Smooth motion generation for 5-axis CNC flank milling through optimal B-spline feed scheduling

Gaizka Gómez Escudero; Pablo Fernández Lucio; Haizea González Barrio; Maialen Martínez Aguirre; Amaia Calleja Ochoa; Pengbo Bo; Michael Bartoň

doi:10.1016/j.jestch.2026.102423

Smooth motion generation for 5-axis CNC flank milling through optimal B-spline feed scheduling

Gaizka Gómez Escudero^*
, Pablo Fernández Lucio
, Haizea González Barrio
, Maialen Martínez Aguirre
, Amaia Calleja Ochoa
, Pengbo Bo
, Michael Bartoň

^*Corresponding author for this work

University of the Basque Country
School of Computer Science and Technology (School of Software), Harbin Institute of Technology Weihai
Basque Center for Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This work presents a motion-planning framework for 5-axis CNC flank milling based on optimal B-spline feed scheduling. The feed profile is modelled as a B-spline function and optimized to minimize jerk at the drive level under machine kinematic constraints while preserving constant machining time. The method incorporates an analytical formulation of axis-level velocity, acceleration, and jerk, and introduces a ruled distance metric (RDM) for smooth parametrization of discrete toolpaths from CL or G-code data. Experimental validation on an industrial 5-axis CNC machine demonstrates improved agreement between programmed and real feed rates, as well as enhanced smoothness of axis motions.

Original language	English
Article number	102423
Journal	Engineering Science and Technology, an International Journal
Volume	80
DOIs	https://doi.org/10.1016/j.jestch.2026.102423
State	Published - Aug 2026
Externally published	Yes

Keywords

5-axis CNC flank milling
B-spline feed scheduling
Freeform flank toolpath
Jerk minimization
Ruling distance metric

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10.1016/j.jestch.2026.102423

Cite this

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title = "Smooth motion generation for 5-axis CNC flank milling through optimal B-spline feed scheduling",

abstract = "This work presents a motion-planning framework for 5-axis CNC flank milling based on optimal B-spline feed scheduling. The feed profile is modelled as a B-spline function and optimized to minimize jerk at the drive level under machine kinematic constraints while preserving constant machining time. The method incorporates an analytical formulation of axis-level velocity, acceleration, and jerk, and introduces a ruled distance metric (RDM) for smooth parametrization of discrete toolpaths from CL or G-code data. Experimental validation on an industrial 5-axis CNC machine demonstrates improved agreement between programmed and real feed rates, as well as enhanced smoothness of axis motions.",

keywords = "5-axis CNC flank milling, B-spline feed scheduling, Freeform flank toolpath, Jerk minimization, Ruling distance metric",

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note = "Publisher Copyright: {\textcopyright} 2026 The Author(s).",

year = "2026",

month = aug,

doi = "10.1016/j.jestch.2026.102423",

language = "英语",

volume = "80",

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publisher = "Elsevier B.V.",

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T1 - Smooth motion generation for 5-axis CNC flank milling through optimal B-spline feed scheduling

AU - Escudero, Gaizka Gómez

AU - Lucio, Pablo Fernández

AU - Barrio, Haizea González

AU - Aguirre, Maialen Martínez

AU - Ochoa, Amaia Calleja

AU - Bo, Pengbo

AU - Bartoň, Michael

PY - 2026/8

Y1 - 2026/8

N2 - This work presents a motion-planning framework for 5-axis CNC flank milling based on optimal B-spline feed scheduling. The feed profile is modelled as a B-spline function and optimized to minimize jerk at the drive level under machine kinematic constraints while preserving constant machining time. The method incorporates an analytical formulation of axis-level velocity, acceleration, and jerk, and introduces a ruled distance metric (RDM) for smooth parametrization of discrete toolpaths from CL or G-code data. Experimental validation on an industrial 5-axis CNC machine demonstrates improved agreement between programmed and real feed rates, as well as enhanced smoothness of axis motions.

AB - This work presents a motion-planning framework for 5-axis CNC flank milling based on optimal B-spline feed scheduling. The feed profile is modelled as a B-spline function and optimized to minimize jerk at the drive level under machine kinematic constraints while preserving constant machining time. The method incorporates an analytical formulation of axis-level velocity, acceleration, and jerk, and introduces a ruled distance metric (RDM) for smooth parametrization of discrete toolpaths from CL or G-code data. Experimental validation on an industrial 5-axis CNC machine demonstrates improved agreement between programmed and real feed rates, as well as enhanced smoothness of axis motions.

KW - 5-axis CNC flank milling

KW - B-spline feed scheduling

KW - Freeform flank toolpath

KW - Jerk minimization

KW - Ruling distance metric

UR - https://www.scopus.com/pages/publications/105041082893

U2 - 10.1016/j.jestch.2026.102423

DO - 10.1016/j.jestch.2026.102423

M3 - 文章

AN - SCOPUS:105041082893

SN - 2215-0986

VL - 80

JO - Engineering Science and Technology, an International Journal

JF - Engineering Science and Technology, an International Journal

M1 - 102423

ER -

Smooth motion generation for 5-axis CNC flank milling through optimal B-spline feed scheduling

Abstract

Keywords

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