FLOW ANALYSIS INSIDE SHEAR AND STREAMLINED EXTRUSION DIES
FOR FEEDER PLATE DESIGN
A Thesis Presented to
The Faculty ofthe
Fritz J. and Dolores H. Russ College ofEngineering and Technology
Ohio University
In Partial Fulfillment
Ofthe Requirement for the Degree
Master ofScience
By
Ibrahim A. AI-Zkeri
November, 1999
OHIO U HSiTY II r~1A~ y ACKNOWLEDGMENTS
I would like to express my sincere appreciation to my advisor, Dr. Bhavin V.
Mehta, for his valuable advice and for providing me with the information and the facilities required for this thesis.
I would also like to thank Mr. Arjaan Bijk from MacNeal-Schwendler
Corporation for his tremendous support during this research.
Last but not least, I would like to thank my parents for their unlimited and continuous care and reassurance, my wife for her endless patience and support, and all my brothers and sisters for their encouragement.
Ibrahim A. AI-Zkeri
November 1999 11
TABLE OF CONTENTS
LIST OF TABLES iv
LIST OF FIGURES v
Chapter I- INTRODUCTION...... •...... 1
1.1 Extrusion History 1
1.2 Extrusion Process 4
1.3 Extrusion Die Design 9
1.4 Objective ofthe Thesis 10
Chapter II - LITERATURE REVIEW 12
Chapter III - ANALYSIS METHODOLOGy 15
3.1 Isothenn.al Extrusion 15
3.2 Steady-State Process 15
3.3 Finite-Element Method 16
3.4 Finite Volume Method 17
Chapter IV - MODELING OF EXTRUSION DIES 18
4.1 Introduction 18
4.2 STREAM 18
4.3 MSCIPATRAN 24 III
Chapter V- SIMULATIONS AND ANALYSIS 30
5.1 Introduction 30
5.2 Common Preprocessing Settings 30
5.3 Simulation Using DEFORMTM-3D 33
5.4 Simulation Using MSC/SuperForge 36
Chapter VI - RESULTS...... •.•...•...... •.•...•.•...... •...... 38
6.1 Extrusion Using Streamlined Die 38
6.1.1 DEFORMTM-3D Simulation Results 38
6.1.2 MSC/SuperForge Simulation Results 41
6.2 Extrusion Using Shear Dies 43
Chapter VII - CONCLUSION AN"D DISCUSSION 51
7.1 Conclusion 51
7.2 Discussion 52
7.3 Future Work 53
REFERENCES ...... •...... •.•...... ••.....•...•...... •.•.•.•..••.•...... 54
APPENDICES...... •.•.•.•...•....•.•.•.•.•.•••...... •...•...... •.•.•...•.•.•...... •.... 59
Appendix A: STREAM RUN 59
Appendix B: DIE1.DAT (The Input Data File) 65 IV
LIST OF TABLES
Table 1: The Input Data for Streamlined Die Profile Design 23
Table 2: The Z-Level Values ofthe Selected B-Spline Curves 27
Table 3: Material Properties for Aluminum Alloy (6061-0) 31
Table 4: DEFORMTM-3D Simulation Control Settings 35 - Table 5: The Maximum Values of Press Load, c , and € for all dies 49
Table 6: Comparison ofSimulations' Results 51 v
LIST OF FIGURES
Figure 1: Bramah's lead-pipe machine 2
Figure 2: Horizontal extrusion press designed by Alexander Dick in 1894 3
Figure 3: Direct and indirect extrusion, with internal shearing 5
Figure 4: Various types of shear dies 7
Figure 5: Feeder plate die; the produced shape is larger than the billet size 8
Figure 6: The product cross-section shape and its dimensions 18
Figure 7: Limitations of previous methods of streamlined die design 20
Figure 8: The new concept of die design used in STREAM 21
Figure 9: Stocke's Theorem applied to die design 22
Figure 10: The mapping of the billet to the product shape 24
Figure 11: Die geometry for the streamlined die 25
Figure 12: Die geometry for the solid-shape and feeder plate dies 26
Figure 13: The billet geometry with different types of mesh 28
Figure 14: The a - £ curve of Aluminum 6061-0 32
Figure 15: Effective stress distribution when streamlined die is used (ksi) 39
Figure 16: Effective strain distribution when streamlined die is used (in/in) 40
Figure 17: The load-stroke curve of the extrusion press 40
Figure 18: Effective stress distribution when streamlined die is used (psi) 41
Figure 19: Effective strain distribution when streamlined die is used (in/in) 42
Figure 20: The load (Ibfj-stroke (in) curve of the extrusion press 43 VI
Figure 21: Effective stress distribution when shape die is used (psi) 44
Figure 22: Effective strain distribution when shape die is used (in/in) 45
Figure 23: The ram load (lbf)-stroke (in) curve when shape die is used 46
Figure 24: Z-Velocity distribution when feeder plate die is used (Z=2.0) 47
Figure 25: Effective stress distribution when feeder plate die is used (Z=2.0) 47
Figure 26: Effective strain distribution when feeder plate die is used (Z=2.0) 48
Figure 27: Load (lbf)-Stroke curve ofthe ram when feeder plate die is used (Z=2.0). 48
Figure 28: Maximum effective stress for all dies used in this study 49
Figure 29: Maximum effective strain for all dies used in this study 50
Figure 30: Maximum ram load for all dies used in this study 50 Chapter I IN·TRODUCTION
Today, with more advanced technology, extrusion process is used in a wide variety of applications--helicopter blades, turbine blades, wing spars, construction material, etc.
Extrusion process offers significant advantages over metal working operations, especially where considerable length of the same cross-section is desired [1]. Extrusion process development revolution began more than 200 years ago with the invention of the first simple lead press and developed into the modem automatic extrusion process. The most important chapter of the extrusion process development revolution began some decades ago using computers to design extrusion dies. Today, extrusion die design is relatively easier and cheaper using the most advanced Computer-Aided Design (CAD) technology.
The designer can design and modify the extrusion dies even for complex shear products without wasting any material and do.so in a relatively shorter time.
1.1 Extrusion History
Extrusion has an industrial history stretching back around 200 years. It is probable that the earliest perception of the principles of extrusion was due to a famous hydraulic engineer, Joseph Bramah. He, in a patent granted in 1797, described a press (see Figure
1), "for making pipes of lead or other soft metals of all dimensions and any given length without joints" [11]. Lead, maintained molten in an iron pot (a), by a fire beneath, was forced by a pump (b) into a long projecting tube (c), which served as a die. A tapered mandrel (d) was supported concentrically with the tube by means of a bridge in its enlarged end. The lead passing through the annular space between the tube and mandrel 2
was kept molten by the fuel gases inside the outer casing until it approached the outlet,
where it was chilled to cause it to solidify so that it emerged in the form of a pipe [11].
The basic principle ofBramah's press is still used today in the manufacture of lead tubes
[2].
Figure 1: Bramah's lead-pipe machine [11].
There was no immediate development of Bramah's idea, and the earlier methods of making lead pipes continued to be used until 1820, when Thomas Burr, a Shrewsbury plumber, constructed a press operated by hydraulic power [11].
The development of metal extrusion processing continued. However, the inventions were limited to the extrusion oflead until 1894, when Alexander Dick got his first patent
for an extrusion press that allowed non-ferrous alloys to be extruded for the first time (see
Figure 2). He built a horizontal extrusion press for the Delta Metal Company in
Dusseldorf, England [11,2]. Upon Dick's inventions, which he continued to improve up to the time ofhis death in 1903, the modern process ofextrusion has been founded [11]. 3
Figure 2: Horizontal extrusion press designed by Alexander Dick in 1894 [11].
Since Dick's death and until the end of the 1960's, the extrusion process has developed technically and some materials, such as steel and unusual metals including titanium, beryllium, and uranium, were added to the extruded metals. Beginning in the early 1950's, many researchers were concerned about studying the extrusion process and modeling the metal flow during the extrusion process mathematically. At the end of the
1960's, many theories that describe the extrusion process and some tips on designing the extrusion dies were available to the extrusion industry. Moreover, many researchers began thinking about modeling some new die shears in order to reduce the stresses on the extruded metal and make the metal flow as uniformly as possible.
