Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves

Abstract

This article presents an online three-axis non-uniform rational B-splines preprocessing and feedrate scheduling method with chord error, axial velocity, acceleration, and jerk limitations. A preprocessing method is proposed to accurately locate the critical points by reducing pre-interpolation feedrate in feedrate limit violation regions. In the preprocessing stage, the non-uniform rational B-splines curve is subdivided into segments by the critical points and the corresponding feedrate constraints are obtained. A sliding look-ahead window-based feedrate scheduling method is proposed to generate smooth feedrate profile for the buffered non-uniform rational B-splines segments. The feedrate profile corresponding to each non-uniform rational B-splines block is constructed according to the block length and the given limits of acceleration and jerk. The feedrate modification method for non-schedulable short blocks is also described which aimed at avoiding feedrate discontinuity at the junction of two non-uniform rational B-splines blocks. With the proposed method, a successful feedrate profile could be generated with sufficient look-ahead trajectory length in the buffer, which enables that the preprocessing and feedrate planning to be performed progressively online. Simulation and experimental tests with different non-uniform rational B-splines curves are carried out to validate the feasibility and advantages of the proposed method. The results show that the proposed method is capable of making a balance between the machining efficiency, machining precision, and computational complexity.

CNC tezgâhlarında dairesel ve helisel hareketler için jerk/ivme sınırlandırmalı yörünge planlama algoritmasının geliştirilmesi

“…Jerk ve ivme sınırlandırmalı hız profilleri Bezier, B-spline, NURBS eğrileri başta olmak üzere birçok eğrisel yörüngeler için farklı yapılarda oluşturulabilmektedir [12]. Şekil 5'te, beş parçalı sabit jerkli ve hız/jerk sınırlandırmalı hız profili [13][14][15] ve buna bağlı oluşan ivme ve jerk profilleri görülmektedir. Şekildeki grafiklerin oluşmasında hızlanma zamanı (t ), sabit hız zamanı (t ) ve yavaşlama zamanı (t ) değerleri büyük öneme sahiptir.…”

Machine tool movement control method combining the benefit of software and real-time interpolator for sculpture surface machining

“…From equation (13), the constraints are nonlinear and coupled for the curve tool path, and it should be solved by the numerical method. There are many methods 7,19 to address this problem. In this work, the method developed in Lu et al 28 is used.…”

“…Finally, the real-time calculating capacity of a CNC controller limits the interpolation accuracy 18 and the feedrate scheduling of a spline tool path. 19 For most curve tool paths, there is no analytical relationship between the arc length and the parameter, 20 and a precise arc length always needs an iterative calculation, which is unsuitable in real-time calculation. Therefore, numerous articles propose various methods to address the interpolation accuracy problem in spline interpolation.…”