G.CampatelliA.Scippa

## Abstract

In High Pressure Die Casting (HPDC), geometrical distortions usually happen during the cooling phase, due to the reduced cooling time and the high thermal gradient inside the product itself. This phenomenon affects most the thin walled products. The usual die design practice considers only the linear shrinking of the product during the cooling as a consequence of the difficult to take in account also the geometrical deformations. In this essay a simple finite element design strategy that allows the designer to improve the die shape is presented. The proposed approach uses an automatic iterative optimization technique based on a heuristic algorithm, which could be easily applied to most of the Finite Element (FE) commercial software: the basic concept of the method is simply to move the nodes defining the die surface in the opposite direction to the error due to the cooling phenomena. An automotive component has been selected as a case study: the aim was to improve the planarity tolerance of a planar surface of the casted product. Results show the efficiency of the proposed method that, despite its simplicity, is able to provide an optimal solution with a small number of iterations.

## Introduction

For many metal components, with perhaps the exception of some powder forming process, the part can rarely be finished exactly to the required final tolerance in a single forming operation. Thus, in general, a forming operation is carried out to produce a ‘near-net-shape’ product, which is subsequently brought into the required tolerance by a finishing operation.

In aluminum casting, High Pressure Die Casting (HPDC) is used when high productivity and good quality of the rough product is required. Both productivity and reduction of finishing operations (neat shape or near net shape processes) allow a heavy reduction in the product manufacturing cost.

Due to the complexity of the process and the number of variables to be controlled, the optimization of HPDC is usually a difficult task with many connections among the process variables.

The mechanical properties of a die-cast product are related principally to the die temperature, the metal velocity at the gate, and the applied casting pressure [7]. The integrity of the cast component is affected by: the combination of die’s thermal profile, mold filling capacity of the molten metal, geometrical complexity of the parts and cooling rate during die casting. The pressure applied to the casting during solidification is crucial to the production of high integrity parts [3]. Porosity reduces with increasing intensification pressure, but enlarges with increasing casting velocity [7], [21]. If these parameters are not controlled adequately, various defects within the finished component will be generated.

The main drawbacks of HPDC are the porosity and the deformation of the product during the cooling phase of the material. The porosity of the product is a well-studied phenomenon [21], [22], while the distortions resulting from the temperature gradients in the product during the cooling phase remain still a critical issue. This kind of deformations could produce variations in the dimensional tolerances of the product of the same order of magnitude of the tolerances usually required to the process. This phenomenon is usual due to the thin-walled feature of most of pressure die casted products, feature due to economical and weight reasons that produce rather weak surfaces. During the solidification phase, the natural casting shrinkage, constrained by the presence of the die, force the component to stretch plastically: this produce residual stresses and complex springback during the cooling phase subsequent to the extraction of the product from the die.

Usually the die’s shape design process takes into account only the thermal shrinkage of the product without considering the geometrical deformation that could arise due to the temperature gradients in the product during the cooling phase. Most of the die designers start from the geometry of the final product and “scale” this geometry using the thermal shrinking coefficient of the material using the company knowhow or a very expensive and time consuming trial-and-error approach. This usually takes place during the die try-out stage in a manufacturing plant, when the die has to be repaired or re-manufactured. The method is highly dependent upon the skill, experience, and luck of those carrying out the procedure.

In the last years Computer Aided Engineering (CAE) technologies have shown a very rapid development and actually are used widespread nearly in all the industrial sectors: the CAE applied to the manufacturing science is playing an important role in process optimization and property prediction for the development of new product.

Simulation of the casting process is now mature and a number of systems are available specifically for this purpose. Recent examples of these can be found in Yoshimura et al. [24] who used Flow3D® software to optimize the design of a die casting plunger tip; Kong et al. [10] used Fluent® to simulate the flow and heat transfer in the HPDC of a representative component; Kokot and Bernbeck [9] used MagmaSoft® to simulate the flow through a two cavity die to produce automotive head caps; Cleary et al. [2] used Smoothed Particle Hydrodynamics (SPH) method to modeling the geometric complexity and high fluid speeds involved in HPDC with strongly three dimensional fluid flow and significant free surface fragmentation and splashing.

