基于预估-校正公式的参数曲线插补算法

为减小插补输出速度的波动，提出基于预估 校正公式的参数曲线插补算法.该算法包括插补预处理和实时插补两部分.插补预处理采用S曲线加减速算法规划插补速度，得出插补速度与时间关系.实时插补用Akima插值法计算插补速度，用五阶龙格 库塔法计算参数的初值，用五阶预估 校正公式计算下一插补参数.对比研究了提出的算法与基于泰勒级数展开插补算法对同一条参数曲线的插补效果，结果表明，与基于泰勒级数展开算法相比，在数控加工中，提出的算法可减小插补输出速度波动，提高机床运动的平稳性，提高加工精度.

Parametric curve interpolation algorithm based on predictor-corrector formula

An interpolation algorithm based on predictor-corrector formula including interpolation preprocessing and realtime interpolation was proposed to reduce feed fluctuation.During interpolation preprocessing,S curve acceleration and deceleration algorithm was used to planning interpolation velocity and the dependence of interpolation velocity on time was obtained. During real-time interpolation,interpolation velocity was calculated with Akima interpolation,5th Runge-Kutta formula was used to calculate starting parameter value and 5th predictor-corrector formula was employed to calculate the next interpolation parameter value.A parameter curve was interpolated with the algorithm and the interpolation algorithm based on Taylor's series expansion for comparison.The interpolation results indicated the algorithm can reduce feed fluctuation,improve feed smoothness of machine tool and increase interpolation precision in computer numerical control(CNC) machining.