current: 6 A Optimum Load Impedance: 4 �

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Signal

Processing:� � �

Hardware Filter for Outputs: 8th order analog low-pass Bessel filter @ 100 Hz

Hardware Filter for Inputs: 16th order digital (FIR) antialiasing (supersampling) filter @ 1000 Hz

Software Filters (Digital SW): 16th order Chebyshev Type-II Zero-Phase Filter @ 100 Hz

(Additional match filters or wavelet noise reduction filters in case of low S/N ratio)

Analysis:� � �

Number of Shaker Configs: 14 Number of Measurement DOFs: 78 Number of Nodes (Mesh Size): 137

Analysis Range: 1 - 75 Hz

Acquired Time Data: 29 GB

Software: Matlab R2008a + Structural Dynamics Toolbox 6.0 + Ident 2.2

Identification Algorithm: Broadband multiple pole optimizer or orthogonal polynomial approach

Data Format: Universal File Format

During the tests two actuators drive the structure at different positions in a chirp-sweep process with force control. The positions of the actuators used to excite the structural normal mode shapes and the control surface modes of the CH-601XL-B are shown in Figure 2.

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Figure 2: Actuator Configurations

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Figure 3: Accelerometer Locations and Channels

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The blue numbers shown in Figure 3 refer to the positions of the sensors used in the measurements whereas the grey points are used within the aeroelastic software package ZAERO for adding mass to the structure as needed for additional payload (fuel, luggage, passenger, control surface balance mass and production tolerances). The evaluation of the time series data recorded during the measurement is performed using the software package, SDT (www.sdtools.com), for the CAE programming system, MATLAB (www.matlab.com).

3.Rigid Body Modes of Control Surfaces Friction in the control system of an airplane as well as the presence of free play measured at the actuator positions when exiting the control surfaces may result in unrealistic values for the relevant modal data. Thus the predicted flutter speed could be wrong. If the control system is locked due to dry friction when excited with the shakers, the resonant frequency found in the test can be too high. Data from the measurements would then only be accurate as long as the aerodynamic forces acting on the control surfaces did not exceed those applied by the actuators in the ground vibration test. This is seldom the case. If strong viscous friction occurs in the control system, the modal mass found when analyzing the time series data of the corresponding measurements will be too high. These values may accurately reflect the current state of the aircraft as it is perceived during the test. However, the flutter speed calculated from these values could be significantly overestimated if the viscous friction decreases over the service life of the aircraft. If free play is found at the control surfaces of an aircraft, reliable modal values cannot be found at all in the ground vibration test. The modal analysis methods are all based on linear theory but free play is a strong nonlinear phenomenon. It is known that free play first leads to so called limit cycles of the control surfaces in flight. Limit cycles are harmonic vibrations and they increase with the service time of the aircraft as the bearings wear. Finally excessive free play might lead to flutter if the control surfaces are not mass balanced. Due to free play along with dry and viscous friction, the measurements at the CH-601XL-B control surfaces were difficult to perform: For the symmetric rigid body mode of the ailerons with locked controls, no mode was found at all in the relevant frequency range. This means that the nonlinearity brought about by friction and free play did not allow reliable resonant responses to the excitation force. It is assumed that only the corresponding eigenfrequency was found correctly for this case. Therefore, the eigenvectors and modal masses have to be calculated based on the design and control- stiffness measurements. For the ant symmetric rigid body mode of the ailerons, an accurate mode shape was found with an inaccurate modal mass. This means that viscous friction did not allow reliable resonant responses to the excitation force. It is assumed in this case that the mode and the corresponding eigenfrequency were found correctly, while the modal mass required correction. A resonant frequency was found for the elevator rigid body motion with locked controls. For the free control scenario, the resonance was found at approximately twice that frequency. This means that when the controls are locked, the elevator vibrates against the elasticity of the control system, whereas the unlocked control stick vibrates counter phase to the elevator motion. Again because of friction the corresponding modal values found in the ground vibration test have to be recalculated based on the design information of the aircraft.

