3.5 Numerical Method
83
the rear wall (ϕ = 180°). Therefore, the center of the laser beam is not at the center
of keyhole, but near the front wall of keyhole.
3.5.1.2 Solution for Energy Absorption Based on Fresnel Absorption
According to the established physical model for the energy interaction on laserkeyhole wall, it is believed that the energy interaction mechanism between laser
and keyhole is mainly the primary and multiple reflection Fresnel absorption. At
present, the scholars at home and abroad in the field of laser/electron beam welding
mainly use the ray tracing method to calculate and determine the Fresnel absorption
coefficients of the keyhole wall.
Although some scholars at home and abroad have studied the Fresnel multiple
reflection absorption mechanism of the keyhole wall surface by using ray tracing
method, in most of these studies, it was assumed that the keyhole is of cone or other
simple shapes. In the actual laser welding process, the shape of the keyhole is very
complex. When the keyhole closes to produce bubbles or spatters, the topological
shape of the keyhole will change dramatically. Therefore, in order to simulate the
complicated transient evolution process of the keyhole, the established ray tracing
method must have high robustness. In addition, in order to ensure the accuracy of
numerical solution, the laser needs to be subdivided into a sufficient number of small
rays during ray tracing calculation, but the calculation speed of ray tracing calculation
will be reduced without doubt. For this reason, certain algorithm skills must be used
to guarantee the ray tracing computational efficiency in the computational process
of pore morphology evolution when mobile laser welding is carried out. Based on
the above two considerations, a fast and robust ray tracing method is proposed and
implemented in this chapter. At the same time, several examples are designed to
logically verify the rationality of the method.
(1) Laser beam subdivision
To calculate the energy density of the keyhole wall by using ray tracing method,
the laser beam needs to be subdivided first, and then the Fresnel absorption between
each beam and the keyhole wall is calculated to obtain the aggregate value.
Considering the feasibility of calculation, the following beam subdivision method
is put forward: assuming that the laser beam is incident on the surface of the material
along a certain direction in the coordinate system (z-axis direction by default), since
most of the energy is concentrated within 1–2 times the radius of the beam, each
difference grid within the beam radius can be divided into several equal parts, each
of which can be regarded as a small beam, and the energy of each beam is the average
area of the laser energy on the equally divided difference grid, i.e. the energy density
I’ of each beam after subdivision is:
I
=
¨
I 0 (r, z)ds/
¨
ds
(3.69)
83
the rear wall (ϕ = 180°). Therefore, the center of the laser beam is not at the center
of keyhole, but near the front wall of keyhole.
3.5.1.2 Solution for Energy Absorption Based on Fresnel Absorption
According to the established physical model for the energy interaction on laserkeyhole wall, it is believed that the energy interaction mechanism between laser
and keyhole is mainly the primary and multiple reflection Fresnel absorption. At
present, the scholars at home and abroad in the field of laser/electron beam welding
mainly use the ray tracing method to calculate and determine the Fresnel absorption
coefficients of the keyhole wall.
Although some scholars at home and abroad have studied the Fresnel multiple
reflection absorption mechanism of the keyhole wall surface by using ray tracing
method, in most of these studies, it was assumed that the keyhole is of cone or other
simple shapes. In the actual laser welding process, the shape of the keyhole is very
complex. When the keyhole closes to produce bubbles or spatters, the topological
shape of the keyhole will change dramatically. Therefore, in order to simulate the
complicated transient evolution process of the keyhole, the established ray tracing
method must have high robustness. In addition, in order to ensure the accuracy of
numerical solution, the laser needs to be subdivided into a sufficient number of small
rays during ray tracing calculation, but the calculation speed of ray tracing calculation
will be reduced without doubt. For this reason, certain algorithm skills must be used
to guarantee the ray tracing computational efficiency in the computational process
of pore morphology evolution when mobile laser welding is carried out. Based on
the above two considerations, a fast and robust ray tracing method is proposed and
implemented in this chapter. At the same time, several examples are designed to
logically verify the rationality of the method.
(1) Laser beam subdivision
To calculate the energy density of the keyhole wall by using ray tracing method,
the laser beam needs to be subdivided first, and then the Fresnel absorption between
each beam and the keyhole wall is calculated to obtain the aggregate value.
Considering the feasibility of calculation, the following beam subdivision method
is put forward: assuming that the laser beam is incident on the surface of the material
along a certain direction in the coordinate system (z-axis direction by default), since
most of the energy is concentrated within 1–2 times the radius of the beam, each
difference grid within the beam radius can be divided into several equal parts, each
of which can be regarded as a small beam, and the energy of each beam is the average
area of the laser energy on the equally divided difference grid, i.e. the energy density
I’ of each beam after subdivision is:
I
=
¨
I 0 (r, z)ds/
¨
ds
(3.69)