Optimization of 3D cooling channels in injection molding using DRBEM and 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. In the numerical solution of three-dimensional boundary value problems, the matrix size can be so large that it is beyond a computer capacity to solve it. To overcome this difficulty, we develop an iterative dual reciprocity boundary element method (DRBEM) to solve Poisson’s equation without the need of assembling a matrix. This yields a reduction of the computational space dimension from 3D to 2D, avoiding full 3D remeshing. Only the surface of the cooling channels needs to be remeshed at each evaluation required by the optimisation algorithm. For more efficiency, DRBEM computing results are extracted stored and exploited in order to construct a model with very few degrees of freedom. This approach is based on a model reduction technique known as proper orthogonal (POD) or Karhunen-Loeve decompositions. We introduce in this paper a practical methodology to optimise both the position and the shape of the cooling channels in 3D injection moulding processes. First, we propose an implementation of the model reduction in the 3D transient BEM solver. This reduction permits to reduce considerably the computing time required by each direct computation. Secondly, we present an optimisation methodology applied to different injection cooling problems. For example, we can minimize the maximal temperature on the cavity surface subject to a temperature uniformity constraint. Thirdly, we compare our results obtained by our approach with experimental results to show that our optimisation methodology is viable.