Arc-intersect method for 5-axis tool positioning

Abstract

A new method for 5-axis CNC tool positioning is presented in this paper that improves upon a previous tool positioning strategy named the rolling ball method (RBM), which was developed by the present authors [Gray P, Bedi F, Ismail S. Rolling ball method for 5-axis surface machining. Comput Aided Des 2003;35(4):347–57]. The special property of the RBM is that it computes tool positions by considering the area beneath the tool that the tool will be positioned to cut instead of using surface curvatures computed at a single point on the surface. This enables the RBM to generate gouge-free tool positions without secondary iterative gouge-check and correction algorithms. However, the RBM generates conservative tilt angles in order to guarantee gouge-free tool positions. The new arc-intersect method (AIM) presented in this paper improves upon the RBM by directly positioning the tool to contact the surface and thereby eliminates the conservative nature of the RBM to give optimal tool positions. Like the RBM, the AIM is an area-based method that generates gouge-free tool positions without the use of iterative gouge-check and correction algorithms. The implementation described in this paper uses triangulated surfaces and the computer's graphics hardware to assist in the tool position calculations. However, the method can be applied to any surface representation since it only uses surface coordinates and surface normals for computation. A section of a stamping die was machined to demonstrate the AIM and to show the improvement over the RBM and for comparison with 3-axis ballnose machining. The results showed that the AIM was 1.33 times faster than the RBM and that the AIM, with single direction parallel tool passes, was 1.62 times faster than a zig-zag pattern 3-axis ballnose tool path for the same feed rate, cusp height and tool diameter. The workpieces were measured with a CMM and the data were compared to the CAD model to show no gouging occurred and to check the cusp heights.

Introduction

The objective of 5-axis surface machining is to generate a better match of the tool's cutting geometry to the surface geometry in order to machine a wider strip width for a given cusp height to reduce the number of passes necessary to finish the workpiece over 3-axis ballnose machining. However, the complexity of the calculations and the potential for gouging the surfaces has led to limited commercial implementation. This section discusses some of the current research topics in the area of 5-axis surface machining.

In the principle axis method (PAM), the tool position is selected based on the local principle curvatures of the surface at a single cutter contact point (ccp). The tool is inclined by an angle such that the effective projected radius of the tool is equal to the minimum radius of curvature of the surface at the ccp [4], [11], [12] (Fig. 1). The problem with curvature matching is that it cannot guarantee gouge-free tool positions. Thus, each tool position must be checked for gouging and adjusted until it is gouge-free. This secondary process of gouge-checking and avoidance strategies complicates the implementation of this technique (examples are Refs. [9], [13]).

Another approach is to match the tool's cutting geometry to a region of the surface beneath it. The multi-point machining (MPM) by Warkentin et al. [18] is an example of this strategy where the area beneath the tool is searched for two contact points that the tool can be positioned to touch tangentially. The rolling ball method (RBM) developed by the present authors [7] is another area-based method. A brief explanation of the RBM is presented in Section 2 since it is the basis of comparison to demonstrate the improvements achieved with the arc-intersect method (AIM).

Generating tool paths that cross surface patch boundaries using equation-based tool positioning strategies can be difficult. In Veeramani and Gau [16] each surface patch is machined separately. For industrial parts with many surface patches, this is not feasible. The main reason for using triangulated surfaces is that it facilitates the generation of tool paths for multiple surface patch workpieces. In Ref. [6], the present authors machined a workpiece with two surface patches connected with C₀ continuity using the RBM with triangulated data.

The goal when triangulating surfaces for CNC machining is to achieve the user-specified accuracy with a minimum set of triangles. Accuracy of the triangulated model generally depends on the number of triangles used to model the surface and, with today's computing power and memory, this is not perceived to be a significant barrier. In [1], Austin et al. addressed the problem of discretizing surfaces into triangulated data set and point data set representations for tool path generation and gouge detection. With regard to accuracy for machining, it was noted that the single source of error for triangular data sets is the maximum distance between the triangle face and the model surface, which depends on the curvature of the surface.

Li and Jerard [10] presented a gouge-check and correction method for Sturz milling using triangulated data. Balasubramaniam et al. [2], [3] presented a 5-axis tool positioning strategy that uses computer graphics to compute visibility for assessing accessibility of surface points. However, as in Ref. [10], the tool orientations were not optimized for curvature matching. Saito and Takahashi [15] developed graphics-assisted strategies for 3-axis rough and finish machining of triangulated surfaces with ballnose and flat endmill tools and Jun et al. [8] also presented a 3-axis ballnose machining strategy for triangulated surfaces, which was used to machine complicated workpieces.