## Abstract

In numerically controlled (NC) machining simulation, a Z-map has been frequently used for representing the workpiece. Since the Z-map is usually represented by a set of z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when automatically programmed tool-type tools move along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these properties, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation is achieved by updating the Z-map properly. Our method can improve accuracy greatly while increasing processing time negligibly in comparison with previous Z-map update methods, making it possible to verify the tool path more accurately and reliably.

Original language | English |
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Pages (from-to) | 995-1009 |

Number of pages | 15 |

Journal | CAD Computer Aided Design |

Volume | 35 |

Issue number | 11 |

DOIs | |

State | Published - Sep 2003 |

## Keywords

- Numerically controlled machining
- Swept surface
- Z-map