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 ...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.展开更多
Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slen...Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.展开更多
The strip with a time-dependent tension moves, namely a harmonically varying tension about a constant initial tension. The nonlinear vibration model of moving strip between two mills with time-dependent tension was es...The strip with a time-dependent tension moves, namely a harmonically varying tension about a constant initial tension. The nonlinear vibration model of moving strip between two mills with time-dependent tension was established. Approximate solutions were obtained using the method of multiple scales. Depending on the variation of the tension, three distinct cases arise： frequency away from zero or two times the natural frequency; frequency close to zero; frequency close to two times the natural frequency. For frequency close to zero and away from zero and two times the natural frequency, the system is always stable. For frequency close to two times the natural frequency, the stability is analyzed respectively when the trivial solution exists and the nontrivial solution exists. Numerical simulation was made on some 1660 mm tandem rolling mill, and the stable regions and unstable regions for parametric resonance are determined with different cases. The rolling speed and the thickness of strip have strong influences on the stability of principle parametric resonances. But the distance between two mills has little influence on the stability of principle parametric resonances.展开更多
基金Item Sponsored by National Natural Science Foundation of China(51005196)Natural Science Foundation of Hebei Province of China(F2010001317,E2012203194)
文摘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.
基金the National Outstanding Young Scientists Foundation of China (Grant No. 10725209)the National Natural Science Foundation of China (Grant No. 10672092)+1 种基金Scientific Research Project of Shanghai Municipal Education Commission (Grant No. 07ZZ07)Shanghai Leading Academic Discipline Project (Grant No. Y0103)
文摘Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.
基金Item Sponsored by National Natural Science Foundation of China (50875231)Great Natural Science Foundation of Hebei Province of China (E2006001038)
文摘The strip with a time-dependent tension moves, namely a harmonically varying tension about a constant initial tension. The nonlinear vibration model of moving strip between two mills with time-dependent tension was established. Approximate solutions were obtained using the method of multiple scales. Depending on the variation of the tension, three distinct cases arise： frequency away from zero or two times the natural frequency; frequency close to zero; frequency close to two times the natural frequency. For frequency close to zero and away from zero and two times the natural frequency, the system is always stable. For frequency close to two times the natural frequency, the stability is analyzed respectively when the trivial solution exists and the nontrivial solution exists. Numerical simulation was made on some 1660 mm tandem rolling mill, and the stable regions and unstable regions for parametric resonance are determined with different cases. The rolling speed and the thickness of strip have strong influences on the stability of principle parametric resonances. But the distance between two mills has little influence on the stability of principle parametric resonances.
