**3.2 New gating system for full mold casting foam residue traps**

By installing a gate at the bottom of the rim, the metal cannot avoid merging in the rim. If the pouring temperature cannot be increased, residue defects are more likely to occur. This requires the discharge of metal that contains residue from the rim. Therefore, we propose a new gating system: foam residue traps. For shrinkage nests, this system allows us to lower the temperature of the pouring metal. Although lowering the pouring temperature may increase the number of defects in the residue, a trap is installed on the side of the rim at the position where the metal joins with the metal to collect the residue, and the metal that is free from residue is recovered. This makes it possible to reduce residue defects.

In order to verify the effect of discharging molten metal entrapped by residue traps, a gating system was designed as shown in **Figure 4**. CFD analysis was performed for this. The analysis conditions are the same as in the previous section, except that a residue trap was installed.

The results of the CFD analysis are shown in **Figure 5**. The results of the analysis are velocity vectors of the metal, which are cross-sections based on the center of the height of the capstan drum. Horizontal cross-sections are set at −120 mm, 0 mm, and 120 mm height, respectively. At the 0 mm and 120 mm cross-sections, there is a vector of the flow from the inside of the residue trap to the rim. Therefore, metal that is entrapped in the residue may flow into the rim. Since the interface between the foam model and the metal is filled with molten metal with resistance due to combustion, it is considered that convection is formed by a flow that has no place to go. Therefore, it is necessary to design an appropriate casting plan to prevent the backflow of metal to the rim side due to convection inside the residue trap.

**77**

**Figure 6.**

*Foam residue traps of capstan drum and design variables.*

*CFD Optimization Method to Design Foam Residue Traps for Full Mold Casting*

Based on the results of the analysis in the previous section, the bottom of the rim is considered the best location for the gate, but in any case, residue defects will be generated by molten metal joining in the rim. In this study, a residue trap is proposed as a gating system for collecting molten metal that can join together and directly collect metal that is entrained with residue, and a new casting method for large castings is presented. The optimal design of the residue trap is used for the capstan drum shown in **Figure 2**. In optimization, the dimensions defined as design variables are varied within a set range to find the optimal combination. This combination increases with the number of design variables, and the time required for optimization becomes enormous. Therefore, the number of design variables must be set to the minimum necessary. The basic shape of the residue trap and the locations where the design variables were set are shown in **Figure 6**. The design variables were defined with five variables, *x*1 to *x*5. Six of these residue traps are installed evenly across the sides of the rim and are interlocked depending on the value of the design variables, all of which

*DOI: http://dx.doi.org/10.5772/intechopen.95505*

**3.3 Optimal design of residue traps**

*The velocity vectors on the horizontal sections for the foam residue trap.*

**Figure 5.**

have the same shape.

**Figure 4.** *Capstan drum with traps for preventing foam residues.*

*CFD Optimization Method to Design Foam Residue Traps for Full Mold Casting DOI: http://dx.doi.org/10.5772/intechopen.95505*

**Figure 5.**

*Casting Processes and Modelling of Metallic Materials*

temperature is required.

pouring temperature is increased to prevent residue defects, the temperature at the completion of filling will also be high, and therefore, to prevent shrinkage defects the pouring temperature should not be increased. Therefore, to prevent both residue defects and the formation of a shrinkage cavity, a new casting plan that allows the suppression of residue defects without increasing the pouring

By installing a gate at the bottom of the rim, the metal cannot avoid merging in the rim. If the pouring temperature cannot be increased, residue defects are more likely to occur. This requires the discharge of metal that contains residue from the rim. Therefore, we propose a new gating system: foam residue traps. For shrinkage nests, this system allows us to lower the temperature of the pouring metal. Although lowering the pouring temperature may increase the number of defects in the residue, a trap is installed on the side of the rim at the position where the metal joins with the metal to collect the residue, and the metal that is free from residue is

