Research On Nonlinear Horizontal Vibration And Control Of Precision Four-high Cold Rolling System

With the advancement of high-accuracy cold rolled sheet technology,the weight of nonlinear factors in the rolling process is increasing,and there is an increasing need to pay attention to the impact of nonlinear vibrations induced by small disturbances in rolling working parameters on the quality of rolling forming.In the roll system structure of the rolling mill,factors such as lateral bending of the roll,movement tilting caused by inconsistent center heights at both ends of the shaft system,gaps between the roll neck and bearing seat as well as the one between the side of bearing seat and the frame window track,can cause small deviations from the ideal motion during the rolling operation of the roll system,which often leads to uncontrollable horizontal non-linear vibration of the rolling system in the error sensitive direction of sheet forming.The uncontrollability of complex nonlinear dynamic behavior will further curb the improvement of rolling productivity and precision.Therefore,this article conducts the following research to clarify the influence mechanism of structural and process factors on the nonlinear horizontal vibration dynamic behavior and rolling accuracy of the precision four roll cold rolling system,aiming to reveal the stability laws and control criteria of the system.(1)Based on the analysis of the structure and working process of a precision four high cold rolling mill,taking into account the elastic bending deformation,gyroscopic effect,and eccentricity effect of the roll system,it is constructed that the Mathieu-Duffing type nonlinear horizontal vibration model of the roll with parametric excitation and cubic stiffness terms under the pseudo-Hamiltonian system;By implementing balanced discretization of the model using the Galerkin method,it is constructed that a nonlinear horizontal internal resonance model of two adjacent modes.The above models provide a research foundation for the subsequent analysis of nonlinear dynamic characteristics as well as the internal resonance instability mechanism and control.(2)It is investigated that the nonlinear characteristics and control of horizontal vibration for rolling system with gyroscopic effect.By constructing Arnold resonance tongue within the effective range of excitation frequency of the horizontal vibration system and using Floquet theory analysis,it is found that increasing systematic damping and axial load would lead to the transfer of the instability critical boundary from the high-frequency region to the low-frequency region.A set of control parameter constraints is constructed when the system satisfies the amplitude dead state under gyroscopic effect by introducing a double-active control factors;Further applying homotopy analysis method to obtain the energy orbit evolution curves of each-order modal amplitude,it is found that the system has multiple frequency-locking regions,which correspond to the nonlinear characteristics of the relevant devil’s staircase morphology;Starting from the global motion characteristics of the horizontal vibration system,the energy manifold change of oscillator group is characterized using the theory of graph cell mapping,which further verifies the modal energy orbit evolution characteristics in steady-state response.The above results to some extent reveal the mechanism of transitional vibration in precision rolling thin plate production.(3)It is investigated that the nonlinear characteristics and control methods of horizontal vibration for rolling system with gyro and eccentricity effects.The chaotic threshold of Smale horseshoe commutation of the roll’s horizontal vibration is given using Melnikov method,and the correctness of the result is verified by the fractal process of the attraction basin.Based on the solved chaos threshold,it is proposed that research mode on exploring stability in unstable state space and instability in stable state space for rolling system.Through the analyses of bifurcation,maximum Lyapunov exponents and bi-parameter bifurcation,it is obtained that the target parameter constraint set when chaos occurs in nonlinear horizontal vibration of rolling system under the condition of maximum Arnold resonance tongue and the quantitative optimal couple of structural and process parameter of precision cold-rolled thin plates during chaotic vibration.The control of nonlinear characteristics is further studied by introducing mixed-delay parameters.The results show that the displacement gain can adjust the resonance frequency,but cannot change the vibration amplitude;velocity gain has almost no effect on the change of resonance frequency,but can significantly change the vibration amplitude;time delay can not only adjust the resonance frequency,but also change the resonance amplitude of the system.(4)It is investigated that the internal resonance mechanism and control method of horizontal vibration for rolling system with gyro and eccentricity effects.The perturbation method is used to analyze the internal resonance control model of the nonlinear horizontal vibration of the roll system with coupling effects,and the Routh-Hurwitz algebraic criterion is used to find the location of the Hopf bifurcation points and trace bifurcation solution of the system under the condition of maximum Arnold resonance tongue,which reveals the instability mechanism of the each mode under different structural and control parameters;simultaneously,the evolution law of the internal resonance on the vibration mode and vibration energy of the roll system in precision cold rolling production are obtained;it is constructed that a four-dimensional average equation model characterizing the bifurcation and chaos characteristics of an internal resonance system,which reveals effects laws of structure and control parameters on the systematic bifurcation and chaos.The results obtained verify the correctness and effectiveness of the theoretical analysis and control method.(5)Conduct experimental research on nonlinear horizontal vibration of rolling mill roll system.Based on the research content,the same mechanical system layout is carried out for the work roll on the four-high rolling mill experimental platform.Combined with the system modal test technology,the dynamic stability experiment and nonlinear characteristics experiment of the roll’s horizontal vibration were completed.Further processing of the time domain curve of the work roll under axial excitation,the dynamic instability domain of parameter resonance in the experimental system are drawn to verify the first-order Arnold resonance instability tongue and the nonlinear characteristics of the amplitude frequency response for the horizontal vibration of the rolling system.It is found that the horizontal vibration made traction movement towards the high frequency direction;The spectrum distribution of the work roll under axial excitation,lateral excitation,and combined excitation is obtained,further revealing the dynamic characteristics and instability mechanism of nonlinear horizontal vibration in the cold rolling system.