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Prediction of turning performances using an equivalent oblique cutting model

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Abstract

The main purpose of this paper is to predict the performances of the turning process using an equivalent oblique cutting model. Based on the real tool, an equivalent cut geometry is performed considering the effects of nose and edge radii. Edge direction and normal cutting angles, uncut chip thickness, and depth of cut were redefined by their equivalent values and then used as new inputs. Turning performances, such as cutting force components, cutting temperatures, and tribology parameters at the tool/chip interface, were predicted over a wide range of cutting conditions. The position of the maximum temperature at the tool/chip interface and its value are determined by solving the heat equation in the chip using the Finite Difference Method. Different assumptions were concluded, and the thermal problem is simply resolved using Laplace transform. It was determined that the maximum tool/chip interface temperature is situated far from the cutting edge about \(0.317{\mathrm{l}}_{\mathrm{c}}\). It was also found that the partition coefficient is strongly related to sliding speed and it decreases about 20% when chip velocity increases from 1 to 5 m/s. Acceptable agreement was concluded between experimental cutting force components and those predicted from the equivalent oblique cutting model. It can thus be concluded that the equivalent model of cut is highly recommended to predict turning performances.

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Availability of data and materials

All data and materials used to produce the results in this article can be obtained upon request from the corresponding authors.

Availability of code

Code used to produce the results in this article can be obtained upon request from the corresponding authors.

Abbreviations

\({a}_{p}\) :

Cutting depth [mm]

\({a}_{p}^{eq}\) :

Equivalent depth of cut [mm]

\({c}^{eq}\) :

Equivalent work material specific heat [J kg−1 K−1]

\(f\) :

Feed rate [mm/rev]

\({\tilde{f }}\) :

Average coefficient of friction at tool–chip interface

\({{\tilde{f }}}^{eq}\) :

Equivalent average coefficient of friction at tool–chip interface

\({F}_{c}^{eq}\) :

Equivalent tangential force [N]

\({F}_{f}^{eq}\) :

Equivalent feed force [N]

\({F}_{r}^{eq}\) :

Equivalent radial force [N]

\({F}_{sh}^{eq}\) :

Equivalent shearing force [N]

\({k}^{eq}\) :

Equivalent work material thermal conductivity [Wm−1 K−1]

\({l}_{c}^{i}\) :

Tool–chip contact length for element i [mm]

\({p}_{0}^{eq}\) :

Equivalent of maximum normal stress at tool–chip contact [N/mm2]

\({r}_{\beta }\) :

Cutting edge radius [mm]

\({r}_{\varepsilon }\) :

Tool-nose radius [mm]

\({t}_{1}\) :

Uncut chip thickness [mm]

\({t}_{2}^{eq}\) :

Equivalent chip thickness [mm]

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

Workpiece melting temperature [K]

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

Initial workpiece temperature [K]

\({T}_{sh}^{eq}\) :

Equivalent shearing temperature [K]

\({\tilde{T }}_{int}^{eq}\) :

Average tool–chip interface temperature [K]

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

Cutting speed [m/min]

\({V}_{chip}^{eq}\) :

Equivalent chip velocity [mm/s]

\({V}_{sh}^{eq}\) :

Equivalent shearing velocity [mm/s]

\({\alpha }_{n}\) :

Normal rake angle [°]

\(\delta\) :

Secondary shear zone thickness ratio to chip thickness

\({\phi }_{n}^{eq}\) :

Equivalent normal shear angle [°]

\({\gamma }_{sh}^{eq}\) :

Equivalent shear strain

\({\dot{\gamma }}_{sh}^{eq}\) :

Equivalent shear strain rate

\({\eta }_{c}^{eq}\) :

Equivalent chip flow angle [°]

\({\eta }_{sh}^{eq}\) :

Shearing direction angle [°]

\({\kappa }_{r}\) :

Edge direction angle [°]

\({\kappa }_{r}^{eq}\) :

Equivalent edge direction angle [°]

\({\lambda }_{s}\) :

Edge inclination angle [°]

\({\rho }^{eq}\) :

Equivalent work material density [kg/m3]

\({\tau }_{sh}^{eq}\) :

Equivalent shear stress [N/mm2

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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 UGPMM, ENIS, Sfax, Tunisia

    Lefi Abdellaoui, Hassen Khlifi & Wassila Bouzid Sai

  2. Université de Carthage (University of Carthage), IPEST, 2078, La Marsa, Tunisia

    Lefi Abdellaoui

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  1. Lefi Abdellaoui
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All the above mentioned authors contributed to the manuscript equally.

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Correspondence to Lefi Abdellaoui.

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Abdellaoui, L., Khlifi, H. & Bouzid Sai, W. Prediction of turning performances using an equivalent oblique cutting model. Int J Adv Manuf Technol 120, 7735–7753 (2022). https://doi.org/10.1007/s00170-022-09243-8

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