In order to verify the effect of discharging molten metal entrapped by residue traps, a gating system was designed as shown in **Figure 4**. CFD analysis was performed for this. The analysis conditions are the same as in the previous section,

The results of the CFD analysis are shown in **Figure 5**. The results of the analysis are velocity vectors of the metal, which are cross-sections based on the center of the height of the capstan drum. Horizontal cross-sections are set at −120 mm, 0 mm, and 120 mm height, respectively. At the 0 mm and 120 mm cross-sections, there is a vector of the flow from the inside of the residue trap to the rim. Therefore, metal that is entrapped in the residue may flow into the rim. Since the interface between the foam model and the metal is filled with molten metal with resistance due to combustion, it is considered that convection is formed by a flow that has no place to go. Therefore, it is necessary to design an appropriate casting plan to prevent the backflow of metal to the rim side due to

**3.2 New gating system for full mold casting foam residue traps**

recovered. This makes it possible to reduce residue defects.

except that a residue trap was installed.

convection inside the residue trap.

*Capstan drum with traps for preventing foam residues.*

**76**

**Figure 4.**

*The velocity vectors on the horizontal sections for the foam residue trap.*

## **3.3 Optimal design of residue traps**

Based on the results of the analysis in the previous section, the bottom of the rim is considered the best location for the gate, but in any case, residue defects will be generated by molten metal joining in the rim. In this study, a residue trap is proposed as a gating system for collecting molten metal that can join together and directly collect metal that is entrained with residue, and a new casting method for large castings is presented.

The optimal design of the residue trap is used for the capstan drum shown in **Figure 2**. In optimization, the dimensions defined as design variables are varied within a set range to find the optimal combination. This combination increases with the number of design variables, and the time required for optimization becomes enormous. Therefore, the number of design variables must be set to the minimum necessary.

The basic shape of the residue trap and the locations where the design variables were set are shown in **Figure 6**. The design variables were defined with five variables, *x*1 to *x*5. Six of these residue traps are installed evenly across the sides of the rim and are interlocked depending on the value of the design variables, all of which have the same shape.

**Figure 6.** *Foam residue traps of capstan drum and design variables.*

Three objective functions are defined as evaluation indices for optimization. The first objective function, *J*1, is an indicator of the amount of residue in the rim. The residue in this CFD software is defined as the diffusion of the transport equation equal to the volume of the foam model replaced by metal. This amount of residue can actually be calculated as the residue volume fraction *a*k for each calculated cell *k*, which represents the volume fraction of the residue contained in the cell in terms of solid time equivalent, and *J*1 is defined as the following equation, where *J*1 is this residue volume fraction averaged for each cell in the rim.

$$J\_1 = \frac{\sum\_{k=1}^{n} a\_k}{n} \tag{4}$$

where *n* is the number of cells in the rim. In other words, *J*1 represents the volume fraction of the residue in the entire rim. The smaller the value of *J*1, the lower the residue defects are expected to be in the actual castings. In this capstan drum simulation, the number of cells in the rim is *n* = 32575, where each side is a cube of 5 mm.

The second objective function, *J*2, is defined as the contact area between the rim and the residue trap. *J*2 is calculated using the design variables *x*1, *x*3, and *x*4 by the following equation.

$$J\_2 = \mathfrak{x}\_1 \mathfrak{x}\_4 + \mathfrak{x}\_3 \mathfrak{x}\_4 \tag{5}$$

The smaller the value of *J*2, the easier it is to remove the residue traps and the better the shape.

