# Adaptive Control of the Aerodynamic Flaps of the Savonius
## 3 Dynamic Analysis of the System
According to (23), we can obtain  
\[\delta_{s}=\frac{459.8\cdot 0.3^{4}}{8\cdot 70\cdot 10^{9}\cdot 4.5\cdot 10^{-9} }=0.04\) mm (24)  
Thus, the deflection of the flap is also insignificant. The gear teeth in the flap control mechanism transmit torque and are subjected to significant contact loads. Under applied forces, elastic deformation occurs on the working surfaces, affecting motion transmission accuracy and wear resistance. Evaluating the elastic deformation of the teeth is necessary for analyzing the overall behavior of the transmission and ensuring its durability [32]:  
\[\delta_{z}=\frac{F_{t}}{kA} \tag{25}\]  
where \(F_{t}=\frac{M_{\rm m}}{r}\) is the tangential force on the gear tooth, and \(k\) is the shear modulus (steel: 80 GPa); \(A\) is the contact area, calculated as \(A=\) bh = 0.008\(\cdot\)0.01 = \(8\cdot 10^{-5}\) m\({}^{2}\). Thus, according to (25), \(\delta_{z}=7.18\cdot 10^{-6}\) mm, which is also negligible. During prolonged operation, the flap control mechanism is subjected to repeated cyclic loads caused by both variable wind forces and actuator operation. These loads can lead to the accumulation of fatigue damage in the materials of the links, eventually resulting in crack formation and failure of individual components. To assess the structural lifespan, a fatigue analysis is required, taking into account material properties, loading type, and the number of cycles. The following section examines the fatigue strength of the lever one of the most heavily loaded elements in the system. The Goodman criterion is used for the calculation, as it allows simultaneous consideration of both mean and alternating stresses [33]:  
\[\sigma_{a}=\frac{\sigma_{max}-\sigma_{min}}{2};\,\sigma_{m}=\frac{\sigma_{max}+ \sigma_{min}}{2} \tag{26}\]  
where \(\sigma_{max}=\frac{M_{s}}{w}\), \(W=\frac{bh^{2}}{6}=3.33\cdot 10^{-6}\)m\({}^{3}\)--axial section modulus, and \(\sigma_{min}\) is minimum stress. According to (26), \(\sigma_{a}=2.06\cdot 10^{6}\) Pa, \(\sigma_{a}=1.03\cdot 10^{6}\) Pa. The stress is below the fatigue limit of aluminum (150 MPa), indicating that the lever will serve reliably over a long period of time. The gear transmission in the flap control mechanism operates under variable loads, which cause both contact and bending stresses on the working surfaces of the teeth. To assess the fatigue strength of gear engagements, the Buchholz criterion is used. This method takes into account local stresses in the contact zone and the effect of stress concentration. Such an approach allows for more accurate prediction of the onset of fatigue damage, crack formation, and wear--which is critical for ensuring the reliability and durability of the entire transmission system [34]:  
\[N_{f}=\left(\frac{\sigma_{fat}}{\sigma_{a}}\right)^{m} \tag{27}\]  
where \(N_{f}\) is the number of cycles to failure; \(m=3\) is the empirical exponent for steel. According to (27), \(N_{f}\approx 1.47\cdot 10^{15}\). Thus, the gearbox teeth will withstand an extremely large number of cycles. The operation of the flap control mechanism in a wind turbine involves not only static but also dynamic loads, which significantly affect its reliability and efficiency. Sudden changes in wind flow are particularly critical, as they generate impact torques and uneven responses within the system. An additional risk factor is the uneven mass distribution of moving links, which leads to increased inertial loads and potential vibrations. To enhance the stability of the mechanism and extend its service life, a comprehensive analysis of dynamic factors is required. The following two key aspects affecting structural reliability are considered:  
* Analysis of dynamic impact loads caused by sudden wind speed changes and actuator operation;
* Optimization of mass distribution within the mechanism to minimize inertial effects and improve system stability.