Heat and Mass Transfer

, Volume 49, Issue 1, pp 129–145 | Cite as

A new heat transfer analysis in machining based on two steps of 3D finite element modelling and experimental validation

  • B. Haddag
  • T. Kagnaya
  • M. Nouari
  • T. Cutard


Modelling machining operations allows estimating cutting parameters which are difficult to obtain experimentally and in particular, include quantities characterizing the tool-workpiece interface. Temperature is one of these quantities which has an impact on the tool wear, thus its estimation is important. This study deals with a new modelling strategy, based on two steps of calculation, for analysis of the heat transfer into the cutting tool. Unlike the classical methods, considering only the cutting tool with application of an approximate heat flux at the cutting face, estimated from experimental data (e.g. measured cutting force, cutting power), the proposed approach consists of two successive 3D Finite Element calculations and fully independent on the experimental measurements; only the definition of the behaviour of the tool-workpiece couple is necessary. The first one is a 3D thermomechanical modelling of the chip formation process, which allows estimating cutting forces, chip morphology and its flow direction. The second calculation is a 3D thermal modelling of the heat diffusion into the cutting tool, by using an adequate thermal loading (applied uniform or non-uniform heat flux). This loading is estimated using some quantities obtained from the first step calculation, such as contact pressure, sliding velocity distributions and contact area. Comparisons in one hand between experimental data and the first calculation and at the other hand between measured temperatures with embedded thermocouples and the second calculation show a good agreement in terms of cutting forces, chip morphology and cutting temperature.


Heat Flux Heat Diffusion Thermal Boundary Condition Chip Morphology Interface Heat Transfer Coefficient 
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List of symbols

Cutting parameters


Cutting speed (m/min)


Feed rate (mm/tr)


Depth of cut (mm)


Approach angle (°)


Tool-rake angle (°)


Inclination angle (°)


Clearance angle (°)


Cutting cut force component (N)


Feed force component (N)


Depth of cut force component (N)


Resultant cutting force (N)

Mechanical quantities


Cauchy stress tensor (MPa)


Body force density vector (N/m3)

\( \ddot{u} \)

Acceleration vector (m/s2)


Material density (kg/m3)


Young modulus (GPa)


Poisson’s ratio


Initial uniaxial tension stress at reference equivalent plastic strain-rate and reference temperature of the workmaterial (MPa)


Strain hardening parameter of the workmaterial (MPa)


Strain hardening exponent parameter of the workmaterial


Strain-rate sensitivity parameter of the workmaterial


Temperature sensitivity parameter of the workmaterial

\( \bar{\varepsilon }^{p} \)

von Mises equivalent plastic strain

\( \dot{\bar{\varepsilon }}^{p} \)

von Mises equivalent plastic strain-rate

\( \dot{\bar{\varepsilon }}_{0} \)

Reference equivalent plastic strain-rate

\( \bar{\sigma } \)

von Mises equivalent stress (MPa)


Normal friction stress (MPa)


Shear friction stress (MPa)


Friction coefficient


Shear stress limit (MPa)

\( \bar{\tau }_{f} \)

Average sliding stress at the tool-chip interface (MPa)

\( \bar{\dot{\gamma }} \)

Average sliding velocity at the tool-workpiece interface (m/s)


Local sliding stress at the tool-workpiece interface (MPa)

\( \dot{\gamma }\left( {x,y} \right) \)

Local sliding velocity at the tool-workpiece interface (m/s)


Displacement along the x axis


Displacement along the y axis


Displacement along the z axis

Thermal quantities


Temperature (°C)


Reference ambient temperature (°C)


Workmaterial melting temperature (°C)


Environment temperature (°C)


Tool temperature (°C)


Toolholder temperature (°C)


Interface workpiece temperature (°C)


Interface tool temperature (°C)


Thermal conductivity (W/m/°C)


Specific heat capacity (J/kg/°C)


Thermal expansion (µm/m/°C)


Plastic work conversion factor (Taylor-Quinney factor)


Fraction of the friction energy conducted into the tool


Heat transfer coefficient for the tool-wokpiece interface (kW/m2/°C)


Heat transfer coefficient for the tool-environment interface (W/m2/°C)


Heat transfer coefficient for the toolhorder-tool interface (W/m2/°C)

\( \dot{q}_{v} \)

Volumetric heat generation in the workmaterial (W/m3)

\( \dot{q}_{p} \)

Volumetric heat generation due to plastic work (W/m3)

\( \dot{q}_{f} \)

Frictional heat flux at the tool-workpiece interface (W/m2)

\( \dot{q}_{c} \)

Heat conduction flux at the tool-workpiece interface (W/m2)

\( \dot{q}_{ \to tool} \)

Heat flux going into the tool at the tool-workpiece interface (W/m2)

\( \dot{q}_{ \to workpiece} \)

Heat flux going into the workpiece at the tool-workpiece interface (W/m2)

\( \dot{q}_{ \to env} \)

Heat flux at the tool-environment interface (W/m2)

\( \dot{q}_{ \to hold} \)

Heat flux at the toolholder-tool interface (W/m2)

\( \bar{\dot{q}}_{ \to tool} \)

Applied uniform heat flux on the tool rake face (W/m2)

\( \dot{q}_{ \to tool} \left( {x,y} \right) \)

Applied non-uniform heat flux on the tool rake face (W/m2)


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Laboratoire d’Énergétique et de Mécanique Théorique et AppliquéeUniversité de Lorraine, LEMTA CNRS-UMR 7563, Mines NancySt-Dié-des-VosgesFrance
  2. 2.Mines Albi, ICA (Institut Clément Ader)Université de ToulouseAlbi cedex 09France

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