During the early 1970's, computers were used to an increasing extent for metal forming applications. For the solution of metal forming problems, two approaches can generally be employed. The first is the usual elastic-plastic approach where the material is treated as elastic-plastic. A good example ofa computer software package utilizing this approach is NlKE2D developed by John Hallquist at the Lawrence Livermore Labs., 4
USA [4]. The second is the rigid-plastic finite-element method developed by Lee and
Kobayashi, which permitted large increments of deformation, therefore reducing computation time. One of the earlier software that worked on Lee and Kobayashi's approach is ALPID (Analysis of Large Plastic Incremental Deformation). ALPID was developed by S. Oh and co-workers at the Battelle Memorial Institute with U.S. Air
Force Sponsorship [4,6].
1.2 Extrusion Process Extrusion is a comparatively process among the industrial methods by which metals are wrought into useful forms, but it has succeeded in establishing itself firmly as one of the foremost of these. Essentially the process is one by which a block of solid metal
(billet) is converted into a continuous length of a uniform cross-section by forcing it to flow, under high pressure, through a die orifice which is so sheard as to impart the required form to the product [11].
Extrusion is mostly carried out under high temperatures. This is dictated by the necessity of lowering the toughness ofthe metal in the pressed state in order to avoid the necessity of applying very large operating stresses. The metals pressed without heating are those with relatively low toughness and with small thermal inertia ofthe blank [3] or the billet. As a result, there are two main types of extrusion processes according to the initial temperature ofthe billet: Cold Extrusion and Hot Extrusion.
Cold Extrusion is so called because the billet enters the extrusion die at room temperature. Any subsequent increase in temperature, which amounts to several hundred degrees, is caused by the conversion ofdeformation work into heat. 5
Hot Extrusion is the process of forcing a heated billet to flow through a sheard die opening [5]. The metal is being heated to give it a suitable degree of softness and plasticity [11]. The temperature at which extrusion is performed depends on the material being extruded; for aluminum alloys, it ranges between 650 to 950 of (5].
The two most significant extrusion processes for aluminum are direct and indirect extrusion, and these are illustrated schematically in Figure 3. With aluminum, lubricant is not normally used. The extrusion method, which uses no lubrication between the billet, the container, and the die, is used to produce complex shears with excellent surface finish and close-dimensional tolerances [6].
(a) Direct
(b) Indirect
Figure 3: Direct and indirect extrusion, with internal shearing [6]. 6
There are two common types ofextrusion dies according to the shear ofthe die:
(a) shear (flat-faced or square) die, which is commonly used in the extrusion of
aluminum; and
(b) sheard (converging) die, which has found applications In the lubricated
extrusion oftitanium, nickel and steel alloys [6].
Shear dies for extruding aluminum are generally classified into four designs: solid
shear, porthole, bridge, and baffle or feeder plate types [6,1]. The shear dies are used for
extruding solid shears. These dies are made by machining an opening ofthe desired shear in the die block, as shown in Figure 4(a). The porthole die design, shown in Figure 4(b), has porthole openings in the top face ofthe die from which material is extruded into two or more segments, and is then, beneath the surface ofthe die, welded and forced through
the final shear configuration to form a part. TIle tubular portion of the extruded shear is
formed by a mandrel attached to the lower side of the top die segment. This provides a
fixed support for the mandrel and a continuous hole in the extruded part. Figure 4(b) shows typical complex parts that can be made through the use of a porthole type arrangement.
Bridge dies are quite similar to the porthole dies and are also used for extruding the hollow products. The bridge divides the metal extending into the container, as shown in
Figure 4(c). Compared to porthole dies, the bridge dies are less rigid. However, the removal of the extrusion left in the container at the end of the extrusion cycle is more difficult with porthole dies than with bridge dies [1]. 7
o• o• ~ i:
(a) Shear die (b) Porthole die
Bortle 0' Wetdin9 Plole (c) Bridge die (d) Feeder plate die
Figure 4: Various types ofshear dies [1, 6,8,9].
The baffle or feeder plate die, according to DeBuigne [9] and Bello [8], as shown in
Figure 4(d), is a solid die designed and manufactured to serve several purposes:
• It provides a uniform feed of metal into the cavity of the die, which induces
flow control and assists in maintaining the contour ofthe extruded section.
• It permits the next billet to partially weld itself to the material in the cavity,
insuring a straight run-out for the next extrusion.
• It helps to extrude straighter and to reduce scrap.
In addition (as mentioned in Bello [8] and shown in Figure 5), the feeder plate die may be used to produce a shear larger than the billet size. It feeds the metal into the die opening in a similar manner to what is done on a hollow die (porthole die), and it forms 8 aluminum pockets toward both ends of the shear to be able to balance the flow with the center and the rest ofthe extrusion.
Feeding angles
.. Metal Flow
~edie
Figure 5: Feeder plate die; the produced shear is larger than the billet size [8].
Converging dies are further classified into conical, parabolic, and streamlined types; the difference between them is the mathematical representation ofthe surface or material path line. In the conical die, the material path line is a linear function; in the parabolic die
(convex or concave), it is a parabolic function (second-order equation); and in the streamlined die, a cubic function has been used [12].
Sheard dies have both disadvantages and advantages over square dies (shear dies).
One disadvantage ofsheard dies is that they are more difficult to design and manufacture, but ifdesigned properly, they offer the following advantages over square dies:
(a) better quality ofproduct (more uniformly deformed product [10]),
(b) less extrusion force, and
(c) greater extrusion speed and productivity [7]. 9
Moreover, according to Patel [10], the streamlined dies have two other advantages over the shear dies--less local adiabatic heating and prevention of hot shortness. Hence, the extrusion must be carried out at a sufficiently low ram (press) speed to avoid adiabatic heating and hot shortness in the product [12,14].
1.3 Extrusion Die Design
Die design has been an art more than a science. The design and manufacture ofdies have been passed down for decades from die and tool designers and tool makers to their apprentices and so on. This process is undergoing some revolutionary change with the advent of computers, Computer-Aided Design (CAD) and Computer-Aided
Manufacturing (CAM) technology and powerful analysis, such as the finite-element method [6].
A good design procedure should always be a precursor to the manufacturing of a quality product. Since the development of the extrusion process in the early eighteenth century, the extrusion process has not seen much of a change. Die design for extrusion processes has been the most difficult part. It has always relied on experimental trial-and error methods and has depended on the knowledge and experience ofthe designer [13].
To design and manufacture an extrusion die, the basic factors to be considered are as follow [9]:
1. Desired shear (shear ofproduct~;
2. Material to be extruded;
3. Billet size;
4. Press capacity (and type [6]); 10
5. Extrusion ratio;
6. Number ofcavities;
7. Shrink factor ofmaterial;
8. Press tool arrangement;
9. Extrusion temperature;
10. Extrusion pressure;
11. Selection ofdie material;
12. Heat-treat procedure ofdie materials.
When items 1 through 10 have been correlated, a decision is then made as to the type ofextrusion tool to be designed and manufactured [9]. In this study, items 4,7,10,1, and
12 have no effect since the designed extrusion process is assumed to be with fixed ,~p~~d
(i.e., unlimited press capacity), plastic deformation, and is isothermal.
1.4 Objective of the Thesis
The main objectives of this study can be summarized on two points: evaluating a new 3-D metal forming simulation package by comparing its simulation results with the simulation results of a validated package for the same process, and optimizing the feeder plate extrusion die design using 3-D metal forming simulation package.
Recently, a new metal forming analysis package--MSC/SuperForge--is provided commercially. This package uses the finite volume analysis method, which is relatively different than the other metal forming analysis methods used by most of the commercial metal forming packages. One objective of this study is to evaluate this package by comparing its simulation results with the simulation results ofone ofthe validated Finite 11
Element Method (FEM) packages--DEFORMTM-3D--using same simulation settings. To satisfy this goal, a 3-D extrusion process using a streamlined die for producing a complex product shear--I-shear--has been used.
The streamlined extrusion dies were considered to be more efficient than the shear dies. The consideration came from a practical view that streamlined dies minimize the load of extrusion and produce a more uniform material flow. However, the streamlined dies are still more expensive and difficult to be designed than the shear dies. Although many researches were concerned about the design of flat-faced (shear) extrusion dies, only a few attempts have been made to analyze the metal flow using a 3-D analysis. In this study, a type ofshear die (the feeder plate die) design is optimized using a 3-D metal fanning simulation package--MSC/S uperForge. 12
Chapter II LITERATURE REVIEW
The most important chapter of the extrusion process development revolution started some decades ago using computers to design extrusion dies. Today, extrusion die design is easier and cheaper using the most advanced Computer-Aided Design (CAD) technology. The designer can design and modify the extrusion dies, even for complex shear products, without wasting any material and in a relatively short time. Recently, many researchers used different computer-aided design packages to design extrusion dies--particularly the streamlined dies--by studying the metal flow.
