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Finite Difference Method

Generally, the pure theoretical methods only gave us very approximate results,
such as average temperature and temperature distribution along the shear
plane and the tool/chip interface.
Finite difference method can be used to calculate the temperature
distributions in the chip, tool and workpiece. And better results can be
expected because the geometry and boundary conditions of chip, tool and
workpiece, as well as the shape of distributed heat sources can be descripted
well.

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Finite Element Method

Finite element method(FEM) has great potential to calculate the temperature
distributions in the chip, tool and workpiece if the geometry, boundary
conditions and the shape of distributed heat sources become very complicate.The
following diagram is the mesh used by O. A. Tay:

In addition, FEM can be used to calculate the temerature distribution
in either toolholder or machined parts and then to obtain the thermal deformation.

Finally, because an accurate distributed heat source model is
needed in order to obtain a better result in the temperature distribution.
FEM can be naturally coupled with some mechanics model, therefore, predicts
the intensity and distribution of the heat sources.

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Boundary Element Method

Boundary Element Method(BEM) was used in calculating the temperature distribution
in the tool by O. A. Tay. BEM has great potential in reducing solid modeling
to surface modeling. A wide application in this field is undoubtable.