A novel S-shape based NURBS interpolation with acc-jerk- Continuity and round-off error elimination

TL;DR

This paper introduces a comprehensive S-shape feedrate scheduling algorithm for NURBS interpolation in CNC machining, improving surface quality and reducing errors by ensuring continuous velocity, acceleration, jerk profiles, and eliminating round-off errors.

Contribution

The paper presents a novel S-shape based feedrate scheduling algorithm with modules for bidirectional scanning, velocity scheduling, and round-off error elimination, enhancing NURBS interpolation accuracy.

Findings

Reduces chord and round-off errors in NURBS interpolation.

Ensures continuous velocity, acceleration, and jerk profiles.

Verifies effectiveness through benchmark comparisons.

Abstract

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.