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3D milling modeling: mechanical actions, strains, strain rates and temperature calculations in the three cutting zones

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Abstract

Analytical and semi-analytical modelling of manufacturing processes involving material removal are of great interest to scientists and industrialists. With this type of modelling, we are able to identify optimal cutting parameters based on geometric and thermomechanical quantities, without having to carry out experimental trials or costly simulations (thus saving time and reducing costs). Compared with other machining techniques, milling involves additional complexities arising from the variation in geometric parameters in the machining configuration and in kinematic parameters when operational. This paper presents a new 3D modelling analysis applied to milling, which takes into account phenomena generated by the three-dimensional kinematics of the process. To complete this thermomechanical approach to cutting, improvements have been made to a basic model configuration. The model that has been developed can now map strains, strain rates, stresses and temperatures along the cutting edge, in the primary, secondary and tertiary shear zones. Forces and cutting moments at the theoretical tool tip are estimated at a local then a global scale, and compared with experimental results from previous work.

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Abbreviations

x c , y c :

Coordinates of a point in the secondary shear zone.

a p ′ :

Apparent depth of cut (m.m i n − 1).

d a :

depth of plastic deformation zone (m m).

f :

Feed rate (m m).

f z :

Tooth feed rate (m m.t o o t h − 1).

r a :

Cutting edge radius (m m).

r β :

Tool nose radius (m m).

α 0 :

Clearance angle (∘).

ϕ :

Shear angle (∘).

γ 0 :

Rake angle (∘).

δ.t 2 :

Thickness of shear band in the secondary shear zone (m m).

α.l c :

Length of shear contact along rake face (m m).

P s1 , P s2 :

Surface power density above and below stagnation point (W.m − 2).

σ e q,S1′ , σ e q,S2′ :

Equivalent stress above and below stag-nation point (M P a).

\({\dot \varepsilon _{eq,S_{1}^{\prime }}}\) , \({\dot \varepsilon _{eq,S_{2}^{\prime }}}\) :

Overall strain rate above and below stag-nation point (s − 1).

h m (𝜃 1) , h m (𝜃 2):

Instantaneous cutting feed for two angle positions 𝜃 1 and 𝜃 2(m m).

ΔT :

Temperature difference (∘ C).

T S S Z :

Temperature in the secondary shear zone (∘ C).

V c h i p :

Chip speed along to cutting edge (m.s − 1).

V c :

Cutting speed (m.m i n − 1).

V g :

Sliding speed of the chip along to cutting edge (m.s − 1).

V S :

Sliding speed in the primary shear zone (m.s − 1).

V t :

Speed of material perpendicular to cutting edge (m.s − 1).

V z :

Speed of material parallel to cutting edge (m.s − 1).

K t h :

Thermal conductivity \(\left ( {W.{m^{ - 1}}.^{\circ } {C^{ - 1}}} \right )\).

a :

Thermal diffusivity \(\left ( {m^{2}.{s^{ - 1}}} \right )\).

d l i :

Elementary length of heat source (m).

R i and R i ′ :

Distance between point M and primary heat source and image respectively.

φ2′ :

Density of heat flux (W.m − 2).

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Authors and Affiliations

  1. University of Bordeaux, I2M UMR 5295, 351 cours de la Libération, 33400, Talence, France

    Wadii Yousfi, Olivier Cahuc, Raynald Laheurte & Philippe Darnis

  2. Arts et Métiers ParisTech, I2M UMR 5295, 351 cours de la Libération, 33400, Talence, France

    Madalina Calamaz

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  1. Wadii Yousfi
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  2. Olivier Cahuc
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  3. Raynald Laheurte
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  4. Philippe Darnis
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  5. Madalina Calamaz
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Correspondence to Wadii Yousfi.

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Yousfi, W., Cahuc, O., Laheurte, R. et al. 3D milling modeling: mechanical actions, strains, strain rates and temperature calculations in the three cutting zones. Int J Adv Manuf Technol 95, 1931–1940 (2018). https://doi.org/10.1007/s00170-017-1351-5

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