F. Faura

On the optimum plunger acceleration law in the slow shot phase of pressure die casting machines

The objective of this paper is to analyse a plunger acceleration law that is expected to minimize air entrapment in the slow shot phase of pressure die casting in horizontal cold chambers, and thus to reduce porosity in manufactured parts. The study is carried out using results from an analytical model of the flow of molten metal in the shot sleeve, which is based on the shallow-water approximation, and whose predicted optimum acceleration parameters are in good agreement with available experimental results. The results for the surface profiles of the wave formed during plunger movement using plunger acceleration laws which are typically used in pressure die casting are compared with those corresponding to the proposed law. Some analytical predictions for the wave profiles and for the mass of trapped air are compared with numerical results obtained from a finite-element code, which solves momentum and mass conservation equations. The limiting values of the initial filling fraction required for appropriate operating conditions are determined for wide ranges of acceleration parameters and pouring hole locations.

Shot Sleeve Wave Dynamics in the Slow Phase of Die Casting Injection

An analysis is carried out on the wave formed during the slow phase of die casting injection processes. Viscous effects are assumed to be negligible and the problem is treated two-dimensionally using finite amplitude wave theory. Two commonly used types of plunger movements are considered, for which all the possible wave profiles are analyzed in depth as a function of the parameters which characterize the law of acceleration applied to the plunger, the initial shot sleeve filling fraction, and the geometrical characteristics of the problem. Different relationships between the relevant dimensionless parameters of the system are proposed, which make it possible to optimize the injection process, and so reduce the entrapment of air which leads to porosity. The validity of such relationships is analyzed in detail for different ranges of parameters. Some of the results obtained for the optimum acceleration are compared with those of other authors and experimental measurements. Finally, a law of plunger acceleration which would completely eliminate the air from the shot sleeve at the end of the slow phase of injection and minimizes the filling time is derived.

A decision support system for sheet metal blanking process parameters selection

Abstract Once manufacturing criteria have been established, a well-founded decision support system (DSS) may solve the problem of selecting the optimum set of parameters. An axiomatic approach has been used in order to quantify final part quality. The present case takes into account form errors in blanking process and an equation model that enables quality quantification through part complexity has been developed. The measurement of complexity in blanked parts may be simplified to a study of the effect of the fundamental parameter (clearance) on the form errors. In order to consider economic influences, technical cost modelling (TCM) has been implemented. With the purpose of uniting both aspects under one common criterion, a function that evaluates them in a single measuring system has been defined. Based on this function, the developed DSS integrates a formal multi-attribute decision model with a relational database. The decision model enables representation of the user’s preferences as regards decision factors. Due to the great number of parameters and variables that intervene in the system, a computerised graphical interface application has been developed allowing decision makers to compare, justify and evaluate different alternatives in a friendly environment.

On the Critical Plunger Speed and Three-Dimensional Effects in High-Pressure Die Casting Injection Chambers

During the initial slow stage of the injection process in high-pressure die casting machines with horizontal cold chamber, a plunger pushes the molten metal which partially fills the injection chamber, causing the formation of a gravity wave. The evolution of the wave surface profile, which depends on the plunger acceleration law, may trap air in the molten metal, causing porosity when the metal solidifies. In this work, a one-dimensional shallow-water model, which is solved numerically using the method of characteristics, and a three-dimensional numerical model, based on a finite element formulation and the volume of fluid (VOF) method for treating the free surface, are used to analyze the flow of molten metal in an injection chamber of circular cross section. The results for the evolution of the free surface obtained from both models for different plunger motion laws and initial filling fractions of the injection chamber were in good agreement for broad ranges of operating conditions. The existence of a critical plunger speed, above which the reflection of the wave of molten metal against the chamber ceiling might appreciably increase air entrapment effects, is investigated. The results for the wave profiles in chambers of circular cross section are compared with those obtained in an equivalent two-dimensional configuration of the injection chamber, for which the shallow-water model is solved analytically. It is shown how the results obtained by applying the one-dimensional model to a two-dimensional chamber configuration can be used to reproduce, with an acceptable degree of accuracy, the salient characteristics of the flow of molten metal in a real injection chamber of circular cross section.

