A Design Approach of Porthole Die for Flow Balance in Extrusion of Complex Solid Aluminum Heatsink Proﬁle with Large Variable Wall Thickness

Article A Design Approach of Porthole Die for Flow Balance in Extrusion of Complex Solid Aluminum Heatsink Proﬁle with Large Variable Wall Thickness

Tat-Tai Truong 1,2 , Quang-Cherng Hsu 2,* , Van-Canh Tong 3 and Jinn-Jong Sheu 4 1 Department of Mechanical Engineering, Hung Yen University of Technology and Education, Dan Tien, Khoai Chau, Hung Yen 17817, Vietnam; [email protected] 2 Department of Mechanical Engineering, National Kaohsiung University of Science and Technology, 415 Chien-Kung Road, Kaohsiung City 80778, Taiwan 3 Department of Ultra-Precision Machines and Systems, Korea Institute of Machinery and Materials, Yuseong-gu, Daejeon 34103, Korea; [email protected] 4 Department of Mold and Die Engineering, National Kaohsiung University of Science and Technology, 415 Chien-Kung Road, Kaohsiung City 80778, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-7-3814526

Received: 30 March 2020; Accepted: 23 April 2020; Published: 25 April 2020

Abstract: In this study, porthole die used for extrusion of a solid heatsink profile with wall thickness variation ratio up to 15.3 was designed using finite element (FE) simulations. To improve the flow balance in the die, a design approach was introduced to find the appropriate die structure, which includes the porthole and pocket geometry correction, the bearing length adjustment, and the port bridge structure modification. Using the proposed die, the predicted velocity relative difference (VRD) and the maximum velocity difference (∆V) of extrudate were significantly lower than those of an initial die, which was preliminarily designed based on general design experiences. The required extrusion force and the residual stress in the product were also reduced significantly. Then, the effects of the port bridge structure and welding chamber height on the behavior of the metal flow in the die were investigated. To verify the proposed die design, experimental extrusions were conducted on a 930-ton extruder. The experiment results showed that the extruded product fulfilled the requirements for dimensional tolerances. The design approach presented in this paper can be useful for practical implementation of die design when extruding similar solid heatsink profiles with large wall thickness variation.

Keywords: metal ﬂow balance; extrusion die design; aluminum heatsink; porthole die; complex aluminum proﬁle

1. Introduction Aluminum alloys are increasingly used in many industrial fields because of their advantages namely, lightweight, high specific strength, good formability, high thermal conductivity, and corrosion resistant. Hot extrusion is an economical process, which has been widely used to manufacture many aluminum alloys products [1]. Among them, aluminum heatsink products can be found in many cooling devices such as CPU coolers, radiators of light-emitting diode (LED) or high-performance electronic systems, etc. [2]. There are two basic types of aluminum heatsink profiles, which include solid and hollow profiles. The geometry of solid profiles is commonly complex, with long fins and variable wall thickness. Increasing the complexity of extruded profiles makes the die design process more challenging. A heatsink with long fins leads to the formation of a weak tongue-shaped cavity structure. Hence,

Metals 2020, 10, 553; doi:10.3390/met10050553 www.mdpi.com/journal/metals Metals 2020, 10, 553 2 of 18 the die can be easily deformed or damaged during the extrusion process. In addition, extruded metal velocity commonly flows faster in the areas of the product with large wall thickness [2], which may cause a tremendous difference in velocity on the extrudate, and therefore defects in the product’s geometry. In general, the design of extrusion dies for heatsink products is always a great challenge for designers to balance the metal flow and ensure product quality. The traditional solution of the extrusion die design is based on the experiences of skillful engineers combined with repeated die tests. In this way, based on the nose geometry of the tested extrudate, an experienced engineer often predicts the possible causes of the die error and then performs a die repair, including die structure modification and/or bearing lengths adjustment. By conducting this modification process several times, a reasonable die structure can be achieved. However, this design process is expensive and time-consuming, especially when designing the die for extrusion of high complex profiles. As a result, the traditional design approach may significantly increase production costs. In recent development of design technology, by using finite element (FE) analysis, a variety of parameters related to the extrusion process such as velocity, temperature, extrusion force, die stress, die deflection, and nose shape of the extrudate can be predicted before the actual fabrication of the die and extrusion production [3]. Therefore, many authors have studied the effects of die structure on the performance of the extrusion process with FE analysis. Based on a non-steady extrusion simulation, Lee et al. [4] numerically investigated the effect of the welding chamber geometry on the elastic deformation of the die during extrusion of condenser tube. They showed that the bottom cone angle and welding chamber height have significant effects on the deflection of the mandrel and die bearing. Wu et al. [5] optimized the structure of the die used for extrusion of a rectangular hollow pipe using numerical simulation. By redesigning the porthole and bearing lengths, they achieved a more uniform velocity distribution in the extrudate. Printer et al. [6] investigated the effects of die geometry and process parameters on the formation of welding seam and die deformation during the extrusion of a hollow tube based on FE analysis with HyperXtrude software. Chen et al. [7] compared the extrusion ability of traditional porthole and pyramid dies using steady-state and transient simulations. They pointed out that the die with a pyramid angle at the porthole entrance offers many advantages over the traditional die such as reducing extrusion force, lessening charge welding length, decreasing stress in the die plates, and increasing welding pressure. However, the pyramid dies caused a negative effect on balancing metal flow and increased length of the butt scrap. Liu et al. [8] optimized the porthole die for extrusion of a small profile with a high ratio of length to width by combining the die modifications and FE analysis. They introduced some modification steps to optimize the die structure, which included porthole correction, adding baffles, and fine-tuning bearing lengths. Xue et al. [9] aimed at improving the flow balance during the extrusion of a thin-walled profile by multi-cavity die. By combining the FE analysis and Taguchi method, they determined preferable parameters for the die structure, such as the undercut angle of porthole entrance, the relief angle of the porthole, and the welding chamber height. Chen et al. [10] investigated the effect of ram speed on extrusion parameters with porthole dies. The related extrusion parameters with the pyramid die, such as velocity, extrusion force, temperature, charge weld, and billet skin were compared to those of the traditional porthole die. Other authors [11,12] investigated the welding seam characteristics in the extrusion of simple solid profiles manufactured by the porthole die. Güley et al. [13] evaluated the capability of the flat-face and porthole dies used for extrusion of simple bar profiles, in which the extruded material was AA6060 aluminum alloy recycled from chips. They pointed out that the welding quality with the porthole die was improved significantly. The ductility of extruded products with the porthole die was 80% higher than that with the traditional flat-face die. For the extrusion of solid heatsink profiles, there are two major types of dies which are widely used: the feeder die and the porthole die with a semi-hollow feeder plate [1]. Recently, optimal design for feeder extrusion dies using FE analysis has been conducted by several researchers. Lee et al. [14] studied the metal flow balance in the die and deflection of the feeder die in the extrusion of a heatsink profile simulated by an FE model with DEFORM-3D software. They highlighted that the feeder Metals 2020, 10, 553 3 of 18 structure plays a vital role in determining the velocity distribution and the die deformation. Hwang et al. [15] optimized the structure of a feeder die for CPU cooling profile extrusion based on non-steady FE simulations. They reported that the position of the die opening and the welding chamber height greatly influenced the balance of flow distribution in the extrudate. Zhang et al. [16] carried out an optimization design for a spread extrusion die by means of FE simulation combined with a response surface and particle swarm optimization algorithms. The geometry of the feeder and the position of the die orifice were optimized to improve the metal flow balance. Previous studies have shown that the design optimization of the extrusion die is essential for the extrusion of aluminum profiles. One of the most important issues in die design is to ensure a good balance of metal flow in the die. This is because the flow balance directly affects the geometry of the extruded product, as well as the die deformation and the extrusion temperature. In the case of complex profiles, the problem of flow balance will become more and more critical. Researchers have made significant efforts to create guidelines for die design, mainly based on numerical simulations. However, studies for the optimal design of porthole dies are still insufficient. So far, studies on porthole dies mainly focus on flow balance for hollow profiles, and welding seam performance when extruding simple solid profiles. Moreover, the existing studies on the flow balance only consider the solid heatsink profiles with a small variable wall thickness by employing a feeder die. However, the flow balance solutions for a complex profile with massive wall thickness change and applying the porthole die have not been discussed. Accordingly, there are very few design guidelines for this type of die. Finally, experimental studies on the extrusion of heatsink profiles with large wall thickness variation have rarely been addressed. In this study, porthole die used for extrusion of a complex solid heatsink profile with large variable wall thickness is designed. First, an initial die is designed based on experience, in which the flow balancing method used includes utilizing a semi-hollow feeder plate, adding a second-step welding chamber, and using variable bearing lengths. Later, modification steps are introduced, including porthole correction, pocket modification, bearing lengths adjustment, and adding a bridge chamfer. Next, the effects of the port bridge structure and the welding chamber height on the behavior of the metal flow in the die are extensively investigated. Steady-state simulations of extrusion performed by HyperXtrude 2019 software are used in the die design process. To verify the designed die, experimental extrusions are conducted on a 930-ton extruder. Then, the geometric dimensions of the extruded product are measured, and the dimensional deviations of the product geometry are evaluated.

