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An equivalent geometry model for turning tool with nose and edge radii

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Abstract

In this study, an equivalent tool geometry was presented, while taking into account the cutting-tool nose and edge radii. The main idea consists in considering that the equivalent geometry induces the same cutting force components as the real tool. In this context, equivalent cutting angle, equivalent direction angle, equivalent uncut chip thickness, and equivalent depth of cut are defined for the new tool geometry. A dual contact at the tool-chip interface, sticking and sliding zones, is considered in the developed thermomechanical model. The influences of the nose and edge radii on the cutting performances are studied. A well agreement was found between analytical and experimental results for different cutting conditions. It is underlined that feed and radial forces are the most sensitive components to nose and edge radii. The proposed equivalent tool has great potential for other applications such as tool wear studying while considering coatings and chip breaker.

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Abbreviations

A, B, n, m, v :

constants of Johnson–Cook Constitutive law

\( {b}_0^{eq} \) :

equivalent width of cut, mm

C 0 :

constant of Oxley

f 0 :

feed rate, mm/rev

F c, F f, F r :

cutting force components, N

h :

thickness of the shear band on the primary shear plane, mm

h c :

length of linear contact at the tool-chip interface, mm

h r :

length of circular contact at the tool-chip interface, mm

h p :

length of the sticking zone at the tool-chip interface, mm

\( {l}_c^{\mathrm{eq}} \) :

equivalent contact length at the tool-chip interface, mm

L AE :

length of the shear plane, mm

N s, T s :

normal and tangential forces at the primary shear zone, N

N hc, N hr :

normal forces at the rake face of the real tool, N

T hc, T hr :

tangential forces at the rake face of the real tool, N

N′c :

normal force at the rake face of the equivalent tool, N

T′c :

tangential force at the rake face of the equivalent tool, N

T int :

average temperature at the tool-chip interface, K

T chip :

average temperature of the chip, K

T m :

melting temperature, K

T max :

maximum variation of temperature in the chip, K

T sh :

average temperature at the primary shear plane, K

p 0 :

depth of cut, mm

\( {p}_0^{eq} \) :

equivalent depth of cut, mm

σ 0 :

maximum hydrostatic pressure at the tool-tip, MPa

σ A :

hydrostatic pressure at the beginning of the shear plane, MPa

σ E :

hydrostatic pressure at the endpoint of the shear plane, MPa

r β :

cutting edge radius, mm

r ε :

nose radius, mm

S real :

real uncut chip area, mm2

S sh :

cross-section on the primary shear plane, mm2

t 1 :

uncut chip thickness, mm

\( {t}_1^{eq} \) :

equivalent uncut chip thickness, mm

t 2 :

chip thickness, mm

V c :

cutting speed, m/min.

V sh :

shear velocity, m/min

α n :

normal clearance angle, °

γ n :

normal rake angle, °

\( {\gamma}_n^{eq} \) :

equivalent normal rake angle, °

γ sh :

strain shear

ε sh :

equivalent strain

κ r :

edge direction angle, °

\( {\kappa}_r^{eq} \) :

equivalent edge direction angle, °

λ s :

inclination angle of the cutting edge, °

λ ap :

apparent friction angle, °

ηc :

chip flow angle, °

ηsh :

shear direction angle, °

μ sl :

sliding friction coefficient

μ ap :

apparent friction coefficient

τ f :

shear yield stress, MPa

τ sh :

shear stress, MPa

ϕ n :

normal shear angle, °

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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, Route Soukra Km 3,5-B.P, 1173-3038, Sfax, Tunisia

    Hassen Khlifi, Lefi Abdellaoui & Wassila Bouzid Sai

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  1. Hassen Khlifi
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  2. Lefi Abdellaoui
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  3. Wassila Bouzid Sai
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Correspondence to Hassen Khlifi.

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Khlifi, H., Abdellaoui, L. & Bouzid Sai, W. An equivalent geometry model for turning tool with nose and edge radii. Int J Adv Manuf Technol 103, 4233–4251 (2019). https://doi.org/10.1007/s00170-019-03787-y

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