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Geometric modeling of the rubbing zone limits in 3-axis ball-end milling

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Abstract

In this paper, an analytical study was performed in order to identify the geometry of the rubbing zone between the flank face of the ball-end tool and the workpiece in terms of radius and altitude from the tool tip point. This research revealed an accurate analytical calculation of the limit angles and altitude of the rubbing zone as a function of cutting parameters. The contact of the tool tip with the workpiece has been investigated experimentally by most researchers without a theoretical model. Furthermore, in addition to the inability of the tool tip to remove material, a noticeable effect of the rubbing zone on the topography, the increasing of cutting forces due to the large zone of rubbing, and the rise of the local cutting temperature have to be avoided. The effect of this contact of the tool flank face on the tool geometry, which favors a flank central wear surrounding the tool tip, was also noted. To validate the model, the simulation results of this analytical model were compared to the experimental studies, and a good agreement was noticed.

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Abbreviations

\(M\) :

Point in the intersection between the cutter and the workpiece

\({R}_{W}\) :

The global coordinate system attached to the workpiece

\({R}_{H}\) :

The local coordinate system attached to the spindle of the mill machine

\({R}_{C}\) :

The local coordinate system centered on the cutter

\({N}_{f}\) :

Teeth number of the tool

\(z\) :

The local height of the point M (mm)

\(R\left(z\right)\) :

The local circumference radius of point \(M\), distance of point \(M\) to axis \({Z}_{C}\) (mm)

\(\gamma\) :

The rake angle (°)

\(\alpha\) :

The clearance angle (°)

\({i}_{0}\) :

The helix angle (°)

\(t\) :

The instant time (s)

\(\theta (t)\) :

Instantaneous rotation angle (°)

\(\varphi \left(z\right)\) :

The location angle (°)

\({\varphi }_{d}\) :

The location angle in flank face (°)

\({R}_{d}(z)\) :

The local circumference radius (mm) of point in flank face

\(e\) :

Runout error (mm), offset distance between \({Z}_{H}\) axis and \({Z}_{C}\) axis

\(\rho\) :

The initial eccentricity angle (°), measured at t = 0, between \({Y}_{C}\) axis and \({Y}_{H}\) axis

\(\chi\) :

Oriented angle between flank face and tool path (°)

\({V}_{f}\) :

The feed rate (mm/min)

\({f}_{z}\) :

Feed per tooth per revolution (mm/z)

\({\theta }_{e}(z)\) :

Start rubbing angle of the flank face with non-milled material (°)

\({\theta }_{s}(z)\) :

Finish rubbing angle of the flank face with non-milled material (°)

\({R}_{lim}\) :

Limit effective radius of rubbing zone (mm)

\({z}_{lim}\) :

Limit altitude of rubbing zone (mm)

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Funding

This work is carried out with the support and funding allocated to the Unit of Mechanical and Materials Production Engineering (UGPMM/UR17ES43) by the Tunisian Ministry of Higher Education and Scientific Research.

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Authors and Affiliations

  1. Unité de Génie de Production Mécanique Et Matériaux, ENIS, Université de Sfax, Sfax, Tunisia

    Amine Regaieg, Rami Belguith, Lotfi Sai & Wassila Bouzid

  2. École Polytechnique de Tunisie, EPT, Université de Carthage, Carthage, Tunisia

    Amine Regaieg

  3. LGCgE, FSA de Béthune, Université d’Artois, Arras, France

    Rami Belguith

  4. Institut Préparatoire Aux Etudes d’Ingénieurs de Nabeul, IPEIN, Université de Carthage, Carthage, Tunisia

    Lotfi Sai

Authors
  1. Amine Regaieg
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  4. Wassila Bouzid
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All the above mentioned authors contributed to the manuscript equally.

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Correspondence to Rami Belguith.

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Regaieg, A., Belguith, R., Sai, L. et al. Geometric modeling of the rubbing zone limits in 3-axis ball-end milling. Int J Adv Manuf Technol 125, 5557–5570 (2023). https://doi.org/10.1007/s00170-023-11037-5

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  • DOI: https://doi.org/10.1007/s00170-023-11037-5

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