刀具螺旋槽磨削接触线的几何求解及其在三维建模中的应用

Geometric method to get contact line in grinding tool helical groove and its application in 3-D modeling

由于解析法求解接触线难以在三维软件中实现参数化,旋转类整体刀具螺旋槽三维建模时尚未利用磨削接触线。提出一种基于极限思想求解螺旋槽磨削接触线的几何方法,首先,阐述该方法的数学原理,然后,将基于极限思想推导的螺旋槽磨削曲面共轭条件与基于包络原理推导的曲面共轭条件进行对比;结果表明二者形式完全一样,证明了几何法求解磨削接触线的可靠性,同时对新方法的具体实施步骤进行说明,最后,通过四刃平头立铣刀三维实体建模的具体实例,论述螺旋槽磨削接触线的极限几何求解法在刀具三维建模中的应用。

As contact line solved by analytic method is difficult to be parameterized in 3-D design software,it has not been applied in 3-D modeling for helical groove of rotary solid tools.A geometric method based on limit thought to get contact line in grinding tool helical groove is proposed.First,the mathematical principle of the geometric method is addressed,and then the derived conditional equation based on limit thought for conjugate surfaces is compared to equation derived based on envelope principle.The result show that the two equations are completely the same in form validates the reliability of the geometric method to solve contact line.Moreover,the concrete implementation steps of the new method are stated.At last,through an example of 3-D modeling a flat end mill with four teeth,the application of the limit geometric method to solve contact line in grinding helical groove is illustrated.Based on the conjugation theory of space surface,the vector relation of gear cutting is ensured.