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Die cavity design of near flashless forging process using FEM-based backward simulation
Journal of Materials Processing Technology 121 (2002) 173–181
Die cavity design of near flashless forging process using FEM-based backward simulation Guoqun Zhaoa,*, Guangchun Wanga, Ramana V. Grandhib a
College of Materials Science and Engineering, Shandong University of Technology, Jinan, Shandong 250061, PR China b Department of Materials and Mechanical Engineering, Wright State University, Dayton, OH 45435, USA Received 26 September 1999
Abstract Preform design in forging processes is an important aspect for improving the forging quality and decreasing the production cost. Forward and backward simulations of the forging process based on rigid visco-plastic finite element methods (FEMs) can directly provide a preform shape from the final forged shape at a given stage. The objective of this effort is to reduce the material lost as flash by the design of an improved busting operation for a track link forging. This paper uses the FEM-based inverse die contact tracking method to design the preform shapes for a representative plane-strain cross section of the track link blocker forging. This procedure establishes a record of the boundary condition time sequence via forward simulation, using a candidate preform, into the final forged shape. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill to satisfy the requirement of material utilization and forging quality. The modified boundary condition sequence is then applied to control die/node separation during the backward deformation simulation. The backward simulation for the section analyzed provided the blocker preform shape from which the buster dies can be designed. The preform for the section is then evaluated by forward FEM simulation and compared with the results from the original busting operation. Performance measures for the comparison includes die fill, flash size, strain variance, frictional power and die load. Use of round billet stock was also investigated for producing the required preform shape. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Die cavity design; Finite element method; Backward simulation
1. Introduction The forged track link with its significantly complex shape provides an interesting challenge for the design of the manufacturing processes. The links are produced in large quantities so that process improvements can provide significant economic pay-off. In view of the current production methods, there are usually two ways to produce this forging. One is nonisothermal die forging using a mechanical press in multiple main stages of forging including flattening, blocking and finishing. The other is a roll forging process where the forming die cavities are sunk into the cylindrical surface of forming rolls. Because of the geometrical complexity of the track link forging, the current material utilization ratio is relatively low. A large amount of flash extruded in the forming process must be trimmed away and discarded. Therefore, reduction of the flash volume becomes a major concern in increasing the material utilization ratio and lowering the production cost. For the track link forged on a mechanical press, the initial billet form starts as rectangular steel melts with rounded *
Corresponding author.
corners or round steel bar. The track link is forged in a 40 000 kN mechanical press. An upsetting operation flattens the billet in the first station. In the second stage, a blocking operation provides the majority of the deformation to form the features of the track link prior to the finishing or third station operation. In the finishing operation, the majority of the material located in the link pin and bushing bores and shoe bolt access recesses is pushed away for later punch-out. The fourth station is the trimming process for flash removal. Currently, a large amount of flash extruded in the blocking operation must be trimmed away and discarded in the fourth station. The objective of this project is to support process improvement efforts through the reduction of the flash volume produced in the blocking stage. The goal is to achieve this objective through the selection and design of a progressive preforming operation. Currently, the press is limited to four stations and knock-out pins for workpiece removal are not available at the current busting station. Therefore, a preforming operation will be designed to replace the existing busting operation with further constraints on geometric complexity to accommodate manual
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removal of the workpiece. In considering the cost and convenience of production, it is not desirable to add an additional forging stage. An additional forging stage would increase die costs and require major capital investment in press equipment. Therefore, the ideal process improvement is to redesign the initial billet size and busting dies and maintain the same forging stage sequence. A proper die design can be derived from the preform shapes developed using isothermal backward tracing finite element methods (FEMs). Although the cross-section of the link varies throughout the length, a three-dimensional problem can be simplified into a series of two-dimensional problems according to the geometric and deformation features of the track link by modeling several sections along the link considered as plane strain deformation processes. To evaluate the utility of the backward deformation simulation method for preform design, the bushing bore cross-section is selected as the representative section for the backward and forward simulation.
