Predictive interpolation algorithm for high-speed and high-precision parameter curve

Abstract

The present invention discloses a predictive interpolation algorithm for a high-speed and high-precision parameter curve. The predictive interpolation algorithm comprises the following steps of S1, calculating the parameter value of each interpolation point of a parameter curve according to the Runge-Kutta method; S2, according to the constraint condition of the machining precision and the normal acceleration, adjusting the feeding speed of the interpolation point in the self-adaptive manner; S3, according to the deviation between a theoretical value and an actual value for the feeding step length, correcting parameters; S4, finding out the extreme point of the feeding speed and subjecting the curve to predictive segmentation; S5, according to the extreme point of the feeding point, sequentially subjecting each prospective interpolation interval to acceleration and deceleration control. According to the technical scheme of the invention, based on the Runge-Kutta method, interpolation parameters are calculated, so that the high-order derivation of the parameter curve is not required. Therefore, the algorithm complexity is reduced and the real-time performance of the algorithm is improved. Based on the relationship between the extreme point of the speed and the length of the interpolation interval, the feeding speed during the rough interpolation process is planned for a second time. Therefore, the fluctuation of the feeding speed is reduced, and the machining precision is improved.

Description

technical field [0001] The invention relates to the technical field of numerical control machining, in particular to a high-speed and high-precision parameter curve forward-looking interpolation algorithm. Background technique [0002] At present, the traditional numerical control system can only realize linear interpolation, circular interpolation and helical interpolation. In most cases, these interpolation methods can meet the basic processing needs. However, some complex curves and surfaces are expressed by parametric curves in CAD / CAM systems, especially non-uniform rational B-spline (Non-Uniform RationalBasis Spline, NURBS) curves can be used for various complex surface modeling Accurate expression, so NURBS parameter curve interpolation is gradually widely used in various high-end CNC equipment. However, in the field of processing, the traditional method is to divide the NURBS curve into a large number of small straight line segments or arc segments, and then perfor...

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Problems solved by technology

The uniform parameter interpolation algorithm calculates the next interpolation parameter with a constant parameter increment, but the error of this method is too large at the position with large curvature. If you want to reduce the error, you need to reduce the increment, and the interpolation efficiency will decrease

The NURBS curve interpolation algorithm of the first-order Taylor expansion method can achieve constant feed rate interpolation, but there is a problem of excessive feed rate fluctuations

The direct interpolation algorithm of the second-order Taylor expansion reduces the feed rate fluctuation, but the algorithm introduces the second-order derivation, which greatly increases the amount of calculation and affects real-time performance

Although the Newton iteration method and the dichotomy method have greatly improved the interpolation accuracy, the number of iterations is too many, which reduces the real-time performance of the interpolation

Although the adaptive speed interpolation algorithm can adaptively adjust the feed rate according to the change of the curvature of the curve to achieve high interpolation accuracy, but for the curve with a large curvature change, it may exceed the acceleration and deceleration performance of the machine tool, which will cause a large impact on the machine tool. shock

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