Dynamic Modeling And Analysis Of Transmission Mechanism With Joint Clearances For Air Rudder

Air rudder is one kind of position servo systems with high precision and rapid dynamic response. The dynamic performances of air rudder directly affect the flight quality of aircraft during the flight. The transmission mechanism is the center of air rudder transmiting motion, which transfers linear motion of the servo to rotation of control surface. Thus perfect dynamic characteristics of transmission mechanism contribute to improve the control accuracy of control surface. The clearance of revolute joints in transmission mechanism not only makes the angle of control surface have a deviation, but also causes contact-impact phenomena among joint elements. Consequently, the clearance reduces the stability and accuracy of movement of the transmission mechanism. It is of great importance to establish the more precise dynamic model of transmission mechanism for guiding the design of mechanism and improving the dynamics performance of rudder system.Based on geometric constraints of conformal deformation and Elastic Foundation Model, the static contact force model between shaft and hole in radial direction is established to get the contact stiffness formula, which is verified by experiments. The static contact force model for revolute joint contact in radial direction is built based on the contact stiffness formula, where the axis length and multi-contact states for joint contact are considered. The static joint contact force model is verified by compressive experiments of single joint.Considering the energy dissipation caused by damping force under the mutable contact stiffness, the hysteresis damping coefficient during the joint collision is derived based on the nonlinear spring-damping model and the static contact model for revolute joint contact. The normal contact-impact model for revolute joints is established where the static contact and damping force model are combined. An collision case, which a pin impacts an stationary semi-hole with a certain initial velocity, is carried out to analysis the influence of contact and impact and verify the validity of contact-impact model. Meanwhile, tangential friction is described based on Coulomb Friction Theorem.According to the structural characteristics of revolute joints in the transmission mechanism, the contact judgment formula is built by the vector method for a reasonable description of joint clearance. Taking advantage of the contact judgment formula, different motion status for revolute joints are described by a uniform contact force model. Then, based on MLSD, the model of impact dynamics with a clearance joint is established. One case of motion with an revolute joint, pendulum swing, is carried out. While the joint clearance is little enough, the validity of the dynamics model is verified by ADAMS simulation.Finally, taking the transmission mechanism in one air rudder system as an research object, the movement of the transmission mechanism are described. The dynamic equations of the transmission mechanism are presented by introducing the clearance joint dynamic model, where three clearance joints in the transmission mechanism are considered. The simulation model by Simulink is built based on the dynamic equations. To carrying out dynamic experiments of the transmission mechanism, a test system is developed. The validity of dynamic equations are verified by experiments.