Steffen Tillmann

As a result of uneven cooling and internal stresses, warpage is a significant challenge in metal casting, particularly when using metal dies. Previous research has sought to reduce warpage by adjusting process parameters, such as the extraction temperature. An alternative approach involves modifying the mold cavity shape to compensate for expected deformation. While this compensation is often based on experience, numerical design optimization offers a systematic alternative. Various optimization methods have been developed for injection molding, but their application to metal casting remains less explored. In this study, we apply and compare two warpage compensation methods in metal casting: the reverse geometry method and a shape optimization‐based approach. Both methods were initially developed for injection molding. We perform coupled thermomechanical simulations using the commercial software Abaqus. Each method is evaluated based on how it adapts the geometry, and we analyze their respective strengths and limitations across different scenarios. Using a simple test geometry, our results demonstrate that the reverse geometry method performs better regarding warpage reduction and computational costs, while the shape optimization‐based method offers superior generalization.

Purpose: In fused deposition modeling (FDM), the nozzle plays a critical role in enabling high printing speeds while maintaining precision. Despite its importance, most applications still rely on standard nozzle designs. This work investigates the influence of nozzle geometry on pressure loss inside the nozzle, a key factor in high-speed printing performance. Design/methodology/approach: We focus on optimizing the nozzle shape to minimize the pressure loss and establish a framework that allows both sim- ple angle-based optimization and more advanced spline-based parametrization. To model the polymer melt flow, we compare two constitutive descriptions commonly employed in the literature: a temperature-dependent, shear-thinning viscous model and an isothermal viscoelastic model. Findings: For the viscous model, the optimal half-opening angle exhibits a strong dependence on the feeding rate, with higher rates favoring half-opening angles near 30°, whereas lower rates are more efficient at larger angles. In con- trast, the viscoelastic model predicts a weaker dependence of the optimal angle on the feeding rate. For both models, spline-based parametrization yields only marginal improvements over angle optimization in terms of reducing pressure loss. Originality/value: This paper presents a comparative study of FDM nozzle shape optimization using different simulation models. We introduce a flexible optimization framework that accommodates both simple and advanced geomet- ric parametrizations. The results highlight the impact of model choice on the optimal nozzle geometry and provide support for improving nozzle design in high-speed printing applications.

In injection molding processes, shrinkage and warpage cause deviations in the size and shape of produced parts compared to the cavity shape. While shrinkage is due to the change of material density during solidification, warpage is caused by uneven cooling and internal stresses within the part. One approach to mitigate these effects is by adjusting the cavity shape to anticipate the deformation. While finding the optimal cavity shape is often experience‐based in practice, numerical design optimization can greatly assist in this process. In this study, we evaluate various numerical algorithms from existing literature to identify the optimal cavity shape. Each method is briefly outlined regarding how it adapts the geometry, and we discuss their respective strengths and weaknesses for different scenarios. We conduct comparisons using 3D geometries of varying complexity. Our findings demonstrate that, for geometric warpage compensation, the node‐based reverse geometry method yields the least warpage and is computationally cost‐effective. Furthermore, it is straightforward to implement and consistently performs well across different geometries.

In the manufacturing process of injection molding, the geometric accuracy of the produced part is affected by shrinkage and warpage. To support efforts to compensate for these effects, this paper presents an extension of the numerical compensation approach known as the reverse geometry method. The reverse geometry method is based on the numerical forward simulation of the displacement field resulting from shrinkage and warpage. It is an iterative method that performs node‐based compensation in each step. The mention of node‐based compensation already indicates that the method is associated with a computational mesh. In particular, in its basic version, it is linked to a specific mesh that must be kept identical during all iteration steps. This requirement is not always compatible with commercial simulation tools for injection molding, which enforce automatic remeshing between simulations. We present an interpolation method that allows to handle changing meshes and illustrate the method with two practical examples.

In injection molding processes, shrinkage and warpage often cause deviations in the shape of produced parts compared to the cavity shape. These deviations arise due to uneven cooling and internal stresses within the part. One approach to mitigate these effects is by adjusting the cavity shape to anticipate the deformation. This can be achieved by simulating the expected deformation using suitable models, which then inform the optimization of the cavity shape for injection molded parts with minimal deformation. \\In this study, we evaluate various numerical algorithms from existing literature to identify the optimal cavity shape. Each method is briefly outlined regarding how it adapts the geometry, and we discuss their respective strengths and weaknesses for different scenarios. We conduct comparisons using 3D geometries of varying complexity. Our findings demonstrate that, for geometric warpage compensation, the node-based reverse geometry method yields the least warpage and is computationally cost-effective. Furthermore, it is straightforward to implement and consistently performs well across different geometries.

In injection molding, shrinkage and warpage lead to a deformation of the produced parts with respect to the cavity shape. One method to mitigate this effect is to adapt the cavity shape to the expected deformation. This deformation can be determined using appropriate simulation models, which then also serve as a basis for determining the optimal cavity shape. Shape optimization usually requires a sequence of forward simulations, which can be computationally expensive. To reduce this computational cost, we use Bayesian optimization which uses Gaussian process regression as a reduced order model. Additionally, Gaussian process regression has the benefit that it allows to account for uncertainty in the model parameters and thus provides a means to investigate their influence on the optimization result. We present a Gaussian process regression trained with samples from a finite‐element solid‐body model. It predicts the deformation of the product after solidification and, together with Bayesian optimization, allows for efficient cavity optimization.

In this paper, we present an approach to efficiently optimize the design of extrusion dies. Extrusion dies, which are relevant to the manufacturing process of plastics profile extrusion, traditionally require time‐consuming iterations between manual testing and die adjustments. As an alternative, numerical optimization can be used to obtain a high quality initial design and thereby reduce the number of adjustments to the actual die. However, numerical optimization can be computationally expensive, so the use of surrogate models can be helpful to improve efficiency. The latter is the goal of this work. Our method uses physics‐informed neural networks (PINNs) that directly incorporate a free‐form deformation (FFD) approach to allow for geometric variations. The FFD approach allows for a wide range of domain deformations, while the fully trained PINN ensures fast evaluation of the objective function. Using a two‐dimensional model of an extrusion die for demonstration, we detail the integration of the FFD method into the PINN model and discuss its potential in the three‐dimensional context.