The third objective function, *J*3, is defined as the volume of the residue trap itself, which is calculated using the design variable *x*5 and the height of the residue trap, *h*, as follows.

$$J\_{\mathfrak{z}} = \mathfrak{x}\_{\mathfrak{z}}^2 \hbar \tag{6}$$

**79**

**Figure 8.**

**Figure 7.**

*Distribution of all analyzed individuals in optimization.*

*Optimized shape of foam residue trap. (a) Foam residue trap. (b) Whole shape of casting.*

*CFD Optimization Method to Design Foam Residue Traps for Full Mold Casting*

the residue traps in which no residue defects occurred in the preliminary experiments. Therefore, in this optimization we selected the individual that is superior for both objective functions as the optimal solution for this C. The final optimal shape is shown in **Figure 8**. The values of the design variables of the optimal solution are

shown in **Table 1** and those of the objective function are shown in **Table 2**.

*DOI: http://dx.doi.org/10.5772/intechopen.95505*

The smaller the value of *J*3, the higher the material yield and the better the gating system.

Based on these definitions, we added geometric constraints and finally formulated this optimization problem.

$$\begin{aligned} \text{Minimize } I\_1(\mathbf{x}\_1, \dots, \mathbf{x}\_5), I\_2(\mathbf{x}\_1, \mathbf{x}\_3, \mathbf{x}\_4), I\_3(\mathbf{x}\_5) \\ \text{Subject to } &0 \, mm \le \mathbf{x}\_1 \le \mathbf{x}\_2 \le 225 \, mm \\ &0 \, mm \le \mathbf{x}\_2 + \mathbf{x}\_3 \le 225 \, mm \\ &10 \, mm \le \mathbf{x}\_4 \le 30 \, mm \\ &30 \, mm \le \mathbf{x}\_5 \le 120 \, mm \end{aligned} \tag{7}$$

We applied NSGA-II [9], a multi-objective genetic algorithm, to this optimization problem. The algorithm was set up with 50 individuals per generation, congestion tournament selection as the selection method, and BLX-α as the mating method. We also decided to terminate the optimization when the percentage of individuals generated more than 2 generations ago in the population of the focused generation exceeded 70%, or when the number of generations reached 30.

The distribution of all the individuals generated by the optimization for the objective function values is shown in **Figure 7**.

The total number of individuals generated was 775. This figure shows that the volume fraction of residue *J*1 and the volume of residue trap *J*3 are in a trade-off relationship with each other. C in the figure shows the objective function values of *CFD Optimization Method to Design Foam Residue Traps for Full Mold Casting DOI: http://dx.doi.org/10.5772/intechopen.95505*

the residue traps in which no residue defects occurred in the preliminary experiments. Therefore, in this optimization we selected the individual that is superior for both objective functions as the optimal solution for this C. The final optimal shape is shown in **Figure 8**. The values of the design variables of the optimal solution are shown in **Table 1** and those of the objective function are shown in **Table 2**.

**Figure 7.** *Distribution of all analyzed individuals in optimization.*

**Figure 8.** *Optimized shape of foam residue trap. (a) Foam residue trap. (b) Whole shape of casting.*

*Casting Processes and Modelling of Metallic Materials*

cube of 5 mm.

following equation.

better the shape.

trap, *h*, as follows.

lated this optimization problem.

ing system.

residue volume fraction averaged for each cell in the rim.

Three objective functions are defined as evaluation indices for optimization. The first objective function, *J*1, is an indicator of the amount of residue in the rim. The residue in this CFD software is defined as the diffusion of the transport equation equal to the volume of the foam model replaced by metal. This amount of residue can actually be calculated as the residue volume fraction *a*k for each calculated cell *k*, which represents the volume fraction of the residue contained in the cell in terms of solid time equivalent, and *J*1 is defined as the following equation, where *J*1 is this

1

<sup>=</sup> <sup>=</sup> ∑ (4)

2 14 34 *J xx xx* = + (5)

3 5 *J xh* = (6)

(7)

*n*

The second objective function, *J*2, is defined as the contact area between the rim and the residue trap. *J*2 is calculated using the design variables *x*1, *x*3, and *x*4 by the

The smaller the value of *J*2, the easier it is to remove the residue traps and the

The third objective function, *J*3, is defined as the volume of the residue trap itself, which is calculated using the design variable *x*5 and the height of the residue

