Research On Horizontal Nonlinear Dynamic Mill Roll System Based On Fractional Order Theory

Rolling is one of the effective ways to produce sheet metal.Under high speed and heavy load rolling conditions,the horizontal vibration of rolling system has an obvious effect on the stability of rolling system and the thickness fluctuation of rolled material,which restricts the quality and efficiency of sheet metal rolling.The traditional research on dynamic characteristics of rolling system is based on the integer order theory.Although nonlinear factors such as stiffness and damping of the system are considered in the rolling process,the accuracy of the model is improved to a certain extent,but the mechanical constitutive relationship of non-ideal materials is not fully considered,resulting in insufficient accuracy of the model,and there is a certain gap between the analysis results and the real state.To solve this problem,this project introduces fractional derivative into the horizontal vibration mechanical model of rolling mill system,and systematically studies the dynamic behavior and stability control of rolling system under the influence of various nonlinear factors.The specific research contents are as follows:(1)The vibration phenomenon of rolling system in the rolling process is measured and analyzed.Taking 150 mm rolling mill in the laboratory as the research object,a vibration test system is built and vibration signals in three directions of rolling system space are collected and analyzed.The results show that obvious horizontal vibration existed in rolling system and coupled with vertical vibration,which aggravated the vertical vibration state of roll system and affected the stability of the system.On this basis,the simulation and experimental study of the horizontal vibration factors of the roll system are carried out.The results show that the main excitation source of the horizontal vibration of the roll system is from the roll gap,and the rolling speed,the reduction amount and the rolling tension at the roll gap have a direct effect on the stability of the rolling system,and the rolling speed and the reduction amount are positively correlated with the horizontal vibration amplitude of the roll system.(2)The horizontal nonlinear principal harmonic vibration of rolling system and its control are studied theoretically.Based on fractional order theory,Van der pol oscillator and Duffing oscillator are introduced to establish the horizontal nonlinear vibration equations of rolling system with fractional order derivatives.The amplitude-frequency characteristic equations and approximate analytical solutions of forced vibration and free vibration are obtained by means of average method.The results of theoretical research are verified by the coincidence between the analytical and numerical solutions.The effects of fractional derivative coefficient,order and excitation amplitude,nonlinear damping,linear stiffness and nonlinear stiffness on the amplitude-frequency characteristics of principal harmonic vibration of roller system are analyzed.On this basis,the stability of the steady solution of the roll system is analyzed,and the necessary conditions for the stability of the steady solution are obtained.Based on the independent mode control method,an independent mode space controller is designed to control the main harmonic vibration of the roll system.(3)On the basis of the study of the principal harmonic vibration,the secondary harmonic vibration and control of rolling mill are further studied.The sub-harmonic vibration and super-harmonic vibration of rolling system are solved by multi-scale method,and the amplitude-frequency characteristic equations and approximate analytical solutions of the two kinds of harmonic vibration are obtained.The effects of excitation amplitude,nonlinear damping,linear stiffness and nonlinear stiffness on the sub-harmonic vibration characteristics of roller system are analyzed.On this basis,a linear and nonlinear optimal feedback controller is designed to control the sub-harmonic vibration of roller system,the optimal control parameters are obtained,and the effectiveness of the controller is verified.(4)Based on the research of harmonic vibration of single frequency excitation,the resonance and control of rolling system vibration under double frequency excitation are further studied.The vibration resonance balance point,vibration resonance critical force and vibration common amplitude gain of rolling system were obtained by the method of fast and slow variable separation.The effects of excitation amplitude F and excitation frequency ω on the vibration resonance of single-well and double-well are both studied.Based on the theory of delay feedback control,a feedback controller with distributed delay term is designed to control the horizontal vibration resonance of roller system.The relationship between the control parameters and the response amplitude gain is obtained,and the effectiveness of the controller is analyzed and verified.(5)On the basis of quantitative analysis of dynamic characteristics of rolling system,the system stability,bifurcation,chaos and control are further studied qualitatively.According to the perturbation theory,the equilibrium point of roll system is obtained and the stability of the equilibrium point is analyzed.The necessary conditions for the stability of roll system are obtained based on Lyapunov second method.The results of geometric and analytical analysis show that the supercritical fork bifurcation is easy to occur in the rolling process.Based on the Melnikov method,the necessary conditions for the chaos of the roll system in the sense of Smale horseshoe are obtained,and the larger the excitation amplitude,the more easily the chaos of the roll system is generated.On the basis of this,a chaotic control strategy is proposed,which takes the vibration displacement of the roll system as the control quantity and changes the critical condition of the chaotic motion by adjusting the control parameters.(6)Experimental research verifies the correctness of theoretical analysis and designs a horizontal vibration damping device for rolling system.The horizontal vibration data of rolling system is collected and analyzed.The measured results are in agreement with the theoretical simulation results,which verifies the correctness of the theoretical research.On this basis,a hydraulic expansion liner vibration damping device is designed.By changing the pressure of the hydraulic system inlet,the liner volume is changed,the system stiffness and damping are controlled,and the purpose of vibration reduction is achieved.In a certain range,the higher the oil pressure,the better the vibration suppression effect,when the oil pressure is7 MPa vibration energy can be reduced by about 28%.Based on the vibration phenomenon of the rolling mill roll system at the rolling site,this project carried out theoretical research on the horizontal principal harmonic vibration,sub-harmonic vibration,vibration resonance,stability,bifurcation and chaos and other dynamic characteristics and control strategies of the rolling mill roll system based on the fractional order theory,and verified the correctness of the theoretical research through experiments,and designed a hydraulic expansion liner damping device,which can effectively reduce the horizontal vibration energy of the roll system by about 28%.This research not only improves the accuracy of the horizontal vibration model of the rolling mill roll system,makes up for the shortcomings of the theoretical research on the horizontal nonlinear dynamic characteristics and stability control of the roll system,but also provides an important reference for the design of the rolling mill system and vibration reduction and suppression.