Dynamic modeling and nonlinear characteristics of a rigid–flexible coupled rudder system with hinge clearance

Hinge clearance in the aircraft rudder system reduces the motion accuracy and stability of the transmission structure, thus affecting the maneuverability, stability and flight safety of the aircraft. Therefore, it is necessary to perform accurate dynamic modeling of rudder systems with hinge clearance and analyze their nonlinear characteristics to guide design and optimization.

The hinge-clearance contact force is modeled using the classical Hertz model and the modified Coulomb model implemented in Automatic Dynamic Analysis of Mechanical Systems (ADAMS). In this study, the rigid–flexible coupled dynamic model of a rudder system with hinge clearance considering a flexible rudder surface was developed using the virtual power principle and the mixed coordinate method. The fixed-step fourth-order Runge–Kutta integral solver was implemented in MATLAB for numerical simulations, and the correctness of the dynamic model was verified by comparing the obtained simulation results with ADAMS dynamic simulation results. Based on the dynamic model, numerical simulation experiments were performed to explore the influence of rigid–flexible coupling on the dynamic characteristics of the rudder system. Based on the theory of nonlinear dynamics, the bifurcation diagrams of a rigid body and a rigid–flexible coupled rudder system under different excitation frequencies were obtained. A specific frequency was selected to construct the phase trajectory diagram and the Poincaré map. The evolution of system dynamics caused by changes in the excitation frequency was analyzed, and the nonlinear coupling effect between the excitation frequency and structural flexibility was explored. The hinge clearance was increased to study its influence on the bifurcation diagrams of the rigid body system.

MATLAB numerical simulation results were overall consistent with the ADAMS dynamic simulation results. When only the first-order natural mode of the flexible rudder surface was considered, the response difference between the rigid–flexible coupled system and the rigid body system was very small. After the introduction of the flexible rudder, mainly the first two natural modes were excited. There was a sudden change in the bifurcation diagram of the rigid rudder system. The phase diagram and Poincaré map showed that the system was in a stable period-1 motion state in the low-frequency band, and that two attractors existed within the relative motion of the clearance. The system gradually transformed into a quasi-periodic motion state near the critical frequency of 21 Hz. Further, increased hinge clearance reduced the critical frequency of the rigid system. The rigid–flexible coupled rudder system resonated due to the excitation of the second-order mode, showing a resonance peak at 27.27 Hz, and the oscillation phenomenon was mitigated in the high-frequency band.

All rigid rudder systems exhibit a critical excitation frequency that is associated with the clearance size. In rudder systems, the presence of a flexible structure reduces stiffness, and a coupling nonlinear effect is observed between the excitation frequency and structural flexibility. These research results clarify the coupling law between the excitation frequency and structural flexibility, which provides a reference for optimizing the structural design of the steering gear and improving the dynamic stability of the rudder system. It is necessary to further explore the coupling nonlinear effects between excitation frequency, structural flexibility and clearance size.