Abstract: To machining of aspheric part of high precision and high quality interpolation algorithm of ultra-precision aspheric numerical control system is very important. According to the aspheric part the bi-arc step length flex numerical control interpolation algorithm a new aspheric curve numerical control interpolation algorithm is adopted. This algorithm adopts bi-arc segment approximating mode it's bi-arc segment is tangent each other first derivative continuous step length transformable numerical control interpolation error controllable. Therefore the machining workpiece surface is smoother the quality of interpolation curve is higher. Moreover applicability of this algorithm is very extensive. In the last a great number of grinding experiments prove that high quality aspheric surface can be machined using this numerical control interpolation algorithm machined profiles accuracy is 0.30 μm the surface roughness Rrms is 11.555 nm Ra is 8.938 nm.

Key words: Bi-arc step length flex Aspheric part Conversion of coor-dinates, Ultra-precision grinding