Introduction
The development of a product involves various phases of calculation and design that provide a series of predefined steps to follow in order to reach mass production. With this aim in mind and considering the high number of parts to be produced, any material saving is advantageous and relevant from an economic perspective. The parties involved in the production need to reduce the waste material (relevant for the foundry) and to reduce the weight of the components (relevant for the end customer).
Optimizing the shape of the product helps both parties (foundry and customer) to reach the right compromise to make the adequate savings while obtaining the highest quality parts.
In this article we will show the design optimization process of a foundry product destined for mass production using an optimization software and a process simulator. The aim is to analyze the solidification of the metal present in the system of interest and to evaluate how the optimization helps both parties to benefit from it.
The component to optimize in this study is produced by sand molded casting technique, one of the oldest, simplest and most economical techniques. The preliminary design phase has provided a prototype in stereolithography format (STL), which is already potentially good for production (courtesy of Flow Science Deutschland). In the image [Figure 1] you can see the feeding system (in yellow) and the geometry of the part to be produced (in red). The weight of the part itself in this starting configuration is 2,197kg, and the whole system weight is 3,126kg. The main objective is, by acting on some details of the geometries themselves, to obtain a total weight of the system as small as possible without having significant porosity in the part.
In order to obtain the best possible result, the parameters chosen to be modified are the size of the feeder [Figure 2], the thickness of the vertical wall closest to the feeder and the thickness of the transition zone between the two walls [Figure 3].
The considered variables are thus potentially multiple and exploring manually all the possible combinations can be a very long and complex work. That is why we have chosen to use a numerical optimizer able to explore the solutions independently. Therefore, IMPROVEit was chosen, which thanks to its simple interface allows to perform both the setup phase and the processing of results easily. FLOW-3D® CAST was chosen as the process simulator for its precision, reliability and simple use in foundry simulations.
As for modifying the geometrical shape, the optimization software allows both to interact directly with parametric CAD if the file is in original format, and to modify an STL file directly inside IMPROVEit if, as it is the case in this test, only the latter is available.
Once the parameters to be corrected have been selected, the software is able to internally modify the shape of the geometries, launch the solidification simulations interacting with the FLOW-3D® CAST process software using the modified geometries, extract the results of the analyses and process them with suitable mathematical nodes to obtain the right optimized quantity. [Figure 4] shows the workflow of our case study.
Figure 4 – Optimization workflow
In order to detect the shrinkage porosity dimension present at the end of the solidification simulation, four control volumes divide the geometry in four distinct zones: the top part is in dark blue, the central part in yellow, the left part in cyan and the right part in magenta. According to the customers’ exigences, among those four parts only three are relevant for optimization: the porosity in the top part (dark blue) is not considered. In the initial configuration, the total shrinkage porosity volume in the three control volumes is 581mm3.
Figure 5 – Control volumes
Execution
For the purpose of the optimization process, two objectives and one constraint were chosen: minimizing the feeding system and the part’s weight while having the amount of porosity in the three control volumes below a threshold low enough to be able to consider the part free from visible defects.
Setting up an optimization with two objectives and a constraint makes the understanding of the problem complex; nevertheless, the IMPROVEit engine being developed specifically for this type of problem, it allows to obtain an excellent result with just a few calls of the process simulator. Since each optimization cycle lasts only a few minutes, it was decided to allow the execution of fifty cycles.
Considerations
After fifty cycles, IMPROVEit was able to propose a wide range of solutions that reduce the weight of the system with tolerable thresholds of porosity, which was our objective. Moreover, by analyzing the panorama of the solutions found, it is possible to understand the influence of the various factors better. In general, as the weight of the system decreases the porosity increases.
The behavior of the system can be deduced from a first set of graphs. The 2D graph shows the best results: the Pareto curves of the two analyzed objectives (the two weights), distributed according to 3 porosity thresholds.
It should be noted that on each curve the points have a very similar level of porosity, increasing from the green curve to the blue curve: a first conclusion is that if you are looking for a very low porosity you have to accept both the size of the part and the feeding system as rather high, and make a compromise in terms of porosity so you can get significant volume reductions.
Similar considerations can be obtained also from the front of Pareto 3D, considering that porosity is also a criterion to be minimized: on the horizontal axes the weights of the part and of the whole casting are reported, while on the vertical axis the shrinkage defects are reported.
The presence of areas with significant concavity in the 3D graphs highlights clearly that it is possible to choose excellent compromising solutions, as in the area circled in red in [Figure 7], with a fairly low overall weight and good results in terms of defects of the structure.
As with any multi-objective optimization, there are several excellent solutions that can be chosen depending on your priorities. In this case, a solution based on the objectives given by the customer was chosen. The compromise is characterized by an absence of default on the left part of the part, the presence of a light porosity that is visible on the lateral parts, a part weight of 2,1625Kg and a total weight of 3,1536Kg. This allows, compared to the initial solution, a material saving in the part of 1.6% and a porosity reduction of 5.2% (551mm3) against an increase in the overall weight of less than 1%.
As an indication, here is another optimal solution with a much higher weight (2.29Kg for the part and 4.09Kg for the total weight) and with a lower and more distributed porosity (490mm in total).
