用单位矢量法求刀具角度

A method of calculating angles of a cutting tool with unit vectors

用数学分析方法精确求解木材切削刀具的角度。在求解过程中,用单位矢量来代表刀刃线和刀面的外法线方向,简化了推导过程和计算公式。同时区分了刀刃在坐标平面上的投影角和刀面相对坐标平面的倾斜角,并用实例计算说明这两种角度有时差值较大。因此,精确计算刀具角度对提高木制品的加工精度,提高刀具的强度、寿命及锋利性是有意义的。

This article introduce a strict mathematical analysis that can exactly calculate angles of wood cutting tool.Unit vectors are used to represent the directions of cutting edges and tool surfaces so that the calculating process and formulats are simplified.Difference between the angles of edge projections and the angles of the intersections of surfaces and coordinate planes are raised in this paper.The calculating result of a sample indicate that the difference may sometimes be considerable so that it is signification to calculate exactly cutting tool angles for improving exactitude of wood products and for increasing strength,life and sharpness of cutting tools.