中国科学院力学研究所机构知识库

激光熔化沉积（Laser melting deposition, LMD）是一种以激光为热源，基于分层制造原理将数字模型逐层加工成三维实体的先进制造技术，目前已经被广泛应用于航空航天、汽车制造、生物医疗等领域。沉积过程中，金属材料在激光的辐射下熔化，形成熔池，冷却、快速凝固成形。熔池是金属增材制造瞬态变化的基本单元，其几何尺寸直接影响打印件的宏观尺寸和微结构，进而影响成形件的力学性能。对熔池几何尺寸的精准预测能够指导工艺参数的选择，从而为制备高精度、高性能打印件提供理论依据。但是，熔池的形成是一个短时、剧烈而复杂的非线性过程，在目前条件下建立精准的与实际熔池相匹配的物理模型对其尺寸进行预测是一项非常困难的任务，因此有必要开发数据驱动的统计学或半定量模型来指导、协助实时监测与反馈控制系统，以获得更加精准的成形结构件。本文针对LMD，通过机器学习和量纲分析建立了较高精度的熔池几何尺寸预测模型。全文的主要研究内容如下：

首先，通过机器学习方法建立了熔池几何尺寸的预测模型。建立了三个结构为“3-4-1”的误差反向传播（Backpropagation, BP）神经网络，通过改变成形过程的三个关键工艺参数（激光功率、扫描速度、送粉速率）对LMD-316L不锈钢材料的熔池的尺寸（包含熔池高度即熔高、熔池深度即熔深、熔池宽度即熔宽）进行了预测，引入了L2正则化和早停法防止模型过拟合。结果表明，BP神经网络模型预测精度较高，三个预测模型的平均相对误差分别为7.6%、8.82%和2.06%，且兼具较高的泛化能力。

其次，通过量纲分析方法对LMD的物理过程进行了分析，建立了适用于多种材料的熔池几何尺寸预测模型。该模型将熔池的形成过程分为能量输入和质量（粉末）输入两部分，用Π定理得到了影响熔池几何尺寸的无量纲数。利用LMD进行了316L不锈钢和Inconel 625两种材料的单道成形实验，根据单道成形实验结果得到了无量纲数与无量纲熔池总高和熔高之间的定量关系，其中模型线性回归的决定系数分别为0.86和0.89，这表明利用量纲分析方法实现了对多材料熔池尺寸较高精度的预测。

最后，讨论了熔高预测模型的必要性、准确性和实用性。本文进行了单道多层薄壁熔高实验，验证了高精度的熔高预测模型能指导LMD层间抬高量的选择，验证了熔高预测的必要性。采用了新的工艺参数组合，进行了单道多层打印，将实际每层熔高和预测值进行比较，最终两个预测模型的平均相对误差分别为1.5%和3.2%，说明预测模型不仅能较为准确地预测熔池几何尺寸，指导工艺参数的选择，还能推广应用于复杂的实际打印模式。

综上所述，本文分别建立了精度和泛化能力较高的BP神经网络模型和精度较高地跨材料量纲分析模型，利用该模型对LMD的熔池几何尺寸进行了预测，预测模型能够指导工艺参数的选择，对制备高质量、高性能的打印件有重要意义。另外，本文还为建立基于数据驱动的模型来处理LMD中复杂的非线性问题提供了新思路。

Laser melting deposition (LMD) is an advanced technology which uses laser as a heat source to process digital models into three-dimensional solid parts layer by layer based on the principle of layered manufacturing. It has been widely applied in many fields such as aerospace, automotive manufacturing, and biomedical engineering. During the process of deposition, metal materials melt under the laser radiation to form the melt pool, which is cooled and rapidly solidified. Melt pool is the basic unit of transient change in metal additive manufacturing, and its geometry affects the macroscopic dimension and microstructure of the printed parts, which in turn affect the performance. Predicting the geometry of the melt pool can guide the selection of process parameters and provide a theoretical basis for the production of high-precision and high-performance printed parts. However, the formation of the melt pool is a short-term, intense, and complex nonlinear process, making it difficult to establish physical models which match to the actual melt pool to predict its geometry. Therefore, it is necessary to develop data-driven statistical or semi-quantitative models to guide and assist real-time monitor and feedback control systems to obtain more accurate formed parts. This paper focus on laser melting deposition (LMD), establishes a high-precision melt pool geometry predictive model using machine learning and dimensional analysis. The content of this paper is as follows.

Firstly, the melt pool geometry predictive model was established by using machine learning method. Three error backpropagation (BP) neural networks with ‘3-4-1’ structure were established. Three LMD process parameters (laser power, scanning speed, and powder feeding rate) were used to predict melt pool geometry (melt pool height, depth and width), respectively. L2 regularization and early stopping were introduced to avoid overfitting problem. The result shows that the BP neural network model had a relatively high predictive accuracy, with relative errors of 7.6%, 8.82% and 2.06%, respectively. Finally, we obtained melt pool geometry predictive model with high generalization ability.

Secondly, the physical process was analyzed by using dimensional analysis and the multi-material melt pool geometry predictive model was established. The melt pool formation process were divided into two parts: energy delivery and mass (powder) delivery. Based on the proper parameters selected by two processes, the Pi theorem was used for dimensional analysis. Single-track forming experiments were conducted using LMD for 316L stainless steel and Inconel 625. The quantitative relationships between dimensionless numbers and normalized melt pool total height and height were established, with determination coefficients of 0.86 and 0.89, respectively. The prediction of multi-material melt pool geometry was achieved using dimensional analysis.

Finally, the necessity, accuracy, and practicality of the melt pool height predictive models were discussed. In this paper, multilayer single-path experiments were conducted to demonstrate the predictive models could guide the selection of robot lifting height. The necessity of height predictive models were verified. A new set of process parameters were selected for multilayer single-path printing, and the actual height of each layer was compared with the predictive values of the predictive model. The average relative errors of the two predictive models are 1.5% and 3.2%, indicating that the predictive models can not only accurately predict the geometry of the melt pool and guide the selection of process parameters, but can also be widely applied to complex printing patterns.

To sum up, this paper has established BP neural network model with relative high precision and high generalization ability and multi-material dimensional analysis model with relatively high accuracy. Based on multiple process parameters, the predictive models can predict the melt pool geometry in LMD process. The predictive models can guide the selection of process parameters to enable the preparation of high-quality and high-performance printed parts. In addition, this paper also provides new ideas for building data-driven models to deal with complex nonlinear problems in LMD.