Discrete Simulation of Numerical Control Machining of Sculptured Surfaces

复杂曲面的数控加工 (NC)是许多行业的常见做法。 复杂曲面 出现在车身、船体、飞机和其他 应用. 主要研究人员想要解决的问题是， 解决方法是：给定一个数学定义的雕刻表面和一个 一组NC刀具运动，刀具切割的形状是否与 在给定的公差范围内的数学形状？ 此前，主要研究人员已经开发出 算法和数据结构，用于快速模拟 一个三轴轧机上的一个精心挑选的样本点上， 面 这种方法可以保证在每一点上的公差， 剩余多余材料区域和 被挖过的洞 曲面离散化是一个新的概念， 一系列的研究问题， 拟解决：1）可模拟方法，目前有限 三轴数控加工，可扩展到五轴数控加工 而不显著降低效率？ 2)如果将 将表面转换成基于三角形边界表示更 比目前的基于点的方法更有效或更可靠？ 3)可以 由模拟产生的误差信息被用来 修正数控程序，离散化表面是否可以 作为算法的基础来生成NC刀具路径？ 4)什么 是点间距和精度之间的权衡 的方法？ 5）通过以下方法可以提高仿真速度吗？ 并行算法

The machining of sculptured surfaces with Numerical Control (NC) is a common practice in many industries. Sculptured surfaces arise in the design of car bodies, ship hulls, aircraft, and other applications. The problem that the principal investigators want to solve is: given a mathematically defined sculptured surface and a set of NC tool movements, does the shape cut by the tool match the mathematical shape within a given tolerance? Previously, the principal investigators have developed algorithms and data structures for rapidly simulating the actions of a three-axis mill on a carefully chosen sample of points on the surface. This method can guarantee tolerances at every point on the surface both for areas where excess material remains and for areas that have been gouged. The concept of surface discretization is a new one and poses a series of research questions which the principal investigators intend to address: 1) Can the simulation method, currently limited to three-axis NC machining, be extended to five-axis NC machining without marked decrease in efficiency? 2) Would a discretization of the surface into a triangle-based boundary representation be more efficient or reliable than the current point-based method? 3) Can the error information generated by the simulation be used to make corrections to the NC program and could the discretized surface be used as a basis for algorithms to generate NC tool paths? 4) What is the trade-off between the spacing between points and the accuracy of the method? and 5) Can the simulation speed be improved through parallel algorithms?