辛普森积分法在双NURBS曲线随动插补中的应用
Application of Simpson Integration Method in Dual-NURBS Curve Follow-up Interpolation

提出一种精确计算插补步长的双NURBS曲线随动插补算法。首先由曲面数控加工的离散刀位数据分别拟合出刀尖点和刀轴点NURBS曲线，并建立两条曲线插补参数间的随动关系模型；然后采用辛普森积分法计算出曲线的总弧长，进行插补运动的加减速规划；再以刀尖点NURBS曲线为基准确定插补参数，采用辛普森法确定各插补周期的进给步长及插补点坐标；最后依据随动关系模型获得刀轴点NURBS曲线对应的插补参数，完成曲面加工刀路规划的刀具位姿插补。仿真实验表明，与同一参数插补法相比，参数随动法可以获得更加稳定的等距效果，便于实时控制插补过程中的刀轴位置和姿态。
A following-up interpolation algorithm for dual-NURBS (Non-uniform rational B-spline) curve was proposed based on precise calculation of interpolation step-length. First, tool-tip and tool-axis NURBS curves are fitted out from the discrete cutter location data for curved surface NC machining, respectively, and after it the follow-up relation model between the two curve interpolation parameters was established. Then, Simpson integral method is used to calculate the total arc length of the curve, and the acceleration/deceleration planning is conducted for interpolation motion. And next, taking tool-tip NURBS curve interpolation parameters as benchmark, and using Simpson method to determine feeding step-length in each interpolation cycle, and the interpolation point coordinates are subsequently gained. The corresponding interpolation parameters of the tool-axis NURBS curve is acquired according to follow-up relationship model, and the tool pose interpolation of the tool-path planning of surface machining is achieved. Simulation experiment shows that compared with the same parameter interpolation method, the follow-up parameters method can obtain more stable isometric effect, which is conducive to real-time control the tool position and posture in the process of interpolation