On the basis, of the condition for demouldability, two levels of visibility, complete and partial visibility, are defined. The viewing directions from which a surface is completely visible can be represented as a convex region on the unit sphere called the visibility map of the surface. Algorithms are given for dividing a given object into pockets, for which visibility and demouldability can be determined independently, for constructing visibility maps, and for selecting an optimal pair of parting directions for a mould that minimizes the number of cores. An example illustrates the algorithms. Keywords: manufacturing, algorithms, computational geometry, injection moulding, die casting, parting directions, visibility In die casting and injection moulding ~-4, a basic mould consists of two plates that form an impression into which molten material is injected. The surfaces on the two plates that meet to form a seal when the mould closes are the parting surfaces; the pair of opposite directions along which the two plates of the mould separate are the partino directions (see Figure 1 ). Recesses or projections on the moulded piece that prevent its removal from the mould along the parting directions are called undercuts. Depending on the types of undercut, different manufacturing devices are used: external recesses and projections are formed by using side cores and side cavities; internal undercuts are formed by using mould pins or inserts. An example of an object requiring a side core for an external recess is shown in Figure 2 and after, the general term core is used to refer to a side cavity, a side core, a mould pin, or an insert. The selection of the parting directions and parting surfaces is important, because it dictates the number and the shapes of cores, and affects all the subsequent steps in the design of a mould. Because the use of cores increases tooling costs, complicates the operation of the mould, and slows down the process, a general rule is emphasized in the literature 1'2'5 that parting directions should be selected so that the number of cores is kept to a minimum. However, the automation of this step has received little attention in the past. Of the few examinations reported, the parting surface is restricted to a plane by assuming that the parting direction is along one of the three principal axes 6-s, or selected from a set of randomly generated directions 9. A drawback of these approaches is the impossibility of knowing whether a feasible parting direction exists at all, and, if more than one exists, whether one is better than the others. Heuristically generated candidate parting directions that consist of the normals of planar faces and the axes of cylindrical surfaces of the given object are also reported 1°. The feasibility of a parting direction is verified by checking sample points on the object for obstruction in the candidate direction. In this paper, a deterministic method is developed for finding an optimal pair of parting directions. Given the geometry of an object, depending on the selection of the pair of parting directions, a different number of cores --, parting directions
Based on the observation that the face normals of the openings of the cavity solid (pocket in REF ) determine a zone of possible directions for clearing the corresponding undercut.
Parting directions for mould and die design
Comput. Aided Des.
Comput. Aided Des.
Mathematics Computer Science