2.2. Problems of multi-piece mold design

As summarized previously, the most significant advantage of multi-piece molds over conventional two-piece molds is that they can be used to handle complex-shaped parts. However, current ap- proaches to multi-piece mold design have two limitations. First, they require simple polyhedral parts or approximate complex parts by facets [18–22], which may not be acceptable in the indus- try. Second, some algorithms have limited application domains. For instance, the algorithms proposed by Dhaliwal [18] and Huang [19] do not handle general partitioning cases such as partitioning along non-planar faces. Moreover, in Huang’s approach, manufacturabil- ity is measured only by the number of cuts involved in the parti- tioning. In reality, manufacturability is more directly related to the number of components and their geometric complexity. In Chen and Rosen’s method [20,21], only local disassemblability evalua- tion is performed when generating parting surfaces. As a result, the current paper proposes a systematic approach to automatic recog- nition of mold-piece regions and parting curves for constructing mold pieces. In the proposed approach, several criteria and tech- niques, such as visibility-ray testing and silhouette detection, are developed to determine moldable surfaces and appropriate surface regions for mold pieces. The algorithm is sufficiently generic to be applied in commercial CAD systems.

2.3. Overview of the proposed algorithm

All curved/free-form surfaces of the input CAD model are in- serted into the proposed system. Information of the geometric en- tities of the model (vertices, edges, and surfaces) is also extracted and used as input for the algorithm. Equations describing edges and surfaces are formed based on such information. The following steps have been developed to generate suitable parting directions and parting curves for the piece.

Fig. 2.    (a) Moldable planar surface, (b) moldable quadric surface, and (c) moldable free-form surface.

(1) A collection D of tentative parting directions is first formed by analyzing the geometric features of the input part. This is described in Section 4.1.

(2) Using these tentative parting directions, as well as the surfaces of the CAD model, surface visibility and moldability are examined for each surface of the model. The set Si of visible- moldable surfaces for each direction di of the collection D is then determined. This is described in Section 4.2.

(3) If there exists a surface that is not in any visible-moldable surface sets, a further accessibility analysis is performed to deter- mine a feasible parting direction for such a surface. This parting di- rection is then inserted into the collection D. This step is described in Section 4.3.

(4) All visible-moldable surfaces of sets Si are used to determine the different regions for mold pieces. In the case where a surface simultaneously belongs to two or more surface sets, the surface is rearranged into the most appropriate mold-piece region. This is described in Section 4.4.

(5) Finally, the algorithm for locating parting curves of mold- piece regions is implemented. All outer and inner loops of the part- ing curves are determined for further generation of mold-piece parting surfaces and structures. This process is detailed in Sec- tion 4.5.

Fig. 3.   Moldable and unmoldable conical surfaces.

of revolution is used, instead of the normal vector, to ascertain whether a revolved surface can be molded. In general, cylinders and cones are present in the design of industrial parts. When the surface is a cylinder, the condition for moldability is