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For the rudder the same arguments hold true as for the elevator, which leads to the conclusion that eigenvectors, modal mass and mass normalized eigenvectors have to be calculated based on design information of the aircraft.

4.Calculation of Modal Values for the Rigid Body Modes of the Control Surfaces of the CH-601XL-B

It is assumed that the resonant frequencies found in the ground vibration test are correct and that the geometry and the mass values together with the tolerances of the ailerons, the rudder and the elevator received from the manufacturer are valid. Only the rigid body modes of the control surfaces need to be updated. The corresponding eigenvectors are easily determined and the generalized mass and the mass normalized eigenvectors can be calculated with confidence. The calculation of the modal parameters of the ailerons starts with the determination of the mass moment of inertia for a rotation about the hinge axis. Figure 4 shows a cross section diagram of the aileron with the location of the counterbalance. The origin of the coordinate system is placed at the center of the hinge line with y pointing into the span wise direction and x pointing in flow direction.

Figure 4: Airfoil cross section of aileron with hinge center and counterbalance point

The mass of the aileron is assumed to be distributed over the surface of the airfoil. The surface of the aileron is found by extruding and shrinking the airfoil profile (Figure 4) in the y- direction. The following discretization of the skin with a Finite Mass Element Method is shown in Figure 5. The centers of gravity of all mass elements and of the complete aileron are then calculated as well as the mass moment of inertia including the balance mass.

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Figure 5: Aileron distributed mass model

The mass moment of inertia for the symmetric aileron mode Tyy is then used to calculate the modal displacements. It is assumed that aileron motion in resonance is independent of the motion of the rest of the aircraft. Thus only the rigid body motion seen at the sensor locations has to be taken into account. As can be seen from Figure 4 only the nodes: 4, 7, 18, and 21 will exhibit motion in the symmetric and antisymmetric modes. An admissible choice of nodal displacements for the symmetric (qs) and antisymmetric (qa) modes can be calculated from the distance of these vertices to the hinge axes of the ailerons. Flutter calculations with ZAERO require mass normalized eigenvectors w such that

1 =wMwT rr

The mass matrix M for linear motion of the six sensors at the rear side of the ailerons is built with the mass moment of inertia Tyy for rotations about the hinge axis y and the square of the sensor distance from the axis y.

��

�

�

��

�

�

=

2

21

2

7

2

4

/000

000

00/0

000/

xTyy

xTyy

xTyy

MO

Mass normalization of the eigenvectors qs and qa is done by multiplication with the constant

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s

T

sqMqvr

1=�

Such that the mass normalized vector is found to be

qwrr

�= ,

and the generalized mass is calculated with

wwm

Tgen rr1

= .

The same procedure also is carried out for the rudder and the elevator:

Figure 6: Half elevator with minimum mass (1.480 kg) according to production tolerances

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Figure 7: Rudder distributed mass model

Figure 7 shows how the aileron hinge stiffness is measured. For the symmetric and ant symmetric modes the control stick is blocked, a weight is placed at the rear of the aileron directly behind the location where the push rod from the control system is connected. By measuring the corresponding displacement xds, the symmetric aileron hinge stiffness cs = 17.46 Nm/deg can be calculated.

Figure 8: Measurement of the aileron hinge stiffness

The resonant frequencies for the ailerons in symmetric and ant symmetric motion are then calculated using the mass moment of inertia found before:

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yy

H

aF

ant

yy

H

sF

sym

T

cx

T

cx22

, == ��

The frequencies found in the ground vibration test compare well with the calculated values.