2. FEM analysis and backward simulation Process modeling for computer simulation has been a major concern in the modern material forming industry. In the past, a number of approximate methods of analysis have been developed and applied to various forming processes. The methods most well known are the slab method, the slipline field method, the visco-plasticity method, upper bound techniques and upper bound elemental techniques [1,2]. These methods have been useful in predicting forming loads, overall geometry changes of the deformed workpiece, material flow, and in determining approximate optimum process conditions. However, accurate determination of the effects of various process parameters on the material flow became possible only when the FEM was developed for the analysis of material forming processes. Since then, the FEM has been found to be widely used in the simulation of material forming process [3–6]. With proper die design, very complex product geometry can be realized. However, production of high quality forgings typically requires one or more preforming operations or stages before the finishing die can produce the final shape. Conventional design methods draw upon the designer’s experience and empirical rules to determine the required number of intermediate stages, the preform or intermediate shapes, the billet dimensions and the process conditions for a given final product shape and material. Many hours of valuable engineering time can be spent in a build-and-try cycle before a workable process is achieved. Therefore, design optimization in these areas would provide great benefit. Computer aided design and manufacturing and FEMs are now available to assist the experienced designer. Raikar et al. [7] gave an empirically based computer aided design procedure for closed-die forgings. Yu and Dean [8] developed a practical computer aided approach to mould design for axisymmetric forging die cavities. Choi and Dean
[9] studied the computer aided design of die block layouts that is an interactive computer program as part of a complete CAD/CAM package for forging hammer die design. Park et al. [10] developed the backward tracing method for preform design using the rigid visco-plastic FEM. Kim and coworkers [11] also applied the FEM backward tracing scheme for the design of preform shapes for an H-shaped cross-section axisymmetric forging problem. Kang and Kobayashi [12] established systematic approaches for the preform design in forging of an airfoil section blade as a twodimensional plane strain problem using the FEM-based back-tracing scheme. Kang et al. [13] have applied this preform design method in three-dimensional ring rolling processes. Han et al. [14] applied optimization techniques in the backward tracing method. Zhao et al. established a node detachment criterion for the inverse deformation and preform design based on minimizing the forging shape complexity factor [15] and gave an inverse die contact tracking method for the preform design in forging processes [16]. Both forward and backward simulation require a converged velocity field in the entire workpiece, but the backward deformation simulation needs an additional geometric adjustment procedure to ensure that the desired forging shape is achieved from the new preform shape. To ensure a correct backward tracing path, the geometry of any backward step must be based on the nodal velocity solution given by the forward simulation of the same step. This velocity field is found in an iterative manner where an initial estimate of preform node coordinates is based on the forward velocity solution of the previous forward step. Fig. 1 gives the schematic illustration of the backward deformation simulation method. The relative error norm of node coordinates is used to determine the convergence of the geometric iteration. Node velocities are found through the solution of the non-linear system of equations after applying the appropriate boundary conditions. Typically, these equations are solved iteratively using the Newton–Raphson method. The primary steps of the backward deformation simulation process shown in Fig. 1 are summarized as follows: 1. The final product geometry, finisher dies and processing conditions are used to establish the initial finite element model for the inverse deformation simulation. 2. The boundary conditions are determined for the current incremental time step. This is done by applying a predefined criterion for detaching nodes from the dies. The type of criteria used will determine the ultimate suitability of the preform shape for the particular forging process. 3. A backward step is taken to update the workpiece geometry and die position based on the velocity field from the previous backward step. This backward step is then verified by completing a forward step in conventional fashion where the updated node velocity field is found by solving the non-linear finite element system of equations using the Newton–Raphson method.
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Fig. 1. Schematic illustration of the backward deformation simulation method (vd : die velocity, X: workpiece geometry, x: coordinates of boundary node).
4. Step 3 is repeated in an iterative manner until the geometry provided by the forward step matches the geometry at the start of the prior backward step. When the geometry comparison is sufficiently close, the current backward step is taken using the last updated velocity field. 5. The inverse simulation progresses by completing steps 3 and 4 at each time step and is usually terminated when only one node remains in contact with each die.
