Boolean operations for 3D simulation of CNC machining of drilling tools Dani Tost*, Anna Puig, Llu?′s Pe′rez-Vidal
Software Department, Polytechnical University of Catalonia, Spain Accepted 25 April 2003
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.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 tiling
1. Introduction
Most 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 path of the grinding wheel. This method is effective for the simulation of sculptured surface polishing, but it is not extensible to complex motions of the tool and/or the grinding wheels. It is mainly useful to detect mistakes in the path suggested
by the presence of abnormally high or small cut vectors. Besides, except for the extension of Ref. [16], it does not yield directly a model of the bit to be machined.
An alternative strategy for machining simulation consists of realizing a sequence of 3D static Boolean operations through time. The main drawback of this strategy is its high computational cost. According to Ref. [11], this is proportional to the number of discrete positions to the fourth. This puts it out of question, in practical terms.Another problem it shows is the granularity of the temporal discretization : it must be very fine if precision in the final tool is required. This means that very little material is cut off in each Boolean operation, and that may entail robustness problems in the computations. A possible method to avoid both problems is to discretize the initial tool model into a voxel or an octree model, [20], to perform all the sequence of Boolean operations on the discrete model and then reconstruct the machined surface, at the end. This approach benefits from the fact that the cost of discrete Boolean operations is much lower and the reconstruction phase at the end of the process is done as late as possible. This option requires the sequence of movements to be specified in terms of relative motion of the grinding wheel, while the tool and its discretization remain fixed. This prerequisite is not always valid and, in particular, it does not hold for the general case of 6-axes machines.
Finally, another option taken into account is that of the computation of the volume swept by the tool and the grinding wheel in their motions. A geometric representation of this volume would allow performing only one Boolean difference operation between the two volumes. The main difficulty of this option is the computation of sweptvolumes. There are several references [1,2,21] on this subject, that contain methods generally applied in CAD for extrusions, collision
detection, and other problems but none of them can be applied to the non-trivial case of simultaneous motion of the two solids in play.
The strategy proposed herein overcomes the disadvantages of these methods. It consists of a double discretization of four dimensional space (3D t time) that reduces the general problem to a sequence of 2D Boolean operations and 3D geometric reconstructions. This algorithm is fast and it provides user-control on simulation accuracy.
3. Scene model
There are different types of machine tools for the fabrication of bores and cutters. They share the same general structure but they differ in the number of degrees of freedom. The method proposed herein deals with machines up to six degrees of freedom. These machines have a static vertical axis (Z in Fig. 1 on which the grinding wheel set can move up and down. One tool is placed on a spindle (the toolholder), that may translate on three axes (X; Y and U) and rotate on two axes (W in relation to the wheel axis and A relative to its own axis). At the beginning of the process, a tool has a piecewise cylindrical or conical shape. Its final shape is the result of a sequence of machining operations consisting of simultaneous movements of the tool and the wheels. The wheel shape is also piecewise cylindrical or conical. It remains unchanged during the process.
The machining process is divided into a set of operations, each one with a specific name in CNC jargon. Each operation is performed using a specific wheel. This information is written in the CNC file.
Specifically, the main operations are (in their usual order):