2. Geometry of the Aluminum Heatsink and Initial Die Structure The cross-section geometry and the three-dimensional (3D) model of the aluminum heatsink product are shown in Figure1. The product consists of 12 fins with four levels of wall thickness: 23.13 mm, 8.32 mm, 2.57 mm, and 1.51 mm, as indicated in Figure1a. Hence, the maximum wall thickness variation ratio is about 15.3. Moreover, in order to increase the heat transfer area, wavy patterns are created in four surfaces of the fins, including two outer surfaces of the left and right fins and two surfaces of the fin at the center position. The thickness of the bottom part of the radiator is 4.04 mm. During the extrusion process, the velocity of the billet in the center region is higher than that in the area near the container wall due to the effect of friction [2]. In addition, the velocity of metal flow in the areas with thicker wall thickness is commonly higher than that in other regions [17]. Thus, it is a great challenge for the die designer to achieve uniform velocity distribution in the extruded product. With a large change in the wall thickness of the product, the solutions such as using a feeder or pocket to support flow balancing are generally less effective. Therefore, the idea of utilizing a porthole die with a port bridge placed at the maximum wall thickness position is considered. Accordingly, an initial porthole die is designed on the basis of empirical experiences, as shown in Figure2. The porthole die consists of an upper and a lower part, with a height and a diameter of 90 and 180 mm, respectively. MetalsMetals 20202020,, 1010,, 553x FOR PEER REVIEW 44 ofof 1819 Metals 2020, 10, x FOR PEER REVIEW 4 of 19

(a) (b) (a) (b) Figure 1. The geometry of aluminum heatsink: (a) the cross-section geometry and main dimensions; FigureFigure 1.1. The geometry of aluminum heatsink: (a) the cross-section geometry and main dimensions; (b) the threeThe-dimensiona geometry ofl ( aluminum3D) model heatsink:(unit: mm). ( ) the cross-section geometry and main dimensions; ((bb)) thethe three-dimensionalthree-dimensional (3D)(3D) modelmodel (unit:(unit: mm).mm).

(a) (b) (a) (b) FigureFigure 2.2. DesignDesign ofof thethe initialinitial extrusionextrusion die:die: (aa)) thethe 2D2D layoutlayout ofof thethe die;die; ((bb)) thethe 3D3D assemblyassembly modelmodel Figure 2. Design of the initial extrusion die: (a) the 2D layout of the die; (b) the 3D assembly model withwith thethe mainmain dimensionsdimensions ofof thethe portport bridgebridge (unit:(unit: mm).mm). with the main dimensions of the port bridge (unit: mm). ItIt isis notednoted thatthat thethe upperupper diedie doesdoes notnot containcontain aa mandrelmandrel asas thethe traditionaltraditional hollowhollow dies.dies. Instead, It is noted that the upper die does not contain a mandrel as the traditional hollow dies. Instead, aa portport bridge of of 18 18 mm mm in in width width is is designed, designed, as as depicted depicted in inFigure Figure 2b2. b.The The rear rear tip tipwidth width of the of theport a port bridge of 18 mm in width is designed, as depicted in Figure 2b. The rear tip width of the port portbridge bridge is 10 ismm, 10 mm,and the and tip the angle tip angle is 50°. is As 50 ◦a. result, As a result, the upper the upperdie consists die consists of two ofportholes, two portholes, which bridge is 10 mm, and the tip angle is 50°. As a result, the upper die consists of two portholes, which whichare symmetric are symmetric through through the Y-axis. the Y-axis. Hence, Hence, this upper this upperdie is also die is called also calledthe semi the-hollow semi-hollow feeder feeder plate. are symmetric through the Y-axis. Hence, this upper die is also called the semi-hollow feeder plate. plate.The profile The profile of porthole of porthole expands expands gradually gradually toward toward the die the center die center with withan opening an opening angle angle of 7°. of The 7◦. The profile of porthole expands gradually toward the die center with an opening angle of 7°. The Theporthole porthole willwill deliver deliver the thematerial material into into the themain main body body area. area. The The center center of the of the port port bridge bridge is chosen is chosen at porthole will deliver the material into the main body area. The center of the port bridge is chosen at atthe the die die center, center, which which corresponds corresponds to to the the largest largest wall wall thickness thickness of of the extrudate. The height of thethe the die center, which corresponds to the largest wall thickness of the extrudate. The height of the weldingwelding chamber chamber is is chosen chosen by byexperience experience as 10% as of10% the of container the container diameter, diameter, so the calculated so the calculated welding welding chamber is chosen by experience as 10% of the container diameter, so the calculated chamberwelding chamber height is 13height mm. is 13 mm. welding chamber height is 13 mm. TheThe lowerlower die die plate plate contains contains a pocket a pocket (also (also called called a second-step a second- weldingstep welding chamber), chamber), which iswhich placed is The lower die plate contains a pocket (also called a second-step welding chamber), which is inplaced front in of front the die of openingthe die opening to control to thecontrol metal the flow metal balance flow inbalance the die in cavity. the die For cavity. the case For ofthe porthole case of placed in front of the die opening to control the metal flow balance in the die cavity. For the case of diesporthole and complex dies and extrusion complex profiles, extrusion a second-step profiles, a second welding-step chamber welding is commonly chamber is used commonly [18]. Hence, used porthole dies and complex extrusion profiles, a second-step welding chamber is commonly used a[18] bow-shaped. Hence, a bow pocket-shaped profile pocket is adopted profile here. is adopted Moreover, here. bearing Moreover, with bearing variable with lengths variable is also lengths utilized is [18]. Hence, a bow-shaped pocket profile is adopted here. Moreover, bearing with variable lengths is toalso aid utilized the balance to aid of the material balance flow. of material Finally, twoflow. run-out Finally, steps two are run designed-out steps so are that designed the extrudate so that does the also utilized to aid the balance of material flow. Finally, two run-out steps are designed so that the notextrudate touch thedoes die not surfaces. touch the They die also surfaces. increase They the also die strength increase during the die the strength extrusion during process. the extrusion extrudate does not touch the die surfaces. They also increase the die strength during the extrusion process.Figure 3 shows the correspondent bearing regions with constant and variable lengths along the process. extrudedFigure profile 3 shows circumference. the correspondent The bearing bearing lengths regions are with calculated constant based and variable on the existing lengths empiricalalong the Figure 3 shows the correspondent bearing regions with constant and variable lengths along the experiencesextruded profile as follows: circumference. The bearing lengths are calculated based on the existing empirical extruded profile circumference. The bearing lengths are calculated based on the existing empirical experiences as follows: 1.experiences The base as bearingfollows: length is approximated as twice the wall thickness of the extrudate. 1. The base bearing length is approximated as twice the wall thickness of the extrudate. 2.1. The base bearing bearing length length at the is thin approximated fin position isas multipliedtwice the wall by a thickness coefficient ofK cthe= 0.75, extrudate. which takes into 2. The bearing length at the thin fin position is multiplied by a coefficient Kc = 0.75, which takes 2. The bearing length at the thin fin position is multiplied by a coefficient Kc = 0.75, which takes intoaccount account the flow the flow obstruction obstruction due todue the to complex the complex geometry. geometry. into account the flow obstruction due to the complex geometry. 3.3. The bearing length at the thick finfin positionposition under the portport bridgebridge isis multipliedmultiplied byby aa coecoefficientfficient 3. TheK = bearing0.52, which length takes at the into thick account fin position the flow under obstruction the port due bridge to the is port multiplied bridge geometry. by a coefficient Thus, Kb = 0.52, which takes into account the flow obstruction due to the port bridge geometry. Thus, Kb = 0.52, which takes into account the flow obstruction due to the port bridge geometry. Thus, the bearing length calculated for this region isis aboutabout 2424 mm.mm. the bearing length calculated for this region is about 24 mm. 4.4. The bearing length at the tip of the extrudate is approximatedapproximated asas 0.60.6 timestimes thethe adjacentadjacent bearingbearing 4. The bearing length at the tip of the extrudate is approximated as 0.6 times the adjacent bearing length [[1919]. length [19].

