锥形球头立铣刀刀刃曲线光滑过渡研究

Research on Smooth Connection for Edge Curves of Conical Ball End Mill

针对锥形球头立铣刀的几何特征,应用广义螺旋运动概念建立了刀刃螺旋线的通用数学模型.利用微分几何的基本原理,研究了锥形球头立铣刀的刀刃曲线建模方法,设计了一种新的锥形球头立铣刀复合型刀刃曲线,解决了复合型刀刃曲线的光滑过渡问题,并应用Matlab软件对所设计的刀刃曲线进行了建模和验证.为锥形球头类刀具的进一步设计提供了理论方法和依据.

According to the geometrical characteristics of conical ball end mills,the general mathematical model of helical edge curves was established by using the concept of generalized helical movement.With the basic principles of differential geometry,the modelling method for edge curves of conical ball end mill was studied and a novel edge curve of conical ball end mill was designed,and the problem on the smooth connection of composite edge curves of conical ball end mill was also studied.Beside,the smooth connection of composite edge curves was modeled and verified by using Matlab.As a result,a theoretical method and basis for the further design of conical ball end mills was provided.