Study on sand stacking law based on FDM 3D printing supported by sand
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摘要: 将颗粒(后面统称砂粒)作为3D打印的支撑材料,避免了传统3轴FDM中因去除支撑而损伤工件的后果。为了归纳出该新型FDM 3D打印技术中的堆砂规律,首先采用Plackett-Burman设计物理实验,选取漏斗孔径X1、漏斗高度X2、漏斗水平移动速度X3以及玻璃砂尺寸X4为参数,研究了砂粒的堆积角规律,其次通过DEM仿真分析了不同漏斗孔径下的砂粒的聚集程度变化。结果表明,参数X1和X3显著影响堆积角,且影响为负效应。随着漏斗孔径的增大,砂粒聚集程度提高。因此在砂作支撑的FDM 3D打印中,增大漏斗孔径可以达到抑制砂道堆积角,提高砂粒堆积聚集性的效果,从而提高工件成型质量。
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关键词:
- Plackett-Burman实验 /
- 堆积角 /
- 离散元仿真 /
- 砂粒聚集性
Abstract: Particle(hereafter referred together as sand) can be used as the supporting material of 3D printing, which avoid the damage to the workpiece caused by removing the supporting in traditional 3D printing. For concluding the sand stacking law in the new FDM 3D printing technology, this paper designed the physical experiment to search the law of sand’s angle of repose by Plackett-Burman at first, in which the funnel aperture X1, the funnel height X2, the funnel horizontal moving speed X3 and the glass sand size X4 were selected as parameters. Secondly, the variation of sand’ accumulation degree under different funnel aperture was analysed by DEM simulation. It was found that the aperture of the hopper X1 and the horizontal movingspeed of the hopper X3 significantly affect the angle of repose, and the influence is negative. Besides, sand’s accumulation degree increases with the increase of funnel aperture. Therefore, in 3D printing supported by sand, increasing the funnel aperture, which inhibit the sand’s angle of repose and improve the sand accumulation, can improve the printing quality. -
表 1 Plackett-Burman试验实验设计及结果
序号 X1 X2 X3 X4 宽D/mm 高H/mm 休止角/(°)
$ \alpha =\dfrac{180}{{\text{π}}}\times \mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\dfrac{H}{0.5D} $1 1 −1 1 −1 48.20 11.55 25.61 2 1 1 −1 1 74.55 19.25 27.31 3 −1 1 1 −1 19.60 4.89 26.52 4 1 −1 1 1 47.45 12.23 27.27 5 1 1 −1 1 74.15 19.27 27.46 6 1 1 1 −1 46.95 12.09 27.25 7 −1 1 1 1 19.25 5.12 28.01 8 −1 −1 1 1 19.00 5.22 28.79 9 −1 −1 −1 1 30.00 8.42 29.31 10 1 −1 −1 −1 73.25 19.12 27.57 11 −1 1 −1 −1 29.10 8.13 29.19 12 −1 −1 −1 −1 30.15 8.29 28.81 13 0 0 0 0 39.54 10.12 27.11 表 2 材料属性
材料 密度/$ (\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}) $ 弹性模量/Pa 泊松比 玻璃砂 2 500 5.5×1010 0.25 不锈钢 7 930 1.94×1011 0.247 表 3 接触属性
材料 静摩擦系数 滚动摩擦系数 恢复系数 玻璃砂-玻璃砂 0.71 0.076 0.62 玻璃砂-不锈钢 0.59 0.05 0.6 表 4 仿真参数
仿真参数 数值 时间步长/s 2.886 04×10−6 网格尺寸/m 0.035 仿真时长/s 10 表 5 Plackett-Burman试验结果方差分析
参数 自由度 调整后的偏差平方和 F值 P值 模型 4 9.824 2 4.65 0.031 X1 1 5.548 8 10.50 0.012 X2 1 0.218 7 0.41 0.538 X3 1 3.203 3 6.06 0.039 X4 1 0.853 3 1.62 0.239 注:P<0.01表示极显著,P<0.05表示显著。
α=29.94−0.907X1−0.009X2−0.017 22X3+0.008 89X4 -
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