Figure 9: Measurement of the elevator hinge stiffness

The procedure for calculating the hinge stiffness for the aileron motions is repeated for the elevator and rudder. The modal data of the basic configuration of the CH-601XL-B (minimum takeoff weight: no fuel, no luggage, no passengers, 75 kg pilot mass) with locked controls can be seen in Table 3. The quality of the time series evaluation can be checked with the help of the phase resonance criterion (PRC). A value of 100% for the PRC is ideal. As a quality criterion for the modal data the value MIF (Modal Indication Function) is shown for each natural mode. A Value of 100 indicates a perfect measurement. A value below 85 is unacceptable. The measurement should be repeated in such a case.

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PROF. DR.- ING. U. WELTIN Table 3: Modal Data for the Basic Configuration of the CH-601XL-B with Fixed Controls

No.�Frequency (Hz)� Modal Mass (kg)� Description�

1� 0,01� 2,53E+00� TX�

2� 0,01� 2,53E+00� TY�

3� 0,01� 2,53E+00� TZ�

4� 0,01� 2,13E+00� RX�

5� 0,01� 1,78E+00� RY�

6� 0,01� 2,24E+00� RZ�

7� 10,50� 2,02E+00� S_WI_BX1�

8� 17,83� 1,66E-01� S_EL_RY2�

9� 19,45� 2,66E-01� A_AI_RY2�

10� 22,83� 2,52E-01� A_AI_RY3�

11� 24,71� 4,15E-01� A_RU_RZ2�

12� 25,78� 6,38E-01� A_HT_BX1�

13� 27,40� 5,94E-01� S_FL_RY1�

14� 28,32� 3,08E-01� A_FL_RY1�

15� 34,14� 5,58E-01� A_WI_BX1�

16� 38,89� 2,45E-01� A_VT_BX1�

17� 39,77� 1,59E-01� A_AI_TY1�

18� 40,77� 2,46E-01� A_FL_TY1�

19� 41,21� 2,38E-01� S_FL_TY1�

20� 41,76� 2,10E-01� A_AI_TY2�

21� 53,12� 1,98E-01� A_EL_TY1�

22� 63,29� 4,07E-01� S_HT_BX1�

23� 65,23� 1,24E-01� A_AI_TY3�

24� 65,46� 1,86E-01� A_AI_TY4�

25� 71,25� 3,61E-01� S_WI_TY1� The MAC matrix (Modal Assurance Criterion) serves as a second quality control means in modal analysis. This matrix is applied here, because the normal mode shapes form the basis of the modeled structural movement in the following flutter calculations, and because the eigenvectors are always supposed to be orthogonal. Ideally, this matrix should only have values of one on its main diagonal, and all other values should be zero. The MAC matrix from the evaluation of the CH-601XL-B with fixed controls can be found in Figure 9.

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Figure 10: Modal Assurance Criterion for controls fixed

If there were an overlap of more than 20 to 30% between any modes evaluated with the time series analysis, any strong aerodynamic coupling between these modes would have to be further examined to determine whether or not the results are reliable. The modal data for the base configuration of the CH-601XL-B with free controls are presented in Table 4.

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Table 4: Modal Data for the Basic Configuration of the CH-601XL-B with Free Controls

