## Numerical Simulation

### 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.

### 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.

### 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.