Many researchers were concerned about the 3-D geometric modeling design of the streamlined dies [10,13-18,20-23]. In Nagpal et al. [15], an ellipse-sheard section of a streamlined die was designed and manufactured with an interactive computer software package called SHEAR. Billets of several metals were extruded experimentally through this streamlined die using suitable lubrication systems. Results ofthese trials showed the validity of SHEAR. Billets of several metals were extruded through this streamlined die using suitable lubrication systems. Later, in Nagpal et a1. [17], a streamlined die for extruding "T" sections was designed and manufactured with the same software package and provided the same results.
Several streamlined die profiles were designed using one or both of two other software packages called STREAM [10,13,14,16,18,21-23,27] and SHEAR [13] that were first developed by Gunasekera [16] for round-to-round extrusion processes.
Recently, a new technique for STREAM has been developed to overcome the re-entry 13
problem, as reported in Kavalauskas et al. [14]. Later, Patel [10] used a CNC machine for
manufacturing a streamlined die that was designed using STREAM. After several
developments, STREAM has proven capable of designing complex shear streamlined
dies, as reported by Altan et al. [18]. Then, Mehta [23] developed it to be able to design
streamlined dies that can be used to produce complex shear products from arbitrary or preformed section billets. Next, STREAM was supplied with a Graphical User Interfaces
(Gill) to be used in different finite-element analysis packages by Wang [21] to he used under Disk Operating System (DOS) with a new name--PcStream--by Gosavi [22]. Both
STREAM and SHEAR were combined and integrated to make users around the world able to use these packages to design either streamlined or shear dies virtually through the internet, as reported by Shivananda [13].
Lam et al. [20] were concerned about demonstrating how an Advance Die Design
System, ADDSTM (a .software from UES, Inc., USA), can be used in the streamlined extrusion die design. Also, they were concerned about how the designed die can be manufactured using computer-aided facilities. They concluded that the methodology used in their paper can be adopted to design and manufacture complex extrusion dies.
Mori et al. [24] investigated 3-D extrusion ofnon-circular sections using rigid-plastic finite-element method to predict the curvature of an extruded bar and calculate the location of the die opening. Later, Yang et al. [25] simulated the extrusion of a complex profile with square dies to generate the loading data necessary to predict the wear of the die land. Shivpuri et al. [26] investigated curvature and twist problems in L-shear extrusion using a shear die by the modification ofthe die geometry including entry angles
• 14 and the die land by simplifying the three-dimensional problem to a two-dimensional analysis problem. Jia [27] simulated the extrusion and drawing of a hollow preform to form a squared hollow shear with a streamlined die. In his study, a rigid-plastic finite element method was employed to simulate both rectangular hollow cold extrusion and drawing processes. The objective was to understand the difference between extrusion and drawing processes.
On the other hand, researches that were concerned about the feeder plate die design through a 3-D simulation were not found. However, there were some investigations about the metal flow of aluminum in weld pocket dies (feeder plate dies) that were analyzed through a metallurgical view like Misiolek [28], Prats [29], and Kialka et al. [38]. All of them were concerned with studying the material's physical response in the extrusion process--particularly studying the change in the microstructure ofthe billet material in the dead metal zone and finding the numerical models that help to control it.
The streamlined dies were considered to be more efficient than the shear dies. This consideration came from a practical view that streamlined dies minimize the load of extrusion and produce a more uniform material flow. However, 3-D finite-element analyses which supports that consideration and shows how much more efficient the streamlined dies are than shear dies, to the author's knowledge, are still not available.
On the other hand, no research was found that was concerned about studying the metal flow in the shear die with feeder plate using a 3-D analysis. Several studies were concerned with studying the change in the microstructure ofthe material flow in the dead metal zone and using 2-D analysis. 15
Chapter III ANALYSIS METHODOLOGY
In this study, the extrusion process is assumed to be an isothermal and steady-state process. These two assumptions were applied on two metal forming analysis packages that represent different analysis methods: finite-element method and finite volume method.
3.1 Isothermal Extrusion
The basic idea of the isothermal extrusion developed from a knowledge of the relationship between the extruded material exit temperature and the ram speed. The exit speed is varied via the pr~ss control system to give a constant exit temperature [2]. It is known that, under the isothermal extrusion conditions, it is feasible to obtain structural stability and constant mechanical properties throughout the length ofan extrusion [30]. In continuous extrusion processes, constant boundary conditions relatively lead to a constant product exit temperature. For isothermal extrusion simulation, the generated deformation and friction heat, the convection and radiation heat loss/gain and the heat exchange between two objects are neglected [31].
3.2 Steady-State Process
Except at the start and the end of the deformation, extrusion processes are kinematically steady-state. Steady-state solutions in these processes are needed for equipment design and die design and for controlling product properties. In nonsteady state forming problems, a mesh that requires continuous updating (Lagrangian) is used. In steady-state problems, a mesh fixed in space (Eulerian) is appropriate, since the process 16 configuration does not change with time. For steady-state problems whose solutions depend on the loading history or strain history of the material, combined Eulerian
Lagrangian approaches are necessary [32].
3.3 Finite-Element Method
The finite-element method (FEM) for elastic-plastic material property is considered to be the most accurate method available at present, but it necessities a very long time to carry out the computation and, further, the method can hardly treat very severe deformation in some metal forming processes. Some codes for computer simulation of metal forming operations (such as DEFORMTM_3D) have been established on the basis of the rigid-plastic finite-element method [33].
The assumption of rigid-plastic or rigid-viscoplastic material implies that the flow stress is a function of strain, strain rate, arid temperature and that the elastic response of the material is neglected. This assumption is very reasonable in analyzing metal forming problems, because the elastic portion of the deformation is negligible in most metal forming operations [4]. The rigid-plastic finite-element method is effective in simulating the metal forming processes undergoing large plastic deformation [24].
For finite-element method, the grid points are defined that are fixed to locations on the body being analyzed. Elements of material are created by connecting the grid points together, and the collection of the elements produces a mesh. As the body deforms, the rigid points move with the material and the elements distort. The finite-element solver is, therefore, calculating the motion of elements of constant mass. Because of the severe 17 element distortion, a frequent finite-element remeshing is necessary to follow the gross material deformation [34].
3.4 Finite Volume Method
Finite volume method has been used for a long time in analyzing the flow of materials in a liquid state. However, in recent years, some codes for computer simulation ofsolid-state metal forming operatio:ns (such as MSC/SuperForge) have been established on the basis ofthis method.
In the finite volume method, the grid points are fixed in space and the elements are simply partitions ofthe space defined by connected grid points. The finite volume mesh is a "fixed frame ofreference." The material ofa billet under analysis moves through the finite volume mesh; the mass, momentum, and energy of the material are transported from element to element. The finite volume solver, therefore, calculates the motion of material through elements ofconstant volume [34]. 18
Chapter IV MODELING OF EXTRUSION DIES
4.1 Introduction
The modeling ofthe extrusion dies is the first stage ofperforming a 3-D simulation after considering the design and manufacturing basic factors, such as the shear of the product, the length ofthe die land, and the billet size, that were mentioned in Section 1.3.
A complex symmetric product shear--I-shear--was used in this study with the dimensions shown in Figure 6. It is assumed to be in the center ofthe billet and the die cross-sections.
The length of the die land was asumed to be 4.0 inches for all dies used since it is acommonly used value. Also, a cylindrical billet with 2.0 inches in diameter and 4.0 inches in length was used in all simulations. -C----,1.- 0.75 in ~I
(0,0) r 1.0 in 0.5 in '-0.25 in-, _L_____1
Figure 6: The product cross-section shear and its dimensions.
4.2 STREAM
STREAM is a software package for extrusion die design developed by Gunasekera
[16] and modified by several other researchers. It is an interactive program for computer- aided design ofextrusion dies for asymmetric parts. The program, which was used in the 19 streamlined die profile design, is a DOS version of STREAM. However, this version has all the required features for doing the streamlined die for round billet to complex product shear design.
The main concept of die design used in STREAM (as mentioned on Nagpal et al.
