Oriented bounding box and octree based global interference detection in 5-axis machining of free-form surfaces

doi:10.1016/S0010-4485(03)00109-X

Computer-Aided Design

Volume 36, Issue 13, November 2004, Pages 1281-1294

https://doi.org/10.1016/S0010-4485(03)00109-X Get rights and content

Abstract

Global interference detection is a critical problem in 5-axis NC machining of free-form surfaces. Based on the hierarchical oriented bounding box (OBB) which is used in virtual reality to detect spatial collisions between 3D objects, a new global interference detection method is developed in this paper. In this method, in order to simplify the computation process of updating tool positions and orientations in 5-axis machining, the cutter and cutter holder are modeled by a hierarchical OBB structure, whereas the workpiece surfaces are approximated by an octree. Interference detection is conducted between the tool OBBs and the gray octants of the surface octree with the separating axis theorem. With the hierarchical structure of octree, if interference is found in one octant, its sub-octants are further processed to locate the exact colliding leaf nodes and the discretized surface points contained in these leaf nodes are tested with a conventional vector calculation method for exact interference detection; if no interference is detected, all the sub-octants are then considered as interference free and are not processed further. Meanwhile, with the hierarchical structure of the tool OBBs, should interference occur between octants and the OBBs in the first level of the hierarchical structure, the sub-OBBs in the second level would be further tested. Otherwise it could be determined with certainty that there is no interference between the tool and the octant.

Introduction

Free-form surfaces have been widely used in aerospace, automobile, shipbuilding and electric appliance industries. For example: the aerodynamic contours of aircrafts and automobiles, turbine blades, mobile phone casings, etc. In manufacturing industry, these free-form surfaces are usually machined through 5-axis NC machines [1], [2], [3], [4], [5], [6], [7], [8], [9]. A 5-axis machine has two extra rotational axes over commonly used 3-axis machines. These two rotational axes provide users with great flexibilities and make it possible to machine high quality complicated free-form shapes which were previously un-machinable. However, because of the two additional rotational axes, interferences are prone to occur in 5-axis machining. These interferences may occur between the moving tool (cutter and cutter holder) and objects on the machine, such as workpieces and fixtures. Sometimes it even occurs between the tool and the machine itself [1]. This greatly affects the wide application of 5-axis machines and has attracted many researches in this area [1], [2], [3], [4], [5], [6], [7], [8], [9].

Tool interferences are usually classified into two categories: local gouging and global interference (Fig. 1). Local gouging refers to the interference between cutter edge and workpiece in the vicinity of the cutter contact (CC) points [2]. It occurs when the cutter curvature is smaller than that of the free-form surface in which case the cutter would over cut the workpiece and excess materials would thus be removed near the CC points. Global interference is the collision between the cylindrical part of the cutter (or cutter holder) and workpieces or fixtures, or between that and the machine tool. In these two types of interferences, global interference is considered to be more serious as accidents may happen if such interference occurs. The consequence of local gouging could just be unqualified workpieces whose errors exceed specified tolerance. However, as for global interference, besides the unacceptable workpieces machined, it may also damage the cutter, fixtures and even the machine structure itself [1].

Due to its wide range of applications, interference detection between geometric models has been studied for many years in various fields [10], [11], [12], for example: in robotic path planning, physical simulation, computer graphics and virtual reality. In CAD/CAM fields, interference detection and avoidance of gouging have been extensively studied by many researchers, and many effective algorithms based on differential geometry or curvature analysis technologies have been developed [9], [13]. However, for global interference detection, there are not many achievements published.

In this paper, based on hierarchical oriented bounding boxes (OBBs) [10], [11] and octree space partition, we developed a new global interference detection method for 5-axis machining of free-form surfaces. In this method a two-level hierarchical OBB structure that consists of five OBBs is used to model the tool, and an octree is applied to partition the free-form surfaces. Unlike geometric modeling, in this algorithm only the gray octants of the octree are used. Interference detection is conducted between the OBBs and octants using the separating axis theorem which is popular in computer graphics. Because of the specialties of the surface octree and these tool OBBs, some simplifications are applied in the testing process to reduce the computation time. With the hierarchical data structure of the octree, if volume interferences were found between OBBs and octants in the first level of the octree, the children nodes of these octants would be further checked to locate the leaf nodes. A conventional vector calculation algorithm is applied in the final phase to determine whether real interference would occur between the tool and the discretized surface points contained in these leaf nodes. Meanwhile, with the hierarchical structure of tool OBBs, if no interference occurs between the first level of tool OBBs and the surface octants, it could be determined with certainty that there is no interference between the tool and the octants. However, if collision is detected, the sub-OBBs of the tool would be further checked to determine whether interference really occurs.

This paper is structured as follows. Section 2 introduces related work of interference detection. Section 3 discusses the structure of OBB and octree. The proposed global interference detection algorithm is presented in Section 4, and some application examples are given in Section 5. The last section is our conclusion.

Section snippets

Related work

Due to its widespread importance, a lot of researches have been carried out to solve the interference detection problems. These include the vector based method [5], [6], convex hull based methods [7], bounding volume method [8], C-space based method [2], [13], analytical method [14], swept volume method [15] and space partition method [16], [17].

Bounding volume collision detection and octree space partition

The idea behind bounding volume is to approximate 3D objects with simple geometric shapes so as to reduce the number of pairs that are needed to be checked for collisions. Spheres, axis aligned bounding boxes (AABBs), OBBs, and k-Discrete oriented polytope (k-DOP) are the bounding volumes that have often been used [10], [11], [19].

Methodology

The bounding volume collision detection algorithm has been a popular technique in solving the spatial collision detection problems between 3D objects in virtual reality and computer graphics. To simplify the computation process of updating tool positions and orientations in 5-axis machining, a two-level hierarchical structure that consists of five OBBs is used to model the tool (cutter and cutter holder). Because the workpiece surfaces are free-form surfaces, to utilize the separating axis

Implementations

The proposed method was successfully implemented in an integrated environment using Visual C++ and OpenGL.

Conclusions

A new hierarchical bounding volume and space partition based global interference detection method for 5-axis machining of free-form surfaces is developed. In this method, in order to reduce the computation burden of updating the moving and rotating tool during the machining process, hierarchical OBBs are applied to model the cutter and the cutter holder. Further, in order to apply the separating axis theory, which is effective in solving 3D object collision problems in computer graphics, an

Songlin Ding received his PhD from the National University of Singapore, MS degree from Tsinghua University and BS degree from Nanjing University of Science and Technology, China. He is currently a senior research engineer in Edison Technology Center of General Electric. His research interests include mechatronics, CAD/CAM and Computer Graphics.

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View full text

Oriented bounding box and octree based global interference detection in 5-axis machining of free-form surfaces

Abstract

Introduction

Section snippets

Related work

Bounding volume collision detection and octree space partition

Methodology

Implementations

Conclusions

Comput Aided Des

Comput Aided Des

Ann CIRP

Comput Aided Des

Comput Aided Des

Comput Aided Des

Comput graphics

Comput Aided Des

J Manufact Syst

Five-axis CNC milling for effective machining of sculptured surfaces

Int J Prod Res

A method for NC toolpath interference detection for a multi-axis milling system