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In the design of plastic injection moulds, the presence of undercut features would affect mould cost and structure. In this paper, the definition, classification of undercut features and the related notions to identify them are presented. Based on the proposed undercut feature definition and taxonomy, the relationships between the undercut features and their mouldability are described. The definition of undercut feature parameters and the computational methodologies to determine them are proposed. The undercut feature draw range and directions are introduced based on the V-maps of undercut features. The recognition criteria from which the undercut features can be identified are presented. In consideration of blending surfaces, two pairs of notions, viz. actual and virtual first adjacent surfaces, actual and virtual edges are proposed. As undercut features can be consistently recognized, the identification criteria for undercut features are given. The industrial case studies show that the methodologies developed are efficient in recognition and extraction of undercut features in complex injection moulded parts.⑥1999 Elsevier Science Ltd. All rights reserved.19708
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1. Introduction
Mould and die making is an important supporting industry since their related products represent more than 70% of the non-standard components in consumer products. The production runs, however, are typically of small lotsize and with great varieties. The high demand for shorter design and manufacturing lead times, good dimensional and overall quality, and rapid design changes has become the bottlenecks in die and mould industries. For mouldmaking companies wishing to maintain the competitive edge,there is the urgent need to shorten the design and manufacturing lead times by automating the design process using advanced manufacturing equipment, processes and improving the skill level of their employees. Currently, some of the mould-making companies use 3-D commercial CAD software tools to design moulds, however, many companies are still designing moulds manually, which is time-consuming and error-prone. The development of a Computer-Aided Injection Mould Design System (CAIMDS) has become the focus of research in both industry and academia.
In CAIMDS, the recognition and extraction of undercut features is one of the prime issues as it affects the determination of parting direction, parting lines and surfaces,generation of the core and cavity, and creation of the local tools and their actuating mechanisms. The determination of optimal parting direction depends on the types, number,volumes, directions and locations of undercut features [1].The optimal parting direction should ideally be in the direction where the number of undercut features and their corresponding volumes are maximal. The rest of the undercut features not considered would need side-cores, side-cavities or other local tools. In automatic determination of parting lines and surfaces, the parting lines and surfaces should include as many undercut features as possible such that the number of the side-cores or side-cavities needed is minimal [2]. In generating the core and cavity, some undercut hole features should be identified and extracted such that they can be “patched” for the Boolean Regularized Difference Operation (BRDO) between the core/cavity box and the moulded part. The core/cavity box contains the moulded part and is separated into core/cavity blocks. In creating local tools (side-cores, side-cavities, form pins and split cores), the “heads” of these local tools are generated based on the geometric entities of the related undercut features. Consequently, all the undercut features in a moulding should be identified first before the other design activities can be carried out.
Although the determination of undercut features is important in CAIMDS, there are relatively few published works because of the complexity of injection-moulded parts. Mostof the previous work in this area addresses the determination of parting direction, rather than providing a complete solution for CAIMDS. The representative work has been presented by Chen et al. [3,4] and Mochizuki et al. [5],where BRDO is used to recognize and extract the undercut features in a moulding by obtaining the regularized difference between the part to be moulded and its convex hull. In Mochizuki’s work, the given moulding Q is denoted as a concave polyhedron. The convex polyhedron is generated by “clay-filling” into the concavities of Q to make it the smallest convex polyhedron, which can just fully contain the original concave polyhedron. After subtracting the convex polyhedron by the given concave polyhedron, the remaining parts are the potential undercut features, which are called “sealed pockets” in Chen’s work [3]. From the viewpoint of solid modeling, the above process is the same as generating the convex hull CH(Q) for a given 3-D concave polyhedron Q and finding the regularized difference between the convex hull CH(Q) and Q. The regularized difference CH Q Q ( denotes a regularized difference operation) represents the potential undercut features.The difficult task in BRDO is the extraction of the potential undercut feature and feature geometric entities from CH Q Q. Since CH Q Q also represents a 3-D solid and all its undercut features are linked together, its decomposition into many single undercut features is equivalent to the recognition and extraction of the features from a 3-D solid model.