Abstract: To solve the problem of complex feedrate planning,low efficiency and severe machine tremor in NURBS curve machining process,a high efficiently NURBS interpolation algorithm was proposed.During the pre-processing stage,the interpolation parameters and error feedrate of NURBS curve were calculated,the acceleration and deceleration regions was analyzed according to the error feedrate curve,and the cubic polynomial equation of feedrate was automatically adjusted according to the length of ACC/DEC interval.Based on Adams-Moulton method,the real-time interpolation process could calculate the initial parameters,and optimize the parameters with bisection method.The feedrate fluctuation in the interpolation process was controlled to the machining precision range to reduce the machine vibration.The feasibility of the proposed algorithm was verified by Matlab simulation,and the simulation result showed that the algorithm could improve the machining efficiency and accuracy in the field of machining complex curves and surfaces.

Key words: non-uniform rational B-spline, feedrate plan, Adams-Moulton method, bisection method, interpolation algorithm, curve machining

摘要： 针对非均匀有理B样条(NURBS)曲线加工过程中速度规划复杂、效率低以及机床震颤剧烈的问题,提出一种高效规划进给速度的NURBS插补算法。预处理过程计算出待加工NURBS曲线插补参数及误差速度,根据误差速度曲线分析加工路径的加减速情况,并基于加/减速区间长度自动调整三次多项式速度方程,实现平滑的速度与加速度曲线;实时插补过程采用基于Adams-Moulton方法计算初始参数,然后采用二分法对参数进行寻优,将插补过程中速度波动控制到加工要求精度范围内,从而降低机床的振动。通过MATLAB仿真,验证了所提算法加减速规划的高效性和参数计算的精确性,表明该算法在复杂曲线曲面加工领域可以提高机床加工效率与精度。

关键词: 非均匀有理B样条, 速度规划, Adams-Moulton方法, 二分法, 插补算法, 曲面加工