4. Certification process

Figure 12. Influence of pitch hinge station (LΘ) on flutter speed (25% = rear; 46% = middle; L = light blades; H = heavy

Figure 13. Influence of mass balance weight station (LW) on flutter speed (0% = front; 100% = rear; L = light blades; H =

heavy blades), rear (25%), and middle (46%) pitch hinge stations.

blades; LW = mass-balance weight station).

152 Flight Physics - Models, Techniques and Technologies

The airworthiness regulation standard requirements for dealing with the aeroelasticity and flutter also include requirements related to the whirl flutter. Essentially, the whirl flutter requirements are applicable only to aircraft powered by a turboprop power plant system. In the following text, the requirements of the FAR/CS 23 regulation standard, which is applicable to smaller turboprop aircraft, are taken into consideration. The whirl flutter related requirement, which is included in §629(e), is applicable regardless of the aircraft configuration or the number of engines (twin wing-mounted, single nose-mounted, twin fuselage mounted pusher, etc.). §629(e)(1) includes the main requirement to evidence the stability within the required V-H envelope, while §629(e)(2) requires the variation of structural parameters such as the stiffness and damping of the power plant attachment. The whirl flutter analysis must, therefore, include all significant aircraft configurations with respect to fuel and payload that are applicable to the aircraft operation. The whirl flutter analysis must also include the influence of the variance of the power plant mount structural parameters when simulating the possible changes due to structural damage (e.g., deterioration of engine mount isolators). Note that further requirements that are applicable to aircraft compliance with the fail-safe criteria come from §629(g).

We can use two main approaches for the analysis:

First is the standard approach, in which the analyses are performed for a known set of structural parameters, and the results are whirl flutter stability characteristics (e.g., whirl flutter speed). The resulting flutter speed is then compared to the certification velocity according to the flight envelope. The analyses are performed sequentially, state by state.

The standard approach is good for complying with the main requirement (§629(e)(1)), which is realized by evaluation of the nominal parameter states. Figure 14 shows an example of a V-g-f diagram of such a calculation. No flutter instability is indicated up to the certification velocity, which is 191.4 m/s in the case, and therefore, the regulation requirement is fulfilled. Calculations are performed for all applicable mass configurations. However, for parametric studies that

Figure 14. Example of whirl flutter calculation (V-g-f) diagram, (a) damping, (b) frequency, nominal state.

may include huge numbers of analyses, such an approach may become ineffective unless some tool for automated analysis, data handling, and processing is used. However, the applicability of such automatic processing systems is always limited.

Therefore, to comply with the parameter variation requirement (§629(e)(2)), the second, optimization-based approach [25] can be used. In this approach, the flutter speed is set equal to the certification speed, and the results are critical values of the structural parameters. The stability margin can then be obtained from these critical structural parameters. The analyzed states are then compared only with respect to the structural parameters and the relationship to the stability margin. Such an approach can save large amounts of time because the number of required whirl flutter analyses is dramatically reduced.

Provided a full-span model is considered, four design variables are defined: (1) effective stiffness of the engine attachment for symmetric pitch, (2) effective stiffness of the engine attachment for antisymmetric pitch, (3) effective stiffness of the engine attachment for symmetric yaw, and (4) effective stiffness of the engine attachment for antisymmetric yaw. The solution includes three frequency ratio constraints: (1) for symmetric engine vibration frequencies, (2) for antisymmetric engine vibration frequencies, and (3) for critical whirl flutter frequencies. Additionally, the flutter constraint, i.e., the requirement of flutter stability, is applied for the certification speed. The objective function is then formally expressed as the minimization of the sum of engine vibration frequencies. Figure 15 shows an example of a V-g-f diagram for the optimizationbased calculation. There is a flutter state of mode nr.2 (engine pitch vibration mode) at the velocity of 191.4 m/s representing the whirl flutter instability. Calculations are performed for several values of the critical frequency ratio to construct a stability margin curve, which is then constructed for all applicable mass configurations, as shown in the example in Figure 16. Stability margins may be constructed with respect to either engine yaw and pitch vibration frequency or engine yaw and pitch attachment effective stiffness. The former type of margin is then compared with the engine vibration frequencies, obtained by the GVT or analytically, to evaluate the rate of reserve. Figure 17 demonstrates an example of such an evaluation. The