The reason for the development of such studies is that nowadays numerical simulation offers a powerful and cost effective way to study the effectiveness of different die designs and filling processes, ultimately leading to improvements in both product quality and process productivity, including a more effective control of the die filling and die thermal performance. In spite of these capabilities, the numerical simulation could be used to evaluate a specific die and process proposal, but not to optimize automatically the die and process parameters.

In the last two decades much effort has been spent in order to develop optimization methods well suited for problems characterized by non-linearity, non-convexity and by continuous and/or discrete design variables, for which the application-requirements of gradient-based algorithms are not fulfilled. These approaches consists in applying optimization heuristics such as evolutionary algorithms (Simulated Annealing, Threshold Accepting), Artificial Neural Networks (ANN), Genetic Algorithms (GA), Tabu Search, and hybrid methods.

Many examples related to HPDC can be found in literature: Tsoukalas [22] used GA to optimizing the porosity formation; Krimpenis et al. [11] developed a hybrid model comprising of ANN and GA for the optimal selection of pressure die casting process parameters; Rai et al. [16] proposed an ANN model for the real-time estimation of the optimal HPDC process parameters; Kong et al. [10] settled a discrete simulation model based on thermography and Computational Fluid Dynamics (CFD) simulation in order to improve the cooling efficiency and improve the productivity of the process.

The main objective is the estimation of optimal HPDC process parameters, no work related to die’s shape optimization to meet the required geometric tolerance of the casting, has been found in literature.

There has been work made on tool compensation for springback in sheet forming, where the geometry is parameterised [19]. This approach could be extended to the die optimization, but the method seems to work only on simple geometries due to the difficulty of the parameterisation of the geometry.

In principle, the trial-and-error method can be applied equally in a simulation framework, but this approach requires accurate prediction capabilities and can be as time consuming as experimental methods when a mechanism for guiding subsequent die design iterations has not been established.

The general aim of the paper is to provide some guideline for the building up of Finite Element (FE) simulation of the cooling phase for a HPDC product and to present an algorithm for the automated optimization of the die geometry, using commercial FE software. It is a heuristic method, based on the difference between the workpiece after cooling and the desired shape. No parameterisation of the die geometry is needed: since no parameters are used to describe the shape of the die geometry, it can be modified in an arbitrary way without the restriction of the design space spanned by design parameters.

## Section snippets

## Proposed approach

Assuming that the deformed shape due to cooling can be predicted accurately, there still remains the problem of how to use such results to obtain a suitable die design able to meet the required tolerances. That is, the cooling predictions allow ‘‘forward’’ analysis, while a ‘‘backward’’ analysis is needed to obtain, from these results, an optimized die design. The proposed approach is based on iteratively comparing a target part shape with the FE simulated part shape after cooling. The

## Setting up the FE simulation

Distortions are basically the result of the temperature gradient inside the piece, the constrained shrinkage during the solidification phase, and the high thermal shock due to the cooling phase: therefore it is necessary to perform a coupled thermal-stress analysis [22]. The thermal stress calculation procedure is as follows (Fig. 2):

For a coupled thermal-stress problem, important topics are:–

the time integration scheme;–

the appropriate integration time step;–

defining both mechanical and thermal

## Case study

The case study of this paper is an automotive component, a water pump cover, with very strict planarity tolerance on the surface (the ones highlighted in Fig. 4) that interfaces with the pump case. The overall dimensions of the component are 178 × 120 × 42 mm.

In order to make the proposed approach more confident, two different condition of cooling has been considered: the water quenching (the cooling condition of the real process) and a gently air cooling, considering a quiescent temperature of 26 °C.

## Die’s shape optimization

The general-purpose explicit and implicit finite element program Ls-Dyna® has been chosen to perform the required simulations. Ls-Dyna® is used to solve multi-physics problems including solid mechanics, heat transfer, either as separate phenomena, or, as in this case, as coupled physics. Moreover Ls-Dyna® provides high-efficiency parallel computation technology like Symmetric Multi-Processing (SMP) and Massively Parallel Processing (MPP), the later much more attractive and effective for complex

## Conclusions

The described method for die geometry compensation has shown to produce a die shape which minimizes the product geometrical error such as planarity. This approach could highly reduce the errors that are generated by the simple die design at nominal geometry or compensated only for uniform shrinkage. The method is characterized by a very short response time: only few cooling simulations are needed and the FE model developed has a very high convergence rate. Moreover the algorithm developed to

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