An integrated mathematical model is proposed to predict the velocity field and strain distribution during multi-pass plate hot rolling.This model is a part of the mixed analytical-numerical method(ANM)aiming at prediction of deformation variables,temperature and microstructure evolution for plate hot rolling.First a velocity field with undetermined coefficients is developed according to the principle of volume constancy and characteristics of metal flow during rolling,and then it is solved by minimizing the total energy consumption rate.Meanwhile a thermal model coupling with the plastic deformation is exploited through series function solution to determine temperature distribution and calculate the flow stress.After that,strain rate field is calculated through geometric equations and strain field is derived by means of difference method.This model is employed in simulation of an industrial seven-pass plate hot rolling process.The velocity field result and strain field result are in good agreement with that from FEM simulation.Furthermore,the rolling force and temperature agree well with the measured ones.The comparisons verify the validity of the presented method.The calculation of temperature,strain and strain rate are helpful in predicting microstructure.Above all,the greatest advantage of the presented method is the high efficiency,it only takes 12 s to simulate a seven-pass schedule,so it is more efficient than other numerical methods such as FEM.
In order to continuously simulate multi-pass plate rolling process,a 3-D elastic hollow-roll model was proposed and an auto mesh-refining module with data passing was developed and integrated with FE software,Marc.The hollow-roll model has equivalent stiffness of bending resistance and deformation to the real solid and much less meshes,so the computational time is greatly reduced.Based on these,the factors influencing plate profile,such as the roll-bending force,initial crown,thermal crown and heat transfer during rolling and inter-pass cooling can be taken into account in the simulation.The auto mesh-refining module with data passing can automatically refine and re-number elements and transfer the nodal and elemental results to the new meshes.Furthermore,the 3-D modeling routine is parametrically developed and can be run independently of Marc pre-processing program.A seven-pass industrial hot rolling process was continuously simulated to validate the accuracy of model.By comparison of the calculated results with the industrial measured data,the rolling force,temperature and plate profile are in good accordance with the measured ones.