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Figure 3. Schematic of bearing lengths for the initial extrusion die (unit: mm). Figure 3. Schematic of bearing lengths for the initial extrusion die (unit: mm). Figure 3. Schematic of bearing lengths for the initial extrusion die (unit: mm). 3. Construction of Finite Element Model 3. Construction of Finite Element Model 3. ConstructionFigure 4a demonstrates of Finite Element the 3D M assemblyodel model of the components, which is built by CATIA Figure4a demonstrates the 3D assembly model of the components, which is built by CATIA V5R20 software (Dassault Systèmes, Vélizy-Villacoublay, France). Figure 4b illustrates the FE V5R20Figure software 4a demonstrates (Dassault Syst theèmes, 3D Vassemblyélizy-Villacoublay, model of France).the components Figure4b, which illustrates is bu theilt FEby modelsCATIA models with different mesh sizes, which will be used for steady-state extrusion simulation with the withV5R20 di ff softwareerent mesh (Dassault sizes, which Systèmes, will be Vélizy used for-Villacoublay, steady-state extrusionFrance). Figure simulation 4b illustrates with the arbitrary the FE arbitrary Lagrangian–Eulerian (ALE) algorithm by HyperXtrude 2019 software (Altair Engineering, Lagrangian–Eulerianmodels with different (ALE)mesh sizes, algorithm which bywill HyperXtrude be used for steady 2019- softwarestate extrusion (Altair simulation Engineering, with Inc., the Inc., Michigan, MA, USA). The entire FE models are divided into six regions, including billet, Michigan,arbitrary Lagrangian MA, USA).–Eulerian The entire (ALE FE) models algorithm are by divided HyperX intotrude six regions,2019 software including (Altair billet, Engineering, porthole, porthole, welding chamber, pocket, bearing, and profile, as shown in Figure 4b. Rough mesh size is weldingInc., Michigan chamber,, MA, pocket, USA bearing,). The entire and profile, FE models as shown are divided in Figure into4b. Roughsix regions, mesh including size is used billet, for used for the billet region, and fine mesh size is adopted for the bearing region, where severe theporthole, billet region,welding and chamber, fine mesh pocket, size bearing, is adopted and for profile, the bearing as shown region, in Figure where 4b. severe Rough deformations mesh size is deformations occur. The tetrahedral element is assigned to the billet, porthole, welding chamber, occur.used for The the tetrahedral billet region, element and is assigned fine mesh to the size billet, is adopted porthole, for welding the bearing chamber, region, and pocket where regions. severe and pocket regions. The triangular prism element is applied to the remaining regions. The meshing Thedeformations triangular occur. prism elementThe tetrahedral is applied element to the remainingis assigned regions. to the billet, The meshing porthole, process welding is carried chamber, out process is carried out automatically as a recommendation by the software with fine mesh level automaticallyand pocket regions. as a recommendation The triangular prism by the element software is with applied fine to mesh the levelremaining selection. regions The. totalThe meshing number selection. The total number of elements used for this simulation model is approximately 760,000. ofprocess elements is carried used for out this automatically simulation model as a is recommendation approximately 760,000. by the software with fine mesh level selection. The total number of elements used for this simulation model is approximately 760,000.

(a) (b)

Figure 4. (a) (b) a Figure 4. FiniteFinite elementelement(FE) (FE) modeling modeling for for steady-state steady -state extrusion extrusion of aluminumof aluminum heatsink heatsink proﬁle: profile: ( ) the(a) 3Dthe assembly3D assembly model model of elements of elements during during extrusion; extrusion; (b) meshing(b) meshing of the of regions.the regions. Figure 4. Finite element (FE) modeling for steady-state extrusion of aluminum heatsink profile: (a) the 3D assembly model of elements during extrusion; (b) meshing of the regions. The material of the the tooling tooling and and the the porthole porthole die die is is H13 H13 tool tool steel. steel. The The material material used used for for billet billet is isAA6063 AA6063 aluminum aluminum alloy. alloy. Rigid Rigid and and viscoplastic viscoplastic simulation simulation models models are are used used for for the the tools tools and the The material of the tooling and the porthole die is H13 tool steel. The material used for billet is billet, respectively. The physical and thermal parameters of these materials are the same as those AA6063 aluminum alloy. Rigid and viscoplastic simulation models are used for the tools and the used by the HyperXtrude software library,library, as shownshown inin TableTable1 1.. The The continuous continuous equationequation basedbased onon billet, respectively. The physical and thermal parameters of these materials are the same as those the Sellar Sellar–Tegart–Tegart model model,, which which is is widely widely used used in in simulations simulations of of aluminum aluminum profile proﬁle extrusion extrusion [9,10] [9,10, is], used by the HyperXtrude software library, as shown in Table 1. The continuous equation based on isapplied applied for for the the simulation, simulation, as asdescribed described in inEquation Equation (1): (1): the Sellar–Tegart model, which is widely used in simulations of aluminum profile extrusion [9,10], is 1/1/nn applied for the simulation, as described in Equation1 -1 (1):Z  휎 = 1 sinh 1( ) (1) σ = βsin h− A 1/n (1) β1 -1 AZ  휎 = sinh ( ) (1) where σ indicates the flow stress of the material;β β andA A are the extruded material coefficients; n is the exponent; Z is the Zener–Hollomon coefficient calculated by Equation (2): where σ indicates the flow stress of the material; β and A are the extruded material coefficients; n is the exponent; Z is the Zener–Hollomon coefficient calculated by Equation (2):

Metals 2020, 10, 553 6 of 18 where σ indicates the flow stress of the material; β and A are the extruded material coefficients; n is the exponent; Z is the Zener–Hollomon coefficient calculated by Equation (2):

Z = ε· eQ/RT (2) where ε· is the eﬀective strain rate; Q, R, and T are the activation energy, gas coeﬃcient, and absolute temperature, respectively. The parameters of AA6063 material used in Equation (1) are as follows [19]: β = 4 10 8 m2/N; Q = 1.4155 105 J/mol; R = 8.314 J/(mol . K); A = 5.90152 109 s 1; n = 5.385. × − × × − Table 1. Material properties of the billet and the tools for extrusion simulation.

Density Heat Capacity Thermal Conductivity Poisson’s Young Modulus Material 3 (Kg/m ) (J/(kg ◦C)) (W/m.K) Ratio (GPa) AA6063 2700 900 198 0.35 40 H13 7870 460 24.3 0.35 210

The stick friction condition is assumed between the extruded material and tools (including dies) with a shear friction coefficient of 1 [8]. The sliding friction condition is assumed between the extruded material and bearing region with a Coulomb coefficient of 0.3 [9]. The heat convection coefficient 2 between the billet and the tooling is 3000 W/m ◦C[9]. The parameters related to the numerical simulation of the extrusion process are summarized in Table2.

Table 2. The parameters used for numerical simulation.

Simulation Parameters Values Container diameter (mm) 130 Billet length (mm) 500 Billet temperature (◦C) 500 Container temperature (◦C) 450 Die temperature (◦C) 490 Ram speed (mm/s) 3 Extrusion ratio 10.73

4. Results and Discussion

4.1. Velocity Distribution with the Initial Die Design The flow velocity distribution during extrusion is a crucial factor that determines the success of an extrusion process. Therefore, it is always the first factor to be considered when designing an extrusion die. The quality of velocity distribution can be monitored through several parameters such as the standard deviation of velocity (SDV)[18] or the velocity relative difference (VRD)[20]. In this study, the VRD is used and calculated by Equation (3):

Pn Vi Va i=1 | V− | VRD = a 100% (3) n × where Vi is the extrusion velocity at node i on the extrudate; Va is the average velocity calculated from all nodes of the extrudate; n is the number of nodes considered in a cross-section of the extrudate. A total of 3269 nodes was used for the VRD calculations. In addition, the difference between the maximum and minimum velocities (∆V) is also used to evaluate the flow balance. This is because geometric defects are likely to occur when significant speed differences arise at any position of the product. Figure5 plots the simulated results of flow velocity distribution and the deformation trend of the extrudate. The minimum flow velocities appear in the regions where the metal contacts with the dies Metals 2020, 10, 553 7 of 18 and the tools because of the sticking friction effect. The maximum velocities occur at the die orifice region. Nonuniform velocity distribution is generally observed, in which the metal on the left side of the product flows faster than that on the right, especially at the thick fin region. The calculated VRD andMetals∆ 2020V are, 10 4.1%, x FOR and PEER 4.72 REVIEW mm/s, respectively. Such uneven velocity distribution will result in bending7 of 19 ofMetals product 2020, 10 geometry, x FOR PEER to REVIEW the right. Therefore, the initial die design needs to be adjusted. 7 of 19

