Application Of Preconditioning Conjugate Gradient Method In Coupling Of Rolling Process

The finite element method could analysis parameters and field variables in metal forming process, so it is often used to simulate the plate rolling process. Rigid-plastic finite element method is applied in this paper and Lagrange multiplier is introduced to couple speed field and temperature field. An improved preconditioning method is introduced to solve the coupling equations in rolling process. The specific steps are follows:(1) In rolling process, the plastic work is converted into heat and temperature of rolled piece changes which has an impact on deformation resistance. So velocity field and temperature field are coupled by introducing the Lagrange multiplier.(2) In the process of plate rolling, the problem is usually converted to solve the minimum of energy functional An improved preconditioning conjugate gradient method is proposed in order to reduce memory consumption and speed up the convergence speed. Considering the characteristics of the Hessian matrix which is sparse and positive definite, the method could make condition number smaller by using the incomplete decomposition, so as to improve the stability and effectiveness in the process of solving equations.(3) The improved algorithms are used in numerical simulation by writing3d finite element program in order to verify the feasibility of the improved method. At the last, comparisons has been done between numerical simulation results and original results.(4) Topsis method is applied to evaluate methods by establishing model and calculate comprehensive distance. Results show that calculated value of rolling force with new method is the closest to the true values, which reflects the superiority of the improved algorithm.