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Simulation and Validation of Die Deformation in Permanent Mould Castings

Digital simulation is already used extensively when designing metallic dies for casting, in particular to design filling and gating systems. Simulations of die cycling to obtain the steady-state temperatures of the dies have also been mastered. Shorter cycle times require temperature regulation (cooling and heating) by a heat transfer fluid (water or oil). For large castings however, the temperature gradient induced between the moulding surface and the rear surfaces of the die leads to deformations that may be large enough to measure and incompatible with the required dimensional accuracy(2,3). The temperature gradient also creates thermal fatigue stresses that may cause cracking of the die surface.

This article by A Chabod, Y Longa, J M Dracon, K Chailler, P Hairy and A Da Silva of CTIF- Centre Technique des Industries de la Fonderie - Sèvres (France) describes validation of a thermo-mechanical simulation system using ProCAST software based on an experimental bench designed by CTIF, capable of detecting measurable levels of deformation. The thermo-mechanical simulation approach increases the possibility of using these high temperature deformation predictions to optimise the die design as early as the design stage to finally obtain a casting part with the initial desired dimensions.

Design of the test bench
A schematic representation of the experimental bench set-up, having a metallic die with a simple cavity to enable casting of an aluminium part, with temperature and displacement sensors is shown in fig.1. The details of this experimental set-up have been described in an earlier CTIF publication(4).

Measuring resources LVDT sensors
The measurement of displacements by LVDT inductive sensors has also been described in a previously published work by CTIF(1). These sensors are metallic, allowing use at high temperature, and their measurement precision is +/- 0.005mm (observed background noise).

Experimental set-up
Instrumented experimental pouring is performed on the tooling. The test bench includes a means of measuring the radial displacement R and vertical displacement Z, using LVDT inductive sensors. A thermocouple is positioned through a drilled steel bolt, with thermal properties comparable to mould material.

The operations necessary for the pouring of five AlSi7Mg0.6 aluminium alloy castings lasted 5,000 seconds (approximately 1hr 20min). The spoon is gauged to control the cast part weight (mean: 3.9kg, scatter: +/- 100g). The casting temperature of the alloy was 700°C, and the metallic tooling was initially at the ambient temperature of 20°C. The die/metal interface was covered by a 50μm thick DYCOTE 39 die coating. 

Correlations between simulation and experimental results

The thermo-mechanical simulations with ProCAST software (fig.3) were intended to model the temperature and displacement fields in the die to compare the results with the experimental tests. The aluminium casting alloy used was AlSi7Mg0.6 and the die was made of tool steel XC38CrMoVa5.3. The simulation involved filling, solidification, die removal / casting ejection at t0+300s, and the die cooling until the beginning of the next casting cycle at t0+1000s. 

The following boundary conditions are applied on the model. The die coating between the die/metal interfaces is modelled using a thermal resistance during filling and solidification. Post die removal and casting ejection, the interface is considered to have a natural convection to account for the contact with atmospheric air. The rest of the surface of the die is subjected to convection with ambient air. Symmetry of the geometry and loads facilitates the modeling of only one quarter of the bench. We can see the central axis and the height adjustable device in mechanical and thermal contact with the mould. Only three cycles are taken into account because of convergence difficulties due to contact between the deformed mould and the height-adjustable device.

The values obtained by simulation are offset by approximately 25°C, from the thermocouple measurements (fig.4).

The measured vertical displacements (fig.5) are the same in shape and of the same order of magnitude in size as the measurements by LVDT sensors. The observations show a first phase in which the die assumes a convex shape (scale strictly positive, cf. fig.3), in the first instants of the cycle, where the heat input is intense, engendering swelling of the die surface. Then, the heat contributed by the alloy diffuses by conduction into the bottom part of the die, and at the same time the moulding surface cools substantially, in particular after shaking out. In the course of this second phase, the temperature is higher in the bottom part of the die, leading to a concave die shape (scale strictly negative). At the end of the cycle, the geometry of the die once again becomes convex.

The radial displacement measurement is made using two LVDT sensors at diametrically opposite positions on the die (fig.6). This arrangement eliminates the effects of any eccentricity of the die during the casting. 

Conclusion
The investigations showed that LVDT inductive sensors yield a measurement precision compatible with the amplitudes of displacement of the die.

The simulation results from ProCAST software are well correlated with the experimental measurements and validate the tools and the calculation methods. This thermo-mechanical approach makes it possible to optimise die design in the foundry and to predict high-temperature deformations as early as the design stage. Knowledge of these deformations makes it possible in turn to anticipate the geometrical and dimensional variations undergone by the castings themselves and so to improve their accuracy. The designer can act on the temperature of the die or the design of the casting, or create a die in which the expected thermal deformation is reversed to produce a casting having the correct dimensions.

Acknowledgments
The research work presented herein forms part of the Promapal Research Program, and obtained funding in response to the 8th request for proposals by the French Single Inter-Ministry Fund (FUI) that supports Competitiveness Clusters research. This research program was also supported by the European Regional Development Fund (FEDER). The authors are grateful to all industrial and research partners (Montupet SA, Evatec, TCPP, Cirtes SRC, Critt Metall 2T, CTIF) for providing useful information based on their experience.

Contact: CTIF - Centre Technique des Industries de la Fonderie, Sèvres (France), emails :
chabod@ctif.com, longa@ctif.com, dracon@ctif.com, chailler@ctif.com, hairy@ctif.com, dasilva@ctif.com

For figures see printed version :-
Fig1 Experimental test bench
Fig 2 Experimental pouring
Fig 3 ProCAST thermo-mechanical simulation 
Fig 4 Comparison of the thermocouple measurements with simulated results
Fig 5 Comparison of the vertical displacements measured by LVDT sensors with simulated results
Fig 6 Radial displacements measured by LVDT sensors

References
1. Journée F and Ogier G, ‘Mesure des déformations en cours de solidification’, Fonderie Fondeur d''Aujourd''hui, vol 214 pp10-23, 2002.
2. Weiss K and Honsel C, ‘Stress in casting dies - simulation and practical example’ Casting Plant and Technology International, vol 02/2008 pp28-33, 2008.
3. Rosbrook C and Kind R, ‘Casting process simulation of stresses and distortion in casting and dies’, Die Casting Engineer, September/October 1999, pp72-76, 1999.
4. Chabod A, Longa Y, Dracon J M, Chailler K, Hairy P, Da Silva A, ‘Simulating the deformation of dies in the foundry’, Fonderie magazine, October 2012, No28, 2012.