一种新的消除舍入误差的加速度连续S形NURBS插值算法
A novel S-shape based NURBS interpolation with acc-jerk- Continuity and round-off error elimination
摘要：
进给速度调度是数控加工的关键环节，它与加工时间和表面质量有着密切的关系，已成为工业界和学术界研究的热点问题。为了减小高弦长误差和舍入误差，生成连续的参数插补速度、加速度和加加速度曲线，提出了一种新的、完整的基于S形的进给速度调度算法。该算法由三个模块组成：双向扫描模块、速度调度模块和舍入误差消除模块。双向扫描模块的目标是保证连续NURBS子曲线连接处进给速度的连续性，并限制了弦误差、法向加速度/加加速度和指令进给速度。在将NURBS子曲线划分为两种情况后，速度调度模块首先计算出实际的最大进给速度，然后根据速度调度函数生成所有NURBS子曲线的进给速度曲线。之后，提出了舍入误差消除模块，使总插补时间成为插补周期的整数倍，从而消除舍入误差。最后，通过与其他方法的比较，验证了该方法的适用性。
英文摘要：
Feedrate scheduling is a key step in computer numerical control (CNC) machining, as it has a close relationship with machining time and surface quality, and has now become a hot issue in industry and academia. To reduce high chord errors and round-off errors, and generate continuous velocity, acceleration, and jerk profile of parametric interpolation, a novel and complete S-shape based feedrate scheduling algorithm is presented in this paper. The algorithm consists of three modules: bidirectional scanning module, velocity scheduling module and round-off error elimination module. The bidirectional scanning module with the limitations of chord error, normal acceleration/jerk and command feedrate aims to guarantee the continuity of the feed rate at the junctions between successive NURBS sub-curves. After the NURBS sub-curves have been classified into two cases, the velocity scheduling module firstly calculates the actual maximum federate, and then generates the feed rate profiles of all NURBS sub-curves according to our velocity scheduling function. Later, the round-off error elimination module is proposed to make the total interpolating time become an integer multiple of the interpolation period, which leads to the elimination of round-off errors. Finally, benchmarks are conducted to verify the applicability of the proposed method compared with some other methods.
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