Optimization of loading path in incremental sheet metal forming

针对非对称扁壳的小批量制造，研制了一种采用轨迹控制球面滚子的柔性板料渐进胀形机。(1)所研制的板材胀形机具有以下性能：行程：x = 200 mm，y = 300 mm，z = 100 mm移动速度：30 mm/sec定位精度：x，y方向<plus-minus>0.03 mm（载荷0.5 kN）z方向<plus-minus>0.03 mm（在载荷2下）（2）计算机控制的胀形机可以进行各种复杂形状的金属板成形，例如锥形壳体，平截头棱锥壳、浅盘和浮雕板。(3)实验表明，在板料渐进成形中，最佳加载路径是使壳体内应变分布均匀的加载路径。(4)为了预测渐进成形的成形极限，采用球凸模对退火铝板进行了新的渐进胀形试验，试验结果表明，当板厚应变达到一定值时，板料发生断裂。(5)利用该断裂极限和几何变形模型，提出了壳体最大胀形高度的近似计算方法。壳的预测与退火铝板的实验值相当一致。(6)通过有限元数值模拟，阐明了渐进成形条件与应变分布、成形极限和回弹的关系。

For the small batch manufacture of non-symmetrical shallow shells, a flexible and incremental sheet metal bulging machine has been developed using a path-controlled spherical roller.The main results of this investigation are as follows.(1) The developed sheet metal bulging machine has the following performances.Stroke : x = 200 mm, y = 300 mm, z = 100 mmTraveling speed : 30 mm/secLocating accuracy : x, y direction <plus-minus>0.03 mm (under load 0.5 kN) z direction <plus-minus>0.03 mm (under load 2(2) The computer controlled bulging machine could perform a wide range of sheet metal shaping of complex shapes, for example pyramidal shells, shells of frustum of pyramid, shallow pans and embossed panels.(3) It was experimentally showed that the optimum loading path in the incremental sheet metal forming was the path which made the strain distribution in the shell uniform.(4) In order to predict the forming limit of the incremental shaping, a new incremental bulging test by a ball punch was performed with annealed aluminum sheet, and the experimental results showed that fracture occurred when the thickness strain reached a constant value.(5) An approximate calculation method of the maximum bulging height of the shell was proposed using this fracture limit and a geometrical deformation model. The predictions for the shells were reasonably in agreement with experimental values of the annealed aluminum sheet.(6) The relationships between the forming conditions of the incremental forming and the strain distribution, the forming limit and the spring-back were clarified by the numerical simulation using the finite element method.