A heuristic approach to meet geometric tolerance in High Pressure Die Casting

                        Engineering Research Paper

Author:

G. Campatelli , A. Scippa

Department of Mechanical Engineering and Industrial Technologies, University of Firenze – Italy, Via di S. Marta, 3, 50139 Firenze, Italy

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 tech-nique 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.

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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. 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. Porosity reduces with increasing intensification pressure, but enlarges with increasing casting velocity. 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. 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.

The general aim 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 work piece 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.

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 displacement vectors at each node are used to adjust the trial die design until the target part geometry is achieved. Thus, the results from one cooling simulation give the input for the next iteration. By making the geometry changes on the FE description of the work piece, new die geometry is directly obtained for the next cooling simulation.

The proposed strategy is based on four phases:

1. Hypothesis of the thermal map of the product before the cooling phase; this could be obtained from the study of similar product (company experience), from technical consideration or by FE simulation of the casting and cooling inside the die.

2. Hypothesis of the heat transfer parameters during cooling: fluid type and temperature, geometry of the product and its orientation in the cooling bath.

3. Determination of the cold product geometry and residual stresses by means of FE simulation.

4. Iterative design process to define the optimized die geometry able to meet the tolerances required for the final product.

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. The thermal stress calculation procedure is as follows:

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

– the time integration scheme;

– the appropriate integration time step;

– defining both mechanical and thermal properties, using a mechanical constitutive model that allows entry of a thermal coefficient of expansion and mechanical properties that are function of temperature;

– realistic boundary conditions;

In a coupled thermal-stress analysis, the thermal time step is independent from the mechanical time step. The rate of mechanical motion, mechanical deformation, and rate of heat transfer must all be considered in selecting an appropriate time step.

 Heat transfer coefficients

To set up a realistic simulation is necessary to provide the heat transfer coefficients for all the phases of the cooling (opening of the die, transport of the product to the cooling bath, etc.), and the thermal map of the work piece at the beginning of the cooling process. This last one can be evaluated knowing the heat transfer from the material to the die, which is usually cooled by water circulation. Some foundry software can provide such information. The heat transfer can be calculated knowing the orientation of the product during transportation and cooling in the bath and the external thermal condition. The approximations of the heat transfer coefficients and of the thermal map constitute the greatest source of error in the simulation.

 Conclusions

The 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 obtain the optimal die geometry, has proven to be very efficient and consists in an iterative procedure that eliminate the trial-and-error optimization by the use of a Matlab_ script that automatically run a sequence of iterations in order to get the final die shape. The different stages in the iteration, i.e., deviation calculation and result mapping are solved by programs written solely for these purposes.

The main advantages of the method are:

– The high generality, so it can easily be applied for modeling other manufacturing processes (e.g. extrusion, welding, sandcasting).

– The ease of implementation that make it easily applicable to most of commercial FE software.

– The excellent convergence rate of the FE simulation, which results in very short response time.

– It is possible to separate the filling phase optimization and the tolerance optimization.

The critical parameters for obtaining a coherent solution are the heat transfer coefficient and the initial thermal map

And the most careful care has to be used for the evaluation of these characteristics in order to obtain a realistic FE simulation and it is most likely that the method will work on a variety of different shapes.