surfaces can be pided into different groups in which the adjacent surfaces are linked together and form an undercut feature. In Fig. 2(a), the target surface is the top surface of the block and the external adjacent surfaces are the foursided surfaces. Its internal adjacent surfaces lying inside the target surface form the two undercut features. Based on these definitions, the internal and external edge-loops are the intersection boundaries of the internal and external adjacent surfaces with the target surface respectively. The IEU is composed of the inside adjacent surfaces, and its intersection boundary with the target surface is the internal edgeloop; while the OEU is a boundary perturbation made up by the whole target surface and its first adjacent surfaces. If the target surface has only one edge-loop and some connecting edges between the target surface and the first adjacent surfaces (SAF) are concave, the target surface and its SAFs will form an OEU. In other words, the OEU is composed of target surface and the SAFs, which connecting edges between target surface and SAF are concave. In Fig. 3, (a) is an OEU (it can also be an OIU). Fig. 3(b) and (c) show the concave and convex edges, the first adjacent surfaces and the second adjacent surfaces (SAS) of the target surface respectively.
The target surface Fi and its SAFs form an OEU or OIU.The undercut features are classified in such a way that it is easy to set up the recognition criteria. Similarly, theinternal undercut features can also be classified into inside internal undercut feature (IIU) and outside internal undercut feature (OIU). The definitions and classification are similar to the above. Fig. 4 shows an IIU which consists of internal adjacent surfaces and the second adjacent surface (SAS). The classification of undercut features is summarized in Fig. 5.Fig. 6 shows a moulding with different undercut features. In the moulding, undercut feature A is an EU since it prevents the moulding from being withdrawn from the cavity. It can also be further classified into an IEU because it consists of internal adjacent surfaces of the target surface. Similarly,undercut feature B is also an IEU. Undercut feature C is an IU because it hinders the moulding from being withdrawn from the core. It can further be classified into IIU since it consists of the internal adjacent surfaces of the target surface. Undercut feature D is an OEU because it consists of the whole target surface and its first adjacent surfaces.
3. Undercut feature parameters
Undercut feature parameters are undercut feature volume and undercut feature direction. The undercut feature volume can be determined based on the geometric entities of the undercut feature, while the undercut directions can be determined by the visibility map (V-map) of the undercut feature surfaces. The V-map of a surface is a notion to describe the surface visibility and is formed by the points on the unit sphere from which the surface is completely visible from infinity [9]. The surface V-map is a twin notion of Gauss map, which is introduced by Gauss through mapping the surface normal of a given point in a surface onto a unit sphere to describe the surface property [10].
3.1. Undercut feature volume
Undercut feature volume UV refers to the 3-D space enclosed by the geometric entities of undercut feature. It is also equal to the volume of the concave portions of the core, cavity or local tools, or the volume of the mould insert or local tool that inserts into the concave portions of the moulding. UV can be determined based on the geometric entities of undercut features. For the IEU, UV can be made up by the internal adjacent surfaces and the common second adjacent surface as shown in Fig. 7(a) and can be approximately calculated based on the area of the internal edge loop, area of the common second adjacent surface (SAS) and the length of undercut feature edges. The method to calculate the area of edge-loop and a surface is presented in Ref.[2]. If the undercut feature consists of only one curved surface, UV is the volume formed by the curved surface as shown in Fig. 7(b). For the OEU in Fig. 8(a), UV is made up by the target surface and its positive undercut feature edges as shown in Fig. 8(b). The undercut feature edges (UE) are the wire frame of undercut features. If one of the vertices of undercut feature edge lies in the target surface, it is necessary to define the vector of these edges. The vector is defined as the ray away from the target surface. If the vector of undercut feature edge VUEi meets Eq.(1), the undercut feature edge is positive, otherwise, it is negative. 侧凹特征在注塑模具设计英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_11168.html