Improving minimum strain energy curve calculations for flexible blade cutting

A flexible blade cutting technique is applied for large physical prototypes. The flexible blade is heated and can shape thick layers of polystyrene foam. For tool path generation a numerical calculation model is available. In practice, the shape calculation time for the hot blade used in the flexible blade cutting process increases with approximately the 3rd power of the number of segments used in the blade model. For better accuracy of the blade shape representation a higher number of segments is required and this results in unacceptable calculation times. A changed procedure of blade shapes calculating has been implemented and tested. The method starts with a small number of segments and after shaping according to the minimum strain energy principle, all segments are subdivided in equal segments of half the length of the previous segments. The resulting blade shaping model is then the starting configuration for the next shaping calculation. This is done until the required number of segments or the requested representation accuracy is reached. A second improvement of the shape representation of the basic calculation method is also implemented, namely the angle setting segments (originally the first and last segments) are extended with two extra segments that fix the setting angles at the blade clamping location. This enables the blade to bend from the first up to the last segment. This provides a higher representation quality and enables more shape freedom resulting in a broader parameter space that can be used. Both enhancements of the blade shaping model provide are demonstrated with a few typical examples