Laser Beam Welding
|Introduction||Solve the PDE Model|
|Heat Transfer Model||Post-processing and Visualization|
|Initial and Boundary Conditions|
Laser beam welding (LBW) is a welding technique used to combine metals or thermoplastics. The laser beam provides concentrated, intense energy that heats up the materials at the welding location, and the parts melt together. In this example two pieces of steel are to be welded together horizontally to form a larger plate. A laser beam follows the edges to be welded and traverses the steel pieces for the time period of . The model and material data are taken from [1, p. 114].
The evolution of the temperature field during the welding process is simulated with a heat transfer model. For a successful welding, the maximum temperature at each time step must be above the melting point of the material used, in this case of steel at .
Once the object is welded after heat continues to escapes through the objects' surfaces by radiation to the surrounding area, and the plate will cool down towards the ambient temperature . We can inspect the cooling process by calculating the time required to drop the plate temperature below a specific temperature .
The symbols and corresponding units used here are summarized in the Nomenclature section.
Please refer to the information provided in "Heat Transfer" for a more general theoretical background for heat transfer analysis.
The heat equation (1) is used to solve for the temperature field in a heat transfer model:
In order to get a good result, a finer than the default grid is used for the mesh generation. Here we set the max edge length to be , which means that there will be at least one hundred elements in the (length) and (width) directions.
In this model the laser beam provides the thermal energy to weld the steel pieces, and is modeled by the heat source term in the heat equation (2). When applying the laser beam all particles within the focal region are irradiated and heated up simultaneously.
Assume the distribution of the laser power is described by a Gaussian bell shape at a focus point , and is homogeneous in the (thickness) direction. A parameter is introduced to control the degree of the laser concentration. A higher number implies a more concentrated beam.
Next we will solve the heat transfer PDE model with NDSolve.
See this note about improving the visual quality of the animation.
During the welding process: , the maximum temperature arises and exceeds the melting point , which confirms the effectiveness of the laser welding. For the joined steel plate gradually cools down by radiating to the surrounding, and drops below the melting point at .