通用刀具扫描体隐式曲面建模方法

Geometric Representation of the Swept Volume of a Generalized Cutter Using Implicit Surfaces

提出五轴加工仿真中基于隐式曲面理论的通用刀具扫描体建模方法。为了提高布尔减运算时间性能,采用隐式曲面能够高效判断扫描体与工件体素数据场点集的位置关系,避免耗时的空间相交计算。定义通用刀具体的隐式曲面模型;根据刚体运动框架理论,建立工件框架与刀具框架的映射关系,利用逆向运动法确定曲面边界范围,将刀具体线性位移和旋转角度作线性插补,推导出工件框架中刀具扫描体的隐函数曲面方程;在分析刀具各部分扫描体方程实数根情况的基础上,给出基于隐式曲面的扫描体构造算法。以典型刀具和运动类型为例,分析扫描体构建过程,试验结果验证方法的正确性和较好的时间性能,方法应用于数控系统中的材料去除仿真。

An implicit surface methodology for computing the swept volume of a generalized cutter in five-axis NC milling simulation is proposed. In order to improve efficiency of boolean subtraction operations, the implicit surface is adopted to determine spatial relationships between the swept volume and set of points representing a workpiece without a time-consuming intersection computation in the three-dimensional space. The geometry of a generalized cutter represented by implicit surfaces is defined. According to the rigid body motion theory in frames, the mapping from a cutter frame to a workpiece frame is built, and surface boundaries are determined via the inversely motion. Translations and rotational angles are interpolated linearly, and implicit functions of the swept volume are deduced in the workpiece frame. Solutions of implicit functions are analyzed, and can be used to generate the swept volume of a generalized cutter based on implicit surfaces. Examples show the approach developed is exact and efficient, and is applied to the material removal simulation in a CNC controller.