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. Component to produce 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]. Figure 2 - First optimization parameter Figure 3 - Second and third optimization parameters 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 … [Read more...]

## Minimizing air entrainment in shot sleeve

M. Barkhudarov, Flow Science Inc., Santa Fe, New Mexico; S. Mascetti, XC Engineering, Italy; R. Pirovano, XC Engineering, Italy Abstract High pressure die casting is one of the most complex processes in the foundry world due to the wide range of physical phenomena and process parameters that control the outcome. A particular challenge is achieving optimal conditions in the shot sleeve from which metal is injected into the die cavity. The speed of the plunger in a horizontal shot sleeve must be carefully controlled to avoid unnecessary entrainment of air in the metal and, at the same time, minimize heat losses in the sleeve. The paper presents a general solution for the flow of metal in a shot sleeve, based on the shallow water approximation of the interaction of the moving plunger and liquid metal. The derived analytical solution allows engineers to precisely control the behavior of metal in the shot sleeve during the slow-shot stage of the high pressure die casting process, minimizing the risk of air entrainment. Results are validated with three-dimensional numerical modeling of the process. Coupled with parametric optimization, the numerical model can improve the process conditions predicted by the analytical model. Introduction The speed of the plunger in a horizontal shot sleeve must be carefully controlled to avoid unnecessary entrainment of air in the metal and at the same time minimize heat losses in the sleeve. If the plunger moves too fast, large waves are created on the surface of the liquid metal that may overturn and entrain air into the metal, which will then be carried into the die cavity. A plunger moving too slow results in waves reflecting from the opposite end of the shot sleeve. The reflected waves prevent proper expulsion of air into the die cavity. In either case, the outcome is excessive porosity in the final casting. Moreover, a slow plunger increases also oxidation of the free surface of liquid metal, and the heat losses because of the long contact time with the mold walls. In this article two approaches are used to limit these effects: a general solution for the plunger speed as a function of time and a full-physics, three-dimensional CFD optimization. Mathematical model The dynamics of waves in a horizontal shot sleeve can be analyzed by drawing an analogy with flow in an open channel. A detailed analysis is possible by modeling the flow of metal in a rectangular shot sleeve of length L and height H (justified for initial fill fractions in the range of 40-60% [1]) using the shallow water approximation [3]. In this approximation the flow in the vertical direction is neglected in comparison with the horizontal velocity component. The flow is modeled in two dimensions, with the x axis directed along the direction of motion of the plunger, and the z axis pointing upwards. If viscous forces are omitted, then the flow has only one velocity component, u, along the length of the channel. The plunger speed in the positive x direction is given by dX/dt=X’(t), where X(t) defines the position of the plunger at time t>0. At the moving surface of the plunger, the velocity is defined as . As the plunger moves along the length of the channel it sends waves traveling forward along the metal surface. Each wave is associated with a small segment of the metal free surface and the column of metal directly below it (Fig. 1). The location, metal speed and depth in a wave that separates from the surface of the plunger at time t=tp are given by [3]: (1) Where According to Eq. (1), the metal speed, u, and depth, h, in each wave are constant and depend only on the time of the wave separation from the plunger, tp. They both increase with the speed of the plunger X’. Therefore, the first conclusion is that to maintain a monotonic slope of the metal surface in the direction away from the plunger, the latter must not decelerate. If this condition is not satisfied, then there will be waves sloped in both directions. When they reflect off the end of the sleeve and travel back towards the plunger, it creates unfavorable conditions for the evacuation of air from the sleeve and into the die cavity. Figure 1: Schematic representation of the flow in a shot sleeve and the coordinate system. Controlling the Waves Once a wave detaches from the plunger it travels at a constant speed given by (2) If the plunger accelerates, then each successive wave will move faster than the waves generated earlier. This will lead to a steepening of the surface slope as the waves travel further down the channel, and can potentialy result in overturning. If the speed of the plunger can be controlled as to limit the wave steepening during the slow shot stage, then the overturning can be avoided. Figure 2: The illustration for calculation of the slope of the metal’s free surface. Let us analyze the evolution … [Read more...]

## Optimisation of the shape of a toilet

The design of sanitary ware not only follows aesthetic criteria but must also be subject to strict regulations that govern its proper functioning. Among these, a sanitary fixture must guarantee a good and effective cleaning of the internal surfaces, making sure that during the drainage phase the water properly removes most of the dirt. This study aims to analyze possible alternative forms for both the water inlet and the toilet bowl itself, which maximize the surface area of the interior of the toilet wetted by water. The variables involved are potentially multiple and interconnected: manually exploring all possible values can be a very long and complex work, as well as understanding the effects on the target set. For this reason we have chosen to use an optimization software that responds to this need: interfacing with the most disparate software you are able to automate the work, analyze the influence of multiple parameters and understand the link between them and the performance you want to improve. The software chosen is IMPROVEit, which thanks to its simple interface allows you to easily perform both the setup phase and the processing of results. https://www.youtube.com/watch?v=7KoQHw1VQfk&feature=youtu.be The software is able to internally modify the shape of STL geometries on the basis of parameters set by the user, launch fluid dynamic simulations interfacing with the CFD software FLOW-3D® using the modified geometries, extract the results of the software and process them with appropriate mathematical nodes or invoking Excel to obtain the quantity to be optimized. FLOW-3D® has been chosen for its excellent capabilities, in terms of speed and accuracy, in the calculation of transient and free surface flows. Three geometric parameters were chosen to vary, so as not to complicate the problem too much: the direction of the inlet, the outlet section of the inlet and the slope of the front part of the sanitary, playing with the curvature present here. Optimisation can certainly be complicated with more time available. The objective is to maximize the wetted surface of the inside of the sanitaryware, calculated as the integral area covered by liquid during the entire discharge time divided by the discharge time itself. Moreover, it has been imposed the constraint that the water must not escape from the upper part of the sanitary, even in small quantities, to discard those solutions that while washing the surface cause unwanted splashes. The fluid dynamics simulation was set up by initializing the water in the tank upstream of the toilet and setting as boundary conditions the exit from the exhaust pipe and the atmospheric pressure of the air. In this way, the water flow is free to enter freely and naturally into the sanitaryware. The simulation is stopped when the tank is completely empty. IMPROVEit has the advantage that it does not require knowledge in the field of optimization to be used, as it is able to independently choose the best strategy to achieve the goal. It only requires you to define a budget, which is the time you want to devote to optimization, because the strategy chosen is such as to seek optimal solutions around the end of this period. Since each calculation cycle (variation of the geometries, fluid dynamics simulation and elaboration of the outputs) lasts approximately 40 minutes, a budget of 25 cycles has been chosen, in order to have the result in little more than a day. Considering that there are 3 variables at play and that the problem is complex, it can be considered a rather challenging case for the optimization software. Nevertheless, IMPROVEit has already been able to propose solutions that increase the surface area of the toilet wetted by water by up to 35%. Moreover, by analysing the panorama of the solutions found, it is possible to better understand the influence of the various factors. It can be seen, in fact, as larger outlet diameters premino because they allow a greater leakage of mass in the unit of time, despite a reduced throttle leads to higher speeds. The direction of the inlet that gives the best results, however, is aligned with the horizontal plane, while the shape of the sanitary has more varied effects, without highlighting such a clear trend. … [Read more...]