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首页> 外文期刊>International Journal of Quality and Innovation >Development of an improved CNC interpolator and performance evaluation in terms of chordal error and feed rate deviation
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Development of an improved CNC interpolator and performance evaluation in terms of chordal error and feed rate deviation

机译：开发改进的CNC插补器，并根据弦误差和进给速率偏差进行性能评估

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摘要

The parametric interpolators of modern CNC machines use Taylor's series approximation to generate successive parameter values which, after substituting into the curve equation, gives the x, y, z coordinates of the tool positions. In order to achieve greater accuracy higher order derivatives are required which complicates the calculation when the curve is represented by NURBS curve. This method calculates the chordal error on a given segment by estimating the curvature which neglects a fraction of the error. In order to avoid calculating higher derivatives and make the calculations easier the classical fourth-order Runge-Kutta (RK) method is proposed in this research, which only requires the first derivative to be calculated, but achieves the accuracy of Taylor's approximation with higher order terms. This paper also proposes the estimation of chordal error on the average value of the parameters at the end points of a given curve segment, which does not require calculation of curvature at every segment. Finally computer simulation is performed on different types of spline curves to show that the proposed method results in reduced chordal error and less fluctuation in feedrate.
机译：现代CNC机床的参数内插器使用泰勒级数逼近来生成连续的参数值，这些参数值代入曲线方程后，给出刀具位置的x，y，z坐标。为了获得更高的精度，需要更高阶的导数，这在使用NURBS曲线表示曲线时会使计算复杂化。该方法通过估计忽略误差一部分的曲率来计算给定段上的弦误差。为了避免计算更高的导数并使计算更容易，本研究提出了经典的四阶Runge-Kutta（RK）方法，该方法只需要计算一阶导数，但可以达到高阶泰勒逼近的精度。条款。本文还提出了在给定曲线段端点的参数平均值上的弦误差估计，该方法不需要计算每个段的曲率。最后，对不同类型的样条曲线进行了计算机仿真，结果表明所提出的方法减少了弦误差，并减小了进给速度的波动。

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