Figure 5. Velocity distribution and deformation trend of the extrudate using the initial die. Figure 5. Velocity distribution and deformation trend of the extrudate using the initial die. 4.2. AdjustingFigure Die 5. SVelocitytructure distribution and deformation trend of the extrudate using the initial die. 4.2. Adjusting Die Structure 4.2. Adjusting Die Structure 4.2.1. Resizing Porthole 4.2.1. Resizing Porthole 4.2.1.From Resizing the P simulatedorthole flow velocity of the initial die, the metal flows faster on the right-hand From the simulated flow velocity of the initial die, the metal flows faster on the right-hand section section of the profile, which contains a fin with 8.32 mm in thickness. Therefore, the first step of of theFrom profile, the which simulated contains flow a velocity fin with of8.32 the mm initial in thickness. die, the metal Therefore, flows the faster first on step the of right correction-hand correction here is to reduce the size of porthole 2. In this way, an offset distance of 3 mm is applied heresection is toof reducethe profile, the sizewhich of portholecontains 2.a fin In thiswith way,8.32 anmm o ffinset thickness distance. ofTherefore, 3 mm is the applied first step for the of for the entrance and bottom edges of this porthole profile. The other geometric parameters of the entrancecorrection and here bottom is to reduce edges of the this size porthole of porthole profile. 2. TheIn this other way, geometric an offset parameters distance of of 3 the mm initial is applied die are initial die are fixed. Figure 6 demonstrates the geometry of porthole 2 before and after correction. By fixed.for the Figure entrance6 demonstrates and bottom the edges geometry of this of porthole porthole profile. 2 before The and other after geometric correction. parameters By applying of this the applying this correction, the area of porthole 2 is reduced to 1702 mm2 compared to the area of correction,initial die are the fixed. area ofFigure porthole 6 demonstrates 2 is reduced the to 1702geometry mm2 ofcompared portholeto 2 before the area and of portholeafter correction. 1 which By is porthole 1 which is 1960 mm2. Consequently, the area ratio of porthole 1 vs. porthole 2 is about 1.15, 1960applying mm2 . this Consequently, correction, the the area area ratio of porthole of porthole 2 is 1 vs.reduced porthole to 1702 2 is about mm2 1.15,compared which approximatelyto the area of which approximately equals to the area ratio of the left- and right-side cross-section of the product equalsporthole to 1 the which area is ratio 1960 of mm the2 left-. Consequently, and right-side the cross-section area ratio of ofporthole the product 1 vs. po (aboutrthole 1.12). 2 is about 1.15, (about 1.12). which approximately equals to the area ratio of the left- and right-side cross-section of the product (about 1.12).

Figure 6. Adjustment scheme of porthole 2 of the upper die (unit: mm). Figure 6. Adjustment scheme of porthole 2 of the upper die (unit: mm). Figure7 shows the simulated velocity distribution of metal flow with porthole 2 correction. Figure 7 showsFigure the 6. simulated Adjustment velocity scheme of distribution porthole 2 of of the metal upper flow die (unit: with mm). porthole 2 correction. This figure indicates that VRD and ∆V are reduced to 1.76% and 2.09 mm/s, respectively. Hence, the This figure indicates that VRD and ΔV are reduced to 1.76% and 2.09 mm/s, respectively. Hence, the velocityFigure distribution 7 shows has the improved. simulated However, velocity distribution the velocity di offf metalerence flow is still with relatively porthole high, 2 whichcorrection. may velocity distribution has improved. However, the velocity difference is still relatively high, which resultThis figure in a defective indicates extruded that VRD product. and ΔV Therefore,are reduced the to extrusion1.76% and die 2.09 still mm/s, needs respectively. further modification Hence, the to may result in a defective extruded product. Therefore, the extrusion die still needs further improvevelocity distribution velocity distribution has improved. as well However, as geometric the accuracy. velocity difference is still relatively high, which modification to improve velocity distribution as well as geometric accuracy. may result in a defective extruded product. Therefore, the extrusion die still needs further modification to improve velocity distribution as well as geometric accuracy.

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FigureFigure 7.7. VelocityVelocity distributiondistribution onon thethe extrudateextrudate withwith thethe extrusionextrusion diedie afterafter correctingcorrecting thethe porthole.porthole. Figure 7. Velocity distribution on the extrudate with the extrusion die after correcting the porthole. 4.2.2.4.2.2. ModifyingFigureModifying 7. Velocity PocketPocket distribution PProfilerofile on the extrudate with the extrusion die after correcting the porthole. 4.2.2. Modifying Pocket Profile 4.2.2.TheThe Modifying secondsecond stepstepPocket ofof thetheProfile weldingwelding chamberchamber solutionsolution isis highlyhighly effectiveeffective forfor extrusionextrusion withwith portholeporthole diedie andandThe complexcomplex second step prodprod ofuctuct the profilesprofiles welding [18,21][18,21] chamber.. However,However, solution isthethe highly geometrygeometry effective ofof the forthe extrusion weldingwelding chamber withchamber porthole usuallyusually die The second step of the welding chamber solution is highly effective for extrusion with porthole needsandneeds complex an an appropriate appropriate product profiles design. design. [18 Therefore,Therefore,,21]. However, the the pocket pocketthe geometry profile profile of of of the the the welding lower lower chamber die die isis modifiedmodified usually needs here here an to to die and complex product profiles [18,21]. However, the geometry of the welding chamber usually improveappropriateimprove thethedesign. metalmetal flowflow Therefore, distributiondistribution the pocket.. OnlyOnly profile thethe geometrygeometry of the lower ofof thethe die pocket ispocket modified profileprofile here isis to furtherfurther improve modifiedmodified the metal inin needs an appropriate design. Therefore, the pocket profile of the lower die is modified here to thisflowthis secondsecond distribution. stepstep,, Onlywhilewhile the thethe geometry otherother geometricgeometric of the pocket parameters parameters profile is fromfrom further thethe modified previousprevious in modificationthis modification second step, step step while areare improve the metal flow distribution. Only the geometry of the pocket profile is further modified in unchangedtheunchanged other geometric.. Figure Figure 8parameters 8 shows shows the the from modification modification the previous scheme scheme modification for for the the steppocket pocket are profile profile unchanged. of of the the Figure lower lower8 shows die. die. In In this second step, while the other geometric parameters from the previous modification step are general,thegeneral, modification thethe leftleft schemeprofileprofile of forof thethe the pocketpocket profileisis enlargedenlarged of the toto lower reducereduce die. thethe In general,influenceinfluence the ofof left frictionfriction profile andand of the thethe pocket deaddead unchanged. Figure 8 shows the modification scheme for the pocket profile of the lower die. In metalismetal enlarged zonezone (DMZ),(DMZ), to reduce therebythereby the influence increasingincreasing of extrusionextrusion friction and speed.speed. the OnOn dead thethe metal contrary,contrary, zone thethe (DMZ), rightright profileprofile thereby isis increasing narrowednarrowed general, the left profile of the pocket is enlarged to reduce the influence of friction and the dead atextrusionat positionspositions speed. ofof highhigh On flowflow the contrary,velocities.velocities. the right profile is narrowed at positions of high flow velocities. metal zone (DMZ), thereby increasing extrusion speed. On the contrary, the right profile is narrowed at positions of high flow velocities.

((aa)) ((bb))

FigureFigure 8. 8. ModificationModificationModification scheme scheme of of the the(a) pocket pocket profile: profile:profile: (( aa)) tt thehehe 2D2D viewview ofof pocketpocket profileprofile profile(b) before before and after thethe change; change; ( (bb)) t thethehe 3D 3D model model of of the the lowe lowerlowerr diedie afterafter modifyingmodifying thethe pocketpocket profileprofileprofile (unit:(unit:(unit: mm).mm)mm).. Figure 8. Modification scheme of the pocket profile: (a) the 2D view of pocket profile before and after FiguretheFigure change; 9 99 presents presentspresents (b) the the3Dthethe model simulated simulatedsimulated of the velocity velocityvelocitylower die distributiondistributiondistribution after modifying usingusingusing the the thethepocket extrusionextrusionextrusion profile die(unit:diedie withwithwith mm) pocketpocketpocket. profileprofileprofile modification.modification.modification. TheThe improvementimprovement in in flow flowflow velocity velocity distributio distributiondistributionn is is clearlyclearly observed.observed. The The values values of of VRDVRD Figure 9 presents the simulated velocity distribution using the extrusion die with pocket profile andand Δ∆ΔVV areare reduced reduced to to 0.87% 0.87% and and 0.89 0.89 mm/s, mmmm/s,/s, respectively. respectively. WithWith th thethee improvement improvement in in flow flowflow velocity velocity modification. The improvement in flow velocity distribution is clearly observed. The values of VRD distribution,distribution, deformations deformations at at the the bottombottom andand leftleft finfinfin regionsregions ofof thethe extrudateextrudate cancancan bebebe reduced.reduced.reduced. and ΔV are reduced to 0.87% and 0.89 mm/s, respectively. With the improvement in flow velocity distribution, deformations at the bottom and left fin regions of the extrudate can be reduced.