Aeroelastic Stability of Turboprop Aircraft: Whirl Flutter http://dx.doi.org/10.5772/intechopen.70171 155

Figure 15. Example of whirl flutter calculation (V-g-f) diagram, (a) damping, (b) frequency, optimization-based calculation.

may include huge numbers of analyses, such an approach may become ineffective unless some tool for automated analysis, data handling, and processing is used. However, the applicability of

Figure 14. Example of whirl flutter calculation (V-g-f) diagram, (a) damping, (b) frequency, nominal state.

Therefore, to comply with the parameter variation requirement (§629(e)(2)), the second, optimization-based approach [25] can be used. In this approach, the flutter speed is set equal to the certification speed, and the results are critical values of the structural parameters. The stability margin can then be obtained from these critical structural parameters. The analyzed states are then compared only with respect to the structural parameters and the relationship to the stability margin. Such an approach can save large amounts of time because the number of

Provided a full-span model is considered, four design variables are defined: (1) effective stiffness of the engine attachment for symmetric pitch, (2) effective stiffness of the engine attachment for antisymmetric pitch, (3) effective stiffness of the engine attachment for symmetric yaw, and (4) effective stiffness of the engine attachment for antisymmetric yaw. The solution includes three frequency ratio constraints: (1) for symmetric engine vibration frequencies, (2) for antisymmetric engine vibration frequencies, and (3) for critical whirl flutter frequencies. Additionally, the flutter constraint, i.e., the requirement of flutter stability, is applied for the certification speed. The objective function is then formally expressed as the minimization of the sum of engine vibration frequencies. Figure 15 shows an example of a V-g-f diagram for the optimizationbased calculation. There is a flutter state of mode nr.2 (engine pitch vibration mode) at the velocity of 191.4 m/s representing the whirl flutter instability. Calculations are performed for several values of the critical frequency ratio to construct a stability margin curve, which is then constructed for all applicable mass configurations, as shown in the example in Figure 16. Stability margins may be constructed with respect to either engine yaw and pitch vibration frequency or engine yaw and pitch attachment effective stiffness. The former type of margin is then compared with the engine vibration frequencies, obtained by the GVT or analytically, to evaluate the rate of reserve. Figure 17 demonstrates an example of such an evaluation. The

such automatic processing systems is always limited.

154 Flight Physics - Models, Techniques and Technologies

required whirl flutter analyses is dramatically reduced.

Figure 16. Example of whirl flutter stability margins for multiple mass configurations.

Figure 17. Example of whirl flutter stability margin evaluation.

dashed line represents the () 30% variance margin in engine attachment stiffness. Another parameter to be evaluated is the damping. This is provided by calculation with very low structural damping, represented by the damping of g = 0.005, while the standard structural damping included in the analyses is g = 0.02. The stability margin for reduced damping is also presented in Figure 17.

As obvious from Figure 17, there is sufficient reserve in stability of the nominal state with respect to the stability margin, and therefore, the regulation requirements would are fulfilled.

#### 5. Conclusion

The presented chapter addresses a specific aeroelastic phenomenon that is applicable for turboprop aircraft structures: whirl flutter. This chapter includes basic facts regarding the physical principles and the analytical solution of the described phenomenon. After that, the experimental research activities are outlined, with a focus on the recent experiments on the W-WING whirl flutter demonstrator. Finally, the approaches to aircraft certification are explained. Comprehensive information on the whirl flutter phenomenon from all aspects can be found in Ref. [26].
