Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization

Abstract

Manufacturing methods using molds, such as casting and injection molding, are widely used in industries. A basic requirement when using such manufacturing methods is that design engineers must design products so that they incorporate certain geometrical features that allow the mold parts to be removed from the created solid object. In the present study, we propose a manufacturability evaluation method especially adapted for the use of molds. To evaluate the manufacturability, we introduce fictitious physical models that are described by steady-state anisotropic advectiondiffusion equations. In these fictitious physical models, material domains have a virtual source term and the advection directions are aligned with the directions along which the mold parts are parted. Void regions, where the values of all fictitious physical fields are high, then represent either undercut geometries that would prevent the mold from being released, or interior voids that cannot be cast. Consequently, manufacturability can be evaluated using these fictitious physical fields. Furthermore, in the present study, we integrate this evaluation method with topology optimization and propose a scheme for imposing a molding constraint within the topology optimization procedure. This newly proposed topology optimization method can consider the position of mold parting lines prior to the detailed optimization procedure. Several numerical examples are provided to demonstrate the validity and effectiveness of the proposed method.

Unified structural optimization method using topology optimization and genetic algorithms

“…To consider the manufacturability of the structure in the topology optimization process, it is needed to detect an inner void and undercut, which are inappropriate to manufacture, and define a mathematical formulation for determining those volumes. The manufacturability evaluation of this research is based on the previous research by Sato et al (Sato et al, 2017) where a fictitious heat flux model is applied. In this fictitious physical model, the fictitious heat fluxes propagate from the outer boundaries of the analysis model in designated directions that demonstrate the movements of the manufacturing tools, such as parting dies in the casting and molding process.…”

“…However, the manufacturing evaluation approaches in DFM, based on intuition of the engineers and lumped parameters, cannot be directly applied to the topology optimization process where the structural configuration is implicitly defined by the topo logical variables. To deal with this issue, several papers have proposed a new problem formulation that incorporates a quantitative manufacturability evaluation technique (Sato et al, 2017) and an updating scheme for the topological design variable regarding the manufacturing constraint (Xia et al, 2010). They utilized predefined parting directions of the molds to define and minimize the total area of nonmanufacturable domain, such as undercuts and interior voids, and to restrict the propagation of the structural boundaries to gain manufacturability during topology optimization process.…”

“…Thus, this paper presents a new integrated topology optimization framework where a metaheuristic algorithm is par tially used for optimization of the manufacturing directions. The optimization problem is formulated to minimize both the mean compliance of the structure and the nonmanufacturable area, which is calculated based on the fictitious flux, the manufacturing direction, and the shadow domains where the heat flux is prevented (Sato et al, 2017). In the begin ning of the optimization process, the initial set of the manufacturing directions is determined by Latin Hypercube(LH) sampling.…”

Geometric shape features extraction using a steady state partial differential equation system

“…In addition, PDE-based approaches are used in many related fields; these are described in the following section. Topology optimization: The use of PDE-based feature evaluation has been proposed for topology optimization [46]. The manufacturability in molding is evaluated by superposition of the solution to the PDE.…”

Thickness Constraints for Topology Optimization Using the Fictitious Physical Model

“…On the other hand, the concept of the fictitious physical model (FPM) [6] for representing geometrical constraint can be avoid such issues. Therefore, the main aim of this paper is to formulate a FPM for representing the thickness constraint.…”