Article: Analytical modelling of the cutter workpiece engagement and the undeformed chip thickness for circular ball end milling path for adaptive feed rate Journal: International Journal of Manufacturing Research (IJMR) 2024 Vol.19 No.3 pp.266 - 293 Abstract: In the ball end milling process, the stability of the process depends on the variations of the cutter workpiece engagement region (CWER) and the instantaneous undeformed chip thickness (IUCT). These two parameters influence cutting forces, tool wear, and machining stability. Previous works have modelled the CWER and the IUCT in the case of linear interpolation, but curvilinear and circular interpolations have not been studied yet. In this study, we focus on the curvilinear path, which is assumed to be the junction of several circular tool paths with a radius equal to the programmed value of the circle circumscribed. The method is described with a geometrical and analytical approach for determining the CWER and the IUCT in the case of concave and convex paths, both in down and up milling. The approach also proposes feed rate optimisation to maintain a constant maximum IUCT along the tool path. [Submitted 17 April 2024; Accepted 27 August 2024] Inderscience Publishers - linking academia, business and industry through research

Title: Analytical modelling of the cutter workpiece engagement and the undeformed chip thickness for circular ball end milling path for adaptive feed rate

Authors: Lotfi Sai; Rami Belguith; Amine Regaieg; Makram Maaloul

Addresses: IPEIN, Université de Carthage, Campus Mrezgua, 8000 Nabeul, Tunisia ' Laboratoire de Génie Civil et géo-Environnement (LGCgE), Univ. Artois, MT Nord Europe, Junia, Univ. Lille, ULR 4515, 62400 Béthune, France ' EPT, Université de Carthage, Tunisia; UGPMM, ENIS, Université de Sfax, Tunisia ' EPT, Université de Carthage, Tunisia; Laboratoire De Physique, Mathématiques, Conception Mécanique et Modélisation Quantique, R18ES45, IPEIN, France

Abstract: In the ball end milling process, the stability of the process depends on the variations of the cutter workpiece engagement region (CWER) and the instantaneous undeformed chip thickness (IUCT). These two parameters influence cutting forces, tool wear, and machining stability. Previous works have modelled the CWER and the IUCT in the case of linear interpolation, but curvilinear and circular interpolations have not been studied yet. In this study, we focus on the curvilinear path, which is assumed to be the junction of several circular tool paths with a radius equal to the programmed value of the circle circumscribed. The method is described with a geometrical and analytical approach for determining the CWER and the IUCT in the case of concave and convex paths, both in down and up milling. The approach also proposes feed rate optimisation to maintain a constant maximum IUCT along the tool path. [Submitted 17 April 2024; Accepted 27 August 2024]

Keywords: ball end milling; cutter workpiece engagement region; CWER; undeformed chip thickness; tooth trajectory; circular interpolation; adaptive feed rate.

DOI: 10.1504/IJMR.2024.143418

International Journal of Manufacturing Research, 2024 Vol.19 No.3, pp.266 - 293

Received: 17 Apr 2024
Accepted: 27 Aug 2024
Published online: 19 Dec 2024 *

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Title: Analytical modelling of the cutter workpiece engagement and the undeformed chip thickness for circular ball end milling path for adaptive feed rate

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