[17], Gunasekera [6], Gunasekera et al. [12,16], Kavalauskas et al. [14], and Mehta [23]) came from an obvious criterion of the deforming material flow in non-lubricated extrusion of shears through shear (or flat-faced) dies. In these types of dies, the deforming material shears internally during the initial stages of extrusion and forms a
"dead-metal zone" on the flat face ofthe die. This zone acts as a streamlined-die surface having a friction factor equal to one (i.e., the shear stress is equal to the shear flow stress ofthe material). The geometry ofthe dead-metal zone (a three-dimensional surface in this case) adjusts itself in such a way that the rate of energy dissipation is minimized. A similar approach has been used by Nagpal et al. [17] and by Gunasekera et al. [16] in designing the geometry of complex product shear streamlined dies. The concept of die design used by these researchers is illustrated in Figure 7. Here, sectors of the billet are mapped onto corresponding sectors of the product, with the same extrusion ratio being maintained. Hence,
Area OPQ_= ER = Area OPR Area OP'Q' Area OP'R' where ER is the extrusion ratio. This criterion ensures a uniform velocity profile at the exit of the die. Thereafter, splines of any order are used to fit the entry and the exit sections. However, the method fails for sections which are re-entrant, as shown in
Figure 7. The reason of this failure is that some radial lines passing through the axis of 20 extrusion (such as OP) cut the perimeter of the product at more than one point (e.g., P',
P", and P). + ~ y IQ' Y! p
MAPING BASED ON ARF:A RE-ENTRY SHEAR PROBLEM PROPORTIONALITY
Figure 7: Limitations ofprevious methods ofstreamlined die design. (after Kavalauskas et al. [14])
A new technique has been developed to overcome this problem. Essentially the method consists of transforming the area-mapping technique to a perimeter- (line-) mapping technique by use ofthe Stoke's Theorem. The method is illustrated in Figure 8.
For re-entry sections, the local line integeral may become negative but can be re- distributed to neighboring areas with little difficulty. For product sections having one perimeter the method applies even ifthe section is re-entrant.
Referring to Figure 7, a sector in the billet such as OPQ can be mapped onto a section OP'Q' in the entry section such that
AreaOPQ =ER AreaOP'Q' 21
...... ························,,··················o·~······ ·"X···~
Figure 8: The new concept ofdie design used in STREAM [6,12,14,16].
The Stoke's Theorem can be used to convert this area mapping to a line-integral technique
JJ(Vx A)ds = fAdf s e where A is a vector function (A = Al i + A2 j + A3 k) and
0. 0 .0 kG v = 1-+ J-+ - OX oy GZ in general. Referring to Figure 9, the line integral for this particular case reduces to
(1. J'Y sin v ds ) 2 Thus, Area ()PQ ~ Area OP'Q'
becomes Line PQ ~ Line P'Q'
The above analysis was used by Gunasekera et al. [6,12,14,16] to develop STREAM, the CAD/CAM package for die design. 22
Figure 9: Stoke's Theorem applied to die design [6,12,14,16].
In general, the STREAM package was developed using this concept and is capable of generating straight (conical), convex, concave, and parabolic die shears in addition to streamlined die shears [23].
STREAM has some important features. The program allows the user to choose one ofthree different modified units systems. The user may choose SI units (Meters), SI units
(Millimeters), or Imperial unit (Inches). Also, the coordinates ofproduct geometry can be entered manually or read by the program from a digitizer, product geometry data file, or mapping data file (if mapping is already performed). In addition, the user can view the product geometry and the mapping of the billet to the product. However, the user can change the mapping parameters until achieving the best mapping. On the other hand, at the end ofthe run, the program gives some important calculated values, such as the cross- sectional areas ofthe billet and ofthe product and the extrusion ratio.
Some specifications for the die that will be designed must be prepared before running STREAM. The user will be asked to key in some input, such as number of 23 sections along die length, length of the die, diameter of the billet, the type of die surface definition, and the coordinates ofproduct geometry. In this study, the input data were as shown in Table I (For more details, a complete run for STREAM can be found in
Appendix A).
Table I: The Input Data for Streamlined Die Profile Design
Specification Assigned Value Units System Modified Imperial Units (Inches) Number ofSections 13 Length ofthe Die 4in Diameter ofthe Billet 2in Die Surface Defmition Cubic Streamlined Product Geometry Coordinates For I-Shear (See App. B for the coordinates) Product Geometry Centroid 0,0 Mapping Parameters 0.25,0.1
The mapping of the billet to the product is the first check point in the die profile design process. It shows if the longitudinal streamlines cross each other or not. It can be controlled by changing the mapping parameters and then viewing the resulted mapping.
The selected mapping parameters for the streamlined die that were used in this study gave a reasonable mapping result (see Figure 10). Moreover, the extrusion ratio for the same die was 6.2832 (see Appendix A), which seems to be reasonable for a streamlined die.
The cross-sections' coordinates of the designed die are stored by STREAM in an output data file as points with X, Y·, and Z coordinates. In this study, the points were keyed in another modeling software called MSC/PATRAN in order to get the 3-D die geometry. More information about this software will be given in the next section. 24
Figure 10: The mapping ofthe billet to the product shear.
4.3 MSC/PATRAN
MSCIPATRAN is an open, flexible, commercial MCAE (Mechanical Computer-
Aided Engineering) software package. It can be used for performing a complete design analysis of mechanical components and systems. It includes a pre- and postprocessor with geometric modeling, meshing, analysis simulation, and results evaluation capabilities. In this study, the last version of MSCIPATRAN, version 8.0, was used to perform two of the previous features: geometric modeling and meshing. MSC/PATRAN provides enough tools to manipulate geometry, plus tools for building new geometry, which makes drawing a complex geometry so simple. In addition, it provides a powerful and flexible meshing with capabilities that range from fully automatic solid meshing to
,detailed node and element editing.
At the beginning, using geometric modeling, the points with x, y, and z coordinates produced by STREAM were entered manually. These points consist ofseveral sets. Each set of points represents an edge curve for one section of the streamlined die. So, the number of sets equals the number of sections along the die length that was assigned by 25 the user at STREAM run plus one. In this study, as mentioned in the previous section, the number ofsections is 13, which means there are 14 sets ofpoints. Then the next steps for geometric modeling were as follows:
• Each set ofpoints was connected to each other using B-spline curve.
• B-spline curves ofall sections' edges were integrated to create a smooth surface.
• Three shell surfaces were built around the die geometry in order to represent the
streamlined die with a solid modeling.
• The closed volume between the die smooth surface and the shell surfaces was
defined as a solid using Create/Solid/Surface option on the main menu.
• The solid broke longitudinally into four symmetric parts in order to reduce the
time and the required memory for meshing and performing simulation.
The streamlined die that was designed using STREAM and modeled USIng
MSC/PATRAN can be seen in Figure 11. The,generated model was checked for defects in order to reduce the meshing errors that come from a bad geometric modeling.
Figure 11: Die geometry for the streamlined die. 26
The next step was performing the geometric modeling for the shear and shear with feeder plate dies. For shear die, all the cross sectional curves were erased except the first curve, which represents the product shear, and the last curve, which represents the billet edge. In order to create the internal shear die surfaces, the first curve was extruded toward the die body (on the negative z-direction) for 1 inch and the last curve was also extruded toward the die body (on the z-direction) for 3 inches. Some shell surfaces were created, then the closed volume between the die internal surface and the external shell surfaces were defined as a solid using the same option as in the streamlined die geometric modeling. For creating the different feeder plate dies, the procedures were almost the same as for the shear die except there was one more curve in each die which was used to form another step on the internal die surface toward the flow exit. One sample of both shear and shear with feeder plate dies, which were used on the simulation, is shown in
Figure 12.
I \ \~\il ~~I/ J--.~
Figure 12: Die geometry for the shear and shear with feeder plate dies.
However, in this study, five feeder plates were modeled by taking five streamlined die's sections' curves with different levels in the z-direction. One of the selected curves 27 was located at the middle of the streamlined die geometry ( Z = 2.0). The other four curves were chosen to be two before the middle curve and two after. The exact z-level values were as shown in Table 2.
Table 2: The Z-Level Values ofthe Selected B-Spline Curves
The selected B-spline curves The Z-level value
Exactly at the middle ofthe streamlined die 2.0
First on the top ofthe middle B-spline curve 2.1538
Second on the top ofthe middle B-spline curve 2.4615
First on the bottom ofthe middle B-spline curve 1.8462
Second on the bottom ofthe middle B-spline curve 1.5385
Meshing the solid models is preferred to be done directly after creating each of die geometries. This procedure makes the remodeling of the solid easier and is done in less time, especially if the solid does not match the mesh engine requirements. The mesh engine might be unable to mesh a solid for unobvious reasons. For example, the arrangement of the model creation steps may cause some unexpected meshing errors.
