高速高精度曲线重构与递推插补研究

为解决中高档计算机数控(Computer numerical control,CNC)中基于多项式基的Hermite样条曲线实时插补算法递推速度低且逼近精度较差的问题,文中利用指数函数e–t快速递推及收敛的优点,在代数指数混合空间构造新的样条曲线并给出基于该曲线的递推插补算法。应用该算法进行的插补试验中,与Hermite曲线相比,新样条曲线的递推速度提高1.7～2.1倍,同时逼近精度提高一个数量级。结果表明基于新曲线的插补算法在提高轮廓加工轨迹精度的同时,也提高加工效率,满足中高档计算机数控中样条曲线的构造要求。

Research on Reconstruction and Recursion Interpolation of Curve with High-speed and High-precision

Aiming at low recursion-rate and poor approximation accuracy of polynomial-basis Hermite curve, which is commonly used in real-time interpolation of middle and top grade computer numerical control(CNC), a new kind of splines based on algebraic-exponential space, which takes full advantage of high recursion-rate and convergence-rate of exponential function e~(-t), is reconstructed. The experiment shows that the recursion rate of new curve is 1.7～2.1 times that of Hermite curve, and at the same time, the approximation precision is improved by one order of magnitude. The result indicates that the interpolation-algorithm based on new curve not only promotes machining precision of profile, but also improves machining efficiency simultaneously, thereby meeting the construction requirement of spline curve in middle and top grade CNC.