Optimization of powder net-shape compacting technology and structural design of 3D complex parts by numerical simulation
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摘要: 基于粉末连续体，运用MSC.Marc有限元软件对粉末净成形压制工艺进行优化，并对减重齿轮的结构设计进行数值模拟。通过与实验数据对比分析，验证了材料模型及仿真模拟的可靠性，在此基础上利用有限元软件研究分析压制方式、压制速度、摩擦系数、压制温度、保压时间等五组因素对压坯密度分布的影响。结果表明，压制方式是最显著的影响因子，采用双向压制、温压成形、低压制速度、小摩擦系数及保压方式的组合压制工艺能有效地改善粉体的密度分布。利用有限元软件对减重齿轮的结构进行优化设计，研究圆环高径比与压坯相对密度的关系，并确定减重孔最佳尺寸。结果表明，采用强制摩擦压制方式代替浮动压制方式，可有效改善孔洞薄壁处密度。此外，结合Workbench有限元软件对减重齿轮进行结构力学模拟仿真，分析薄壁处的受力情况，以满足对齿轮强度的要求。Abstract: The optimization of powder net-shape compacting technology and the structural design of weight reduction gear were simulated by MSC.Marc software based on the finite element method (FEM). The reliability and accuracy of the proposed FEM model were validated by the experimental results. The influences of compacting mode, compacting speed, friction coefficient, compacting temperature, and dwell time on the relative density distribution of compaction were studied by the finite element software. In the result, the combined compacting process can effectively improve the density distribution of powders as double-action pressing + warm compacting + low compacting speed + small friction coefficient + pressure maintaining. The optimal structure of weight reduction gear was carried out by the proposed FEM model, the relationship between the height-diameter ratio of spur gear and the relative density of compaction was studied, and the optimum size of weight reducing hole was determined. The results show that, the density on the thin wall of the hole can be effectively improved by using the forced friction pressing mode instead of floating pressing mode. The structural mechanics of weight reduction gear was simulated by Workbench software, the force condition on the thin wall was analyzed to reach the strength requirements of gear.
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图 1 弹性模量与相对密度关系（a）、泊松比与相对密度关系（b）及流动应力‒应变曲线（c）
Figure 1. Relationship between the relative density and elasticity modulus (a), relationship between the relative density and Poisson's ratio (b), and the flow stress‒strain curve (c)
图 3 相对密度随压坯轴向位移变化
Figure 3. Relationship between the relative density and axial displacement of compaction
图 4 不同工艺下压坯等效应力（σeq）分布状况：（a）优化工艺；（b）基准工艺
Figure 4. Distribution of equivalent stress (σeq) in different process: (a) optimization simulation; (b) standard simulation
图 5 优化工艺与基准工艺下相对密度与压坯轴向位移的关系
Figure 5. Relationship between the relative density and axial displacement of compaction in optimization simulation and standard simulation
图 6 不同尺寸孔洞1/6直齿轮相对密度分布：（a）2 mm；（b）3 mm；（c）4 mm；（d）5 mm
Figure 6. Relative density distributions of 1/6 gears in different hole sizes: (a) 2 mm; (b) 3 mm; (c) 4 mm; (d) 5 mm
图 7 不同侧压系数下相对密度与压坯轴向位移的关系
Figure 7. Relationship between the relative density and axial displacement of compaction at different K values
图 9 强制摩擦压制（a）与浮动压制（b）模型对比
Figure 9. Compaction model of suppressed friction compaction (a) and floating compaction (b)
图 10 不同压制方式下压坯相对密度（ρ）分布状况：（a）强制摩擦压制；（b）浮动压制
Figure 10. Distribution of relative density (ρ) in different compaction styles: (a) suppressed friction compaction; (b) floating compaction
图 11 强制摩擦压制与浮动压制下相对密度与压坯轴向位移的关系
Figure 11. Relationship of the relative density and axial displacement in suppressed friction compaction and floating compaction
图 12 不同尺寸孔洞的齿轮转动过程中等效应力分布：（a）3 mm；（b）5 mm
Figure 12. Equivalent stress distribution during gear transmission process in different hole sizes: (a) 3 mm; (b) 5 mm
表 1 相对密度实验值与模拟值
Table 1. Relative density in simulation and experiment
数值 位置1 位置2 位置3 位置4 位置5 模拟值 0.8074 0.7862 0.7712 0.7862 0.8074 实验值 0.8168 0.7899 0.7551 0.7763 0.8136 误差/% 1.15 0.47 2.13 1.28 0.76 
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表 2 正交试验设计与结果
Table 2. Design and results of orthogonal experiments
模型编号 压制方式 温度/℃ 速度/(mm·s-1) 摩擦系数 保压时间/s 标准差，Y 1 单向压制 20 9.8 0.1 0 4.55×10-3 2 单向压制 20 9.8 0.2 1 8.93×10-3 3 单向压制 120 4.9 0.1 1 2.58×10-3 4 单向压制 120 4.9 0.2 0 5.29×10-3 5 双向压制 20 4.9 0.1 1 2.15×10-3 6 双向压制 20 4.9 0.2 0 3.88×10-3 7 双向压制 120 9.8 0.1 0 1.03×10-3 8 双向压制 120 9.8 0.2 1 2.02×10-3 标准差平均值，Y1 5.34×10-3 4.88×10-3 3.48×10-3 2.58×10-3 3.92×10-3 — 标准差平均值，Y2 2.22×10-3 2.73×10-3 4.13×10-3 5.03×10-3 3.69×10-3 — 标准差相对差值 3.12×10-3 2.15×10-3 6.5×10-4 2.45×10-3 2.3×10-4 —
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