Boolean operations for 3D simulation of CNC machining of drilling tools Dani Tost*, Anna Puig, Llus Perez-VidalSoftware Department, Polytechnical University of Catalonia, Spain Accepted 25 April 2003AbstractThis paper addresses the simulation of drilling tools CNC machining. It describes a novel approach for the computation of the boundary representation of the machined tools. Machining consists of a sequence of Boolean operations of difference between the tool and the grinding wheels through time. The proposed method performs the dynamic Boolean operations on cross sections of the tool and it reconstructs the 3Dmodel by tiling between the cross sections. The method is based on classical computational geometry algorithms such as intersection tests,hull computations, 2D Boolean operations and surface tiling. This approach is efficient and it provides user control on the resolution of the operations.Abstract This paper addresses the simulation of drilling tools CNC machining. It describes a novel approach for the computation of the boundary representation of the machined tools. Machining consists of a sequence of Boolean operations of difference between the tool and the grinding wheels through time. The proposed method performs the dynamic Boolean operations on cross sections of the tool and it reconstructs the 3Dmodel by tiling between the cross sections. The method is based on classical computational geometry algorithms such as intersection tests,hull computations, 2D Boolean operations and surface tiling. This approach is efficient and it provides user control on the resolution of the operations.q 2003 Elsevier Ltd. All rights reserved.Keywords: CNC simulations; Bores machining; Computational geometry; Boolean operations; Surface tiling1. IntroductionMost of the research on CNC in CAD is centered on theautomatic computation of tool paths 5,13. Given a final tool design, the optimal trajectories of the tool and the grinding wheels must be computed yielding as final result the CNC code. Machining simulation and verification hasexactly the opposite goal: to calculate the tool starting from the CNC code and from a geometrical model of the machine, the wheels and the tool before machining. This simulation has three main applications 6. First, it detects eventual collisions between the tool or any of the grinding wheels and the rest of the machine. It is important to avoid collisions because serious damages to the machines can follow. Next, simulation provides a means of visually verifying the efficiency of the trajectories, which may result in faster and cheaper processes. Finally, the simulation allows users to check if the surface of the resulting tool is effectively the desired one. In the routine practice of machining, experienced operators have enough skills to imagine the tool final shape by only reading the CNC code. However, they are generally not able to do so with new or non-standard designs. Therefore, the use of a simulation system decreases considerably the tool production cost because it avoids the trial and error process on the real machine with costly materials that is otherwise necessary. This paper addresses a particular type of CNC machining simulation: the grinding of bores and cutters. Conventional CAD systems do not provide a means of realizing this type of simulations and specific applications are needed. Until recently, most of the simulation applications dealt only with the machining of 2D cross-sections of the tools and they were restricted to the main fluting operation 3. Three dimensional applications are rather recent 4,23. They provide a machining simulation for specific 5-axes machines and they are not applicable to general movements. This paper presents a novel approach for the computation of the external shape of the tools through a sequence of coordinated movements of the tool and the wheels on machines of up to 6-axes. The proposed method reduces the 3D problem to 2D dynamic Boolean operations followed by a surface tiling. The 2D solution involves different techniques of planar computational geometry: from intersections to hull computations. The paper is structured as follows. In Section 2 we review previous approaches on machining simulations.Section 3 describes briefly the contour conditions of the simulation. Finally, Section 4 describes the computation of Boolean operations and the results of the implementation are shown in Section 5. 2. Previous work Machining can be considered a dynamic Boolean operation of difference between the grinding wheel and the tool. It is dynamic, because both the tool and the wheels move along time through rotations and translations. The Vector Cut 8,10, is probably the most referenced numerical control simulation method. It is an approximate solution that represents the frontier as a set of points and normal vectors that will be cut along the pat