Effect of critical eccentricity on forming accuracy of tubes in 3D free bending process
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摘要:
三维自由弯曲成形过程中弯管处于少约束状态，弯管弯曲半径的大小及轴线形状取决于相应的弯曲模偏距值。为了准确成形出预设弯管的形状，提高弯管的自由弯曲成形精度，基于弯曲模临界偏距
U e建立了弯曲模偏距U 和弯管弯曲半径R （U -R ）关系数学模型。采用有限元模拟与实验相结合的方法，研究了不同摩擦系数及材料参数条件下临界偏距的演化规律及其对弯管成形精度的影响。研究结果表明：引入临界偏距的U -R 关系拟合结果更加符合实验结果。随着摩擦系数的增加，弯管塑性变形程度增加，临界偏距的数值降低，弯管弯曲半径减小。相比于SS304不锈钢弯管，相同工艺参数下6061铝合金弯管的弯曲半径增大，临界偏距降低。Abstract:The tube is less limited during 3D free bending, and the eccentricity of the bending die determines the radius of the bend and the form of the bending axis. In order to accurately process the shape of the tube and improve the forming accuracy during the free bending process, a new free bending mechanical model was established for critical eccentricity. The influence of different friction coefficients and material parameters on the change of critical eccentricity were studied by using the finite element simulation and free bending tests. The findings have demonstrated that the experimental findings and the fitting outcomes of the
U -R relationship with critical eccentricity are in a good agreement. With the increase of friction coefficient, the degree of plastic deformation of the bending tube increases, and the value of critical eccentricity and the bending radius are decreasing. Compared with SS304 tubes, the bending radius of the 6061 Al tube increases and the critical eccentricity decreases at the same process parameters.-
Key words:
- tube /
- 3D free bending /
- elastic-plastic deformation /
- friction coefficient /
- material parameters
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图 2 三维自由弯曲弯管应力状态和几何参数示意图
Figure 2. Schematic diagram of stress state and geometric parameters of a 3D free bending bent tube
图 3 平面螺旋典型弯曲构件的U-R映射原理图
Figure 3. Schematic mapping of dimension characteristics and U-R relationship of planar involute components
图 5 三维自由弯曲数值模拟有限元模型
Figure 5. Finite element model for numerical simulation of 3D free bending
图 6 三维自由弯曲有限元模拟结果以及相应的U-R关系
Figure 6. Finite element simulation results and corresponding U-R relationship of 3D free bending
图 8 三维自由弯曲成形实验弯管以及相应的U-R关系
Figure 8. Experimental bends and corresponding U-R relationship of 3D free bending
图 9 三维自由弯曲成形U-R关系曲线及拟合结果
Figure 9. U-R curves and fitting results of 3D free bending molding
图 10 连续变曲率构件自由弯曲成形实验
Figure 10. Experiment on free bending forming of planar involute components
图 11 不同摩擦系数条件下临界偏距Ue演化情况
Figure 11. Evolution of critical eccentricity under different friction coefficients
图 13 不同材料参数条件下的临界偏距模拟情况对比
Figure 13. Simulation results of critical eccentricity under different material parameters
表 1 SS304管材力学性能参数
Table 1. Mechanics performance parameters of SS304 tube
弹性模量E/GPa 延伸率△/% 屈服强度σ0.2/MPa 抗拉强度σb/MPa 强度系数K/MPa 硬化指数n 194 15.72 235.42 265.76 1040.88 0.33 
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表 2 SS304管材自由弯曲有限元模拟工艺参数设置
Table 2. Setting parameters of free bending finite element simulation of SS304 tube
管材尺寸（D×t）/
（mm×mm）推进速度
v/（mm·s−1）管模间隙
△c/mm摩擦
系数f20×1 15 0.1 0.1
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表 3 U-R关系拟合结果
Table 3. The fitting results of U-R relationship
公式 k c R2（COD） 式（17） 7834.610 ± 225.709 202.246 ± 35.888 0.99752 式（18） 11044.577 ± 185.952 141.952 ± 885 0.99915
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表 4 6061管材自由弯曲有限元模拟工艺参数设置
Table 4. Setting parameters of free bending finite element simulation of 6061 tube
管材尺寸（D×t）/
（mm×mm)推进速度
v/（mm·s−1）管模间隙
△c/mm摩擦
系数f20×1 15 0.1 0.1
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