# Simulation Analysis of Porthole Die Extrusion Process and Die Structure Modifications for an Aluminum Profile with High Length–Width Ratio and Small Cavity

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Porthole Die Design and Simulation Procedures

#### 2.1. Traditional Design Scheme and Geometry Modeling

^{2}, with the ratio of length to width up to 42.6. Thus, the metal flow behavior in porthole die is quite complex and it is a challenging task to obtain a uniform velocity distribution on the cross-section of die exit. In addition, the profile had a small cavity with diameter of 4.04 mm at the outer end of profile, which further aggravates the difficulty of extrusion.

#### 2.2. Establishment of 3D-FE Model

^{–1}with a true strain of 1 (Figure 4). Those flow stress dates obtained were then corrected for flow softening due to deformation heating during hot compression tests, and then were used to determine the material parameters. For AA6063 aluminum alloy used in the present simulations, the parameters in Equations (1) and (2) were as follows: Q = 1.71 × 10

^{5}J/mol, A = 1.18 × 10

^{9}s

^{–1}, β = 3.66 × 10

^{–8}m

^{2}/N, n = 7.89, R = 8314 J/(mol·k).

^{2}·°C [22,23]. When the extrusion temperature was greater than 400 °C, the friction type at the interface between the billet and porthole dies (except die bearing) was considered to be sticking friction [24]. However, at the interface between the billet and die bearing was defined as sliding friction and the friction coefficient was set to be 0.3 [7].

## 3. FE Simulation of Traditional Die Design

_{i}is the normal velocity for node i, $\overline{v}$ is the average velocity, and n is the nodes number. In order to obtain a more actual velocity distribution, the velocity values of all nodes on the cross-section of extruded profile were extracted. The smaller the value of SDV, the better the extruded quality is.

## 4. Redesign of Porthole Die

#### 4.1. First Step: Rearranging the Welding Chamber in Upper Die

#### 4.2. Second Step: Introducing the Baffle Plates

#### 4.3. Third Step: Adjusting the Die Bearings

## 5. Comparison between the Initial and Optimal Porthole Dies

#### 5.1. Metal Flow Pattern

#### 5.2. Welding Pressure

#### 5.3. Temperature Distribution

#### 5.4. Extrusion Load

#### 5.5. Die Displacement

## 6. Experimental Verification

## 7. Conclusions

- The metal flow behavior in the porthole die at different stages of extrusion process for the initial die scheme is severely not uniform. The SDV at the die exit is 19.63 mm/s. The maximum displacement in the upper die and mandrel are 0.107 and 0.0925 mm, respectively.
- By three steps of die structure modifications, the SDV at the die exit is reduced to 0.448 mm/s. The distortion of the profile is avoided effectively. The mean welding pressure in the welding zones for the optimal die is 197.3 MPa, being 331.72% higher than that of the initial die. The maximum temperature of extrudate at the die exit for the optimal die is 539.3 °C, being 8.6 °C higher than that of the initial die. The maximum displacement in the upper die is decreased from 0.107 to 0.0656 mm, and the mandrel deflection is decreased from 0.0925 to 0.04648 mm.
- The good agreement between the simulation and experimental results shows the modification strategy of porthole die based ALE formulation is practicable and it can provide theoretical guidance for porthole die design of any other similar profiles.
- A design route of porthole die for aluminum profile with a small mandrel is proposed, including sunken port bridges to design the welding chamber in the upper die, increasing the inlet angle of portholes, adding the baffle plates, and adjusting the die bearings.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometric model of aluminum profile with small cavity: (

**a**) 3D shape and (

**b**) cross-section. (unit: mm).

**Figure 2.**3D models of the traditional designed die with the welding chamber designed in lower die: (

**a**) the upper die and (

**b**) the lower die.

**Figure 4.**True stress–strain curves of AA6063 aluminum alloy: (

**a**) at different strain rates in 480 °C; (

**b**) at different temperatures in strain rate 1 s

^{–1}.

