دانلود رایگان مقاله مدل منیفولد مبتنی بر یادگیری برای بررسی خصوصیات شکل اسپرینگ بک

Abstract

The parameters of a stamping process include the geometry of the tools, the shape of the initial sheet blank, the material constitutive law and the process parameters. When designing the overall process, one has to also take into account the springback effect that appears when the tools are removed and additional surfaces are cut-off. The goal then is to obtain a final shape as close as possible to the desired shape, while satisfying the admissibility constraints on the variable parameters as well as the feasibility constraints frequently expressed in the form of forming limit diagrams. In the present paper we represent the postspringback shape by a level set function. Then, rather than rely on arbitrarily selected case-dependent measurement locations as in the NUMISHEET benchmark problems, we build a reduced order “shape space” where this level set evolves, by extending our recent shape manifold approach to the problem of springback assessment for 3D shapes. Next, we propose an optimization algorithm designed to minimize the gap between the post-springback and the desired final shapes. The required level set functions are generated from a corresponding set of springback shapes predicted by Finite Element simulations. Using our approach, we determine the minimal number of parameters needed in order to uniquely characterize the final formed shape regardless of complexity. Finally, we demonstrate the approach using an industrial test-case: springback assessment of the deep drawing operation of an automotive strut tower.

4. Conclusions

In this paper, we have presented an objective approach to characterize the complex non-geometric 3D shapes obtained after springback in a deep drawing process, using the level set approach and a shape space meta-model based on the fundamental hypothesis of the continuous shape manifold. The transition from a “point-set manifold” to a smooth shape manifold is then achieved by interpolating between level set functions in POD coefficient-space using the Diffuse Approximation. The approach was then demonstrated in the problem of springback assessment for the deep drawing process of an automotive strut tower. This allows us to achieve a variety of goals in a single shot: we can directly determine the tool geometry needed for a desired final post-springback shape needed by the manufacturer, thus being better able to take springback into account at the tool design stage. Level sets, arguably the best tool to represent complex and “non geometric” shapes like those post-springback, suffer from excessive dimensionality due to the number of grid points needed for adequate precision (1,204,938 in the test case in this article) This is alleviated by the use of the POD that allows us to represent this massive information using only a handful of αs for a given shape.