Mathematical Modeling of Laser Beam Welding

本课题研究的是高能束焊接工艺。 的 第一个目标是建立一个现实的数学模型， 包括了所有重要的物理学--锁眼，非平衡态 蒸发和随后的蒸汽膨胀， 液体区域和固体区域内的传导。 第二 目的是发展一种更有效的数值格式， 计算 为实现这一目标，将采用模块化方法， 就业。 最适合每个特定区域的不同方法是 以供使用。 在固体区域内，边界元法将 可以用来求解热传递。 边界层理论将是 应用于模拟熔融区内的对流。 的 非平衡蒸发将用Mott-Smith型模型来模拟 溶液 随后的蒸汽膨胀将由一个- 三维气体动力学方程 这些不同的地区将成为 通过沿固体沿着匹配边界条件组合在一起， 液体和液体-蒸汽界面。 边界匹配 沿着固液界面的条件决定了其形状， 从而形成熔融区域的形状。 边界匹配 沿着液-气界面的条件决定了小孔 形状 预计这种技术将是计算效率高的 并且将提供对焊缝熔深的更现实的预测， 熔体形状、冷却速度和热影响区。 将进行实验以验证数学模型。

This project deals with the process of high energy beam welding. The first objective is to develop a realistic mathematical model which includes all of the important physics -- keyholing, nonequilibrium vaporization and subsequent vapor expansion, convection within the liquid region, and conduction within the solid region. The second objective is to develop a more efficient numerical scheme for computation. To achieve this objective, a modular approach will be employed. Different methods best suited for each specific region are to be used. Within the solid region the boundary element method will be used to solve for the heat transfer. Boundary layer theory will be applied to model the convection within the melt region. The nonequilibrium vaporization will be modeled with a Mott-Smith type solution. The subsequent vapor expansion will be modeled by a one- dimensional gas dynamic equation. These different regions are to be combined together by matching boundary conditions along the solid- liquid and liquid-vapor interfaces. The matching of boundary conditions along the solid-liquid interface determines its shape, hence the shape of the molten region. The matching of boundary conditions along the liquid-vapor interface determines the keyhole shape. It is expected that this technique will be computationally efficient and will provide more realistic predictions of the weld penetration, the molten shape, the cooling rate and the heat affected zone. Experiments will be performed to verify the mathematical model.