Figure 9. FFigureigure 9. 9. SimulatedSimulatedSimulated flow flowflow velocity velocity velocity distribution distribution distribution using using using the extrusion the the extrusion extrusion die after die die modifying after after modifying modifying the pocket the the profile.pocket pocket profile.profile. 4.2.3.F Adjustingigure 9. Simulated Bearing flow Lengths velocity distribution using the extrusion die after modifying the pocket 4.2.3.4.2.3.Adjustingprofile. AdjustingAdjusting bearing BearingBearing lengthsLLengthsengthsusually takes place at the end of the design process to make some fine-tune adjustments for the die structure, something considered by many authors [3,8]. The main AdjustingAdjusting bearingbearing lengthslengths usuallyusually taketakess placeplace atat thethe endend ofof thethe designdesign processprocess toto makemake somesome objective4.2.3. Adjusting of adjusting Bearing bearing Lengths lengths is to precisely control the product geometry. In this modified step finefine--tunetune adjustmentsadjustments forfor thethe diedie structure,structure, somethingsomething consideredconsidered byby manymany authorsauthors [3,8][3,8].. TheThe mainmain 3, adjustingAdjusting bearing bearing lengths lengths is performed, usually take whiles place the otherat the die end parameters of the design are keptprocess the sameto make as stepsome 2. objectiveobjective ofof adjustingadjusting bearingbearing lengthslengths isis toto preciselyprecisely controlcontrol thethe productproduct geometry.geometry. InIn thisthis modifimodifieded fine-tune adjustments for the die structure, something considered by many authors [3,8]. The main objective of adjusting bearing lengths is to precisely control the product geometry. In this modified

Metals 2020, 10, x FOR PEER REVIEW 9 of 19 step 3, adjusting bearing lengths is performed, while the other die parameters are kept the same as step 2. MetalsFigure 2020, 10 10, x FORdemonstrates PEER REVIEW the distribution of bearing lengths after modification. The general9 rule of 19 for adjusting bearing lengths is based on the velocity distribution in the extrudate. The bearing lengthsstepMetals 3 2020, adjusting are, 10 , reduced x FOR bearing PEER at REVIEW the lengths slower is performed, flow velocity while areas, the whereasother die theyparameters are increased are kept at the the same faster9 of as 19 Metals 2020, 10, 553 9 of 18 velocitystep 2. zones. Accordingly, the bearing lengths on the left side of the product profile are reduced slightly.step Figure3, adjusting For 10the demonstrates bearing bearing regions lengths the on distribution is the performed, right side, of whilebearing the bearing the lengths other lengths dieafter parameters atmodification. the bottom are andkeptThe the generalthe corner same rule ofas step 2. thefor profadjustingFigureile are 10 bearingincreased.demonstrates lengths the is distribution based on ofthe bearing velocity lengths distribution after modification. in the extrudate. The general The bearing rule for Figure 10 demonstrates the distribution of bearing lengths after modification. The general rule adjustinglengthsFigure are bearing 11 reduced shows lengths at simulated the is based slower flow on flow the velocity velocity velocity distribution distribution areas, whereas using in the they the extrudate. die are withincreased The adjusted bearing at the bearing lengths faster for adjusting bearing lengths is based on the velocity distribution in the extrudate. The bearing lengths.arevelocity reduced Itzones. can at bethe Accordingly, seen slower that flow a fairly the velocity bearing uniform areas, lengths velocity whereas on distribution the they left are side increased is of obtained. the product atthe The faster profilevalues velocity ofare VRD reduced zones. and lengths are reduced at the slower flow velocity areas, whereas they are increased at the faster ΔVAccordingly,slightly. are decreasedFor the the bearing bearing to only regions lengths 0.75% on on and the the right 0.78 left sidemm/s,side, ofthe therespectively. bearing product lengthsprofile As aat result,arethe reducedbottom the productand slightly. the corner without For the of velocity zones. Accordingly, the bearing lengths on the left side of the product profile are reduced geometricbearingthe profile regions defectsare increased. on can the be right extruded. side, the Hence, bearing the lengths bearing at thelength bottom adjustment and the solution corner of successfully the profile slightly. For the bearing regions on the right side, the bearing lengths at the bottom and the corner of enhancesare increased.Figure the 11flow shows balancing. simulated flow velocity distribution using the die with adjusted bearing lengths.the prof ileIt canare beincreased. seen that a fairly uniform velocity distribution is obtained. The values of VRD and ΔV areFigure decreased 11 shows to only simulated 0.75% flow and 0.78 velocity mm/s, distribution respectively. using As the a result, die with the adjustedproduct without bearing geometriclengths. It can defects be seen can that be extruded.a fairly uniform Hence, velocity the bearing distribution length is adjustmentobtained. The solution values successfullyof VRD and enhancesΔV are decreased the flow balancing. to only 0.75% and 0.78 mm/s, respectively. As a result, the product without geometric defects can be extruded. Hence, the bearing length adjustment solution successfully enhances the flow balancing.

Figure 10. SchemeScheme of of recalculated recalculated bearing lengths (unit: mm) mm).. Figure 11 shows simulated ﬂow velocity distribution using the die with adjusted bearing lengths. It can be seen that a fairly uniform velocity distribution is obtained. The values of VRD and ∆V are decreased to only 0.75% and 0.78 mm/s, respectively. As a result, the product without geometric Figure 10. Scheme of recalculated bearing lengths (unit: mm). defects can be extruded. Hence, the bearing length adjustment solution successfully enhances the ﬂow balancing. Figure 10. Scheme of recalculated bearing lengths (unit: mm).

Figure 11. Flow velocity distribution using the die with adjusted bearing lengths.

4.3. Effects of the Port Bridge Structural Parameters and the Welding Chamber Height

In the initial die, the parameters of the port bridge and the welding chamber were roughly chosen based Figureon practical 11. Flow experience. velocity distribution Therefore, using parameters the die with related adjust toed bridge bearing structure lengths. such as the port bridge widthFigure ( 11.W),Flow chamfered velocity distribution bridge, rear using tip the width die with (Wt), adjusted and welding bearing lengths. chamber height (H) 4.3. Effects of theFigure Port 11.Bridge Flow S velocitytructural distribution Parameters using and thethe Weldingdie with Chamberadjusted bearingHeight lengths. (Figure 12), are further investigated to determine the appropriate values. The other parameters in 4.3. Eﬀects of the Port Bridge Structural Parameters and the Welding Chamber Height step4.3. Effects3In remain the of initial the the Port same die, Bridge . theMoreover, S parameterstructur theal P behavior arametersof the port ofand metal bridge the Welding flow and with the Chamber varweldingied H dieeight chamber structural were parameters roughly ischosen alsoIn examined. thebased initial on die,practical the parameters experience. of Therefore, the port bridge parameters and the related welding to chamber bridge structure were roughly such chosen as the In the initial die, the parameters of the port bridge and the welding chamber were roughly basedport bridge on practical width experience. (W), chamfered Therefore, bridge,parameters rear tip width related (Wt to), and bridge welding structure chamber such as height theport (H) chosen based on practical experience. Therefore, parameters related to bridge structure such as the bridge(Figure width 12), are (W ),further chamfered investigated bridge, rearto determine tip width (theWt ),appropriate and welding values chamber. The height other (Hparameters) (Figure 12 in), arestepport further 3 bridge remain investigated width the same (W),. to Moreover, chamfered determine the the bridge, behavior appropriate rear of tip metal values. width flow The (W witht other), and var parameters weldingied die structural chamber in step 3 parametersremain height the(H) same.is(Figure also Moreover,examined. 12), are further the behavior investigated of metal to ﬂow determine with varied the appropriate die structural values parameters. The other is also parameters examined. in step 3 remain the same. Moreover, the behavior of metal flow with varied die structural parameters is also examined.

Figure 12. The die geometry with the chamfered bridge. The geometric parameters shown include the

port bridge width (W), rear tip width (Wt), and welding chamber height (H).

Metals 2020, 10, x FOR PEER REVIEW 10 of 19

Figure 12. The die geometry with the chamfered bridge. The geometric parameters shown include

the port bridge width (W), rear tip width (Wt), and welding chamber height (H).

Metals 2020, 10, 553 10 of 18 4.3.1. Effect of the Port Bridge Parameters Two types of portholes are considered, including the ones with and without the chamfered 4.3.1.bridge. E ffToect investigate of the Port the Bridge effect Parameters of the port bridge’s width, W varying from 18 to 26 mm is examined. The parametersTwo types ofWt portholesand the tip are angle considered, are set to including 10 mm and the 50°, ones respectively. with and withoutThe chamfer the chamfereddimension bridge.of the port To investigate bridge is theselected effect ofat the4 × port 25°, bridge’swhich is width, commonlyW varying usedfrom for the 18 to die 26 with mm is a examined.container Thediameter parameters of 130 Wmmt and in practical the tip angle extrusion are set. to 10 mm and 50◦, respectively. The chamfer dimension of the portFigure bridge 13 shows is selected the effects at 4 25of W, which on ΔV is and commonly the required used forextrusion the die force. with aIt containercan be observed diameter that of × ◦ 130the mmrequired in practical extrusion extrusion. force increases with increasing W. This can be explained by the fact that increasingFigure W 13 will shows increase the e theffects dead of Wmaterialon ∆V zoneand the(DMZ required) under extrusion the bridge force. and reduce It can bethe observed entrance thatsize theof the required porthole extrusion. Moreover, force t increaseshe extrusion with force increasing of the W porthole. This can die be with explained the chamfered by the fact bridge that increasingsignificantlyW reducewill increases compared the dead to the material traditional zone porthole (DMZ) underdie, as the shown bridge in andFigure reduce 13. T thehe entrancereduced sizeamount of the of porthole.extrusion force Moreover, estimated the extrusionfor W = 18 force mm ofis about the porthole 9.7 tons die. This with is because the chamfered the size bridge of the significantlyDMZ formed reduces before the compared port bridge to the is decreased traditional in porthole the die with die, asthe shown chamfered in Figure bridge 13. The reduced amountFigure of extrusion 13 also shows force estimatedthat increasing for W W= 18leads mm to is an about increas 9.7e tons. of Δ ThisV. However, is because ΔV the of sizeboth of die thes DMZwith and formed without before chamfered the port bridgebridges is is decreased almost the in same the die. with the chamfered bridge.

