三阶局部切触在5坐标加工椭球模腔中的应用

Application of Third-order Part Contact in 5-AXIS Sculptured Surface Machining

运用微分几何中的切触原理,研究了在多轴数控机床中铣刀铣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,并用截形对铣刀铣削圆与曲面的贴近程度进行了分析。相对于现有文献的论述,本文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,计算过程确切(曲率的导数很难求),求解方便(只要解一阶非线性方程)。

This paper researches the part third-order contact condition of tool and the surfaces by the contact principle of deferential geometry in to the 5-axis NC machining and analyzes the contact degree of the intersection line of the cutter and the surfaces. The paper explains surface third-order parameters instead of two-order parameter curvature which is not only fit for preliminary analytic surface but calculation of geometric fitting surface. Calculation process is accuracy and solution procedure is convenient.