Multiscale, Thermomechanical Topology Optimization of Cellular Structures for Porous Injection Molds

Abstract

During the injection molding cycle, molten material is injected at high pressure inside the mold and cooled down to form a solid part. This creates thermomechanical stresses that are alleviated by the correct design of a cooling system. In conventional molds, the cooling system consists of straight-line cooling channels, which can be manufactured using machining processes; however, they are thermally inefficient and unable to cool the injected part uniformly. The emergence of metal-based additive manufacturing techniques such as direct metal laser sintering (DMLS) allows the fabrication of molds with conformal cooling channels. Conformal cooling molds cool down the part faster and more uniformly; however, they face limitations. First, their fabrication cost is 10 to 20 times higher than the one of a conventional mold. Second, the DMLS process, which is the most popular fabrication method of conformal cooling molds, produces internal thermal stresses that distort the mold. The development of structural optimization methods such as multiscale topology optimization offers the potential to create novel and complex cellular structures that alleviate these current limitations. The objective of this research is to establish a multiscale topology optimization method for the optimal design of non-periodic cellular structures subjected to thermomechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable, and suitable for additive manufacturing. The proposed method seeks to minimize the mold mass at the macroscale, while satisfying the thermomechanical constraints at the mesoscale. The thermomechanical properties of the mesoscale cellular unit cells are estimated using homogenization theory. A gradient-based optimization algorithm is used for which macroscale and mesoscale sensitivity coefficients are derived. The design and evaluation of a porous injection mold is presented to demonstrate the proposed optimization method.