Figure 13. W V Figure 13. InfluenceInfluence of of W onon Δ∆V andand the the extrusion extrusion force force in in two two types of dies with and without without chamfered bridges. chamfered bridges. Figure 13 also shows that increasing W leads to an increase of ∆V. However, ∆V of both dies with Figure 14 presents the effect of W on the flatness of the profile nose (ΔD). It is seen that the and without chamfered bridges is almost the same. behavior of ΔD with respect to W is fairly similar to that of ΔV (in Figure 13). The maximum values Figure 14 presents the effect of W on the flatness of the profile nose (∆D). It is seen that the of the profile nose (Dmax) are found at the 8.32 mm fin area. In the extrusion process, the velocity in behavior of ∆D with respect to W is fairly similar to that of ∆V (in Figure 13). The maximum values of the porthole tends to be fast in its center. Increasing W will push the high-velocity zone away from the profile nose (D ) are found at the 8.32 mm fin area. In the extrusion process, the velocity in the the die center, whichmax leads to increasing the velocity mainly at the 8.32 mm fin area, and therefore porthole tends to be fast in its center. Increasing W will push the high-velocity zone away from the die Dmax. center, which leads to increasing the velocity mainly at the 8.32 mm fin area, and therefore Dmax. From Figure 13, the porthole die with the chamfered bridge is recommended because it reduces the extrusion force significantly while the velocity difference is negligible. In this way, the width W = 18 mm is selected as the appropriate value for this die design.

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Metals 2020, 10, 553 11 of 18 Metals 2020, 10, x FOR PEER REVIEW 11 of 19

Figure 14. Effect of W on ΔD of the porthole die with the chamfered bridge.

From Figure 13, the porthole die with the chamfered bridge is recommended because it reduces the extrusion force significantly while the velocity difference is negligible. In this way, the width W = FigureFigure 14.14. EEffectffect ofof WW on ∆ΔD of the porthole die with the chamfered bridge. 18 mm is selected as the appropriate value for this die design. FigureFigure 15 illustratesillustrates the the effect effect of of WWtt varyingvarying from from 2 to 2 to10 10mm mm on onΔV∆,, ΔD,V, ∆ andD, and the themaximum maximum exit From Figure 13, the porthole die witht the chamfered bridge is recommended because it reduces exitprofile profile temperatur temperature.e.. It can It can be seenbe seen that that ΔV∆ Vandand ΔD∆ Dallall have have the the same same reduction reduction tendency with with the extrusion force significantly while the velocity difference is negligible. In this way, the width W = increasingincreasing WWtt.. Therefore, Therefore, thethe flowflowflow balancebalance isis improvedimproved withwith increasingincreasing WWtt... However, However, thethethe maximummaximummaximum 18 mm is selectedt as the appropriate value for this die design. t temperaturetemperature inin thethe exitexit profileprofile risesrises slightly.slightly. ThisThis isis becausebecause whenwhen WWttt increaseincreases,s,, the the size of thethe DMZDMZ Figure 15 illustrates the effect of Wt varying from 2 to 10 mm on ΔV, ΔD, and the maximum exit underunder the bridge is increased (see Figure 1166),), resulting resulting in in a a higher higher d degreeegree of metal deformation deformation... profile temperature. It can be seen that ΔV and ΔD all have the same reduction tendency with Moreover,Moreover, the increase in exitexit temperaturetemperature isis alsoalso attributedattributed toto thethe flowflow obstructionobstruction causedcaused byby the increasing Wt. Therefore, the flow balance is improved with increasing Wt. However, the maximum DMZ.DMZ.. FigureFigure 17 17 depicts depicts the the velocity velocity distribution distribution of materialof material estimated estimated for Wfort = W2tt mm = 2 mm and Wandt = W10tt mm.= 10 temperature in the exit profile rises slightly. This is because when Wt increases, the size of the DMZ Themm. flow The velocityflow velocity under under the port thebridge port bridge with Wwith= W10tt mm= 10 ismm significantly is significantly reduced reduced compared compared to that to under the bridge is increased (see Figure 16), resultingt in a higher degree of metal deformation. withthat withW = W2ttmm. = 2 mm.. Moreover,t the increase in exit temperature is also attributed to the flow obstruction caused by the DMZ. Figure 17 depicts the velocity distribution of material estimated for Wt = 2 mm and Wt = 10 mm. The flow velocity under the port bridge with Wt = 10 mm is significantly reduced compared to that with Wt = 2 mm.

(a) (b)

FigureFigure 15.15. The The eeffectsﬀects ofofW Wttt onon ((aa)) ∆ΔV andand the the maximum maximum exit exit profile proﬁle temperature; ( b) on Δ∆DD...

(a) (b)

Figure 15. The effects of Wt on (a) ΔV and the maximum exit profile temperature; (b) on ΔD.

(a) (b)

FigureFigure 16. 16.Distribution Distribution of of strain strain rate rate of of material material inside inside the the die: die::( a((a))W Wttt = = 2 mm mm;;; ( (b) Wtt == 1010 mm mm...

(a) (b)

Figure 16. Distribution of strain rate of material inside the die: (a) Wt = 2 mm; (b) Wt = 10 mm.

Metals 2020, 10, 553 12 of 18 Metals 2020, 10, x FOR PEER REVIEW 12 of 19

(a) (b)

FigureFigure 17. 17.Distribution Distribution of of velocity velocity inside inside the the die: die:( a(a))W Wt t= = 2 mm; ((b)) Wtt = 1010 mm mm..

InIn summary,summary, bridge bridge parameters parametersW Wand andWt Wsignificantlyt significantly influence influence the velocity the velocity distribution distribution of metal of duringmetal during extrusion. extrusion The chamfered. The chamfered bridge bridge shows shows a little a little effect effect on the on flow the flow balance; balance however,; however, it can it significantlycan significantly reduce reduce the extrusion the extrusion force. force. From From the presented the presented results, results the proper, the proper values values of W and of W tandfor obtainingWt for obtaining a good a flow good balance flow b arealance 18 andare 18 10 and mm, 10 respectively. mm, respectively.

4.3.2.4.3.2. EEffectffect ofof thethe WeldingWelding ChamberChamber HeightHeight InIn thisthis section,section, thethe eeffectsffects ofof weldingwelding chamberchamber heightheight ((HH)) varyingvarying fromfrom 99 andand 1717 mmmm onon thethe extrusionextrusion processprocess parameters parameters are are analyzed. analyzed. Figure Figure 18 18shows shows the the behavior behavior of ∆ ofV ,Δ∆VD,, ΔD,and and maximum maximum exit profileexit profile temperature. temperature. It can It be can seen be thatseen the that eff theects effects of H on of theH on extrusion the extrusion process process parameters parameters are totally are ditotallyfferent different compared compared to the eff toects the of effectsW and ofW tWrepresented and Wt represented earlier in Figures earlier 14 in and Figures 15. As 14 indicated and 15. As in FigureMetalsindicated 2020 18,, 10in the, xFigure FOR unbalance PEER 18, REVIEWthe of unbalance flow increases of flow as increasesH becomes as veryH becomes high or very very high small. or veryH = 13small. mm 13His of= the 1319 bestmm valueis the tobest achieve value theto achieve flow balance the flow as bothbalance∆V asand both∆D ΔreachV and their ΔD reach minimum their values.minimum values. Figure 18 also illustrates that the maximum exit temperature of the profile decreases with increasing H. This is caused by the effect of the DMZ, which exists under the port bridge. For the die with a lower value of H, the DMZ causes greater obstruction to the metal flow at the die opening compared to that of the die with a larger H, as demonstrated in Figure 19. Moreover, reducing H also increases the deformation of metal in front of the die orifice, as shown in Figure 20.

(a)

Figure 18. Cont.

(b)

Figure 18. The effects of H on the extrusion process parameters: (a) ΔV and the maximum exit temperature profile; (b) ΔD.

(a) (b)

Figure 19. Distribution of velocity in dies: (a) the die with H = 9 mm; (b) the die with H = 17 mm. Metals 2020, 10, x FOR PEER REVIEW 13 of 19

Metals 2020, 10, x FOR PEER REVIEW 13 of 19

Metals 2020, 10, 553 13 of 18

(a)

(b)

FigureFigure 18. 18. The e effectsﬀects of of HH on on the the extrusion extrusion process process parameters: parameters: ( (aa)) ∆ ΔVV andand the the maximum maximum exit exit temperaturetemperature proﬁle;profile; ( (bb))∆ ΔDD..

