70
3 Coupling Model and Numerical Computation Method of Keyhole and Weld Pool
− →
I
Normalized laser beam direction;
n
Normalized normal vector of the keyhole wall;
ε
Constant related to the laser device and material;
I 0 (r, z)
Energy distribution function of laser beam;
I m (r, z) Remaining energy density of the laser beam after the m reflection.
The constant ε is theoretically determined by the following equation.
ε
2
=
2ε 2
ε 1 +
ε
2
1 + (σ st /ωε 0 )
2
1/2
(3.13)
where:
σ st
Electrical conductivity per unit depth of metallic material;
ε 1 , ε 2
Real component of the metal and plasma dielectric constants;
ε 0
Vacuum transmittance;
ω
Laser angular frequency.
As a matter of fact, ε value is normally determined by trial-and-error method,
which is larger than the theoretical value in general. There are main two reasons for
using the trial-and-error method: ➀ The keyhole wall has an extreme high temperature, close to boiling point, which is likely to affect the Fresnel absorption effect; ➁
The approximation error can be compensated by a large ε value, because the formula
used for calculating the Fresnel absorption is an approximation by itself. For CO 2
laser welding, ε is normally equal to 0.08; for YAG laser, ε is normally equal to
0.2–0.25. Considering the fiber laser has a better beam quality than YAG in general,
this study proposes that for the fiber laser welding, ε can be determined as 0.2–0.5,
which varies with the laser power.
3.3 Free-Surface Tracking Method
The keyhole normally has a changing transient morphology in the laser welding
process, and its shape may even be highly topologically deformed, such as metal
spatter and porosity. In addition, the normal vector and the curvature at any position
of the keyhole wall should be calculated precisely in order to accurately consider the
influence of Fresnel effect and surface tension on the transient behavior of keyhole.
The aforesaid two problems cause great difficulty in choosing a reasonable numerical
method to track the moving surface of transient keyhole.
It is very difficult to use Lagrangian-based surface tracking methods such as
MAC (Mark and Cell) and Front Tracking to deal with the topological deformation
of complex surface. Now, two main surface tracking methods are VOF (Volume
of Fluid) method and Level Set method, with the advantages of high calculation
accuracy, short calculation time and less memory. So, this chapter mainly introduces
the Level Set and VOF methods to track the keyhole free-surface movement.
3 Coupling Model and Numerical Computation Method of Keyhole and Weld Pool
− →
I
Normalized laser beam direction;
n
Normalized normal vector of the keyhole wall;
ε
Constant related to the laser device and material;
I 0 (r, z)
Energy distribution function of laser beam;
I m (r, z) Remaining energy density of the laser beam after the m reflection.
The constant ε is theoretically determined by the following equation.
ε
2
=
2ε 2
ε 1 +
ε
2
1 + (σ st /ωε 0 )
2
1/2
(3.13)
where:
σ st
Electrical conductivity per unit depth of metallic material;
ε 1 , ε 2
Real component of the metal and plasma dielectric constants;
ε 0
Vacuum transmittance;
ω
Laser angular frequency.
As a matter of fact, ε value is normally determined by trial-and-error method,
which is larger than the theoretical value in general. There are main two reasons for
using the trial-and-error method: ➀ The keyhole wall has an extreme high temperature, close to boiling point, which is likely to affect the Fresnel absorption effect; ➁
The approximation error can be compensated by a large ε value, because the formula
used for calculating the Fresnel absorption is an approximation by itself. For CO 2
laser welding, ε is normally equal to 0.08; for YAG laser, ε is normally equal to
0.2–0.25. Considering the fiber laser has a better beam quality than YAG in general,
this study proposes that for the fiber laser welding, ε can be determined as 0.2–0.5,
which varies with the laser power.
3.3 Free-Surface Tracking Method
The keyhole normally has a changing transient morphology in the laser welding
process, and its shape may even be highly topologically deformed, such as metal
spatter and porosity. In addition, the normal vector and the curvature at any position
of the keyhole wall should be calculated precisely in order to accurately consider the
influence of Fresnel effect and surface tension on the transient behavior of keyhole.
The aforesaid two problems cause great difficulty in choosing a reasonable numerical
method to track the moving surface of transient keyhole.
It is very difficult to use Lagrangian-based surface tracking methods such as
MAC (Mark and Cell) and Front Tracking to deal with the topological deformation
of complex surface. Now, two main surface tracking methods are VOF (Volume
of Fluid) method and Level Set method, with the advantages of high calculation
accuracy, short calculation time and less memory. So, this chapter mainly introduces
the Level Set and VOF methods to track the keyhole free-surface movement.