No.� Frequency (Hz)� Modal Mass (kg)� Description�

1� 0,01� 2,53E+00� TX�

2� 0,01� 2,53E+00� TY�

3� 0,01� 2,53E+00� TZ�

4� 0,01� 2,13E+00� RX�

5� 0,01� 1,78E+00� RY�

6� 0,01� 2,24E+00� RZ�

7� 0,01� 1,13E-01� A_AI_RY1�

8� 0,01� 3,02E-01� S_EL_RY1�

9� 0,01� 3,63E-01� A_RU_RZ1�

10� 10,50� 2,02E+00� S_WI_BX1�

11� 25,78� 6,38E-01� A_HT_BX1�

12� 27,40� 5,94E-01� S_FL_RY1�

13� 28,32� 3,08E-01� A_FL_RY1�

14� 34,14� 5,58E-01� A_WI_BX1�

15� 38,89� 2,45E-01� A_VT_BX1�

16� 39,77� 1,59E-01� A_AI_TY1�

17� 40,77� 2,46E-01� A_FL_TY1�

18� 41,21� 2,38E-01� S_FL_TY1�

19� 41,76� 2,10E-01� A_AI_TY2�

20� 53,12� 1,98E-01� A_EL_TY1�

21� 63,29� 4,07E-01� S_HT_BX1�

22� 65,23� 1,24E-01� A_AI_TY3�

23� 65,46� 1,86E-01� A_AI_TY4�

24� 71,25� 3,61E-01� S_WI_TY1�

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Figure 11: Matrix for the Base Configuration of the CH-601XL-B with Free Controls

The MAC matrix of the normal mode shapes for the base configuration of the CH-601XL-B with free controls is shown in Figure 10. It can be seen here that the results of the measurement of the CH-601XL-B with free controls are satisfactory as well.

5. Computational Model The numerical model of the CH-601XL-B was calculated using finite element theory to match measured results of the tested aircraft as precisely as possible. The model was assembled using 6 DOF Bernoulli beam elements connecting the vertices of the GVT model in a physically meaningful manner intended to mimic the original structure. In total, the FE model consisted of 912 degrees of freedom over 152 vertices connected by 256 beam elements. The mass parameters of the FE model were determined based on a surface mass distribution of the aircraft’s exterior. Initial estimates were made for stiffness parameters, which were then altered using a numerical model updating procedure. The model was divided into sections for the updating calculations as per the following table. Stiffness parameters were identified for each section separately, adding to a total of 11 updating parameters.

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Stiffness Section

Wings

Fuselage

Horizontal Tail

Ailerons

Elevator

Rudder

Flaps

Aileron Hinges

Flap Hinges

Elevator Hinges

Rudder Hinges

Table 5: Updated Model Sections

The parameters were updated iteratively based on a match between the FE model and the following measured mode shapes:

DESC FREQ (HZ)

S_WI_BX1 10.10

S_EL_RY2 17.81

A_AI_RY2 19.52

A_RU_RZ2 20.06

S_FL_RY1 29.61

A_FL_RY1 28.31

A_WI_BX1 28.22

A_AI_TY1 39.80

S_HT_BX1 62.76

S_WI_TY1 64.28

Table 6: Measured Resonance Frequencies

The updating process was performed using an iterative least squares sensitivity method. A

measurement vector was constructed from the mode shapes, , and eigenvalues, ,

measured in the GVT.

Similarly, the corresponding computed vector can be calculated and assembled out of the FE model.

The error vector is simply the difference between the two.

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The sensitivity of each error parameter to each updating parameter is computed and added to the

sensitivity matrix completing the following equation, in which represents a vector of minimal deviations to the updating parameters.

The updating parameters are calculated iteratively using the following least squares approach until convergence.

At convergence the FE model yielded eigenvalues and mode shapes that corresponded well to those from the GVT.

DESC FREQ (HZ)

S_WI_BX1 10.50

S_EL_RY2 17.83

A_AI_RY2 19.45

A_RU_RZ2 24.71

S_FL_RY1 27.40

A_FL_RY1 28.32

A_WI_BX1 34.14

A_AI_TY1 39.77

S_HT_BX1 63.29

S_WI_TY1 71.25

Table 7: Computed Resonance Frequencies

After completion of the updating process, the updated FE model was used to extrapolate the remaining flutter relevant eigenvalues and mode shapes.

5.Flutter Calculation For the flutter calculation, the aerodynamic model of the CH-601XL-B first has to be constructed using the software package, ZAERO (www.zonatech.com). In Figure 11, the aeroelastic model created for the CH-601XL-B is shown.