MSCIPATRAN, as stated on the beginning of this section, is equipped with a powerful and flexible meshing engine. However, it may need a defect-free model in order to perform a surface or a solid mesh.
In this study, the internal surfaces ofall dies were meshed as fine as possible in order to get smooth surfaces since the smooth internal surfaces minimize the frictional forces that occur from the contact between the billet and the die. The mesh edge length for these surfaces was between 0.01 to 0.08 inches for all dies. However, a larger value for the mesh edge length (0.16 inch) was used for meshing the external surfaces ofall dies since 28 the billet material has no contact with them during the extrusion process. On the other hand, the sharp comers ofthe product shear were rounded, as seen in Figures 11 and 12, since it was not possible to generate a finer mesh in order to avoid the crossing of mesh elements.
Solid Tetrahedron with Solid Tetrahedron hidden inside elements
7 ~
7 1
Surface Triangular for
~' .'-' . ..1 Surface Triangular 1-/...... • shown surfaces only
Figure 13: The billet geometry with different types ofmesh.
The billet was easier to create since its geometry is simple compared to the extrusion dies' geometry. The billet was modeled as a quarter of a cylinder because of the symmetry of the problem (see Figure 13). Two types of mesh were used for the billet depending on the definition of geometry. The billet on the DEFORMTM_3D simulation was meshed using a solid type ofmesh (tetrahedron mesh type with 0.08 inch as element 29
edge length was used), while MSC/SuperForge requires the billet to be meshed with a
surface mesh (triangular mesh type with 0.08 in element edge length was used).
Finally, the ram (press) was created as a surface with a quarter circle shear and meshed with the same type and size of mesh used for meshing the billet surfaces. Then, all of the objects--the dies, the billet and the ram geometries--were exported in Neutral
files in order to be imported by the simulation packages. 30
Chapter V SIMULATIONS AND ANALYSIS
5.1 Introduction
The simulation and analysis stage is the most difficult stage of this study. The simulation process may run for more than two days in some cases. Moreover, it might stop because ofa divergence problem or negative bad elements meshing. So, handling the simulation seems to be a matter related to user experience more than the information that is given in the simulation package's user manual, particularly for DEFORMTM_3D.
DEFORMTM_3D is one of the commercial packages that were used for performing the simulation ofthe extrusion process using the streamlined die. The other package used is
MSC/SuperForge, and it was used to perform six more simulations in addition to the simulation of the extrusion process using the streamlined die--one simulation using the shear die and five simulations using five different feeder plate dies. However, in addition to the billet and the die dimensions, there are some common settings, such as the properties ofthe material used, the ram speed, the initial temperature, and the friction coefficients, which were identical in all simulations since using identical setting is one of the requirements for performing a comparison between any simulation process.
5.2 Common Preprocessing Settings In addition to the billet and the different dies dimensions, there are four common settings which must be equal for all simulations in order to perform the comparison the properties of the material used, the ram speed, the initial temperature, and the friction coefficients. These settings--except the material properties--were assumed depending on 31 the type of extrusion process that was simulated--cold extrusion process with no lubrication.
The forming process is a material oriented process. In other words, the properties of the material specify what type of forming processing should be selected. Since the forming process used in this study is the extrusion process, an aluminum alloy was selected to be the billet material. Aluminum alloys are common materials for both cold and hot extrusion. The excellent formability of aluminum alloys makes them strong candidates for extrusion processes.
Table 3: Material Properties for Aluminum Alloy (6061-0) [36,37].
Imperial British Quantity (in/slug/s/rR)• (in/lb/s/oF)
Density Ibf-s2/in4 2.53E-4 k lb/in' 9.75E-4 Temperature OR 527.27 OF 68 Initial Temperature OR 527.27 OF 68 Young's Modulus (E) lbf/in' 10100£+3 ksi 10100 Min. Yield Stress (S) lbf/in' 8000 ksi 8 Yield Stress Constant (C) lbf/in' 32500 ksi 32.5 Strain hardening exponent (n) - 0.209 - 0.209 Poisson's Ratio - 0.33 - 0.33 •slug = Ibf-s//in
However, the different aluminum alloys have different mechanical and thermal properties. Aluminum 6061-0. alloy was selected to be the billet material since it is commonly used for cold extrusion. The properties ofthis alloy, illustrated in Table 3 and
Figure 14, were used in all simulations performed in DEFORMTM-3D and
MSC/SuperForge packages. As a results of each package's limitations, a different units 32 system was used in each package; the British units system was used in DEFORMTM_3D and the Imperial units system was used in MSC/SuperForge.
45 -r-----.-----~--...------_____,
40
35
~ ~ 30 ~ ~ 25 ~ .....a. rJ1 20 ~ e ~ 15 10 ------
5 ------
O-+------.----i----;.-.---r----i----.------f o 0.5 1.5 2 2.5 3 3.5 Effective Strain (in/in)
Figure 14: The O"-E curve ofAluminum 6061-0.
On the other hand, the flow stress, o , was represented with a simplified function of - - effective strain, E, effective strain rate, e , and some constants in order to eliminate the complexity ofthe problem:
-n-m o = CE i: + y
where, C and n have the same values as listed in Table 3
m = 0 (the strain-rate hardening exponent)
y = 0 (the material constant)
The other three settings were assumed to be 68°F as initial temperature, 2.5 in/sec as ram speed, 0.2 as friction coefficient for the contact between the billet and the die surfaces and 0.3 as friction coefficient for the contact between the billet and the ram 33 surfaces. The previous settings were implied in all types of simulations performed in this study.
5.3 Simulation Using DEFORMTM..3D
DEFORMTM_3D is a commercial package developed by SFTC (Scientific Forming
Technology Corporation). It is a Finite-element Method (FEM) based process simulation system designed to analyze three-dimensional flow ofvarious metal-forming processes. It provides vital information about material and thermal flow during forming processes. The capabilities of the FEM code, DEFORMTM_3D, had been evaluated and validated by applying it to several isothermal or non-isothermal applications [19, 31].
Typical DEFORMTM_3D applications include forging, extrusion, heading, rolling, and many others. It is an ideal tool to model a complex 3-D material flow. Its simulation engine is capable of analyzing large deformation and thermal behavior of multiple interacting objects during the metal forming processes. An automatic mesh generator
(AMG) that generates an optimized mesh system wherever necessary is integrated in the system. This facilitates the generation of finer elements in regions where greater solution accuracy is required, thus reducing the overall problem size and computing requirement
[35]. Only one type of mesh--paver--can be generated by AMG. Paver mesh does not fit as well as isometric mesh, especially on the curved surfaces. On the other hand,
DEFORMTM_3D accepts the solids that are meshed with tetrahedron mesh type. Most of the time, it can remesh the solids that were meshed using a tetrahedron mesh type. In this study, the billet was meshed in MSC/Patran using solid tetrahedron isometric mesh type, 34 as shown before in Figure 13, since it gives better results than using paver mesh type provided by the AMG ofDEFORMTM-3D.
Opening the DEFORMTM_3D Pre-Processor is the first step toward performing the complete simulation. It includes all the extrusion process specifications and the simulation control parameters. The preprocessing stage can be summarized in the following steps:
• Import the streamlined die geometry that is stored in a neutral file after meshing
it with a surface mesh using MSC/Patran.
• Import the meshed billet and the ram geometries.
• Define the die and the ram as rigid objects and the billet as a plastic object.
• Add Aluminum 6061 to the defined materials list with the properties listed in
Table 3.
• Assign the material to be the billet material.
• Set the initial temperature ofthe billet to be 68°F.
• Set the two symmetry surfaces ofthe billet to be fixed (have zero velocity) on the
directions normal to them--one on x-direction and the other on y-direction--as
boundary conditions for the billet.
• Set the die to be fixed in all directions.
• Set the ram to have a velocity in the positive z-direction with value 2.5 in/sec.
• Set the simulation controls parameters to the default settings, except the
parameters listed in Table 4. 35
Table 4: DEFORMTM_3D Simulation Control Settings
Parameter Value
Units English
Simulation mode Isothermal
Starting step number -1
Number ofsimulation steps 50
Step increment to save 1
Primary die 1
Steps are controlled by Stroke
Maximum stroke per step 0.1
• Set the inter-object relation to be as follows:
Objects Relation Separation Friction Die-Billet Master-Slave Yes Shear 0.2 Ram-Billet Master-Slave No Shear 0.3
• Generate the inter-object boundary conditions with 0.0001 as a tolerance.