**Figure 6.**Metal flow at different stages during the whole extrusion process: (

**a**) velocity distribution at the entrance of the portholes; (

**b**) velocity distribution in the portholes, (

**c**) metal flowing the welding chamber, (

**d**) metal flowing in the mid-height welding chamber, and (

**e**) velocity distribution at the entrance of the die orifice.

**Figure 9.**Displacement distribution of the first modification scheme: (

**a**) the upper die and (

**b**) the lower die.

**Figure 13.**Velocity distribution in the extruded profiles at different positions of baffle plates: (

**a**) d = 55 mm; (

**b**) d = 57.5 mm; (

**c**) d = 60 mm; (

**d**) d = 65 mm.

**Figure 16.**Comparison of metal flow patterns in porthole die: (

**a**) the initial die and (

**b**) the optimal die.

**Figure 17.**Comparison of the welding pressure distribution in middle height of the welding chamber (

**a**) the initial die and (

**b**) the optimal die.

**Figure 18.**Comparison of the temperature distribution of billet (

**a**) the initial die and (

**b**) the optimal die.

**Figure 19.**The displacement distribution in the upper die (

**a**) the initial design scheme and (

**b**) the optimal design scheme.

**Figure 22.**Optical micrographs in different observation points of (

**a**) 1#, (

**b**) 2#, and (

**c**) 3# on the profile.

Physical Properties | AA6063 Aluminum Alloy | AISI H13 Steel |
---|---|---|

Density (Kg/m^{3}) | 2700 | 7870 |

Young’s modulus (MPa) | 68,900 | 210,000 |

Poisson’s ratio | 0.3 | 0.33 |

Thermal conductivity (W/(m·K)) | 198 | 24.3 |

Specific heat (J/(kg·K)) | 900 | 460 |

Thermal expansion coefficient (1/K) | 1.0 × 10^{–5} | - |

Conditions | Values |
---|---|

Billet diameter (mm) | 210 |

Billet length (mm) | 350 |

Extrusion ratio | 75.8 |

Extrusion speed (mm/s) | 2 |

Billet temperature (°C) | 480 |

Container and die temperature (°C) | 430 |

Friction coefficient at billet/container and die | Sticking |

Friction coefficient at billet/die bearing | 0.3 |

Heat thermal coefficient between billet/container and die (W/(m^{2}·°C)) | 3000 |

**Table 3.**Comparison of maximum and minimum velocities, SDVs, and displacements of extruded profiles at different position of baffle plates.

Design Schemes of Baffle Plates | Case 1 | Case 2 | Case 3 | Case 4 |
---|---|---|---|---|

Length of d (mm) | 55 | 57.5 | 60 | 65 |

Max. velocity (mm/s) | 217.8 | 157.7 | 162.8 | 168.8 |

Min. velocity (mm/s) | 141.2 | 149.9 | 149.8 | 140.8 |

SDV | 16.266 | 1.892 | 3.656 | 8.825 |

Displacement of profiles (mm) | 6.657 | 0.927 | 1.499 | 3.318 |

Position | l_{1} | l_{2} | l_{3} | l_{4} | l_{5} |
---|---|---|---|---|---|

Initial design (mm) | 2 | 4 | 6.4 | 4.3 | 2.8 |

Optimal design (mm) | 2.75 | 4.06 | 6.35 | 4.18 | 3.32 |

Design Schemes | Initial Design | Modification Scheme 1 | Modification Scheme 2 | Modification Scheme 3 |
---|---|---|---|---|

Extrusion load (KN) | 10,617.3 | 10,140.6 | 13,718.4 | 13,903.2 |

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**MDPI and ACS Style**

Liu, Z.; Li, L.; Li, S.; Yi, J.; Wang, G.
Simulation Analysis of Porthole Die Extrusion Process and Die Structure Modifications for an Aluminum Profile with High Length–Width Ratio and Small Cavity. *Materials* **2018**, *11*, 1517.
https://doi.org/10.3390/ma11091517

**AMA Style**

Liu Z, Li L, Li S, Yi J, Wang G.
Simulation Analysis of Porthole Die Extrusion Process and Die Structure Modifications for an Aluminum Profile with High Length–Width Ratio and Small Cavity. *Materials*. 2018; 11(9):1517.
https://doi.org/10.3390/ma11091517

**Chicago/Turabian Style**

Liu, Zhiwen, Luoxing Li, Shikang Li, Jie Yi, and Guan Wang.
2018. "Simulation Analysis of Porthole Die Extrusion Process and Die Structure Modifications for an Aluminum Profile with High Length–Width Ratio and Small Cavity" *Materials* 11, no. 9: 1517.
https://doi.org/10.3390/ma11091517