Study of the aspheric curve algorithm based on the bi-arc step length flex numerical control interpolation

To the machining of aspheric part of high precision and high quality, the 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, its bi-arc segment is tangent to each other with continuous first derivative continuous, transformable step length, and controllable numerical control interpolation error. Therefore the machining workpiece surface is smoother, and the quality of interpolation curve is higher. A great number of grinding experiments prove that high quality aspheric surface can be machined by using this numerical control interpolation algorithm. The machined profiles accuracy is 0.30 μm, the surface roughness R_rms is 11.555 nm, and R_a is 8.938 nm.