• Generate the database file, save the key file, and exit the preprocessor.
The next stage is starting the simulation after entering the suitable memory size to be used for the integral and the real arrays. The approximate memory sizes needed for each ofthe two arrays are given at the database file generation step. In this simulation, 30 MB and 60 MB were reserved for integer arrays and real arrays, respectively. The checking of the simulation process while it is running was available by using the Process Monitor 36 option. It shows the DEFORMTM_3D simulation processes that run on the same machine with their current step number and allows for any process to be aborted.
After the end of simulation, the database file that contains all the simulation results' database can be browsed using the Post-Processor provided by DEFORMTM_3D. Also, the wanted figures can be captured and saved as an image file.
5.4 Simulation Using MSC/SuperForge MSC/SuperForge is a new software package for the computer simulation of industrial forging processes. It combines a robust finite volume solver with an easy-to use graphical interface specifically designed for the simulation of 3-D bulk forming operations. MSC/SuperForge is being effectively utilized by forging companies and suppliers worldwide to successfully simulate the forging of a variety of practical industrial parts. Ohio University was selected as one of the Beta Sites for evaluation and testing ofthis software package.
The first step in a forging analysis is to build a model consisting of dies, billet, and finite volume mesh (representing the flow domain of the billet). The latter entities are considered as separate objects. Each object is geometrically modeled and meshed in the object modeler of MSC/SuperForge, called SFObject. SFObject can directly import geometry from several CAD or design system.
After creating geometry for the different objects of the forming process assembly, the individual objects need to be meshed. SFObject provides the following automated meshers: IsoMesh and Paver. For relevant corner regions of the dies, IsoMesh is preferred over Paver as much as possible. A finite-volume mesh must be created for the 37 flow domain, i.e., a domain in which billet material is anticipated to flow throughout the analysis. Ifthe billet flows out ofthis domain, the analysis will stop immediately.
After building a model consisting ofdies, billet, and finite volume mesh, the fanning process must be defined using the process editor of MSC/SuperForge called SFPre. At this stage, some data must be provided regarding press, friction, and material characteristics, as well as setup of the tooling. All data selected was same as in
DEFORMTM_3D simulation--the hydraulic press with constant speed 2.5 in/sec in the z direction, friction coefficients: 0.2 between the billet and the die and 0.3 between the billet and the press, and the material characteristics were as illustrated in Table 3. In this step, material properties are assigned to the dies and billet. Also during this step the extrusion layout will be built with the help of the positioner. The billet and dies are automatically positioned on top of each other to form the forging assembly. During this step, the kind of results output to be obtained from the analysis can be defined. At the end, the analysis input file that contains all the simulation settings was generated.
The results of an MSC/SuperForge analysis run can be evaluated using SFPost.
SFPost enables the user to visualize the analysis results and create animations of the simulated fonning process. SFPost does not work with a results database, but imports the binary MSC/SuperForge analysis results files (archive files) into memory and after importing allows the user to perform the post-processing. When SFPost is closed, the data is released from memory and for the next post-processing session the user needs to import the MSC/SuperForge Archive files again. 38
Chapter VI RESULTS
In order to obtain the final results ofthis study, more than four months were spent on continuous trials and modifications of the required simulations. This long time for performing several successful simulations summarized the difficulties ofperforming a 3
D metal forming simulations. These results include the extrusion simulations using streamlined die and using various types ofshear dies.
6.1 Extrusion Using Streamlined Die
The extrusion streamlined die was used in two simulations with same setting and in two different software packages, DEFORM3DTM_3D (version 3.0) and MSC/SuperForge
(version 1.0). Both simulations were performed on a Silicon Graphics machine. Similar number of meshing elements were used in both simulation in order to make the comparison ofthe two packages more precise.
6.1.1 DEFORMTM..3D Simulation Results
The results of the simulation can be easily visualized using the post-processor of
DEFORMTM_3D. This post-processor supplies the user with six different types of distributions: stress, strain, strain rate, velocity, temperature, and damage distributions. It also gives several curves that represent the relation of some variables, such as the press load and the velocity, versus the forming process time or the press stroke. In addition to the load-stroke plot, two distributions--effective stress and effective strain distributions- were selected to be used in the comparison between the DEFORMTM_3D and the
MSC/SuperForge simulation results. 39
Figure 15: Effective stress distribution when streamlined die is used (ksi).
The effective flow stress value, as shown in Figure 15, increases gradually as the cross-sectional area decreases and it reaches its maximum value near the final shear of the product, especially at its rib. However, the maximum effective flow stress was 38.966 ksi and the minimum effective flow stress value was around 1.2 ksi.
From Figure 16, the stain distribution increases gradually with the cross-sectional area decreasing as with the flow stress distribution. It also gets its maximum value at the product rib. "From the figure, the strain maximum value is 2.415 in/in and the minimum value was 0.004 in/in. On the other hand, the maximum load of the extrusion process for a quarter model using the streamlined die was around 90,000 lbf(i.e., 360,000 for the full model), as shown in Figure 17. This load is reached at a stroke value of 2.5 inch.
However, the consumed time in performing this simulation was around 21 hours. 40
----,------
Figure 16: Effective strain distribution when streamlined die is used (in/in).
80
------.~ I I
- - •. - - -- - _. ------I , I I I
I I - - - - .- - I I
I I 20 ~ ~ -- _. -
a +----=*==:::.--+--...L....-,--f---.L..-~f___--L--_+_-----'--______t 0.00 0.50 1.00 1.50 2.00 2.50 Stroke (inch)
Figure 17: The load-stroke curve ofthe extrusion press. 41
6.1.2 MSC/SuperForge Simu lation. Results As in DEFORMTM_3D, the post-processor of MSC/SuperForge (Version 1.0) is an interactive and friendly browser. This post-processor gives more parameter distributions, such as density, pressure and contact. However, it gives a poor curve fitting plots. The user cannot change the axes' limits, the curve fitting order, or even the axes' labels. The plot comes with a fluctuating curve that makes the reading ofthe results difficult.
In MSC/SuperForge simulation, the effective flow stress distribution on the extruded billet using a streamlined die as 'used in DEFORMTM_3D simulation changes gradually and is inversely proportional with the cross-sectional area until it reaches its maximum values on the product rib, as shown in Figure 18. The maximum and the minimum flow stress values are 37.66 ksi and 3.139 ksi, respectively.
______•.!,:~;: ··l~._._.
3139 8071 1.3e+04 1.793e+04 2.267e+04 2.78e+04 3.273e+04 3.766e+04
Figure 18: Effective stress distribution when streamlined die is used (psi). 42
From Figure 19, the stain distribution increases gradually with the cross-sectional area decreasing as on the flow stress distribution. It also gets its maximum value at the product rib and near the product shear section. From the figure, the maximum strain value is 2.021 in/in and the minimum value was 0.021 in/in. The maximum load of the extrusion process for the full model using the streamlined die was around 360,000 lbf, as shown in Figure 20. This load is reached at a stroke value of 2.5 inches. However, the consumed time in performing this simulation was around 9 hours.
'I /' ~z X 0.02118 0.3069 0.5925 0.8782 1.164 1A5 1.735 2.021
Figure 19: Effective strain distribution when streamlined die is used (in/in). 43
. . · ..~ ------_'.· ------_._ ------..------.t. ______· .." · .. 3.0*1 as---.---+---t-----+----+----+---+---+---+--i-· .. Load'(lbf) ------r------Str~~~-(i~~ )- ----r------
~ 2.0*1 as--t----;------t-----;----+----;----+----..T----+--t...... -----t o .....:l ------.------· ------.....------.--.---- · .. · .. 1 .0*1 OS --t------+------tl-----+-r--~~-+_--_____t· ... ------1------::------1------i& l l ~ 0.0*1 0°.....--...--"----+------..-----+------1-----... ~ 0.0 0.005 0.01 0.015 0.02 0.025 "'102 stroke
Figure 20: The load-stroke curve ofthe extrusion press.