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Figure 12: Aeroelastic Model of the CH-601XL-B

The deformations that were determined in the ground vibration test (eigenvectors for each resonant frequency) at the positions of the accelerometers (green dots in Figure 11) are transferred over to the discrete surface of the CH-601XL-B model. Using spline operations, a three dimensional movement is allocated to every aeroelastic element (the red rectangles seen in Figure 11)

6. Normal Modes of the CH-601XL-B The resulting normal modes of the CH-601XL-B as interpolated in ZAERO are presented in the following section both with free and with fixed controls. The results shown in Figures 12 through 32 are sorted by increasing resonant frequency. The notation for the normal modes is clarified in Table 3 and Table 4.

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Figure 13:

Figure 14:

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Figure 15:

Figure 16:

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Figure 17:

Figure 18:

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Figure 19:

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Figure 20:

Figure 21:

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Figure 22:

Figure 23:

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Figure 24:

Figure 25:

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Figure 26:

Figure 27:

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Figure 28:

Figure 29:

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Figure 30:

Figure 31:

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Figure 32:

Figure 33:

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After interpolating the normal modes with the software package, ZAERO, the aerodynamic forces on each element are calculated with respect to air stream velocity. Afterwards, Eigen values are determined for the structure with coupled aerodynamic forces. At the point where the calculated damping becomes positive, energy from the air stream begins to be converted into vibration energy of the structure. The velocity of the air stream at which this begins is identified as the critical flutter velocity. Exceeding the flutter velocity does not necessarily mean that the amplitudes of the structural normal mode shapes will climb as would be the case with resonant excitation. Before flutter can occur, a certain initial deformation of the flutter-causing mode shape needs to be present. This can be initiated by a gust, by turbulence or by flight maneuvers. Once a critical structural deformation has taken shape, the vibration amplitudes of the affected normal modes start climbing. In fact, this gain in amplitude is significantly more dangerous than is seen in resonant excitation. In resonance, the vibration amplitudes increase linearly, which usually leaves time to react. In the case of flutter, which presents a dynamic instability, the vibration amplitudes increase exponentially over time. Within just a few oscillations of the right normal mode at the right frequency, the maximum allowed material stress is exceeded and the aircraft breaks apart in the air. There is usually no time to react! In a test flight, it is not possible to induce all of the conditions that could lead to a critical deformation of the aircraft structure. If the deformation that leads to flutter has not been identified, then one cannot be certain that this deformation would not occur during flight maneuvers. Therefore, an in-flight flutter investigation conducted before attaining this information is insufficient. For this reason, a computer investigation of flutter risk is absolutely necessary. In the flutter calculations for the CH-601XL-B the minimal flutter velocity required for the flight certification is determined and the vibration modes that cause the flutter are presented up to a flight velocity of 500 km/h. According to the results of the aeroelastic investigation, there is no cause for concern in certifying the aircraft as long as the minimum flutter velocity (VFL) is at least 20% greater than the Design or Dive Velocity (VD). The empirically determined safety margin of 20% with respect to the design velocity is defined in the JAR23. It accounts for deviations that could occur in the test-based calculations due to the fact that only one prototype is measured in the ground vibration test. Unknown deviations in parameters between prototypes could affect the results. At this time common practice does not entail specifying a confidence interval for a flutter speed calculated based upon ground vibration testing.

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7. CH-601XL-B with Minimum Loading In Figures 33 and 34, results are presented for the CH-601XL-B with fixed controls and minimum take-off weight flying at sea level (1.225 kg/m� air density).

Figure 34: Aerodynamic Damping Values over Velocity for the CH-601XL-B with Fixed Controls and Minimum Loading at Sea Level

Figure 35: Resonant Frequencies over Velocity for the CH-601XL-B with Fixed Controls

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The results of the flutter calculations for the CH-601XL-B with minimal loading and fixed controls at an altitude of 5000m (0.736 kg/m� air density) are shown in Figures 35 and 36.

