Vertical Vibration of Moving Strip in Rolling Process Based on Beam Theory

The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.

Non-Linear Vibration and Stability of Moving Strip With Time-Dependent Tension in Rolling Process

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.

Vibration of Moving Strip With Distributed Stress in Rolling Process

Taking the moving strip between two stands of some tandem rolling mill in rolling process as a subject for investigation, according to the Poisson-Kirchhoff sheet theory, the vibration model of the moving strip in rolling process was established. Model of distributed stress was built based on rolling theory. And then, vibration model of moving strip with distributed stress was established. The partial differential equation was discretized by Galerkin truncation. The natural frequency and stability of the moving strip were investigated and simulation in time domain was made by numerical method. Taking the moving strip between the second stand and third stand of some tandem mill as a subject for investigation, distributions of stress, natural frequencies and stability of moving strip were de- termined under six different rolling conditions which are ＂uniform distribution of stress＂, ＂flat roll flat＂, ＂flat roll convex＂, ＂flat roll concave＂, ＂convex roll flat＂ and ＂concave roll flat＂. At last, three-dimensional dynamic simulation was made and the moving law of the strip was determined. This model can be used to study the stability of moving strip, depress the shape wave of strip and develop new rolling technology from the aspect of dynamics.

Tandem Strip Mill's Multi-parameter Coupling Dynamic Modeling Based on the Thickness Control

The rolling process is determined by the interaction of a number of different movements,during which the relative movement occurs between the vibrating roll system and the rolled piece,and the roll system＇s vibration interacts with the strip＇s deformation and rigid movement.So many parameters being involved leads to a complex mechanism of this coupling effect.Through testing and analyzing the vibration signals of the mill in the rolling process,the rolling mill＇s coupled model is established with comprehensive consideration of the coupling interaction between the mill＇s vertical vibration,its torsional vibration and the working roll＇s horizontal vibration,and vibration characteristics of different forms of rolling mill＇s vibration are analyzed under the coupling effect.With comprehensive attention to the relationship between the roll system,the moving strip and the rolling parameters＇dynamic properties,and also from the strip thickness control point of view,further research is done on the coupling mechanism between the roll system＇s movement and the moving strip＇s characteristics in the rolling process.As a result,the law of inertial coupling and the stiffness coupling effect caused by different forms of the roll system＇s vibration is determined and the existence of nonlinear characteristics caused by the elastic deformation of moving strip is also found.Furthermore,a multi-parameter coupling-dynamic model is established which takes the tandem strip mill as its research object by making a detailed kinematics analysis of the roll system and using the principle of virtual work.The coupling-dynamic model proposes the instruction to describe the roll system＇s movement,and analyzes its dynamic response and working stability,and provides a theoretical basis for the realization of the strip thickness＇dynamic control.