6.2 Extrusion Using Shear Dies
Performing a 3-D simulation of an' extrusion process using a shear die is still full of difficulties. This type of metal forming processes includes a severe metal deformation that, for the most part, leads to analysis meshing problems. Most of the metal forming packages, including DEFORMTM-3D, are still incapable of doing 3-D extrusion process simulations using the shear dies. However, MSC/SuperForge has the capability to handle such a severe deformation. Using the finite volume method enables MSC/SuperForge to avoid most of the meshing problems that usually happen to packages which work with the finite element method. As a result, MSC/SuperForge was used for performing the 3-D extrusion process simulations using a shear die and several shear with feeder-plate dies. 44
While the flow stress distribution for the extrusion process using streamlined die changes gradually, the flow stress distribution for the extrusion process using shear die is concentrated 011 different places of the extruded billet geometry. From Figure 21, it is clear that the maximum effective stress is concentrated near the product shear beginning and also near the contact surface between the billet and the ram. The maximum and minimum flow stress values are 39.66 ksi and 7.652 ksi, respectively.
7652 1.222e+04 1.68e+04 2.137e+04 2.594e+04 3.052e+04 3.50ge+04 3.966e+04
Figure 21: Effective stress distribution when shear die is used (psi).
Similar to the flow stress distribution, the effective strain distribution, as a result of using the shear die, is concentrated on the contact surface of the billet with the ram and the sharp change ofthe cross-sectional area, from the billet area to the product shear area.
From Figure 22, the maximum and the minimum effective strain values are 2.59 in/in and 45 around 0.035 in/in, respectively. The xy-plane ofthe dead metal zone at the sharp change of the die cross-sectional area, as may be noticed in Figures 18 and 19, follows the product shape.
From Figure 23, the ram load has a sharp increment once it reaches the sharp decrement of the die cross-sectional area, from billet area to the product shear area. This sharp increase in the load value is combined with a severe deformation for th.e extruded billet. The ram load elevates from 40 klbf to more than 300 klbf within a stroke increment less than 0.25 in.
______i!Jr".,"c·
0.3998 0.7648 1.13 1.495 , .86 2.225 2.59
Figure 22: Effective strain distribution when shear die is used (in/in). 46
.... ------~_·.-- - -.. _.. ------..--. --- .. -- -- _.. -~-. -_ -- - --_ .... ·., . ., · , ., 5 ·, . . 4.0*10 -+-----;----+-----;i---+----r---+-----t---f-HI~• I • ·..Load (lbf) ········r······ -r ··Str~~~·(i;;~ .) ,. .
3.0*1 Os-t------+--· __. ~~-__, +___- "'C cd .... -_ .. --- ~-_· _ -- -,--". -- -- .. --- -_ •• -r", ------_ ------o ·., . ., ~ ··.... ., 2.0*1 OS --+----+----+-----;:....-.--+----+-----+-----+-tF-+-lo--i·. .
· , . . ------~-.------..... ----..... ------_.~.-_ ... ------._- ·• ..a • ...• ·.·• ..,• .,• .I 1.0*1 OS --....-----+----+------+------+----i·. , . a 2s 1 ~ 0.0*10°...... -----+----+------+------. 0.0 0.001 0.002 0.003 0.004 *103 Stroke
Figure 23: The ram load-stroke curve when shear die is used.
The metal flow through the feeder plate die achieves its maximum flow stress and effective strain values in one place in addition to what the flow in shear die achieves.
Since there are two flat faces, the deforming material shears internally during the initial stages of extrusion and forms two dead-metal zones on the two flat faces of the feeder plate die (see Figure 24). These zones act as a streamlined-die surface having a friction factor equal to one (i.e., the shear stress is equal to the shear flow stress ofthe material).
As an example ofthe results of using feeder plate dies, Figures 25,26, and 27 show the effective stress distribution, the effective strain distribution, and the load-stroke curve of the feeder plate that has the shear of the middle longitudinal cross-section of the streamlined die (Z-level equals 2.0) and is placed on the same Z-level. 47
10 12 14
Figure 24: Z-Velocity distribution when feeder plate die is used (Z=2.0).
7719 1.544e+04 2.316e+04 3.086e+04 3.86e+04 4.631 e+04 5403e+04
Figure 25: Effective stress distribution when feeder plate die is used (Z=2.0). 48
______.~f:· :J?l'g.__
0.6514 1.:303 1.954 2.606 3.257 3.909 4.56
Figure 26: Effective strain distribution when feeder plate die is used (Z=2.0).
' , I• I · ., Load _____ L__ .. _--_.--1----- ~~~~----- iaI , ·I .• ·,I .• S~ok~ (inFh) 6 ·, ., 1.5*10
------_..- ---
..... -_ -...._------~------....------
I _____' ____ - ~ -----,----- 1--- ...... ----JJ ..,..: .,.. \1 .-...... :. .-. .J. ~ I ~ ~ ~ .... '-"""11'" ~ l/ 0.0*10° ....b....--r- 0.0 0.001 0.002 0.003 *103 Stroke
Figure 27: Load-Stroke curve ofthe ram when feeder plate die is used (Z=2.0).
The simulation results of using different feeder plate dies are illustrated in Table 5 and Figures 28,29, and 30. The maximum effective stress, the maximum effective strain, 49 and the maximum ram load for all of the extrusion dies used in this study are illustrated on a bar chart for easy comparison.
Table 5: The Maximum Values ofPress Load, c , and E for All Dies.
Maximum Load Level Die Type Maximum o Maximum E (klbf) (ksi) (in/in) Streamlined 360 37.66 2.02 Shear 420 39.66 2.59 Z=2.4615 370 37.49 1.977 .s c~-0.) Z=2.1538 530 41.49 3.215 o > .= .£ u 0.) Z=2.0 600 54.03 4.56 Q) ~ E Q) ~ ..c tI) Z=1.8462 570 49.24 4.15 t- Z=1.5385 430 40.12 2.736 .5 Z=2.4615 420 39.04 2.4 c-til Q) ._0"'0"'0 Z=2.1538 520 50.33 3.4 ~ g .-E til Q) Z=1.8462 540 47.87 3.5 Q)..c ..c~ r- Z=1.5385 430 39.46 2.528
60 ~------.,
0 ... Vi QC) N Vi Vi QC) N Vi ~ ell f"') \C QC) f"') \C QC) ~ N ~ Vi = ~ f"') ~ ~ ~ f"') .5 .c: ~ II ~ ": ~ ~ ": i fI1 N N N N N ell II II i r II II r r ~ N N N N N N N N en I , I I
The' sections in the same level The sections in the middle (Z=2.0)
Die Type
Figure 28: Maximum effective stress for all dies used in this study. 50
5
4.5 :5 ! 4 .;c 3.5 ...... ~ 3 QI .';:> u 2.5 t! ~ 2 E 1.5 =E .~ ~ ~ 0.5
0 .. V') QC M Vj V') QC M V') -=~ at ~ \C QC ~ \C QC) ~ ~ N= ~ ~ ~ ~ .5 .= ~ ~ II ~ ~ ~ ~ ~ ~ i VJ N N N M M at ii ii II ii ii ..~ N" N" N N N" N N N ~ I I I I
The sections in the same level The sections in the middle (Z=2.0)
Die Type
Figure 29: Maximum effective strain for all dies used in this study.
700
600
g 500 ~ -0 400 =0 ~ e :s 300 -;;e ~= 200
100
0 .. at i ~ .s .c E VJ eCllI ()j
The sections in the same level The sections in the middle (Z=2.0)
Die Type
Figure 30: Maximum ram load for all dies used in this study. 51
Chapter VII CONCLUSION AND DISCUSSION
7.1 Conclusion
In order to evaluate a new 3-D finite volume analysis package--MSC/SuperForge-- two cold extrusion process simulations using streamlined die with a complex product shear--I-shear--were performed, One simulation was performed using this new package and the other was performed using a validated 3-D finite element analysis package,
DEFORMTM-3D. The simulation results obtained from both DEFORMTM_3D and
MSC/SuperForge packages were comparable. The maximum effective stresses (o max) and the maximum ram load (Pmax) for both packages' simulation results were very similar, - while the maximum effective strain ( E max) for both was slightly different, as can be seen in the Table 6.
