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Towards an accurate pressure estimation in injection molding simulation using surrogate modeling

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Abstract

The computational cost of high-fidelity injection molding simulations has been growing in the past years making it more and more challenging to use them for performing analyses such as optimizations or uncertainty quantification. Surrogate modeling offers a cheaper way to realize such studies and has been gaining attention in the field of injection molding simulation. In this work, we propose to compare three surrogate modeling techniques along with two design of experiment methods in their ability to predict the pressure signal at a surface node in a Moldflow simulation by varying process and modeling parameters. A Sobol sensitivity analysis is performed to study the contribution of the varied parameters on the pressure results. In addition, one of the generated models is used along with experimental pressure sensor data to improve the pressure estimation by calibrating the heat transfer coefficients during filling and packing as well as the pressure-dependency coefficient in the Cross-WLF viscosity model. This resulted in major improvements of the pressure predictions for all 27 considered cases in comparison to using the default heat transfer coefficients and viscosity model parameter.

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Acknowledgements

The authors wish to thank Dr. Michael Schick (Robert Bosch GmbH) for the helpful discussions concerning the Python Uncertainty Quantification library.

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Authors and Affiliations

  1. Corporate Sector Research and Advance Engineering, Robert Bosch GmbH, Robert-Bosch-Campus 1, Renningen, 71272, Germany

    Sandra Saad & Camilo Cruz

  2. LAMPA Laboratory, Arts et Métiers Institute of Technology, Boulevard du Ronceray 2, Angers, 49035, France

    Sandra Saad & Amine Ammar

  3. Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstrasse 18, Aachen, 52062, Germany

    Alankar Sinha

  4. PIMM Laboratory, Arts et Métiers Institute of Technology, Boulevard de l’Hôpital 151, Paris, 75013, France

    Gilles Régnier

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Appendix A: Cross-WLF viscosity model

Appendix A: Cross-WLF viscosity model

The Cross-WLF viscosity model [15] describes the temperature, shear rate, and pressure dependency of the viscosity for thermoplastic materials. This model is used in Autodesk Moldflow Insight 2021.1 to calculate the viscosity of the polymer during its injection molding.

$$\eta = \frac{\eta_{0}}{1 + \left(\frac{\eta_{0}\dot{\gamma}}{\tau^{*}}\right)^{1-n}}$$
(A1)

where:

  • η is the viscosity of the melt,

  • η0 is the zero shear viscosity,

  • \(\dot {\gamma }\) is the shear rate,

  • τ∗ is the critical stress at the transition to shear thinning,

  • n is the power law index in the high shear rate regime.

The zero shear viscosity parameter, η0, in the above equation is given by the WLF model [16]:

$$\eta_{0} = D_{1} \exp{\left[-\frac{A_{1}(T-T^{*})}{A_{2} + (T-T^{*})} \right]}$$
(A2)

where:

  • T is the temperature,

  • T∗ = D2 + D3P is the glass transition temperature,

  • A2 = A3 + D3P,

  • P is the pressure,

  • A1, A2, D1, D2 and D3 are data-fitted coefficients.

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Saad, S., Sinha, A., Cruz, C. et al. Towards an accurate pressure estimation in injection molding simulation using surrogate modeling. Int J Mater Form 15, 72 (2022). https://doi.org/10.1007/s12289-022-01717-0

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