# Helicopter Rotor Thickness Noise Control Using Unsteady Force Excitation
## 3 Validation of Noise Reduction Method
### Results and Discussions
When the observations were at the same azimuthal angle, e.g., P3, P6, and P8 at 180\({}^{\circ}\), the noise reduction in the rotor plane was the most obvious (P6) and gradually reduced with the elevation angle increase. The same trend was observed in other azimuths. This was because the anti-noise generated by the trailing edge winglet reached the largest value in the rotor plane. Comparing the observations in the rotor plane (P15, P6, P21), the noise reduction of the observations at 180\({}^{\circ}\) was the best and was lower at 150\({}^{\circ}\)and 210\({}^{\circ}\). For the hovering condition, due to the axisymmetric distribution of SPL, the control method could only reduce the noise in the areas of interest. However, for forward flight, the area with strong SPL was located in the front of the rotor, thus the peak SPL could be reduced by adjusting the control phase angle and amplitude. Although the noise behind the rotor increased, the overall SPL was reduced. Figure 12: The comparison of the signal at the P22 microphone with and without filtering: (**a**) original signal, (**b**) filtered signal. Then, the effects of the winglet control parameters (frequency, amplitude, and phase) on noise reduction were further analyzed. The variation of differential SPL (SPL\({}_{\text{on}}\)-SPL\({}_{\text{off}}\)) with a deflection frequency at the P6 microphone is shown in Figure 14. The alternating voltage was kept at 60 \(\pm\) 40 V.  
Figure 13: The noise reduction in the condition of \(H_{f}=1,\psi_{f}=270^{\circ},60\pm 40\) V: (**a**) contour plot of differential sound pressure level (SPL), (**b**) time history of sound pressure. It can be seen that there was an optimal excitation angle at any frequency where the maximum noise reduction could be achieved. The optimal excitation angles corresponded to different frequencies. The angle for the first-order excitation was 270\({}^{\circ}\), and those of the second-order and third-order controls were 180\({}^{\circ}\) and 90\({}^{\circ}\), respectively. In the hover condition, the distribution of SPL was axisymmetric, thus the optimal angle could be directly obtained through theoretical analysis. Learning from Equations (4) and (5), we know that the peaks of thickness and load noise were generated from the source at the azimuthal station that was 90\({}^{\circ}\) ahead of the observer, also explained by Figure 15. If an observer was at a 180\({}^{\circ}\) azimuth, the source at the azimuth of 90\({}^{\circ}+\delta\) caused the greatest noise at this location. \(\delta\) was the angle between the position and the radiation vector and could be neglected when the observer was far away from the rotor center. Therefore, the change rate (time derivative) of the exciting force needed to be maximized at an angle of 90\({}^{\circ}\) ahead of the observation position to reduce noise effectively. This meant that the time derivative of the deflection function should have been maximal at that azimuth. Taking the second-order frequency as an example, the deflection law of the winglet is: \(\theta_{f}=A_{f}\sin(2\cdot\psi+\psi_{f})\) to maximize the time derivative \(\dot{\theta}_{f}\)= \(2A_{f}\cos(2\times 90^{\circ}+\psi_{f})\) at azimuth of 90\({}^{\circ}\), the initial excitation angle \(\psi_{f}\) is 180\({}^{\circ}\). The test results given in Figure 14 are consistent with the theoretical analysis. Strictly speaking, the angle \(\delta\) should have been included to obtain the exact angle of \(\psi_{f}\) in this analysis because the observers were not located in far-field. However, due to the large interval (30\({}^{\circ}\)) used in the phase sweeping test, it covered the effect of \(\delta\), thus the results were similar to the theoretical analysis. The four observations on the right and the left sides of the rotor (azimuth 150\({}^{\circ}\) and azimuth 210\({}^{\circ}\)) were selected to study the influence of the excitation phase angle.