A topological approach for the flow behaviourcharacterization in LCM processes

In this work we propose a topological approach to explain the dynamical behaviour of a LCM flow. To this end we shall use a class of homotopy maps in order to characterize an idealized mould filling process. By means this benchmark model we can construct a functional that can be used to give the reference in an on-line control system. In our previous work, [1], is proposed the use of the artificial vision technique to sense the mould as a discretized mesh that can be simulated off-line and used as a benchmark model in real-time control systems. The resulting FEM simulation represents theoretical flow behaviour. In this sense, the ideal flow behaviour must be defined based on the optimal criterion. For instance in [2, 3], the flow front in each time instant is desirable to be vent-oriented for dry spot prevention. Whatever of these optimal laws can be defined as a homotopy map where the flow front is defined as a parametric curve that moves with the flow. In order to reduce the sampling rate control system, the homotopy map is defined in a Flow Pattern Configuration Space (FPCS). This tool permits to represent the mould filling in an alternative space representation developed with the optimal criterion [5–7]. Using this space, the homotopy map is defined as a mono-dimensional parametric function for whatever mould dimension. Some numerical examples are given at the end of the paper.