Table 6: Comparison ofSimulations' Results
Variable DEFORMTM_3D MSC/SuperForge - 0"max 38.966 ksi 37.660 ksi - £ max 2.415 in/in 2.021 in/in
Pmax 360,0001bf 360,0001bf Tiine 21 hours 9 hours
On the other hand, several extrusion processes using different feeder plate dies were simulated in order to study the effect of using different streamlined die longitudinal cross-sections on the material flow on these dies and to see which shear with feeder plate die confiquration yields better results. Aluminum alloy 6061-0 was chosen to be the 52 extruded material since aluminum alloys are common materials for cold extrusion. The excellent formability of aluminum alloys makes them strong candidates for extrusion processes. The variables of the simulation results for the extrusion processes using the different cross-section and Z-level feeder plate dies ranged between 600 to 370 ksi for the maximum effective stress--4.56 to 1.98 in/in for the maximum effective strain and 54.00 to 37.49 klbf for the maximum ram load (see Table 5). The maximum values of all variables were obtained as a result of using the middle cross-section of the streamlined die for the 2.0 Z-level feeder plate die, while the minimum values of all variables were obtained as a result of using the 2.4615-inch z-level cross-section of the streamlined die for the same Z-level feeder plate die. Moreover, by placing all of the five selected streamlined die cross-sections in one Z-level, the maximum and the minimum values of all variables were obtained with the same previous feeder plate dies.
By comparing the results of the extrusion simulations using the streamlined die, the shear die, and the optimized shear with feeder plate die, it can be concluded that using streamlined die has no great advantage over using the shear die in aluminum extrusion.
The results of using all of these three extrusion dies were close enough to make the streamlined die with the more designing and manufacturing difficulties less advantageous than the shear die--especially the feeder plate shear die--for aluminum extrusion.
7.2 Discussion From the previous conclusion, it is clear that MSC/SuperForge package using the semi-new analysis method--finite volume method--gives results very close to the results that were obtained from a validated analysis package. However, the simulation time 53
required by MSC/SuperForge was less than half the time required by DEFORMTM_3D in
performing identical simulations using the same computing machine. Moreover, the finite
volume technique used in MSC/SuperForge eliminates the meshing problems that makes
simulating a metal-forming process with severe deformation, such as the extrusion
process with using a shear die, full ofdifficulties and failures.
By comparing the results of using the streamlined die, the shear die, and the
optimized feeder plate die, shear dies and optimized feeder plate dies are a strong
competitor for streamlined dies in aluminum extrusion since they relatively give the same metal flow mechanical characteristics.
7.3 Future Work
Although MSC/SuperForge has several advantages, it has a limited use. It can be
used only on up-setting forging and extrusion processes. Moreover, some features should be improved such as the poor quality of curve fitting and the ability of visualizing the process while it is running.
Regarding optimizing the feeder plate dies, simulations might be performed for feeder plate dies by choosing several streamlined die cross-sections and several Z-levels.
A Design of Expennent (DOE) should be performed before a detailed simulations.
Simulations using all ofthe different cross-sections in each Z-level should be performed in order to obtain several curves that might indicate the effect ofchanging the Z-level and the cross-section shear on the shear die with feeder plate. 54 REFERENCES
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APPENDICES
Appendix A: STREAM Run
MICRO-STREAM 2.0 THIS IS AN INTERACTIVE PROGRAM FOR COMPUTER AIDED DESIGN OF EXTRUSION DIES FOR ASYMMETRIC PARTS STREAM CAN DESIGN THE FOLLOWING TYPES OF DIE (1) STRAIGHT CONVERGING (2) CONVEX - EXTRUSION TYPE (3) CONCAVE- DRAWING TYPE (4) PARABOLIC (5) CUBIC STREAMLINE (6) THIRD ORDER AREA BASIS STREAMLINE (7) CONICAL/STREAMLINED (8) CONSTANT STRAIN-RATE --- Press Return to Continue
DO YOU WANT TO CHOOSE UNITS ( YIN) ======> Y
************************************************ THE FOLLOWING UNITS ARE AVAILABLE 1. MODIFIED SI UNITS-METERS 2. MODIFIED SI UNITS- MILLIMETERS 3. MODIFIED IMPERIAL UNITS- INCHES *********************************************** CHOOSE ONE BY ENTERING 1 2 OR 3 »»> 3 60
************************************************ MODIFIED IMPERIAL UNITS
LENGTH = INCH ------IN
AREA = SQUARE INCH. --- SQ.IN
VOLUME = CUBIC INCH ---- CD.IN
FORCE = POUND FORCE --- LBF STRESS = LBF PER SQ.IN - LBF/SQ.IN
VELOCITY = IN PER SECOND - IN/S
STRAIN RATE = PER SECOND ---- /S
TEMPERATURE = FARENHEIT ----- F ************************************************ NUMBER OF SECTIONS ALONG DIE LENGTH? ======> 11
LENGTH OF DIE? ======> 4
DIAMETER OF BILLET? ======> 2
DIE SURFACE DEFINITION TYPE 1 FOR STRAIGHT CONVERGING DIE 2 CONVEX - EXTRUSION TYPE 3 CONCAVE - DRAWING TYPE 4 PARABOLIC 5 CUBIC STREAMLINE 6 THIRD ORDER AREA BASIS STREAMLINE 7 CONICAL/STREAMLINED 8 CONSTANT STRAIN-RATE ======> 5 61
COORDS. OF PRODUCT GEOMETRY TYPE 1 IF INPUT IS MANUAL 2 FROM PRODUCT GEOMETRY DATAFILE 3 IF PRODUCT GEOMETRY IS A CIRCLE 4 IF MAPPING IS ALREADY PERFORMED ======> 2
NAME OF DATAFILE WITH PRODUCT GEOMETRY COORDS. ======> DIEl.DAT (See Appendix B)
DO YOU WANT TO VIEW PRODUCT GEOMETRY? ( YIN) ======> Y
MODIFY/CORRECT ANY NODE? TYPE 1 IF YES OTHER NUMBER IF NO ======> 2
TYPE 1 TO FILE PRODUCT GEOMETRY COORDS. 2 OTHERWISE 62
======> 2
DO YOU' NEED RADII CALCULATION? TYPE (Y/ N) ======> N
*********************************************** TRANSFERRING PRODUCT CENTROID TO BILLET CENTER IF PRODUCT HAS TO BE MOVED IN X OR Y DIRECTION ENTER X AND Y DISPLACEMENTS IF NOT ENTER 0, 0 *********************************************** ======> 0,0
********************************************** MAPPING OF BILLE~r 1~O PRODUCT ENTER MAPPING PARAMETERS NEGATIVE AREA PARAMETER - TYPICAL 0.1 PERIMETER BASE PARAMETER - TYPICAL 0.1 EXAMPLE .5 .5 SEPARATED BY COMMA OR SPACE **********************************************
======> 0.25, 0.1
TYPE 1 TO VIEW MAPPING 2 TO VIEW AND FILE MAPPING OTHERWISE TYPE ANY OTHER NUMBER ======> 1 63
DO YOU WANT TO CHANGE MAPPING PARAMETERS? TYPE (YIN) ======> N
DO YOU WANT TO PRINT PRODUCT COORDS AND ANGLE TYPE (Y IN) ======> N
************************************************ X-SECTIONAL AREA OF BILLET = 3.1416 X-SECTIONAL AREA OF PRODUCT = 0.5000 PERIMETER OF PRODUCT SECTION = 4.5000 EXTRUSION RATIO = 6.2832 VOLUME INSIDE DIE = 6.8483 TOTAL SURFACE AREA OF DIE = 22.8709 ************************************************** *** PRESS
BILLET DIAMETER OPTIMIZATION? (YIN) ======> N 64
TYPE 1 IF FORCE CALCULATION REQUIRED 2 OTHERWISE ======> 2
TITLE OF MOVIE COMPATIBLE OUTPUT FILE-START WITH M TYPE 0 FOR NULL SPECIFICATION ======> 0
TITLE OF APT COMPATIBLE OUTPUT FILE-START WITH A TYPE 0 FOR NULL SPECIFICATION ======> DIEI.DAT
STREAM WAS SUCCESFULLY EXECUTED 65
Appendix B: DIEt.DAT (The Input Data File) : < Number ofnodes: > 14 < Nodes Coordinates (X,Y,Z): >
0.0000 0.0000 0.0 -0.3750 0.0000 0.0 -0.3750 -0.2500 0.0 -0.1250 -0.2500 0.0 -0.1250 -0.7500 0.0 -0.3750 -0.7500 0.0 -0.3750 -1.0000 0.0 0.0000 -1.0000 0.0 0.3750 -1.0000 0.0 0.3750 -0.7500 0.0 0.1250 -0.7500 0.0 0.1250 -0.2500 0.0 0.3750 -0.2500 0.0 0.3750 0.0000 0.0