Abstract
With the complexity of automobile body forming and the improvement of process quality requirements, more efficient and accurate metal forming simulation methods are urgently needed. In the frame of one step positive forming algorithm, the improved perturbation method is introduced in Newton-Raphson iterative calculation. Along the tangent plane of the node on the spatial initial solution, a small displacement perturbation is applied to make the unbalance force on the spatial initial solution changed. The simplified method to process the perturbation of the node normal vector is applied to calculate the unbalance force gradient in the node tangent plane, which can be transformed into the one in the space coordinate system through the coordinate transformation matrix. The node coordinates of the spatial initial solution can be modified according to the unbalance force gradient descent direction. When calculating the unbalance force gradient, the region dependent on the perturbation can be found. Then the unbalanced force vector is calculated only in the region dependent on the perturbation, and the repetitive calculation of the unbalanced force vector in uncorrelated nodes is avoided. Because the method proposed does not involve solving of the system of equations, the ill condition of stiffness matrix is avoided, which is caused by local material yield deformation destabilization, and lead to instability or non-convergence of the computation process. Thus, the solving process is more stable. The validity of the algorithm proposed is proved by comparing the measurement of the practical drawn parts with the simulation results obtained by one step positive forming algorithm based on improved perturbation method, one step positive forming algorithm based on solving system of equations and one step inverse forming algorithm of DYNAFORM on the calculation accuracy and computational efficiency.
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