曲面的三阶局部切触在5坐标曲面加工中应用

运用微分几何中的切触原理，研究了在多轴数控机床中刀具切削圆与零件曲面的切触条件和局部坐标系下的局部三阶切触条件，并用截形对刀具切削圆与曲面的贴近程度进行了分析。相对于现有献本理论更严密，深入到曲面三阶参数而不仅是二阶参数曲率，既适合初等解析曲面又适合计算几何的拟合曲面，计算过程准确(曲率的导数很难求)，求解方便(只要解一阶非线性方程)。

The Three Order Local Contacte of the Scurptrued Surfaces in 5-axis Machining of scuptrued Surfaces

This paper applied the contact principle of deferential geometry in to the 5-axis NC machining,researched the best contact condition of tool and the surfaces,analysis the contact degree of the intersection line of the cutter and the surfaces.Compared with other references,the theory of this paper is more restrict,going deep into the parameter of third order instead of the second order,suitable to the primary analytical geometry and the simulation surface of the numerical geometry,with definite procedure of calculation,and easy to solve the function.