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Analysis of the heat transfer at the tool–workpiece interface in machining: determination of heat generation and heat transfer coefficients

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Abstract

This paper deals with the modelling and identification of the heat exchange at the tool–workpiece interface in machining. A thermomechanical modelling has been established including heat balance equations of the tool–workpiece interface which take into account the heat generated by friction and the heat transfer by conduction due to the thermal contact resistance. The interface heat balance equations involve two coefficients: heat generation coefficient (HGC) of the frictional heat and heat transfer coefficient (HTC) of the heat conduction (inverse of the thermal contact resistance coefficient). Using experimental average heat flux in the tool, estimated for several cutting speeds, an identification procedure of the HGC–HTC couple, involved in the established thermomechanical FE-based modelling of the cutting process, has been proposed, which gives the numerical heat flux equal the measured one for each cutting speed. Using identified values of the HGC–HTC couple, evolution laws are proposed for the HGC as function of cutting speed, and then as function of sliding velocity at the tool–workpiece interface. Such laws can be implemented for instance in a Finite Element code for machining simulations.

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Abbreviations

\(V_{c}\) :

Cutting speed (m/min)

\(f\) :

Feed rate (mm/rev)

\(w\) :

Depth of cut (mm)

\(\alpha\) :

Tool rake angle (°)

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x}\) :

Vector position

\(p_{w}\), \(p_{t}\) :

Points in the workmaterial and tool, respectively

t :

Time or cutting time (s)

\(\Omega_{w}\), \(\Omega_{t}\) :

Workmaterial and tool domains, respectively

\(\partial \Omega_{w}\), \(\partial \Omega_{t}\) :

Workmaterial and tool boundaries, respectively

\(\partial \Omega_{c}\) :

Tool–workpiece contact interface

T :

Temperature (°C)

\(T_{0}\) :

Reference ambient temperature (°C)

\(T_{m}\) :

Workmaterial melting temperature (°C)

\(T_{w}\), \(T_{t}\) :

Temperatures, respectively, of workpiece and tool at the tool–workpiece interface (°C)

\(T_{tool}\) :

Average tool rake face temperature (°C)

\(\lambda\) :

Thermal conductivity (W/m/°C)

\(c_{p}\) :

Specific heat capacity (J/kg/°C)

\(\alpha\) :

Thermal expansion (µm/m/°C)

\(\eta_{p}\) :

Plastic work conversion factor (Taylor-Quinney factor)

\(\beta\) or HGC:

Heat generation coefficient (fraction of the friction energy generated in the tool side)

\(h\) or HTC:

Heat transfer coefficient for the tool–workpiece interface (kW/m2/°C)

\(\eta_{f}\) :

Frictional work conversion factor

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

Volumetric heat generation in the workmaterial (W/m3)

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

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

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

Heat generation by friction at the tool–workpiece interface (W/m2)

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

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

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

Heat flux density in the tool at the tool–workpiece interface (W/m2)

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

Heat flux density in the workpiece at the tool–workpiece interface (W/m2)

\(\dot{Q}_{ \to tool}\) :

Average heat flux in the tool (W)

\(\dot{Q}_{num}\) :

Numerical (from FE) average heat flux in the tool (W)

\(\varvec{\sigma}\) :

Cauchy stress tensor (MPa)

\(f_{v}\) :

Body force density (N/m3)

\(\textit{\"{u}}\) :

Acceleration (m/s2)

\(\rho\) :

Material density (kg/m3)

\(E\), \(\nu\) :

Young modulus (GPa) and Poisson’s ratio

\(A\), \(B\), \(C\), \(m\),\(n\) :

Workmaterial parameters of Johnson–Cook flow stress law

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

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)

\(d\) :

Damage variable

\(\tilde{\varvec{\sigma }}\) :

Effective stress (MPa)

\(\sigma_{n}\) :

Normal friction stress (MPa)

\(\tau_{f}\) :

Shear friction stress (MPa)

\(\mu\) :

Friction coefficient

\(\tau_{\hbox{max} }\) :

Shear stress limit (MPa)

\(V_{s}\) :

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

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Authors and Affiliations

  1. University of Lorraine, Laboratoire d’Energétique et de Mécanique Théorique et Appliquée, LEMTA CNRS-UMR 7563, Mines Albi, Mines Nancy, GIP-InSIC, 27 rue d’Hellieule, 88100 St-Dié-des-Vosges, France

    B. Haddag, S. Atlati & M. Nouari

  2. University of Mohamed I, Equipe de Mécanique et Calcul Scientifique (EMCS), ENSAO, Oujda, Morocco

    S. Atlati & M. Zenasni

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  1. B. Haddag
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  2. S. Atlati
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  3. M. Nouari
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  4. M. Zenasni
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Correspondence to B. Haddag.

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Haddag, B., Atlati, S., Nouari, M. et al. Analysis of the heat transfer at the tool–workpiece interface in machining: determination of heat generation and heat transfer coefficients. Heat Mass Transfer 51, 1355–1370 (2015). https://doi.org/10.1007/s00231-015-1499-1

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