Research And Application On Surface Unfolding Of One Step Inverse Forming FEM

Along with the rapid development of the automotive industry, CAE technology is gradually applied to all aspects of the design and manufacture of automotive products. Especially in the design and manufacture process of automotive body part, CAE technology has become inseparable as the technical support power. The research works are supported by the key project of National Natural Science Funds"The basic theory, calculation method and key technique of stamping and die design"(19832020) , the key project of National Outstanding Scientific Youth Funds"The CAD expert system theory of stamping design based on KBE and the research on the polymer forming theory and calculation method"(10125208) and the key project of National Automotive Electric Industrialization (No.2004-2563). The research works have been carried out in-depth with the surface unfolding forming and the springback forming of automotive body part, which are based on the surface unfolding of one step inverse forming FEM. They rely on the independent development of the sheet metal stamping CAE analysis software KMASTM / One-step and the CAE integration module of UG software.Currently, the one step inverse forming FEM can unfold the whole part on blank plane along with the stamping direction. But the surface unfolding of one step inverse forming FEM has even broader application fields, which just unfold the local part. The method can unfold the binder regions and the flanging regions of auto body part. It also can predict the flanging lines. Because most of the local parts are surface unfolding, the deformation processes are very complex and could not been predicted by experience formula.The surface unfolding of one step inverse forming FEM is the further study on one step inverse forming FEM. In the production forming processes, one step inverse forming FEM bases on the proportional loading assumption and unfolds the auto body part to blank. It only considers the initial and the final state without considering the medium state. But the surface unfolding of one step inverse forming FEM considers every forming step and just unfolds the local part on surface region, special the region is plane.The surface unfolding of one step inverse forming FEM have two steps. The first step is unfolding the local part on plane along with the stamping direction, which is named intermediate configuration. The second step is mapping intermediate configuration on the target surface, which is named the initial configuration.The surface unfolding method adopts the initial solution of one step inverse forming FEM. The surface unfolding of one step inverse forming FEM get the initial solution of local part, instead of the whole one. The basic idea is that we assume the initial flat blank translate into the final part by linear elastic reverse deformation neglecting all of external load. Then the equilibrium equations are established by the linear elastic FEM in the initial flat blank. The nodal residual force vector in the initial flat blank will satisfy the initial convergence conditions by iterative calculation. Finally we can get the initial solution.Surface reconstruction is the hot and difficult question in reverse engineering. As one of the key technologies in surface unfolding of one step inverse forming FEM, there are three methods which could chose automatically. They are Implicit Surface Construction Method which bases on Radial Basis Function, Geometry Construction Method and NURBS Curve Construction Method.The basic idea of Implicit Surface Construction Method which bases on Radial Basis Function is to establish an implicit surface function which bases on the FEM surface of target region at first.And then approach the nodes of the intermediate configuration to map on the implicit surface and make the surface smoothly blended with its vicinity by a Gradient Descending Algorithm.The Gradient Descending Algorithm is an iterative optimization method aiming at some rule functions. One Assume that f (r ) is a rule function, in which r is a vector. The fastest reduce direction of f (r ) is the negative gradient direction of the vectorr and the approached points can be obtained full out in this direction. Grads of the implicit surface formula is written asIn whichThe iterative formula isGeometry Construction Method bases on the existing FEM and establishes geometry relationship between surfaces. According to the relationship between flanging surfaces and target surfaces, it uses geometry transform matrix to get the unfolded FEM surface. Assuming that the node P is (x_p,y_p,z_p ) and the unfolded new node is P~* (x_p~* , y_p~*,z_p~*), then the unfolding formula is written as:In which, Ra bis a rotational transform matrix, given byNURBS curve construction method avoids constructing the complicated surface directly. It can construct the outer boundary curve along with the tangent direction of reference surface by the good use of NURBS curves. Then according to the required surface precision, it spreads discrete points evenly and establishes the mesh topology, generates the FEM surface.In order to eliminate the effect of Complex surface and meet the calculation requirements, there are three key algorithms in the surface unfolding of one step inverse forming FEM, including normal consistency algorithm, mesh smoothing algorithm and the main direction of curvature optimization algorithm. Normal consistency algorithm guarantees the FEM normal direction consistent of the part. Mesh smoothing algorithm guarantees the smoothness of boundary curve in the surface construction. The main direction of curvature optimization algorithm guarantees the FEM Results along with the expected direction by controlling the unfolding direction. All these algorithms will affect the surface unfolding result directly.In the automotive products of modern design and manufacture, computer simulation technology is becoming the integration trend of CAD / CAE / CAM systems. Based on the bottom code development platform of Unigraphics NX software, the surface unfolding of one step inverse forming FEM developed the CAE module "One-step Formability Analysis". To the CAD models which are built by UG-Modeling model (or interoperated other CAD software), the model can do the meshing, the data preparation of pre-processing, the surface unfolding of solver, the physical distribution show of post-processing, the result analysis and so on. It achieved a seamless integration of CAD and CAE. It is a unified database and achieved the free exchange of data among the CAD / CAE / CAM modules. It also supports the concurrent engineering.In the springback simulation analysis of the Auto Body Part, it is been proved feasible that the forming process is simulated by the one step inverse forming FEM, and then predicated the unloading springback by the nonlinear elastic static implicit FEM. The Auto Body Parts are simulated the forming process by the surface unfolding of one step inverse forming FEM, and then predicated the unloading springback by the nonlinear elastic static implicit FEM. All of the simulation results show that the efficiency of the method for the prediction of unloading springback in forming process. The foundation of the nonlinear elastic static implicit FEM is the elastic-plastic large deformation FEM. The finite element model is the Belytschko-Lin-Tsay shell element based on the Mindlin theory. As the physical model removed the plastic deformation and the elastic deformation is only considered, the method can simulate the nonlinear FEM with large displacement and large rotation in space.