Digital twin of functional gating system in 3D printed molds for sand casting using a neural network

Abstract

The filling stage is a critical phenomenon in sand casting for making reliable castings. Latest research has demonstrated that for most liquid engineering alloys, the critical meniscus velocity of the melt at the ingate is in the range of 0.4–0.6 m s⁻¹. The work described in this research paper is to use neural network (NN) technology to propose digital twin approach for gating system design that allow to understand and model its performances faster and more reliable than traditional methods. This approach was applied in the case of sand casting of liquid aluminum alloy (EN AC-44200). The approach is based first on a digital representation of filling process to perform the melt flow simulations using a combination of the gating system design parameters, selected as a training cases from Taguchi orthogonal array (OA). The second step of the approach is the data capture of functional gating design system to train up the feed-forward back-propagation NN model. The validation of the well-trained NN model is assessed by interrogating predicted ingate velocity to it and making reliable predictions with high accuracy. The claim is that such digital twin approach is an effective solution to recognize the functional design parameters from the entire filling systems used during casting process.

Appendix

The relationship between the selected gating design variables and their corresponding ingate velocity is described by the response surface methodology (RSM). A central composite design (CCD) with three level factorial design was employed in this study to construct an accurate RSM. Equation (10) shows the first-order regression model in RSM.

$$ Y = \beta_{0} + \sum\limits_{j = 1}^{m} {\beta_{j} } x_{j} + \sum\limits_{j = 1}^{m - 1} {\sum\limits_{p = 1}^{m} {\beta_{jp} } x_{j} } x_{p} $$

(10)

where Y is the response objective, x_j is the independent design variables and x_j x_p is the interaction term. β₀ is the constant term, β_j is the jth linear coefficient, and β_jp is the jpth interaction coefficient.

The six factors derived from the ANOVA results were used to construct the response objective. As shown in Table 6, the significant design variables three level CCD experiment, which are coded as − 1 and + 1 and the midpoint coded as 0, was employed to determine the response surface model V_ingate (Chen et al. 2016).

Table 6 Factors and levels selected from ANOVA test

According to the first order regression equations (Eq. 3) the relationship between selected parameters and objective was established as shown in Eq. (11) after eliminating the insignificant terms.

$$ \begin{aligned} V_{ingate} & = 0.75 + 0.04 \times {\text{A}} + 0.06 \times {\text{B}} + 0.035 \times {\text{C}} + 0.03 \times {\text{D}} - 0.036 \times {\text{I}} - 0.05 \times {\text{J}} - 0.024 \times {\text{AB}} - 0.055 \times {\text{AC}} \\ & \quad - 0.047 \times {\text{AD}} + 0.017 \times {\text{AI}} - 0.024 \times {\text{BD}} + 0.024 \times {\text{CD}} - 0.012 \times {\text{CI}} - 0.006 \times {\text{DJ}} - 0.016 \times {\text{IJ}} \\ \end{aligned} $$

(11)