Abstract Mathematical modelling of the shape-forming process of multi-layer multi-bead parts dealing with (i) a single layer, (ii) inclination angles and (iii) various slopes, is carried out. In the layers-overlapping model, material shortage areas are generated at the edges of layers. To solve the problem, the deposition amount of beads at the edges of the second and above layers should be modified, in association with the parameters applied to fabricate the slope. Various basic inclined components were deposited to validate the proposed mathematical formulation. Findings from the basic experiments were: (i) depositing additional material to compensate for the material shortage areas is necessary for realizing the designed geometries of the layers, (ii) depositing the bead at the layer edges alongside an already-deposited neighboring bead enables a better shape-forming in the case of negative slopes and (iii) the deposition order of beads in a layer has little influence on the shape formation of positive slopes. A complex part was also fabricated as a case study to validate the model and findings in the real-life context. Practical issues with regard to using the model and the solutions to the issues were discussed.

中文翻译：

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基于 GMAW 的平面位置沉积倾斜多层多焊道零件的增材制造

摘要 对处理 (i) 单层、(ii) 倾角和 (iii) 各种坡度的多层多胎圈零件的成形过程进行数学建模。在层重叠模型中，材料短缺区域在层的边缘产生。为了解决这个问题，应该修改第二层及以上层边缘的珠子的沉积量，并结合用于制造斜坡的参数。沉积了各种基本倾斜分量以验证所提出的数学公式。基本实验的结果是：（i）沉积额外的材料以补偿材料短缺区域对于实现层的设计几何形状是必要的，(ii) 将珠粒沉积在与已经沉积的相邻珠粒一起的层边缘，可以在负斜率的情况下形成更好的形状，并且 (iii) 层中珠粒的沉积顺序对正斜率的形状形成几乎没有影响连续下坡。还制作了一个复杂的部分作为案例研究，以在现实生活中验证模型和发现。讨论了有关使用该模型的实际问题和问题的解决方案。