Figure 18 also illustrates that the maximum exit temperature of the profile decreases with increasing H. This is caused by the effect of the DMZ, which(b) exists under the port bridge. For the die with a lower value of H, the DMZ causes greater obstruction to the metal flow at the die opening compared to Figure 18. The effects of H on the extrusion process parameters: (a) ΔV and the maximum exit that of the die with a larger H, as demonstrated in Figure 19. Moreover, reducing H also increases the temperature profile; (b) ΔD. deformation of metal in front of the die orifice, as shown in Figure 20.

(a) (b)

Figure 19. Distribution of velocity in dies: (a) the die with H = 9 mm; (b) the die with H = 17 mm.

(a) (b)

MetalsFigureFigure 2020, 10 19. 19., xDistribution DistributionFOR PEER REVIEW ofof velocityvelocity in in dies: dies: ((aa)) thethe diedie withwithH H= = 99 mm;mm; ((bb)) thethe diedie withwith HH == 17 mm mm.. 14 of 19

(a) (b)

FigureFigure 20. 20.Distribution Distribution of strainof strain rate rate with with diﬀ differenterent H values: H values: (a) H(a)= H9 = mm; 9 mm; (b) (Hb)= H17 = 17 mm. mm.

FromFrom Figure Figure 18 ,18 it, can it can be be concluded concluded that that the the welding welding chamber chamber height height remarkably remarkably influences influences the the flowflow balance. balance. A weldingA welding chamber chamber height height of 13of 13 mm mm is theis the preferable preferable parameter parameter for for the the present present die. die. 4.4. The Final Die Structure 4.4. The Final Die Structure The ultimate die is obtained after the presented modification steps of die structure. Table3 The ultimate die is obtained after the presented modification steps of die structure. Table 3 summarizes the simulation results corresponding to the die modification steps. Steps 1–3 mainly aim summarizes the simulation results corresponding to the die modification steps. Steps 1–3 mainly aim at improving the flow balance of metal (reducing VRD, ΔV, and ΔD), which, however, increases the extrusion force because the extruded material experiences a higher degree of deformation. In the last step, by designing a chamfered bridge structure, the extrusion force is reduced to a minimum, whilst the other parameters VRD, ΔV, and ΔD do not change significantly. Figure 21 presents the 2D layout and 3D model of the proposed extrusion die. Figure 22 shows the velocity distribution of metal in the initial and proposed dies. It can be seen that the velocity distribution of the proposed die is significantly improved compared to the original one. The deformation of the extrudate with the proposed extrusion die is also reduced.

Table 3. Summary of simulation results of dies corresponding to modifying steps.

Simulation results Step Modification VRD (%) ΔV (mm/s) ΔD (mm) Extrusion force (ton) 0 Initial die design 4.10 4.72 12.42 479.55 1 Reducing porthole 1.76 2.09 5.76 481.88 2 Modifying pocket 0.87 0.89 2.69 487.07 3 Adjusting bearing lengths 0.78 0.78 2.38 487.59 4 Chamfering port bridge 0.82 0.86 2.58 477.88

Metals 2020, 10, 553 14 of 18 at improving the ﬂow balance of metal (reducing VRD, ∆V, and ∆D), which, however, increases the extrusion force because the extruded material experiences a higher degree of deformation. In the last step, by designing a chamfered bridge structure, the extrusion force is reduced to a minimum, whilst the other parameters VRD, ∆V, and ∆D do not change signiﬁcantly. Figure 21 presents the 2D layout and 3D model of the proposed extrusion die.

Table 3. Summary of simulation results of dies corresponding to modifying steps.

Simulation Results Step Modiﬁcation VRD (%) ∆V (mm/s) ∆D (mm) Extrusion Force (ton) 0 Initial die design 4.10 4.72 12.42 479.55 1 Reducing porthole 1.76 2.09 5.76 481.88 2 Modifying pocket 0.87 0.89 2.69 487.07 3 Adjusting bearing lengths 0.78 0.78 2.38 487.59 Metals 2020, 10, x FOR PEER REVIEW 15 of 19 4 Chamfering port bridge 0.82 0.86 2.58 477.88

(a)

(b)

FigureFigure 21.21. TheThe proposedproposed diedie forfor extrusionextrusion ofof thethealuminum aluminumheatsink heatsink proﬁle:profile: ((aa)) thethe 2D2D layoutlayout ofof thethe proposedproposed die;die; ((bb)) the the 3D3D assemblyassembly modelmodel of of the the upper upper and and lower lower dies dies (unit: (unit: mm). mm).

Figure 22 shows the velocity distribution of metal in the initial and proposed dies. It can be seen that the velocity distribution of the proposed die is signiﬁcantly improved compared to the original one. The deformation of the extrudate with the proposed extrusion die is also reduced.

(a) (b)

Figure 22. Velocity distribution on the extrudate: (a) the initial die; (b) the proposed die.

Figure 23 displays the temperature distribution during the extrusion process of the original and proposed dies. In general, maximum temperatures of proposed and original dies are well approximated. Higher temperature occurs near porthole 2 due to the increase of material deformation in this region. Figure 24 highlights the distribution of residual stress in the extrudate of the initial and proposed dies. The maximum residual stress in the extrudate with the proposed die is smaller compared to the original die (12.83 MPa vs. 16.19 MPa). High residual stresses are mainly concentrated at the intersection regions between fins with a large wall thickness and the main body

Metals 2020, 10, x FOR PEER REVIEW 15 of 19

(a)

(b)

Figure 21. The proposed die for extrusion of the aluminum heatsink profile: (a) the 2D layout of the Metals 2020, 10, 553 15 of 18 proposed die; (b) the 3D assembly model of the upper and lower dies (unit: mm).

(a) (b)

Figure 22. Velocity distribution on the extrudate:extrudate: (a) the initial die; (b) the proposed die. Metals 2020, 10, x FOR PEER REVIEW 16 of 19 Figure 23 displays the temperature distribution during the extrusion process of the original and proposedof the heatsink dies.dies In., which In general, general, are maximum caused maximum by temperatures the temperaturedifference of proposeds sin ofvelocity proposed and and original temperatureand dies original are well of diesthe approximated. respective are well Higherregions.approximate temperature d. Higher occurs temperature near porthole occurs 2 due near to the porthole increase of 2 materialdue to deformationthe increase in of this material region. deformation in this region. Figure 24 highlights the distribution of residual stress in the extrudate of the initial and proposedMetals 2020 , 10die, xs FOR. The PEER maximum REVIEW residual stress in the extrudate with the proposed die is smaller16 of 19 compared to the original die (12.83 MPa vs. 16.19 MPa). High residual stresses are mainly concentratedof the heatsink at ,the which intersection are caused regions by the between difference finss with in velocity a large andwall temperaturethickness and of the the main respective body regions.

(a) (b)

Figure 23. TemperatureTemperature distribution during the extrusion: ( a) t thehe initial die; (b) thethe proposed die.

Figure 24 highlights the distribution of residual stress in the extrudate of the initial and proposed dies. The maximum residual stress in the extrudate with the proposed die is smaller compared to the original die (12.83 MPa vs. 16.19 MPa). High residual stresses are mainly concentrated at the intersection regions between(a) ﬁns with a large wall thickness and the main body(b) of the heatsink, which are causedFigure by 23. the Temperature diﬀerences distribution in velocity during and temperature the extrusion: of ( thea) the respective initial die; regions. (b) the proposed die.

(a) (b)

Figure 24. Distribution of residual stress in the extrudate: (a) the initial die; (b) the proposed die.

