Optimization of BEM-based Cooling Channels Injection Moulding Using Model Reduction
Today, around 30% of manufactured plastic goods rely on injection moulding. The cooling time can represent more than 70% of the injection cycle. In this process, heat transfer during the cooling step has a great influence both on the quality of the final parts that are produced, and on the moulding cycle time. Models based on a full 3D finite element method renders unpractical the use of optimization of the design and placement of the cooling channel in injection moulds. We have extended the use of boundary element method (BEM) to this process. We introduce in this paper a practical methodology to optimize both the position and the shape of the cooling channels in injection moulding processes. We couple the direct computation with an optimization algorithm such as SQP (Sequential Quadratic Programming). First, we propose an implementation of the model reduction in the BEM solver. This technique permits to reduce considerably the computing time during the linear system resolution (unsteady case). Secondly, we couple it with an optimization algorithm to evaluate its potentiality. For example, we can minimize the maximal temperature on the cavity surface subject to a temperature uniformity constraint. Thirdly, we present encouraging computational results on plastic parts that show that our optimization methodology is viable.
KEY WORDSBEM optimization reduction model injection moulding SQP.
Unable to display preview. Download preview PDF.
- 1.C. S. Chen, C. A. Brebbia, H. Power. Dual reciprocity method using compactly supported radial basis functions Communications in NumericalMethods in Engineering, editors John Wiley & Sons, Vol 15, 2, pp. 137–150, 1999.Google Scholar
- 2.E Mathey, L Penazzi, FM Schmidt, F Rond-Oustau. Automatic optimization of the cooling of injection mold based on the boundary element method Materials Processing and Design: Modeling, Simulation and Applications, Proc. NUMIFORM” 04, Vol 712, pp. 222–227, 2004.Google Scholar
- 3.F. Chinesta, A. Ammar, F. Lemarchand, P. Beauchchene, F. Boust. Alleviating mesh constraints: model reduction, parallel time integration and high resolution homogenization. Comput. Methods Appl. Mech. Engrg, editors Elsevier, 2007.Google Scholar
- 4.J. Nocedal and S. S. J.Wright Numerical optimization series in operation research, editors springer, 1999.Google Scholar
- 5.N. Pirc, F. Schmidt, M. Mongeau, F. Bugarin,. BEM-based cooling optimization for 3D injectionmolding. International Journal of Mechanical Sciences, Proc. ASMDO’07, Vol 48, 4, pp. 430–439, 2006.Google Scholar
- 6.S. Kenig, M.R. Kamal. Cooling molded parts, a rigorous analysis. Soc. Plast. Eng. J., Vol 26, pp. 5057, 1970.Google Scholar
- 7.B. A. Davis,P.J. Gramann, J.C. Mätzig,T.A. Osswald. The dual reciprocity method for heat transfer in polymer processing. Eng. anal. bound. elem., editor, Elsevier, vol. 13, 3, pp. 249–261, 1994.Google Scholar