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摘要: 不同形状金属粉末制品在高速压制下的压制行为不一致，从而导致其相对密度以及致密均匀性发生改变。粉末制品零件多含有锥角结构，在压制过程中，金属粉末的致密化程度会随锥角角度的不同而发生变化。借助离散元PFC3D探究锥形零件在冲击加载下不同角度的相对密度。结果表明，锥角角度在30°～60°之间，相对密度表现为波动式变化，有着多个波峰波谷，但整体呈上升趋势；锥角角度在45°～60°之间，相对密度在波动式变化中达到最大值；当锥角角度大于60°，相对密度会下降。随摩擦系数增大，相对密度减小的同时对小锥角零件影响加大。综合分析发现，45°与60°锥角总会处于相对密度峰值附近，而其均匀度系数也相对其他角度较小，45°为锥角零件的优秀角度，相对密度高且较为均匀。实验验证了模拟结论的准确性，为锥角零件的最佳压制成型提供理论依据。Abstract: Metal powder products with the different shapes have the different pressing behaviors under the high speed pressing, easily leading to the change in relative density and density uniformity. Most of powder products contain the taper angle structure, and the densification degree of metal powders will change with the taper angle in the process of pressing. The relative density of the conical parts at different angles under impact loading was investigated by discrete element software PFC3D in this paper. It is found that, the relative density shows the fluctuating variation with the multiple peaks and troughs when the taper angle is between 30° and 60°, but the overall trend is upward, and the relative density reaches the maximum value in the trough change with the taper angle between 45° and 60°. When the taper angle is greater than 60°, the relative density decreases. With the increase of the friction coefficient, the relative density decreases, and the effect on the small taper angle parts increases. The comprehensive analysis shows that, the taper angles at 45° and 60° are always near the peak relative density, and the uniformity coefficient is smaller than other angles. 45° is the excellent angle for the taper angle parts, showing the higher relative density and uniformity. The experimental results verify the accuracy of the simulation, providing the theoretical basis for the optimal pressing of conical parts.
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Key words:
- taper angle /
- discrete element method /
- relative density /
- impact loading /
- uniformity
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图 2 考虑两颗粒法向重叠量和切向位移且不考虑颗粒表面变形的软球模型
Figure 2. Soft ball model considering without particle surface deformation and with normal overlap and tangential displacement
图 3 软球模型接触力简化处理：（a）法向力；（b）切向力
Figure 3. Simplified treatment of the particle contact force by soft sphere model: (a) normal force; (b) tangential force
图 4 圆锥模型（a）以及圆锥部分相对密度（b）测量示意图
Figure 4. Schematic diagram of the taper model (a) and the measurement of the relative density (b)
图 5 锥角角度与相对密度的变化曲线
Figure 5. Relationship between the taper angle and relative density
图 6 不同锥角下颗粒速度分布规律：（a）30°；（b）45°；（c）60°
Figure 6. Distribution of particle velocity at different taper angles: (a) 30°; (b) 45°; (c) 60°
图 7 不同模壁摩擦系数下相对密度与锥角角度之间的关系
Figure 7. Relationship between relative density and taper angle at different mold wall friction coefficients
图 8 不同材料不同锥角零件的部分试样图
Figure 8. Partial samples of the different materials with the different taper angles
图 9 预压后锥角与相对密度关系：（a）铝粉；（b）铁粉
Figure 9. Relationship between the relative density and taper angle after pre-compression: (a) aluminum powders; (b) iron powders
图 10 锥形零件冲击模型（a）与测量球布置模型图（b）
Figure 10. Impact model of taper part (a) and the model of measurement unit layout (b)
图 11 不同锥角下的轴向相对密度分布云图：（a）30°；（b）35°；（c）40°；（d）45°；（e）50°；（f）55°；（g）60°；（h）65°；（i）70°
Figure 11. Relative density distribution clouds in axial direction at different taper angles: (a) 30°; (b) 35°; (c) 40°; (d) 45°; (e) 50°; (f) 55°; (g) 60°; (h) 65°; (i) 70°
表 1 锥形模型尺寸
Table 1. Dimensions of the taper model
锥角角度 / (°) 底模总高度 / mm 底模锥角部分高度 / mm 底模上端面直径 / mm 底模下端面直径 / mm 30 6 3 12 1.61 35 6 3 12 3.43 40 6 3 12 4.85 45 6 3 12 6.00 50 6 3 12 6.96 55 6 3 12 7.80 60 6 3 12 8.54 65 6 3 12 9.20 70 6 3 12 9.82 
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表 2 底模参数汇总
Table 2. Summary of the bottom mold parameters
锥角角度 / (°) 底模总高度 / mm 底模锥角部分高度 / mm 底模上端面直径 / mm 底模下端面直径 / mm 30 8.6 3.6 14.4 1.9 35 8.6 3.6 14.4 4.1 40 8.6 3.6 14.4 5.8 45 8.6 3.6 14.4 7.2 50 8.6 3.6 14.4 8.4 55 8.6 3.6 14.4 9.4 60 8.6 3.6 14.4 10.2 65 8.6 3.6 14.4 11.0 70 8.6 3.6 14.4 11.8
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