Effect of Tool-Modeling Accuracy on Square-Cup Deep-Drawing Simulation

Abstract

In this study, the effect of tool-modeling accuracy on a finite-element simulation of a square-cup deep-drawing process is examined. First, the accuracy of tool modeling using a conventional approach, in which polyhedral surfaces are used, is compared with that of an alternative approach, in which the quadratic parametric surfaces proposed by Nagata [Nagata, Comput. Aided Geom. D 22 (2005) 327-347] (Nagata patch) are used. It is clear that the Nagata patch yields a much more accurate tool geometry than the conventional approach with regard to the shape and normal vectors of the tool. Next, simulations of the square-cup deep-drawing process are carried out for die models with various numbers of tool elements. It was found that a polyhedral model with at least 10 divisions at the die shoulder is required to carry out accurate simulations. The simulated result of the Nagata patch model with two patches at the die shoulder corresponds well to that of the polyhedral model with more than 10 patches. From this point of view, it is concluded that the number of tool elements can be markedly decreased using the Nagata patch model. In the present case, the number of tool elements can be reduced to about 10% of that of the polyhedral model.

Sensitivity analysis of the of the square cup stamping process using a polynomial chaos expansion

“…This work presents a numerical study on the influence of the material and process uncertainty in the results of a square cup forming process. The square cup test was chosen for two main reasons: (i) it is a commonly used benchmark test to represent sheet metal forming processes [1,6,[15][16][17][18]; (ii) it is a relatively fast process to simulate, which is suitable for performing a large number of numerical simulations. A polynomial chaos expansion (PCE) metamodel is used for reducing the computational cost of the Sobol's indices assessment [19].…”

Numerical study of the square cup stamping process: a stochastic analysis

“…With this knowledge it is expected to identify the uncertainty factors that most affect the results in different regions of the cup, and that are essential to control in order to guarantee product conformity with the intended requirements. Additionally, this work intends to fill the lack of research studies associated with the variability of the square cup benchmark, which is one of the most used test cases [7,[14][15][16][17].…”