A mathematical model integrating analytical method with numerical method was established to simulate the multi-pass plate hot rolling process, predicting its strain, strain rate, stress and temperature. Firstly, a temperature analytical model was derived through series function solution, the coefficients in which for successive processes were smoothly transformed from the former process to the latter. Therefore, the continuous computation of temperature for multi-operation and multi-pass was accomplished. Secondly, kinematically-admissible velocity function was developed in Eulerian coordinate system according to the principle of volume constancy and characteristics of metal flow during rolling with undetermined coefficients — which were eventually solved by Markov variational principle. Thirdly, strain rate was calculated through geometric equations and the difference-equations for solving strain and a subsequent recurrent solution were established. Fourthly, rolling force was calculated on the base of Orowan equilibrium equation, considering the contribution to flow stress of strain, strain rate and temperature, rather than taking the flow stress as a constant. Consequently, the thermo-mechanics and deformation variables are iteratively solved. This model was employed in the simulation of an industrial seven-pass plate hot rolling schedule. The comparisons of calculated results with the measured ones and the FEM simulation results indicate that this mathematical model is able to reasonably represent the evolutions of various variables during hot rolling so it can be used in the analysis of practical rolling. Above all, the greatest advantage of the presented is the high efficiency. It costs only 12 seconds to simulate a seven-pass schedule, more efficient than any other numerical methods.
A mathematical model for evaluating the work of the heart left ventrical segments and a numerical method for deformation curve restoration
