Integration von Fertigungsrestriktionen bei 3D-Fräsverfahren in die Topologieoptimierung mit der Level-Set-Methode
The optimization of mechanical structures is becoming increasingly important in the development of technical products. The goal of this process is to find out what shape and topology a structure must adopt to fulfill its design objective in the best possible way. For example, with the help of optimization methods, it is possible to determine in a targeted manner how far the weight of a structure can be reduced without falling below the minimum requirements for its mechanical properties. The result of such a process is an optimized structure. In order to guarantee the manufacturability of the optimized structures, current research is striving to integrate information about the manufacturing processes in the form of manufacturing constraints directly into the related optimization methods. In this work, a methodology for integrating the manufacturing constraints of 3D milling processes into level set based topology optimization is developed. The constraints considered are ensuring tool accessibility of each machining point and maintaining a minimum wall thickness. The approach followed is based on the induction of structural growth in areas that are either inaccessible or too thin. To identify these areas, a method is developed in which the level set function is interpolated along the outer contours of realistic tool geometries, considering available machining directions. A potential is defined in regular steps for the subsequent induction of structural growth. This potential has greater values inside the structure than outside and changes linearly normal to the structural boundary. Minimization of the potential present on the structural boundary is converted into structural growth. For this purpose, the sensitivities of the potential with respect to deformations of the structural boundary are determined and coupled with the evolution velocities of the corresponding level set function. In the course of this approach, both manufacturing constraints are transformed into a single mathematical constraint and explicitly integrated into the optimization problem.
