基于双圆弧步长伸缩数控插补非圆曲线算法的研究

STUDY ON THE ASPHERIC CURVE ALGORITHM BASED ON THE BI-ARC STEP LENGTH FLEX NUMERICAL CONTROL INTERPOLATION

为了加工出高质量的非球曲面器件,超精密非球曲面数控系统的数控插补算法非常重要。根据所要加工的非球曲面零件,采用了一种新的非圆曲线数控插补算法“双圆弧步长伸缩数控插补算法”。这种算法采用双圆弧段逼近方式,其双圆弧段彼此相切,一阶导数连续,并且步长可伸缩,其数控插补误差可进行控制。因此加工后的工件表面整体光滑,插补曲线的质量很高,而且适用性很广泛。最后用所研制的数控插补算法进行了大量的磨削加工试验,试验结果表明:该插补算法能加工出高质量的非球曲面零件,加工后的零件面形精度为O.30μm,其表面粗糙度Rrms=11.555nm,Ra=8.538 nm。

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 Rms is 11.555 nm, Ra is 8.938 nm.