Figure 36: Aerodynamic Damping Factors over Velocity for the CH-601XL-B with Fixed Controls at an Altitude of 5000m

Figure 37: Resonant Frequencies over Velocity for the CH-601XL-B with Fixed Controls at an Altitude of 5000m

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The results for the CH-601XL-B with minimal loading and free controls at sea level are shown in Figures 37 and 38.

Figure 38: Damping Factors over Velocity for the CH-601XL-B with Free Controls at Sea Level

Figure 39: Frequencies over Velocity for the CH-601XL-B with Fixed Controls at Sea Level

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The results of the flutter calculations for the CH-601XL-B with minimal loading and free controls at an altitude of 5000m (0.736 kg/m� air density) are shown in Figures 39 and 40.

Figure 40: CH-601XL-B with Minimal Loading and Free Controls at an Altitude of 5000m

Figure 41: CH-601XL-B with Minimal Loading and Free Controls at an Altitude of 5000m

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8.Flutter Calculation Results for the CH-601XL-B with Maximum Loading

The mass distributions for maximum loading that were previously shown in Figure 3 are introduced to their corresponding positions (also indicated in Figure 3) before the model is simulated with the help of the software package, ZAERO. The modal parameters of this modified structure are updated using the corresponding eigenvalue calculations. In general, the resonant frequencies are reduced with the introduction of the additional mass to the structure. This poses a new risk that aerodynamic force may couple with the modified structure and enable flutter vibrations. The results for the configuration at sea level with maximum loading and fixed controls are shown in Figures 41 and 42.

Figure 42: Damping Factors over Velocity for the CH-601XL-B at Sea Level with Maximum Loading and Fixed Controls

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Figure 43: CH-601XL-B at Sea Level with Maximum Loading and Fixed Controls

The results shown in Figures 43 and 44 are for the configuration with maximum loading and fixed controls at an altitude of 5000m.

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Figure 44: CH-601XL-B with Maximum Loading and Fixed Controls at an Altitude of 5000m

Figure 45: CH-601XL-B with Maximum Loading and Fixed Controls at an Altitude of 5000m

The results presented in Figures 45 and 46 are for the CH-601XL-B at sea level with free controls and maximum loading.

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Figure 46: CH-601XL-B at Sea Level with Maximum Loading and Free Controls

Figure 47: CH-601XL-B at Sea Level with Maximum Loading and Free Controls

The results for the configurations of the CH-601XL-B with free controls and maximum loading at a 5000m altitude are shown in Figures 47 and 48

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Figure 48: CH-601XL-B at 5000m with Maximum Loading and Free Controls

Figure 49: CH-601XL-B at 5000m with Maximum Loading and Free Controls

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9.Flutter Calculation for Control Surfaces with Maximum Mass

The results shown in Figures 49 and 50 are for the CH-601XL-B at sea level with minimum loading, free controls, and with the maximum control surface masses. The control surface masses are increased as seen in Table 5 to the upper tolerance limits. All additional mass is added to the trailing edges of the control surfaces assuming the worst possible unbalance scenario.

Table 8: Control Surface Masses and Tolerances from the Manufacturer

Minimum Maximum

Left / right Aileron without balance mass

1.500 kg

+30%

1.950 kg

Elevator 2.500 kg +25% 3.125 kg

Rudder 2.750 kg +25% 3.375 kg

Figure 50: Damping Factors over Velocity for the CH-601XL-B at Sea Level with Maximum Control Surface Masses

Flutter Analysis

LH10

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Figure 51: CH-601XL-B at Sea Level with Maximum Control Surface Masses

10.Summary and Recommendations The CH-601XL-B is free of flutter under ICAO standard atmospheric conditions from sea level to an altitude of 5000m for velocities up to 500 km/h (TAS). This was confirmed for free and fixed controls, as well as maximum and minimum loadings. This aircraft is found to be in accordance with the JAR-23 fulfilling the requirements for certification.

Hamburg, December 18, 2011

Prof. Dr.-Ing. Uwe Weltin

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