Abstract
In vector based machining simulations sampling only along one direction misses surface portions, such as sharp edges and vertical walls. This drawback can be removed when sampling along multiple directions, even without increasing the number of vectors. Therefore, given the same total number of vectors, vector hits are likely to be better distributed over the surface in a multiple-rayrep model than in a single one. But in this case, although we have a better in-process workpiece representation, we face with another problem: computational expense in the vector/envelope intersections. Computations are easy when the workpiece is represented by unidirectional vectors and when the tool axis is positioned along these vectors. On the other hand, a more complicated situation occurs when the machining simulations are performed in the multiple-reyrep based environments with tools having high-order geometries. In this case, the extensive usage of nonlinear root finding algorithms makes machining simulations impractical. One solution might be to eliminate the variable representing a vector from calculations. This leads to a union of 3D-points (i.e. polyhedral, voxel and Octree representations), at the loss of accuracy Therefore, from a geometric viewpoint we can consider the aggregate of 3D-points as a special version of the multiple-rayrep model, in which the orthogonal vectors are discretized. In this paper, first the above mentioned drawbacks are presented for the triple-vector model based environments with arbitrarily oriented tool surfaces. Later, since each NC sequence is described by using the toolpath parameter, the above problems are reduced to a single equation with collection of toolpath parameters for the given 3D-points. Since its geometric complexity is highest among other APT-type cutter surfaces, the toroidal surface is chosen for the analysis.