| 其他摘要 | The precision of the mathematical models based on the traditional rolling theories has reached its limited point. In order to improve the precision of the online model, most researchers focus on the artificial intelligence and the finite element method (FEM). FEM has been widely used for the offline analysis in strip rolling, but it is unavailable for the online application due to the long computational time involved. The research on the fast algorithm of FEM for online application is a great challenge task with important theoretical value and practical significance. In this work, the fast online calculation theory for rigid plastic FEM (RPFEM) in strip rolling is researched, and then the fast online calculation for the various rolling parameters is carried out including rolling force, rolling torque, rolling power and forward slip etc..
Firstly, the basic fast calculation theory of RPFEM for strip rolling is established. The finite element model is simplified by only meshing the deformation zone of the workpiece under the contact area with roll. The arc tangent frictional shear stress model is used to deal with the neutral point problem in strip rolling. The shear deformation work rate on the discontinuous velocity sections is adopted in the total energy functional of RPFEM to resolve the first singular point. The fast calculation software of RPFEM in strip rolling FAR-2D ParL has been developed, and the distribution rule of computational time is investigated, as a result the major ways to increase the solution speed of RPFEM are fixed on the most time-consuming parts including the integration of the Hessian matrix and the one dimensional line search.
During the Newton-Rapshon solution of RPFEM, the closer the initial guess approaches the real velocity field, the easier the convergence can be obtained. Thus the setup of initial guess to speed up the convergence rate is studied systematically. The traditional methods including the Engineering Method and G Functional to set up the initial guess are discussed, and the Neural Network method is newly proposed. In order to establish an accurate and efficient neural network model, a correlation analysis of the input data is performed to remove the insignificant input parameters, thus the number of the input variables for the Neural Network model is reduced. The neural network model has been trained using the momentum amended back propagation algorithm from a huge amount of samples calculated by the rigid plastic finite element code. Comparisions for the three methods to set up the initial guess are performed, and the results show that the initial guess and the initial energy functional are very close to the real values, thus FEM can get the convergence through several steps iteration. Therefore, the solution speed of FEM can be increased greatly by using the Neural Network model; this provides a better method to set up the initial guess for the fast calculation of RPFEM.
A fast line searh algorithm for the relaxation factor is developed. Firstly, the Golden –Parabola method is introduced to bracket an initial interval containing the minimum point. Secondly, the one dimensional optimization algorithms including the Fibonacci’s method and the Brent’s method without derivatives are introduced to reduce the interval and to obtain the relaxation factor. Compared with the traditional trial method for bracketing the minimum point and the Golden Section line search, the new fast line search using the Golden–Parabola method and the Brent’s method presents great advantages of reducing the frequency for evaluating the energy functional. By adopting the new fast line search algorithm, the computational time of the line search can be reduced greatly, thus the solution speed of FEM can be increased remarkably.
Parallel algorithms for the rigid plastic finite element solution of strip rolling are developed. The computation for the Hessian matrix and the energy functional during the Newton-Raphson solution of RPFEM is parallelized using the shared memory parallelism. During a multi-pass solution for continuous strip rolling, a multi-pass parallel algorithm with the distributed memory parallelism is developed, and a multi-pass mixed parallel algorithm by adopting the shared memory parallelization for the Newton-Raphson solution within a pass and the distributed memory parallelization across passes is also proposed. The parallel performance has been tested by the numerical examples of the practical rolling data for the multi-pass continuous strip rolling. The results show that the parallelization for the Hessian matrix can obtain high speedup, while the parallelization for the energy function presents a small ability to increase the solution speed of FEM. The multi-pass distributed memory parallelization presents a great effectiveness to speed up the solution of RPFEM; the speedup approaching to the number of processes can be obtained. The multi-pass mixed parallel algorithm is the best way to speed up the solution of RPFEM, the speedup exceeding the number of processes can be obtained.
The opitimization tests for the computer software and hardware platform to increase the solution speed of RPFEM have been performed, and the theoretical schemes of the fast online finite element calculation are proposed. In order to obtain a high efficient computer software and hardware platform for the fast online finite element calculation, the optimization tests have been performed on the operation system, programming language and compiler software, hardware etc.. An energy method for calculating the rolling force with a high numerical stability is newly proposed. Four theoretical schemes for the fast online calcaulation by RPFEM are constructed, and the seven-pass continuous strip rolling data from the production line have been used to test the feasibility of the four theoretical schemes. In order to finish the computation for seven passes, the fastest scheme consumes less than 60ms, the the slowest scheme consumes less than 190ms, thus the computational time for the four schemes can meet the requirements of online control. The predicted rolling force is compared with the measured values and presents a high precision; hence, the online application of FEM can improve the precision and flexibility of the online control model. |
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