Fast Solution And Application Of Finite Element In Hot Strip Rolling

The paper is based on the project "Online fast algorithm of finite element method in strip rolling", which was sponsored by National Natural Science Foundation of China and the project "Program of precise temperature prediction model in hot rolling process", sponsored by POSCO. The influent factors on calculating time and convergence stability of solution to hot rolling by finite element method are investigated. The FEM model in the fast solution of rolling is developed based on the actual rolling data. The fast solution of FEM is put into the control system for Tianjin RockCheck 750mm medium-width hot strip rolling production line. FEM have been realized online application through theoretical analysis and online test. The chief original work and results of this paper are expressed as follows:(1) The methods to improve the computing speed of energy functional and optimization were discussed based on the compressible rigid plastic FEM. Programming, matrix storage, solution of equations and linear search methods have important influence on the solution. The procedure of program was designed and the FFE-RF2D was developed by the Compaq Visual Fortran. The rolling parameters were solved by the FFE-RF2D and the calculating time of main subprogram module was analysized according to the rolling data from a certain plant. The influence of compiling method, element division, initial velocity field prediction and the other parameters on the computing speed were discussed. The computing speed has been improved and the calculating time has been shortened in a certain extent.(2) The Cholesky method to force positive definite Hessian matrix was discussed in order to improve convergence stability and computing speed. The NR-C (NR-Cholesky) was proposed based on one dimension variation bandwidth storage and Cholesky decomposition methods. The calculating time is shortened within 200ms for solving one pass rolling and the solution efficiency is improved. Golden section and Brent methods were discussed according to different rolling process. The NR-C-B (NR-Cholesky-Brent) algorithm was proposed based on considering the advantage of Cholesky decomposition and Brent search methods. The iteration step is reduced and convergence stability is improved greatly by NR-C-B algorithm compared to NR method. The calculating time is less than 150ms by NR-C-B for solution of one pass rolling.(3) The trust region and quais-newton methods were discussed to reduce the calculating time of one dimension search and solution of Hessian matrix respectively. The TR-NR and NR-BFGS algorithm were proposed to improve the solution efficiency. TR-NR algorithm had more iteration steps than these of NR. However, the convergence stability is improved by TR-NR compared to the calculated results by NR method. The iteration steps changed from 30 to 40 by TR-NR algorithm. The calculating time is shortened and the convergence stability improved greatly by NR-BFGS algorithm. These algorithms were tested according to the same rolling data. The order of iteration step from more to less is NR, TR-NR, NR-C, NR-C-B and NR-BFGS algorithm. The order of convergence stability from high to low is NR, NR-C, NR-C-B, TR-NR and NR-BFGS. The calculating time is less than 100ms the iteration steps are less than 25 by NR-BFGS algorithm for solution of one pass rolling with finite element mesh 16×8.(4) The influence of element division and time step on solution of temperature and calculating time was investigated in order to improve the solution efficiency by the developed program FFE-TEMP2D. The layer-by-layer refined mesh method was proposed to restrain the solution oscillations. Layer-by-layer refined mesh method not only can restrain the solution oscillations but also reduce the calculating time greatly compared to uniform refined mesh method. The custom hot strip rolling of a certain plant was solved and the calculated results had a good agreement with the measured values. The calculating time is consumed about 700ms for solution of hot strip rolling process.(5) The heat generate rate of electromagnetic field was discussed by ANSYS. A new heat generate rate model was obtained according to analysis of the induction heating on the basis of requirement from a certain plant. The influence of work frequency, source current density, air gap between induction coil and slab and distance of node to edge in skin depth on the heat generate rate distribution was investigated. The temperature distribution of induction heating was solved by the developed program through considering the heat generate rate as the inner heat resource into the thermal analysis. The temperature evolution of induction heating in hot strip rolling was discussed and the calculated results had a good agreement with the measured values. In order to analyze the phase-transformation in hot rolling, the coupled model of temperature, deformation and phase transformation was set up. The temperature, stress and phase fraction distribution had been solved according to the resistance of deformation of W20 obtained by test. The results provided the important theory for analyzing the head curling.(6) The control system was discussed and the database of material property parameters, stratification data, system constant and the other control parameters was developed, which assured the data exchange and transfer in the FEM online application. The offline simulation software was developed based on the conventional mathematical model and fast solution of FEM. The software provided a platform for rolling parameters calculating, model testing and results analysis which improved FEM online application.(7) According to the control system for Tianjin RockCheck 750mm medium-width hot strip rolling production line the prediction flowchart of rolling parameters, data transfer and communication methods were investigated. The fast solution model of rolling force and temperature by FEM has been put into the control system through the dynamic link method. It is successful to realize the online prediction of rolling parameter and temperature by FEM. The prediction error of rolling force and temperature are less than 5% and 2% respectively between calculated results and measured values. The research has broken the bottleneck of calculating time by FEM for online application and achieved the expected target.