4.5. Extrusion Experiment To verify the proposed die design, the real porthole die is fabricated according to the geometry parameters of the proposed(a) die. After that, the extrusion experiment is (b conducted) on a 930-ton extruder. Figure 25a shows the experimental extrusion process. Figure 25b presents the final Figure 24. Distribution of residual stress in the extrudate: (a) the initial die; (b) the proposed die. extrudedFigure product. 24. Distribution It can be of seen residual that stress a defect in the-free extrudate: product (a) t washe initial produced. die; (b) t Thehe proposed geometry die. of the 4.5.product Extrusion is generally Experiment consistent with the simulation results. To check the geometric dimensions of the 4.5. Extrusion Experiment extruded product, measurements were carried out using electronic calipers. The deviations in the To verify the proposed die design, the real porthole die is fabricated according to the geometry wall thicknessTo verify ofthe the proposed product die are design, within the realallowable porthole lim dieits of is ±0.15fabricated mm, andaccording dimensional to the geometryerrors of parameters of the proposed die. After that, the extrusion experiment is conducted on a 930-ton theparameters length and of the width proposed of the die. product After are that, less the than extrusion 0.25 mm. experiment Hence, is the conducted extrudate on meets a 930 - theton requirementextruder. Figure for dimensional 25a shows tolerance. the experimen tal extrusion process. Figure 25b presents the final extrudedIt is worth product. noting It canthat bethe seenproposed that adie defect successfully-free product extrudes was for produced. the first time The wi geometrythout the of need the forproduct die modifications. is generally consistent Therefore, with the theproposed simulation design results. approach To check is very the useful geometric and dimensionsreliable. It is of also the notedextruded here product, that the effectsmeasurements of die deformation were carried on outthe usingdimensional electronic tolerance calipers. of theThe extruded deviations product in the werewall thicknessassumed negligible.of the product This are is becauwithinse the the allowable extrusion lim processits of ±0.15used mm,a porthole and dimensional die, which reducederrors of thethe direct length impact and width from the of the billet product to the die are orifice. less than Therefore, 0.25 mm. the Hence, deformation the extrudate of this die meets will the be smallerrequirement than for the dimensional traditional tolerance. flat-face di es. Secondly, the extrusion ratio is quite low (= 10.73), resultingIt is worth in a small noting required that the extrusionproposed die force, successfully and therefore extrudes small for die the deflection.first time wi Lastly,thout the the need die containsfor die modifications. two run-out Therefore, steps, which the supportproposed the design die openingapproach and is very increase useful the and die reliable. strength. It is Thealso runnoted-out here steps that also the ensure effects that of die the deformation extrudate does on thenot dimensionaltouch the die tolerance surface. Hence,of the extruded die deformation product canwere be assumed minimized. negligible. This is because the extrusion process used a porthole die, which reduced the direct impact from the billet to the die orifice. Therefore, the deformation of this die will be smaller than the traditional flat-face dies. Secondly, the extrusion ratio is quite low (= 10.73), resulting in a small required extrusion force, and therefore small die deflection. Lastly, the die contains two run-out steps, which support the die opening and increase the die strength. The run-out steps also ensure that the extrudate does not touch the die surface. Hence, die deformation can be minimized.

Metals 2020, 10, 553 16 of 18 extruder. Figure 25a shows the experimental extrusion process. Figure 25b presents the ﬁnal extruded product. It can be seen that a defect-free product was produced. The geometry of the product is generally consistent with the simulation results. To check the geometric dimensions of the extruded product, measurements were carried out using electronic calipers. The deviations in the wall thickness of the product are within the allowable limits of 0.15 mm, and dimensional errors of the length ± and width of the product are less than 0.25 mm. Hence, the extrudate meets the requirement for dimensionalMetals 2020, 10, x tolerance. FOR PEER REVIEW 17 of 19

(a) (b)

Figure 25.25. Extrusion experiments:experiments: ((aa)) thethe aluminumaluminum porthole porthole extrusion extrusion process process of of a heatsinka heatsink proﬁle profile in practice;in practice; (b) ( theb) the sample sample of theof the real real product product after after extrusion. extrusion.

5. ConclusionsIt is worth noting that the proposed die successfully extrudes for the first time without the need for die modifications. Therefore, the proposed design approach is very useful and reliable. It is also notedIn here thisthat study, the an eff ectsappropriate of die deformation die for extrusion on the dimensionalof a complex tolerance heatsink ofaluminum the extruded profile product with werelarge assumed variable negligible. wall thickness This is was because designed. the extrusion The die processdesign usedwas a implemented porthole die, whichby combining reduced the directexisting impact design from experiences the billet to and the steady die orifice.-state Therefore, extrusion thesimulation deformation with of the this ALE die algorithm. will be smaller The thaneffects the of traditionalthe structural flat-face parameters dies. Secondly, of the port the bridge extrusion and the ratio welding is quite chamber low (=10.73), height resulting on the metal in a smallflow were required examined. extrusion Experiments force, and thereforewere conducted small die to deflection. verify the Lastly,proposed the diedie. containsThe conclusions two run-out are steps,obtained which as follows: support the die opening and increase the die strength. The run-out steps also ensure that the1. extrudateThe following does not step touchs are the proposed die surface. to obtain Hence, suitable die deformation porthole can extrusion be minimized. die: 1) resizing the porthole and pocket profiles; 2) adjusting the bearing lengths; 3) modifying the port bridge 5. Conclusionsstructure. The simulation results indicate that using the proposed die, the quality of flow balance of metal in the die was improved considerably. Comparing to the initial die, the In this study, an appropriate die for extrusion of a complex heatsink aluminum profile with large velocity distribution measures of the proposed solution such as VRD and ΔV are reduced from variable wall thickness was designed. The die design was implemented by combining the existing 4.1% and 4.72 mm/s to 0.82% and 0.86 mm/s, respectively; the required extrusion force and design experiences and steady-state extrusion simulation with the ALE algorithm. The effects of the residual stresses in the extrudate are also reduced from 479.55 tons and 16.19 MPa to 477.88 tons structural parameters of the port bridge and the welding chamber height on the metal flow were and 12.83 MPa, respectively. The maximum exit temperature of the extrudate increases slightly examined. Experiments were conducted to verify the proposed die. The conclusions are obtained as as compared to the initial die. follows: 2. The entrance of a porthole with a chamfered bridge significantly reduces the required extrusion 1. forceThe following. However steps, it has are a negligible proposed influence to obtain on suitable the velocity porthole distribution extrusion of die:flow (1)in the resizing extruded the product.porthole and pocket profiles; (2) adjusting the bearing lengths; (3) modifying the port bridge 3. Tstructure.he die parameters The simulation including results the width indicate of th thate port using bridge the proposed(W), the rear die, tip the wi qualitydth of the of flowport bridgebalance (W oft) metal, and the in the welding die was chamber improved height considerably. (H) all influenc Comparinge the metal to the flow initial velocity die, the due velocity to the brakingdistribution effect measures of the dead of the metal proposed zone solution(DMZ) formed such as VRDunderand the∆ portV are bridge. reduced Moreover, from 4.1% th andese parameters4.72 mm/s to have 0.82% different and 0.86 effects mm/s, respectively;on velocity distribution the required on extrusion the extrudate. force and In residual particular, stresses the velocityin the extrudate distribution are alsobecomes reduced more from uniform 479.55 with tons increasing and 16.19 MPaWt from to 477.88 2 to 10 tons mm. and On 12.83 the other MPa, handrespectively., increasing The W maximum from 18 exitto 20 temperature mm results ofinthe uneven extrudate velocity increases distribution slightly in as the compared extrudate. to Verythe initial high die.(above 17 mm) or very small (below 9 mm) values of welding chamber height H all have a negative effect on the balance of metal flow. 4. In conclusion, appropriate porthole extrusion die is the key to success of the extrusion of heatsink products with significant wall thickness variation. The main concern in designing this die type is to determine the position and structure of the port bridge, which plays a vital role in balancing the metal flow on the extrudate, especially at the location where the wall thickness is very thick. Although the proposed die is highly suitable for metal flow balance, this die type commonly generates longitudinal weld seams in the extrudates. Moreover, it may cause poor surface quality of the products after anodizing, and higher extrusion force when compared to the flat-face die. Hence, design optimization of porthole dies needs to be extended further.

Metals 2020, 10, 553 17 of 18

2. The entrance of a porthole with a chamfered bridge significantly reduces the required extrusion force. However, it has a negligible influence on the velocity distribution of flow in the extruded product. 3. The die parameters including the width of the port bridge (W), the rear tip width of the port bridge (Wt), and the welding chamber height (H) all influence the metal flow velocity due to the braking effect of the dead metal zone (DMZ) formed under the port bridge. Moreover, these parameters have different effects on velocity distribution on the extrudate. In particular, the velocity distribution becomes more uniform with increasing Wt from 2 to 10 mm. On the other hand, increasing W from 18 to 20 mm results in uneven velocity distribution in the extrudate. Very high (above 17 mm) or very small (below 9 mm) values of welding chamber height H all have a negative effect on the balance of metal flow. 4. In conclusion, appropriate porthole extrusion die is the key to success of the extrusion of heatsink products with significant wall thickness variation. The main concern in designing this die type is to determine the position and structure of the port bridge, which plays a vital role in balancing the metal flow on the extrudate, especially at the location where the wall thickness is very thick. Although the proposed die is highly suitable for metal flow balance, this die type commonly generates longitudinal weld seams in the extrudates. Moreover, it may cause poor surface quality of the products after anodizing, and higher extrusion force when compared to the flat-face die. Hence, design optimization of porthole dies needs to be extended further.

Author Contributions: T.-T.T. synthesized data, designed and simulated extrusion dies, conducted experiments, and wrote the original manuscript; Q.-C.H. instructed, supervised, and edited the content; V.-C.T. analyzed the results, reviewed, and edited the manuscript. J.-J.S. reviewed and edited the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was partially funded by the Ministry of Science and Technology, Taiwan, under grant number MOST 108-2221-E-992-066-. Acknowledgments: The authors would like to acknowledge the financial support from the Ministry of Science and Technology, Taiwan. Conflicts of Interest: The authors declare no conflicts of interest.

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