Directed energy deposition (DED) is a metal additive manufacturing process, where dimensional accuracy and repeatability are traditionally challenging to achieve. Strategies for computationally inexpensive process modelling and fast-response process controls of the laser deposition process are necessary to keep the geometric features close to the required dimensional tolerances. The deposition geometry depends highly on the complex local laser-material interaction and global thermal history of the substrate. In order to control the deposition geometry, an accurate and computationally inexpensive discretized state space thermal history model coupled with an analytical deposition geometry model is developed in this work. The model accounts for the local laser-material interaction using the mass and energy equilibrium equations coupled in a lumped parameter solution, as well as the global thermal history of the product using a state space thermomechanical discretization. In literature, studies have only focused on 1D toolpaths with constant process parameters such as speed, powder feedrate, and laser power. As it is possible to achieve highly complex geometric shapes with additive manufacturing, it is important to have models compatible with 2D/3D complex toolpaths. In this paper, an analytical thermomechanical model and a coupled deposition geometry model for DED process are presented and experimentally validated. As such, the thermal history of the deposited part is predicted throughout the process and the geometric features are predicted for 2D toolpaths.

定向能量沉积（DED）是一种金属增材制造工艺，传统上很难实现尺寸精度和可重复性。为了使几何特征保持在所需的尺寸公差附近，需要用于激光沉积过程的计算上廉价的过程建模和快速响应过程控制的策略。沉积的几何形状在很大程度上取决于复杂的局部激光材料相互作用和衬底的整体热历史。为了控制沉积几何形状，在这项工作中开发了精确且计算成本低的离散状态空间热历史模型以及分析性沉积几何形状模型。该模型使用集总参数解决方案中耦合的质量和能量平衡方程来说明局部激光与材料的相互作用，并使用状态空间热机械离散化说明产品的全局热历史。在文献中，研究仅集中于具有恒定工艺参数（例如速度，粉末进给速度和激光功率）的一维刀具路径。由于可以通过增材制造获得高度复杂的几何形状，因此具有与2D / 3D复杂刀具路径兼容的模型很重要。本文提出了一种用于DED工艺的热力学分析模型和一个耦合的沉积几何模型，并进行了实验验证。这样，在整个过程中将预测沉积零件的热历史，并为2D刀具路径预测几何特征。