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Analytical model of cutting temperature field in workpiece including uncut chip layer

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Abstract

To understand the nature of chip formation in cutting, the study of temperature field in the uncut chip layer of the workpiece is extremely important. In this study, the temperature field for the uncut chip layer is modeled using the heat source projection at different depths of the layer along the cutting speed direction to obtain the different heating times of points at corresponding depths. It is based on the model of the cutting temperature field in the machined surface layer of the workpiece, as proposed in the previous paper of the authors. The temperature distribution in both uncut chip and machined surface layers are thus achieved, and the temperature penetration depths in the machined surface layer are compared with experiment results. The results show that the computed isotherms on the boundary of the uncut chip and machined surface layers are continuous and smooth, indicating that the temperature field model for the uncut chip layer is correct. The temperature field for the nonplanar primary shear plane heat source is also modeled by introducing the curve integral. This is considerably significant in the conduct of further research on the temperature field in micromachining considering size effects and in machining using restricted contact tools, such as groove-type chip breaker tool, double-rake-angled tool, rounded-edge tool, and tool with built-up edge.

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Abbreviations

B :

Fraction of shear plane heat conducted into workpiece

B rubbing :

Fraction of tool flank–workpiece rubbing heat conducted into workpiece

α :

Rake angle (°)

q shear :

Heat liberation intensity in shear plane (W/mm2)

q rubbing :

Heat liberation intensity in tool flank–workpiece rubbing zone (W/mm2)

λ :

Thermal conductivity (W/(mm °C))

F t :

Feed force (N)

F cw :

Frictional force between tool flank and workpiece machined surface (N).

F c :

Cutting force (N)

L :

Shear plane heat source width (mm)

VB :

Width of tool flank–workpiece contact zone (mm)

t c :

Cut depth or undeformed chip thickness (mm)

φ :

Shear angle (°)

w :

Cut width (mm)

V :

Velocity of moving plane heat source or cutting speed (mm/s)

a :

Thermal diffusivity (mm2/s)

μ :

Friction coefficient between tool flank and workpiece machined surface

N th :

Thermal number (=tcV/a)

K 0 :

Modified Bessel function of second kind of order zero

K ω :

Dimensionless coefficient of K0 modification

\( {K}_{\omega}^{shear} \) :

Dimensionless coefficient of K0 modification corresponding to shear plane heat source

\( {K}_{\omega}^{\mathrm{rubbing}} \) :

Dimensionless coefficient of K0 modification form corresponding to tool flank–workpiece rubbing heat source

t :

Heating time (s)

t shear :

Heating time of point M(x, z) caused by shear plane heat source (s)

t rubbing :

Heating time of point M(x, z) caused by tool flank–workpiece rubbing heat source (s)

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Funding

This work is supported by the Major State Basic Research Development Program of China (973 Program, Grant No. 2014CB046704).

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Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yi Gao, Kun Huang & Wenyu Yang

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  1. Yi Gao
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  2. Kun Huang
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  3. Wenyu Yang
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Correspondence to Wenyu Yang.

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Gao, Y., Huang, K. & Yang, W. Analytical model of cutting temperature field in workpiece including uncut chip layer. Int J Adv Manuf Technol 107, 3943–3952 (2020). https://doi.org/10.1007/s00170-020-05260-7

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