2

The smaller the value of *J*3, the higher the material yield and the better the gat-

Based on these definitions, we added geometric constraints and finally formu-

We applied NSGA-II [9], a multi-objective genetic algorithm, to this optimization problem. The algorithm was set up with 50 individuals per generation, congestion tournament selection as the selection method, and BLX-α as the mating method. We also decided to terminate the optimization when the percentage of individuals generated more than 2 generations ago in the population of the focused

The distribution of all the individuals generated by the optimization for the

The total number of individuals generated was 775. This figure shows that the volume fraction of residue *J*1 and the volume of residue trap *J*3 are in a trade-off relationship with each other. C in the figure shows the objective function values of

≤+≤ ≤ ≤ ≤ ≤

*mm x x mm mm x mm mm x mm*

*Minimize J x x J x x x J x*

Subject to 0 225 0 225 10 30 30 120

…

generation exceeded 70%, or when the number of generations reached 30.

objective function values is shown in **Figure 7**.

11 5 213 4 35 ( ) ( ) ( ) 1 2

*mm x x mm*

,, ,, , ,, ,, ,

≤≤≤

*n <sup>k</sup> <sup>k</sup> a*

1

where *n* is the number of cells in the rim. In other words, *J*1 represents the volume fraction of the residue in the entire rim. The smaller the value of *J*1, the lower the residue defects are expected to be in the actual castings. In this capstan drum simulation, the number of cells in the rim is *n* = 32575, where each side is a

*J*

**78**


#### **Table 1.**

*Values of design variables for optimal solution.*


#### **Table 2.**

*Values of objective functions for optimal solution.*

**81**

**Figure 10.**

*Fluid behavior with shape-optimized foam residue trap.*

*CFD Optimization Method to Design Foam Residue Traps for Full Mold Casting*

In order to verify the effectiveness of the optimal shape, CFD analysis was performed and compared between the conventional method without a residue trap and the residue trap method with the optimal shape. The flows for the conventional

and residue-trapping methods are shown in **Figures 9** and **10**, respectively.

*DOI: http://dx.doi.org/10.5772/intechopen.95505*

**Figure 9.** *Fluid behavior without foam residue trap.*

*CFD Optimization Method to Design Foam Residue Traps for Full Mold Casting DOI: http://dx.doi.org/10.5772/intechopen.95505*

**Figure 10.** *Fluid behavior with shape-optimized foam residue trap.*

In order to verify the effectiveness of the optimal shape, CFD analysis was performed and compared between the conventional method without a residue trap and the residue trap method with the optimal shape. The flows for the conventional and residue-trapping methods are shown in **Figures 9** and **10**, respectively.

*Casting Processes and Modelling of Metallic Materials*

*Values of design variables for optimal solution.*

*Values of objective functions for optimal solution.*

*J***1 [**−**]** *J***2 [m2**

**Table 1.**

**Table 2.**

*x***1 [mm]** *x***2 [mm]** *x***3 [mm]** *x***4 [mm]** *x***5 [mm]** 11.58 76.50 108.82 27.05 57.57

6.906 × 10−1 3.257 × 10−3 7.456 × 10−4

**]** *J***3 [m3**

**]**

**80**

**Figure 9.**

*Fluid behavior without foam residue trap.*

In the conventional gating system, the metal flow shows that the residue is spreading inside the rim, and it is thought that the following factors influence the development of residue defects. The volume fraction of the residue in this case was *J*1 = 1.013. On the other hand, the residue trapping method has an opening in the residue trap where the metal containing residue agglomerates, through which residue is effectively collected into the trap. The part of the rim that is not in contact with the residue trap suppresses the backflow of metal containing residue. Due to these effects, the optimal shape of the residue trap is efficient for collecting residue and effective for capturing residue. The volume fraction of residue is 0.6906, which is more than 30% lower than that of the conventional method.