Analysis of the Flow in a High-Pressure Die Casting Injection Chamber

The flow in the injection chamber of pressure die casting machines is analyzed using a model based on the shallow-water approximation which takes into account trie effects of wave reflection against the end wall of the chamber. The governing equations are solved numerically using the method of characteristics and a finite difference grid based on the inverse marching method. The results of the model for wave profiles, volume of air remaining in the injection chamber at the instant at which the molten metal reaches the gate to the die cavity, and optimum values of the parameters characterizing the law of plunger motion, are compared with the numerical results obtained from a finite element code, which solves the two-dimensional momentum and mass conservation equations, taking into account nonhydrostatic and viscous effects

A new volume conservation enforcement method for PLIC reconstruction in general convex grids

A comprehensive study is made of methods for resolving the volume conservation enforcement problem in the PLIC reconstruction of an interface in general 3D convex grids. Different procedures to bracket the solution when solving the problem using previous standard methods are analyzed in detail. A new interpolation bracketing procedure and an improved analytical method to find the interface plane constant are proposed. These techniques are combined in a new method to enforce volume conservation, which does not require the sequential polyhedra truncation operations typically used in standard methods. The new methods have been implemented into existing geometrical routines described in Lopez and Hernandez 15, which are further improved by using more efficient formulae to compute areas and volumes of general convex 2 and 3D polytopes. Different tests using regular and irregular cell geometries are carried out to demonstrate the robustness and substantial improvement in computational efficiency of the proposed techniques, which increase the computation speed of the mentioned routines by up to 3 times for the 3D problems considered in this work.

An Experimental and Numerical Study of Flow Patterns and Air Entrapment Phenomena During the Filling of a Vertical Die Cavity

One of the most important problems encountered in die-casting processes is porosity due to air entrapment in the molten metal during the injection process. The aim of this work is to study experimentally and numerically the different air entrapment phenomena that may take place in the early stages of the filling of a vertical die cavity with a rectangular shape for operating conditions typically used in low and medium-pressure die-casting processes. Special attention is given to determining the influence of the gravitational forces on the flow pattern. Numerical simulation of the flow in the die cavity is carried out for the liquid phase using a commercial computational fluid dynamics (CFD) code (FLOW-3D) based on the solution algorithm-volume of fluid (SOLA-VOF) approach to solve the coupling between the momentum and mass conservation equations and to treat the free-surface, while the amount of air evacuated through vents is calculated by using an unsteady one-dimensional adiabatic model that retains friction effects. The main characteristics of the flow at the early instants of the die cavity filling are analyzed for different operating conditions, and the different flow patterns are summarized in a map as a function of the Reynolds and Froude numbers. Also, filling visualization experiments are carried out on a test bench using water as working fluid in a transparent die model and a high-speed camera. The numerical and experimental results obtained for the free-surface profile evolution are compared for different inlet velocities of the fluid and the viability of the numerical tools used to predict the final amount of trapped air in the die cavity is discussed.

Influence of Unsteady Effects on Air Venting in Pressure Die Casting

The influence of unsteady effects on the evacuation of air through vents in pressure die casting processes is analyzed. A model is proposed which considers the air flow as one-dimensional and adiabatic, and which retains friction effects. Venting conditions for wide ranges of the relevant dimensionless parameters are analyzed for both atmospheric and vacuum venting systems. The model is solved numerically using the method of characteristics and its results are compared with those obtained for quasi-steady models. It is shown that wide ranges of operating conditions can exist in practical situations, for which unsteady effects, neglected in previous models, are important and must be taken into account to determine the air mass entrapped at the end of the filling process. The selection of parameters which will reduce the amount of trapped air and thus porosity in manufactured parts is also discussed.

VOFTools - A software package of calculation tools for volume of fluid methods using general convex grids

The VOFTools library includes efficient analytical and geometrical routines for (1) area/volume computation, (2) truncation operations that typically arise in VOF (volume of fluid) methods, (3) area/volume conservation enforcement (VCE) in PLIC (piecewise linear interface calculation) reconstruction and(4) computation of the distance from a given point to the reconstructed interface. The computation of a polyhedron volume uses an efficient formula based on a quadrilateral decomposition and a 2D projection of each polyhedron face. The analytical VCE method is based on coupling an interpolation procedure to bracket the solution with an improved final calculation step based on the above volume computation formula. Although the library was originally created to help develop highly accurate advection and reconstruction schemes in the context of VOF methods, it may have more general applications. To assess the performance of the supplied routines, different tests, which are provided in FORTRAN and C, were implemented for several 2D and 3D geometries. Program summary: Program Title: VOFTools Program Files doi: http://dx.doi.org/10.17632/brrgt645bh.1 Licensing provisions: GNU General Public License, version 3. Programming language: FORTRAN and C, with C interfaces. Nature of problem: The package of routines includes simple and efficient analytical and geometrical tools for area/volume computation, truncation operations that typically arise in VOF (volume of fluid) methods, area/volume conservation enforcement (VCE) in PLIC (piecewise linear interface calculation) reconstruction and computation of the distance from a given point to the reconstructed interface. Solution method: The volume (area in 2D) computation of a polyhedron (polygon in 2D) uses an efficient formula based on a quadrilateral decomposition and a 2D projection of each polyhedron face. The analytical VCE method is based on coupling an interpolation bracketing procedure with an improved final calculation step based on the above volume computation formula. Also, the exact distance from a given point to a reconstructed polygonal interface is calculated. Restrictions: Convex 2D and 3D polytopes.

Numerical Simulation of Breaking Waves Using a Level Set Method

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.Copyright