Compensation Algorithm For Springback In Multi-point Forming And Its Validation By Numerical Simulation And Experimental Methods

At present, Sheet metal forming processes are widely used to produce three-dimensionalsurface in many fields, such as aerospace, automotive, aircraft manufacturing, vehicle body,shipbuilding and pressure vessel forming and so on. Stamping is one of the most commonsheet metal forming methods. For conventional stamping process, which involves a matchedsolid die set, its advantages are a short production time and high productivity. Nevertheless,large initial investments and long setup time make its processes inflexible and onlyprofitable for mass production and economically unsuitable for single or small batchproducts. Multi-point forming (MPF), a novel flexible forming technology develops wellrecent years. In MPF, conventional solid stamping dies are replaced by a pair of opposedreconfigurable dies comprised by punch matrices. Based on this technology, dieless, rapidand digital manufacturing of sheet metal parts can be realized. Comparing with conventionalstamping, MPF technology is more suitable for small-lot and individualized production, andresponding to customers’ requirements quickly, meanwhile, accelerating the productrenovation.Comparing with conventional stamping, MPF technology is with advantages of rapid andflexible forming. However, whether it is conventional stamping or MPF, springback is aninevitable phenomenon in sheet metal forming, and it greatly affects the geometricalaccuracy of products. Springback caused by elastic recovery and release of residual stressafter forming, and the final shape of part depends on the value of springback. Once the valueof springback exceeds the allowable tolerance, it becomes defects and affects the wholeassembly of other parts. Moreover, it is an accumulated effect of the entire processing history.Hence the prediction of springback is difficult and remains an important problem in themanufacturing industry. The die surface of MPF can be adjusted quickly, realizing thereconfiguration of various curve surfaces; therefore, springback compensation method isvery suitable for MPF. Compensation method is an effective, practical method for controlling MPF springback. An algorithm was established for springback compensation inMPF by combination methods of theoretical analysis, numerical simulation and formingexperiment. Calculation formula for curvature before springback was obtained basing onthree material models, the method describing the shape of die-face after springbackmodification was proposed, Simulation and experimental results shows that thecompensation algorithm can effectively control errors caused by springback in MPF.The main contents and conclusions are as follows:(1)Calculation formulas for curvature before springback for single-curvature surface wasobtained basing on three material models, For irregular single curvature surface,interpolation and difference method are used to obtain continuous surface with first-orderderivative, then a cubic B-spline fitting method are used to obtain the smooth and continuoussurface. Comparison of the interpolation and difference method, it is found that theinterpolation method is with excellent accuracy.(2) For irregular doubly curved surface, the calculation formula for curvature beforespringback was obtained basing on three material models. Then, with discrete method, thewhole surface was divided into tiny pieces, interpolation processing and Bezier surfaceblending methods are used to describe the surface after springback compensation. Due to thedie-face of MPF is composed by a series of discrete punch elements, the center position andthe points of tangency of punch elements are obtained basing on the surface after springbackcompensation, the adjusting heights of punch elements can be achieved for MPF diecompensation surface.(3)Based on the ABAQUS software, the finite element models were established, and theunite selection, contact definition, friction coefficient, constraint and displacement boundarywere described in simulation. Simulating the process of MPF and springback, and theSpringback process is simulated combining explicit and implicit algorithm. The influencingfactors on the springback, such as, using cushion, material, thickness, radius of curvature,were researched. The results show: the greater the thickness is, the springback decreasesgradually; the greater elastic modulus is, smaller the springback after unloading is; with theradius of curvature decreases, the springback is reduced; in addition, with the increase ofcompensation coefficient, the error value is decreasing.(4)Simulating the springback process of MPF on single-curvature surface and doubly curvedsurface. Effective stress distribution and Z-displacement distribution are achieved.Comparing the simulation result with the target shapes, it is found that the single-curvature surface is easily to generate large springback; for doubly curved surface, if the bendingdirection is coincident, the springback is smaller, otherwise, the springback is bigger.Comparing the simulation result with and without springback compensation, we found thatthe errors is very small with springback compensation, otherwise, the errors is relativelylarge.(5) A series of experiments were carried out by means of MPF equipment, comparing theresults with compensation and without compensation, it is observed that simulated andmeasured results with compensation matched well with target shapes, and overall errors arerelatively small and satisfied processing precision. The compensation method presented inthis paper provides an effective calculation method to springback compensation ofsingle-curvature and doubly curved surface, and it is of good springback predition effect andapplication value.