Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state va...Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state variables of the system, the complete set of nonlinear equations of motion including an effective linear control function was solved for A-4D and Mig-21 Aircraft. The roll angle responding to the linear control function for both models was estimated when the systems were tested under different damping ratios. The numerical re- suits show that a linear control function including both the roll attitude and the roll rate is sufficient to suppress the wing rock motion with an acceptable error in desired time. A good agreement between the numerical results and the published work is obtained for the limit cycle oscillation existence at different damping ratios.展开更多
Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-D...Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.展开更多
文摘Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state variables of the system, the complete set of nonlinear equations of motion including an effective linear control function was solved for A-4D and Mig-21 Aircraft. The roll angle responding to the linear control function for both models was estimated when the systems were tested under different damping ratios. The numerical re- suits show that a linear control function including both the roll attitude and the roll rate is sufficient to suppress the wing rock motion with an acceptable error in desired time. A good agreement between the numerical results and the published work is obtained for the limit cycle oscillation existence at different damping ratios.
基金Supported by National Natural Science Foundation of China (No.50905061)the Fundamental Research Funds for Central Universities
文摘Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.
