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首页> 外文期刊>Computer-Aided Design >Complete swept volume generation, Part I: Swept volume of a piecewise C~1-continuous cutter at five-axis milling via Gauss map
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Complete swept volume generation, Part I: Swept volume of a piecewise C~1-continuous cutter at five-axis milling via Gauss map

机译：完整的扫掠体积生成，第一部分：通过高斯图在五轴铣削中分段C〜1连续刀具的扫掠体积

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摘要

In this paper, we present a methodology to generate swept volume of prevailing cutting tools undergoing multi-axis motion and it is proved to be robust and amenable for practical purposes with the help of a series of tests. The exact and complete SV, which is closed from the tool bottom to the top of the shaft, is generated by stitching up envelope profiles calculated by Gauss map. The novel approach finds the swept volume boundary for five-axis milling by extending the basic idea behind Gauss map. It takes piecewise C~1-continuous tool shape into account. At first, the tool shape is transformed from Euclidean space into Tool map (T-Map) on the unit sphere and the velocity vector of a cutter is transformed into Contact map (C-Map) using Gauss map. Then, closed intersection curve is found between T-Map and C-Map on the Gaussian sphere. At last, the inverse Gauss map is exploited to get envelope profile in Euclidean space from the closed curve in the range. To demonstrate its validity, a cutting simulation kernel for five-axis machining has been implemented and applied to mold and die machining.
机译：在本文中，我们提出了一种方法来生成进行多轴运动的主流切削刀具的扫掠量，并且在一系列测试的帮助下，该方法被证明是可靠的和实用的。通过缝合由高斯图计算得出的包络轮廓，可以生成从工具底部到轴顶部闭合的精确且完整的SV。通过扩展高斯图背后的基本思想，新方法找到了五轴铣削的扫掠体积边界。它考虑了C-1连续刀具的分段形状。首先，将刀具形状从欧式空间转换为单位球面上的刀具图（T-Map），然后使用高斯图将刀具的速度矢量转换为接触图（C-Map）。然后，在高斯球面上的T-Map和C-Map之间找到闭合的相交曲线。最后，利用高斯逆映射从该范围内的闭合曲线获得欧几里得空间中的包络线轮廓。为了证明其有效性，已经实现了用于五轴加工的切削仿真内核，并将其应用于模具加工。

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