A new approach to z-level contour machining of triangulated surface models using fillet endmills

Abstract

Precision z-level contour machining is important for various computer-aided manufacturing (CAM) applications such as pocket machining and high-speed machining (HSM). This paper presents a new z-level contour tool-path generation algorithm for NC machining of triangulated surface models. Traditional approaches of z-level machining rely on the creation of accurate CL (cutter location) surfaces by surface offsetting or high-density z-map generation, which is computationally expensive and memory demanding. In contrast, this paper presents a novel approach to the generation of CL data directly from the section polygon of a triangulated surface model. For each polygon vertex of the contour, the offset direction is determined by the normal to the edge, while the offset distance is not fixed but is determined from the cutter shape and the part surface. An interference-free tool-path computation algorithm using fillet endmills is developed. Since there is no need to create a complete CL surface or high-density z-map grids, this proposed method is highly efficient and more flexible, and can be directly applied to triangulated surfaces either tessellated from CAD models, or reconstructed from 3D scanned data for reverse engineering (RE) applications.

Introduction

In recent years, triangulated surface models have gained acceptance in the CAD/CAM community, and the stereolithography (STL) format [1] has, thus, become a de facto standard. Usually, the STL format contains only the coordinates of triangle vertices and the normals of triangle facets so that topological information can be clearly and easily translated between different graphics systems. For most CAD systems, complex triangulated surface models, as described by Piegl [2], [3], can be created directly from design surfaces or solid models. The use of triangulated surface format for representing a CAD model has been widely accepted in industry. The popular application of triangulated surface models is their use in rapid prototyping (RP) as well as in reverse engineering (RE) [4], [5]. In computer-aided manufacturing (CAM) system, finding effective ways to directly cut the triangulated surfaces is of interest due to the easy representation for design models and the existence of robust surface triangulation algorithm. This technology provides an important platform for tool-making applications because the surface models of a work-piece are often assemblies of many surface patches, and by tessellating these surface patches to form a group of triangle patches we can take advantage of established methods for handling intersections, trimming, shading, hidden surface removal and gouge protection [6].

The essential task is to generate interference-free tool-paths for NC machining of triangulated surface models. The tool-paths consist of a series of gouge-free cutter location (CL) data. For machining triangulated surface models, there are different methods to compute the gouge-free CL data. One approach is the point-based method, by which a CL point is found by lowering the cutter along the z-axis until the cutter contacts with the part surface [7], [8], [9], [10]. Another approach is called CL-based method. A CL-surface is generated by offsetting the part surface along the surface normal with a constant cutter radius. The CL data are then computed by slicing the offset CL-surface [11], [12], [13]. After the tool-paths are generated, the machining operation is to control the cutter tip to move through all CL data on the tool-paths to complete machining.

Usually, in 3-axis machining the height of CL point will vary with the contour of the part surface (which is called z-projection machining, see Fig. 1(b)). But for some machining operations such as rough machining and pocket machining, the height of the cutter will be kept constant (called z-level machining, see Fig. 1(a)). The main advantage of the z-level machining is to maintain a stable cutting load during machining and increase the cutter life. Moreover, in the past few years, with the technology advancement in machine tools and cutting tool materials, high-speed machining (HSM) has become a cost-effective manufacturing process that produces parts with high surface quality [14]. For a successful application of HSM technology, the critical factors in tool-path planning that are generally considered include: collision avoidance, chip-load leveling, cutting-load smoothing, and generation of smooth tool-paths [15]. To satisfy these critical factors, the z-level machining approach is usually applied to the planning of tool-paths for HSM [16]. There are many studies describing the tool-path generation for z-level machining, and most of the present methods mainly focus on tool-path generation for pocket machining [17], [18], [19], [20], [21], [22]. Flat endmills are primarily selected to enable pocket or rough machining to achieve maximum productivity. However, the square shoulder profile of a flat endmill is not suitable for the z-level finishing operation for sculptured surface machining. As shown in Fig. 2, when a flat endmill is used for z-level machining, more material remains after machining when compared with the use of a fillet endmill. Therefore, the fillet endmills (also called ballnose or toroidal endmills) are usually selected for z-level finishing and semi-finishing operations.

The z-level tool-paths for finish machining are usually generated by cutting the CL surface with a series of horizontal planes. The CL surface of an STL model is a compound surface consisting of patch-offset (triangle facet offset) surfaces and edge-offset (convex edge or boundary edge) surfaces [15], [18]. It is, however, expected that a great deal of computational effort is needed for the offset-surface intersection, and it may be unstable as the surface complexity increases or if a non-manifold triangulated surface exists. A z-map based approach is provided to quickly compute a CL surface based on hardware-rendered polygons [13]. To achieve good accuracy, dense sampling points on a z-map model are needed due to the discrete nature of the z-map.

In this paper, a new approach to z-level contour machining of triangulated surface model with fillet endmills is proposed. The overall approach consists of five major steps described as follows.

• The triangulated surface model is sectioned by a horizontal drive plane and the section polygons are created along the intersection contour curve. Those section polygons are used as the guide lines for generating the following tool-paths.

• The vertexes on the section polygon are treated as the original CL points. For every vertex, an offset vector is created for the computation of limited offset distance measured from the original CL point to the interference-free CL point.

• After the offset vector is created, compute the interference-free CL data based on the geometry of cutter and the triangulated surface along the section polygon and generate a raw tool-path.

• Detect the intersection loops existing in the raw tool-path and remove them.

• If there are multiple section polygons, then check if global intersections exist between different tool-path loops and remove them.

As pointed out, traditional z-level contour machining requires the generation of CL surfaces. No matter by the surface offset of the z-map based method, intensive computation and a large amount of grid data are needed for generating precision tool-paths. In comparison, this paper presents a novel approach to the generation of CL points directly from the sliced contours of triangulated surface models. Based on the proposed method, it is not necessary to create high density grids or a complete CL surface. Hence, it is highly efficient and more flexible for applications such as pocket machining and high-speed machining that require precision z-level contour machining.