Research On Control Mathematical Models Of Force And Shape In Plate And Strip Rolling Based On Energy Approach

Mathematical model is an important foundation for computer control system of plate and strip rolling,and accurate prediction model is a significant guarantee for obtaining high quality plate and strip products.The energy approach integrates the whole deformation body based on continuum model.The results of force and shape obtained by this approach can clearly reflect the mechanical relationships between different variables.In order to improve the forecast accuracy of rolling force and shape parameters' models in plate and strip rolling production,the exact prediction of these models in hot rolling,cold rolling,as well as variable gauge rolling processes are established based on energy approach.These models have great theoretical value and practical application value to optimize the forming process parameters,as well as understand,analyze and solve the relationships between each parameter in rolling from the physical point of view.The main research contents and results are as follows:(1)The deformation characteristics of slab in vertical rolling were studied by finite element simulation.The sine function dog-bone model and corresponding kinematically admissible velocity field were firstly built based on the character of stream function and the incompressibility condition using plane strain assumption in vertical rolling.The cubic curve dog-bone model and corresponding velocity field in three-dimensional deformation were set up based on the nature of dual stream function in order to overcome the deviation caused by plane strain assumption.The above two models and methods were successfully applied to vertical rolling,and the numerical and analytical solutions of total power functional,rolling force and the dog-bone shape parameters were obtained.The effects of various rolling arguments such as width reduction rate,slab thickness and vertical roll radius on dog-bone shape after edge rolling and stress state coefficient were discussed respectively using present models.The prediction results of dog-bone shape and rolling force are in good agreement with other models' results and actual production data,which are significance for width control and rolling force prediction in vertical rolling.(2)According to the fact that the natural width spread and dog-bone width spread may exist in rough horizontal rolling,natural width spread was researched using rectangular slab through horizontal rolling,and the numerical solutions of rolling force and width spread were got on the basis of energy approach.The regression models of natural width spread and weight coefficient in velocity field were proposed according to the data of theoretical solution.The percentage model of dog-bone shape spread after horizontal rolling was put forward combining finite element simulation with BP neural network for the complex deformation in vertical-horizontal rolling.Dog-bone width spread in different rolling schedules was received based on percentage model and dog-bone shape area calculated by its model.The results show that the width spread increases with the increasing of reduction or roll radius,and decreases with the increasing of width.The maximum deviations between width and rolling force calculated by above models and actual production data are no more than 4.79%in vertical-horizontal rolling,and these predictions have a high hit rate.(3)A new exponent velocity and corresponding strain rate field which satisfy kinematically admissible condition were firstly proposed to analyze the rolling force of hot strip finish rolling,and then the analytical solutions of total power functional,rolling torque and rolling force were gained based on energy approach.The influence of roll flattening and the effects of various rolling parameters on location of neutral point and stress state coefficient were discussed respectively using proposed models.The neutral point is close to the entrance of the strip in finish rolling.The deviation of analytical solutions of rolling force and actual production data is less than 7.59%.(4)Due to the existence of large elastic compression zone at entry side and elastic recovery zone at exit side in cold rolling,accurate rolling force model of elastic zone was obtained considering the influence of forward and backward tensions on deformation zone size based on generalized Hooke's law.A hyperbolic sine velocity and strain rate fields which satisfy kinematically admissible condition in cold rolling deformation were established.The analytical solution of total rolling force was got by iterating through taking the effect of roll flattening,forward and backward tensions on rolling force into account.According to BP neural network,the arm factor model was firstly presented combining finite element simulation with the data of rolling plant for the difficulty to determine arm factor in cold rolling.Moreover,the effects of rolling parameters on stress state coefficient and location of neutral point were researched respectively using proposed models.The present calculated rolling forces are slightly higher than the actual measured ones,but the deviation is with 3.31%.Additionally,the neutral point is close to the exit of the strip in cold rolling deformation.(5)The velocity and strain rate fields were set up based on the incompressibility condition in variable gauge rolling considering the influence of roll lifting or dropping,and then analytical solutions of rolling force in upward and downward rolling were firstly obtained based on energy approach.The variations law of bite angle,neutral angle and stress state coefficient with rolling time during variable gauge rolling were studied according to this model.The measured data of MAS rolling in plate rolling plant and tailor rolled blanks have verified the correctness of the analytical results.The above method provides a new idea for obtaining analytical solution of dynamic rolling process by energy approach.