# High-Fidelity Fin-Actuator System Modeling and Aeroelastic Analysis Considering Friction Effect
## 1 Introduction
The coupling between these equations often makes the modeling process cumbersome and the solving process complex. Therefore, a new actuator modeling method is needed. Based on modularization, a high-fidelity and systematic modeling method for an actuator is formed that can ensure accuracy, ease of use, and consider freeplay and friction at the same time. It can be easily extended to different configurations of actuators. Using this model, the characteristics of the actuator can be obtained directly for the analysis of aeroservoelasticity. In addition to the natural friction at the joints of the system, engineers, based on experience, take measures to increase friction in order to suppress flutter. For example, friction sheets [11] or friction rings [12] were added to some actuators to increase friction. Friction  
Figure 1: Model comparison for flutter analysis, where (**a**) is the model of the conventional fin–actuator system and (**b**) is the fin–actuator system considering the characteristics of an actuator. plays a positive role in the aeroelastic system, but friction in servomechanism systems dissipates power [13] and may cause position signal steady-state errors or oscillations. The added friction sheet is often set empirically. So far, the mechanism of friction on the aeroelastic characteristics of the system is still unclear, and relevant research or analysis has not been reported. How can we reduce friction while ensuring the effect of friction on flutter stability? How can we achieve a balance between ensuring aeroelastic stability and reducing power loss? These are the issues that this article explores in the study of the friction influence mechanism. Friction is a nonlinear and complex phenomenon that is determined by the relative motion between the two contact surfaces. Friction is related to interface material and operating conditions, such as loads acting on the contact [14]. Introducing nonlinearity significantly complicates all aspects of already complicated aeroelastic equations of motion, to the point that friction is typically omitted from a flutter-related analytical workflow or approximated by a constant value. Some researchers use simple friction models to analyze the influence of friction on aeroelastic characteristics. [PERSON] [15] researched stability criteria with consideration of mechanical damping, which was assumed constant. [PERSON] et al. [16] considered friction as a hysteretic spring with damping to study the blade response. The blade was simplified as a single degree of freedom system, and then the maximum response amplitude of it was analyzed using the Ritz method. [PERSON] and the team [17] studied the possibility of dry friction for flutter suppression. The results showed that the aeroelastic stability boundary can be enhanced by changing the position of friction and the geometry of the interfaces. [PERSON] et al. [18] validated for the first time that friction may play a stabilizing role in LCOs that occur after flutter. [PERSON] et al. [19] studied the stability of an aeroelastic system with 1.5 degrees of freedom. The results showed that different friction stiffness has an influence on the critical aerodynamic damping ratio and the stability boundary of the system, but it has little influence on the stability boundary. [PERSON] et al. [20] studied the effect of the Coulomb friction on airfoil aeroelastic stability by a numerical method and the harmonic balance method. The results showed that Coulomb friction can increase the flutter velocity, and it is affected by the initial condition. [PERSON] et al. [21] regarded Coulomb friction as a linear damping ratio and analyzed the influence of the Coulomb friction on LCOs caused by symmetric and asymmetric freeplay. The results show that friction is dissipative, but it is not enough to restrain LCOs. The friction model used in the above work is relatively simple and is a preliminary exploration of the friction effect mechanism and cannot fully reflect the friction characteristics.