A novel feed rate scheduling method with acc-jerk-continuity and round-off error elimination for non-uniform rational B-spline interpolation

Abstract

Feed rate scheduling is a critical step in computer numerical control (CNC) machining, as it has a close relationship with machining time and surface quality. It has now become a hot issue in both industry and academia. In this article, we present a novel and complete S-shape-based feed rate scheduling method for three-axis NURBS tool paths, which can reduce high chord errors and round-off errors, and generate continuous velocity, acceleration, and jerk profile. The proposed feed rate scheduling method consists of three modules: a bidirectional scanning module, a velocity scheduling module, and a round-off error elimination module. The bidirectional scanning module aims to guarantee the continuity of the feed rate at the junctions between successive NURBS blocks, where the chord error, tangential acceleration, and tangential jerk limitations are considered. After the NURBS blocks have been classified into two cases by the previous module, the velocity scheduling module first calculates the actual maximum feed rate. It then generates the feed rate profiles of all NURBS blocks according to the proposed velocity profile. Later, the round-off error elimination module is applied to adjust the actual maximum feed rate so that the total interpolation time becomes 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 the traditional method, the proposed method can save the interpolation time by $4.67\% $ to $14.26\% $.

A novel method for calculating interpolation points of NURBS curves based on chord length-parameter ratio

“…The accuracy of conventional methods is evaluated using the 2D butterfly-shaped NURBS curve shown in Fig. 1b as a benchmark, and our previous work [31] is applied to plan the feedrate profile on the NURBS curve. The resulting feedrate fluctuations and chord length deviations of these conventional methods are presented in Figs.…”

“…The purpose of using these different NURBS curves was to evaluate the performance of the proposed method across a range of path complexities. The feedrate scheduling method in our previous work [31] is applied to plan the feedrate profile on the NURBS curve, and the interpolation parameters are listed in Table 2.…”

Reducing the contour error of leading and trailing edge through feedrate scheduling in 5-axis machining of blisk

“…providing reliable assurance of high machining efficiency and motion stability. However, this is a challenging task due to the nonlinear relationship between the five axes and the end cutter [3,4]. The GBFS strategy focuses on ensuring that the machining error stays within the required tolerance during high-speed machining, which is primarily caused by static arc length approximation error and dynamic contour error.…”