基于量纲分析法的金属板材折弯回弹数学模型

Springback Model for Air-bending of Sheet Metal Based on Dimensional Analysis Method

回弹是影响金属板材工件成形精度的一个非常重要因素。准确控制回弹是工件精密成形和模具设计的关键所在。针对用于修正回弹的传统试错法的不足,提出一种基于量纲分析和正交试验相结合的方法来建立金属板材折弯回弹半径数学模型。并讨论回弹数学模型的适用范围。该模型定量求解了板料回弹半径与凸模半径、板材厚度、屈服强度、弹性模量之间的非线性关系。将此应用于折弯凸模的设计制造,且用该凸模多道次渐进成形了一半椭圆形工件,它的平均误差是+0.63/-0.65mm。该制造结果表明,基于量纲分析法和正交试验法建立的板料回弹半径数学模型是合理有效的,该建模方法有助于加快模具设计进程,降低生产成本,为金属板料折弯成形及模具设计提供了一条新的途径。

Springback is a very important factor to influence forming accuracy of sheet metal.Accurate controlling of springback is the key to precision forming and tool design.In view of the shortcoming of traditional trial-and-error method used to correct springback,a technique based on dimensional analysis and orthogonal test is proposed to establish springback radius model for air-bending of sheet metal.And the scope of application of mathematical model for springback is discussed.With this model,the non-linear relation between springback radius of sheet metal and punch radius,sheet thickness,yield strength,Young＇s modulus can be quantitatively solved,and it is used to design and make air-bending punch.Then,a semiellipse-shape workpiece,whose average errors are ＋0.63 /-0.65 mm,is made with the punch.The manufacturing results show that springback radius model,established with dimensional analysis and orthogonal test,is reasonable and effective.The modeling method is helpful to speeding up the progress of tool design and reducing production cost.It can be taken as a new approach for air-bending forming of sheet metal and tool design.