Study On Variational Principles Of Springback For Bending And Its Numerical Simulation

Stamping is one of the most common sheet metal forming technique, and bendingtypes of forming operation is the most important process of sheet metal stamping. Partshape error due to springback is common manufacturing defect in sheet metal formingprocesses, specially in bending operation. Recently, more and more high strength steel aswell as aluminum alloys sheets are used by the automobile makers in making automobilebody. The springback problem becomes more prominent. Because springback is one ofthe key factors to influence on the quality of stamped sheet metal parts, it is must be doneto compensate shape deviation caused by springback in mould designing stage in order toget target part. To compensate shape deviation caused by springback, the traditionalpractice in shop floor is using the trial-and-error approaches to obtain desired part. Itseconomic impact in terms of delayed production, tooling revision costs, and rejection ofunqualified parts is tremendous. If accurate springback prediction was available forcompensate shape deviation before designing mould, we can reduce the expensive andtime consuming trial-and-error method. Therefore, finding an accurate method forspringback prediction following forming of arbitrary shapes to get desired parts is animportant task in sheet metal forming fields. The accuracy of springback prediction isaffected by many parameters, there is no accurate theoretical expression by now, the finiteelement method (FEM) is popularly used to predict the springback in sheet metalstamping.The simulation of sheet metal forming is a crossover subject made up of technique ofplastic forming of metals, theory of finite element, CAD, and so on. It is difficult tosimulate sheet metal forming for its strong nonlinear factors, which include geometry,material characters and contact. Springback occurs when sheet undergoes deformation,the accumulated error of forming simulation will make it more difficult to improve theprecision of the springback prediction. Therefore, the results of springback prediction ofsheet metal forming are not satisfied and research on improving springback prediction ofsheet metal forming is still hotspot and nodus at present.In this paper, the dynamic explicit method and time integration schemes forsimulating sheet metal forming were analyzed, the result is that the method of thedynamic explicit approach in loading and the static implicit one in unloading is mostsuitable for springback simulation. This thesis analyses the material models used in sheetmetal forming simulation such as von Mises isotropic yield criterion, Hill anisotropicyield criterion and 3-Parameter Barlat anisotropic yield criterion. This thesis analyses thecommon penalty function method and modified coulomb friction model used for contactanalysis in sheet metal forming simulation.In this paper, in order to investigate springback variational principle which istheoretical basis of springback finite element methods, based on anti-coupled systems andequations of springback the potential energy principle and generalized potential energy ofspringback for small forming are established. And the springback principle of potentialenergy for small flexibility bending and springback variational principle for largeflexibility bending of straight beam are developed. Solving formulae of the finite elementmethod for calculating springback of straight beam bending are established. The finiteelement method programs are compiled for calculating springback of straight beambending, the beam was applied single point load. The calculated results of the program arecontrasted with the results calculated by existing equations, commercial software andthose of three-point bend experiment. It is concluded that the principle of potential energyand finite element method for calculating springback of straight beam bending are right.Otherwise, for the excellence of high precision of which only needs displaces and strainsof forming body for calculating springback and avoids influence brought by untruematerial models, the complementary energy principle of springback for sheet bending areestablished. The theoretical basis is established for calculating complicated springback ofsheet forming using variational principles in the future.In this paper, the springback in U-bending is simulated by ANSYS/LS-DYNA codes.Sensitive factors, such as dumpy velocity of punch, number of element on punch and dieradius, the blank mesh size and number of integration points, are studied. From a greatnumber of calculating examples and results compared with experiment, the reasonablevalue of them for the explicit method in springback simulation is obtained. Based on these,the definition of arc bottom radius which compensated springback method of U-bendingis investigated.Two methods for designing sheet metal stamping dies to produce desired final partshape, based on springback prediction, are compared. The method for designing generalsheet forming dies to produce a desired final part shape, based on reverse compensatingspringback, was developed. Firstly, the CAD model of stamping dies is established basedon the CAD model of desired part. Secondly, the CAE analysis of stamping process iscarried out. Then, according to the springback deviation obtained by numerical simulation,the initial FEM model of dies is modified to be able to compensate springback error.Finally, based on the final FEM model of tools, the CAD model of them could be gainedby reverse compensating method. Hence, the method for die shape design of smallcurvature parts based on springback prediction is established. The die design of bendingof a small part of three dimensional geometries was considered, the correspondingexperiment was carried out, the result is that the designed tools obtained by repeateddisplace compensating method can produce the desired part shapes with small error.