论文标题
粉末床融合应用的移动热源的梯度模型
Gradient models of moving heat sources for powder bed fusion applications
论文作者
论文摘要
在本文中，我们得出了在传热梯度理论中移动热源的准平台问题的封闭形式解决方案。该理论可以从两个温度模型正式推导，并且可以将其视为具有第四阶控制方程的Guyer-Krumhansl模型的广义变体。我们表明，考虑到梯度理论的变体允许为移动点和线热源获得有用的无奇异溶液，该解决方案可用于对激光粉末床融合过程中熔体池形状的精制分析。派生的解决方案包含单个额外的长度比例参数，这些参数可能与粉末床的平均颗粒大小有关。也就是说，我们表明开发的梯度模型可以描述熔体池深度的减小，而粉末颗粒的大小的增加，这在实验中观察到。我们还得出了无量纲关系，可用于对不同材料的模型长度比例参数的实验识别。基于考虑理论中的绿色功能方法，还得出了高斯激光束的半分析溶液。
In this paper, we derive closed form solutions for the quasi-stationary problems of moving heat sources within the gradient theory of heat transfer. This theory can be formally deduced from the two-temperature model and it can be treated as a generalized variant of the Guyer-Krumhansl model with the fourth order governing equation. We show that considered variant of the gradient theory allows to obtain a useful singularity-free solutions for the moving point and line heat sources that can be used for the refined analysis of the melt pool shape in the laser powder bed fusion processes. Derived solutions contain single additional length scale parameter that can be related to the mean particles size of the powder bed. Namely, we show that developed gradient models allow to describe the decrease of the melt pool depth with the increase of the powder's particles size that was observed previously in the experiments. We also derive the dimensionless relations that can be used for the experimental identification of the model's length scale parameter for different materials. Semi-analytical solution for the Gaussian laser beam is also derived and studied based on the Green function method within the considered theory.
