Figure 2 The flowchart of the automatic optimisation strategy
Related Figures (9)
Then the unknown parameters @ and £ can be estimated as follows: The correlation function is defined in 3D as follows: Figure 3 Schematic illustration and FE model of the clinched joints studied This application involves a large deformation of sheets. High local plastic strains are developed during the clinching operation, resulting in severe local mesh distortion (Figure 4a). In order to obtain an accurate clinched joint shape, the adaptive meshing technique is used (Figure 4b). On the other hand, small time steps are adopted to obtain an accurate solution, in particular, during the separation step (Figure 5). Figure 4 Deformed meshes: (a) without re-meshing, (b) with re-meshing The FE-analysis includes two simulation stages: 3.2 Optimisation results and discussion The optimisation strategy adopted clearly showed its capacity to improve the strength of the joint above that previously achieved using Moving Least Squares (MLS) approximation. The reason is that the kriging interpolation is more accurate and is improved by increasing the number of evaluation points in the vicinity of the optimum. Note that the die groove width (variable B) and punch radius (variable G) change and reduce to 0.82 mm and 0.10 mm (Figure 7a and Figure 7c), respectively. On the other hand, the die diameter (variable D) is significantly increased (Figure 7b). It shifts from 3.0 mm to 3.28 mm. Table 1 Parameters before and after optimisation Figure 8 shows the tensile force curves obtained during the separation step for initial and optimised tool geometry. It can be observed that the load carrying capacity of the Figure 7 Evolution of the optimisation variables during the optimisation iterations (see online version for colours) Table 1 summarises the results obtained with the initial and optimal tool shape design. It can be seen that the strength of the clinched joint increased significantly when optimised using the kriging interpolation compared to the non- optimised joint. It increased from 623 N to 834 N. The use of MLS approximation in previous work also showed improvement of the strength of the joint but was still lower than that obtained using the kriging interpolation. 4 Conclusion clinched joints is significantly improved by optimising the tool geometry. It was increased by 10% when compared to that previously achieved using the MLS approximation (Oudjene et al., 2009). The optimisation strategy clearly showed its capacity to obtain a better optimal solution with a very fast convergence. The aim of this paper was to optimise the tool geometry of the clinch forming process towards the improvement of clinched joints’ tensile strength. An improved and automatic optimisation procedure, based on RSM and SQP programming methods, is proposed and implemented in ABAQUS finite element code. The response surfaces are built using kriging interpolation. In order to improve the RSM accuracy and to deal with the local optimum problem, an efficient optimisation strategy allowing the updating of the search space is presented. The optimisation procedure eads to very satisfactory results and allows further improvement of the clinched joints’ strength to that previously achieved. In fact, the use of the kriging technique seems to be efficient when the objective function presents several optima. This work is an improvement on previous one presented in Oudjene and Ben-Ayed (2008) and Oudjene et al. (2009). The optimisation procedure developed will have extensive applications and can also be helpful in designing various forming processes.
