The jointed shaft in the drivelines of the rolling mill, with its angle continuously varying in the production, has obvious impact on the stability of the main drive system. Considering the effect caused by the joint angle and friction force of roller gap, the nonlinear vibration model of the main drive system which contains parametric excitation stiffness and nonlinear friction damping was established. The amplitude-frequency characteristic equation and bifurcation response equation were obtained by using the method of multiple scales. Depending on the bifurcation response equation, the transition set and the topology structure of bifurcation curve of the system were obtained by using the singularity theory. The transition set can separate the system into seven areas, which has different bifurcation forms respectively. By taking the 1 780 rolling mill of Chengde Steel Co for example, the simulation and analysis were performed. The amplitude-frequency curves under different joint angles, damping coefficients, and nonlinear stiffness were given. The variations of these parameters have strong influences on the stability of electromechanical resonances and the characteristic of the response curves. The best angle of the jointed shaft is 4.761 3° in this rolling mill.
SHI Pei-mingLI Ji-zhaoJIANG Jin-shuiLIU BinHAN Dong-ying
This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincar map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.
