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Abstract: 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.
Key words: CAD/CAM 5-Axis NC machining Cylindrical cutter Second order
osculation Cusp height Line contact Asymptotic direction
CLC No: TP391
国家自然科学基金资助项目(50105001). Received 20020510, received in revised form
20030128
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