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In a nesting operation, the part is positioned such that the remaining metal (scrap) is minimized. For this purpose differ- ent algorithms have been used.
The algorithms developed for this software are all alge- braic based. The geometrical abilities of Solidworks have not been used for this purpose. The nesting algorithm is described below.
annealing algorithm in layout design minimizing the bending 4.1. Mathematical model
moment acting on the die. Smaller bending moments create
smaller die deflections which in turn result in greater die accu- racy and quality of the produced parts. Recent work in this area has concentrated on blanking and fine blanking simu- lation by various F.E. methods (Chen et al., 2004; Chan et al., 2004). In 2007, Kumar and Singh introduced a material selec- tion rule based expert system for selecting progressive die components (Kumar and Singh, 2007). This system catego- rized die components into active and inactive components. The system also determined the hardness range for active components.
Generally speaking, different aspects of computer-aided progressive die design have been considered in the last decade. However, problems persist. Algorithms which have been used for nesting are not general and can only nest some special geo- metrical shapes. Usually shapes containing arcs and free-form curves are not considered. Some algorithms are considerably time-consuming. There are no general algorithms for indirect pilot design and semi-direct piloting has been totally ignored. These limitations often originate from limitations due to fea- ture recognition.
In this paper, a software is introduced which can auto- mate the nesting of different parts according to minimum scrap strategy. The software is also capable of selecting direct pilots (if there are any) or creating semi-direct or indirect pilots for the strip. It compares these pilot systems with each other and selects the best one or two according to minimum scrap strategy and other technical limitations. Suitable algorithms is developed for recognizing the shape of the components and the scrap part of the sheet metal. Also Heuristic methods were used in the software which resulted in greater efficiency and a reduction in the run time.
Initially a copy of the part is produced and positioned on
the side of the original part. This part is then fed towards the copy of itself in small increments (without any rotations), until
the first intersection takes place (Fig. 1). This Figure demon- strates that the part is closest to its copy when an element of its shape is tangent to an element of its copy (Fig. 1A) or there is an intersection point between the two shapesIf a circumscribing rectangle is drawn around these two shapes, then the area of the rectangle is directly related to the scrap (Fig. 2A). As shown in Fig. 2B, the next step is to draw all horizontal lines passing through the critical points of the shape. The critical points of a shape are the points where they may be tangential to or intersect the copied shape. In more general terms it can be said that for any shape consisting only of lines, all vertices can be regarded
where Pcrij is the jth critical point on the ith element. Áijk is the kth intersection point of the line passing through the point
Pcrij. ijk is the critical distance between Pcrij and Áijk; is a set
of all critical distances; imax is the number of all elements in
shape; jmax is the number of critical points; kmax is the number
of intersection points of each horizontal line with the shape
elements.
as critical points. In Section 4.1.1, it is shown how these critical points for straight line elements can be found. In Section 4.1.2, critical points for shapes including arcs are
is the maximum element of
4.1.1. Critical points on lines «= YPij 1 i imax , 1 j jmax (4)