基于五坐标数控圆柱形刀具线接触加工自由曲面的几何学原理

从微分几何学的角度，探讨了在五坐标数控机床上采用圆柱形刀具线接触加工自由曲面的几何学原理，分析了刀具面与被加工曲面二阶密切的条件。通过对二次型半正定的判别，求得了刀具轴线的位置，给出了点邻域内三阶离差的计算公式，证明了圆柱形刀具与被加工曲面的密切条件等价于刀具轴线与被加工曲面的等距面的密切条件，通过实例验证了所提方法的正确性。

GEOMETRICAL THEORY OF MACHINING FREE FORM SURFACE BY CYLINDRICAL CUTTER IN 5-AXIS NC MACHINE TOOLS

On the basis of the differential geometry, the geometrical theory of machining free form surface by cylindrical cutter in 5-axis NC machine tool is investigated. The second order osculating condition between the cutter and the theoretical surface is analyzed. By means of the condition of positive semidefinite of a quadratic form, the location of the tool-axis can be acquired. The osculating condition between the cutter and the theoretical surface is equivalent to the osculating condition between the tool-axis and the offset surface of the theoretical surface and has been demonstrated. By means of the proposed machining method, the cusp height can be limited within the third order infinitesimal. The machining precision and the efficiency can be improved, and the potential ability of the 5-axis NC machine tools could be developed.