3. Preform design method The configuration of the final forging die cavity is usually designed according to the required shape of hot forging. Similarly, the configuration of the preforming die cavity can also be designed from the preforming shapes. Therefore, the design of the intermediate die shapes can be derived from the final forging shape if there is a methodology for designing a preform shape from a given final shape. During forward simulation, nodal boundary conditions of non-steady material forming processes constantly change as die filling progresses. The manner in which the nodes make contact with or separate from the die is dictated by the given die shape and the form of the workpiece at the previous simulation time step. For the backward tracing simulation, the final die shape is known but the shape of the preceding stage is unknown, and so there is no predetermined manner in which nodes will separate from the dies. Due to the irreversibility of the forging process, the backward tracing path is not unique and any number of preform shapes can be found by changing the sequence in which boundary nodes separate from the dies. In order to obtain optimum preform design, the proper criteria for controlling the boundary conditions must be established in some way before backward tracing can be done. The inverse die contact tracking method developed by Zhao et al. [16] was selected for this
project. A finite element code called PREFORMS (PReform Engineering using FOrward and Reverse Modeling Simulation) was developed and used for this project. The inverse die contact tracking method utilizes both the forward and inverse finite element simulations to design the preform shapes in forging processes. The procedure starts with the forward simulation of a candidate preform into the final forging shape or, in this case, the shape of the blocker. During the forward simulation, a record of the boundary condition changes is produced by identifying when a particular location on the die surface makes contact with the workpiece surfaces. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill to satisfy the requirement of material utilization and forging quality. The modified boundary conditions are finally used as the boundary condition control criterion for the inverse deformation simulation. The method can be used to design the preform shapes for forging processes in which the deformation is severe and remeshing procedures are required. As a part of the pre-processing tasks, all die surfaces are divided into a number of straight line or arc segments. During the forward simulation with a trial preform, the time at which each die segment comes into contact with the deforming body is calculated and recorded. In this way, it is not necessary to retain the original mesh division or the same position of the workpiece of the boundary nodes. If a die segment were to repeatedly separate and make contact with the workpiece, the last moment of segment contact is used for the record. To adequately reflect the change of the boundary condition using the contact time of the die segments, the length of each die segment should be less than the minimum side length of the workpiece boundary elements. With this die segment spacing, some segments that are between workpiece surface nodes will never make contact with a boundary node. The contact time for these central die segments is determined through linear interpolation using the contact times of the two
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nearest adjacent die segments as the end data points. This provides a continuous time sequence record for the segments that touch the workpiece between the nodes. The boundary condition sequence derived directly from the trial forward simulation must be modified according to the die fill state and material flow characteristics if the trial preform does not satisfy the design objectives. The extent of the modification depends on how close the selected trial preform is to the desired shape. Several guidelines were developed and used for modifying the boundary conditions [16]. During inverse simulation, if a die segment is scheduled to separate from the workpiece in the current step according to the modified record, then the boundary nodes that lie in this die segment will be detached from the die. The last die segments which come into contact with the deforming workpiece during trial forward simulation become the first die segments to break away from the dies during inverse simulation. All the die segments except the initial contact segments will become free at the completion of the inverse simulation. The intermediate workpiece shape at the completion of inverse simulation is typically selected for the preform shape.
4. Preform design in track link forging The cross-section (bushing bore) of the blocker dies and the original busting or preform shapes are shown in Fig. 2. A non-strain hardening material having the constitutive relation 0:145 s ¼ Y0 e_ with Y0 ¼ 4:93 kpsi (28.21 MN/m2) was recommended. A constant shear friction factor of 0.3 was assumed between the workpiece and the dies. The velocity of the upper die was assumed as a constant 10 in./s (254 mm/s) for
Fig. 2. Bushing bore cross-sectional shapes of the blocker dies and busting of the original design.
design purposes, while the lower die was held stationary. The design objective is to determine the buster die or the busting shape which will produce a sound blocking forging free of fold-over defects, underfill and with as little extrusion of flash as possible over the whole blocking process. Fig. 3 shows the material flow patterns in forward simulation of the blocking stage using the original preform shape. Because the two lateral cavities are shallow, they are easily filled with the closure of the upper and lower die. When the upper die moves to the position shown in Fig. 3(b), the two cavities are nearly completely filled and the material begins to be extruded into the flash gutters. Further closure of the dies only results in the movement of material to the two lateral flash gutters. This material flow pattern causes the forging load to increase abruptly. This load, combined with the excessive sliding velocity between the workpiece and dies near the flash gutter inlets, also causes the die surface at the flash gutter inlets to be worn severely.
Fig. 3. Material flow patterns in the forward simulation of the blocking stage using the original preform design.
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When the upper die moves down to the required position at a flash height shown in Fig. 3(c), the blocking stage is finished. At this point, the flash volume for this plane strain section is nearly one-third of the initial section volume. All of this material is trimmed away and discarded after forging, and so the waste is considerable. In addition, Fig. 3(c) illustrates that the volume of the left flash is larger than that of the right flash. This indicates the need for repositioning the billet further to the right at the start of the blocking stage. Analysis of the improved design should also provide the initial billet position within the blocker die cavity to ensure an even material distribution. During this trial forward simulation, both the upper die and lower die are divided into a series of die segments for recording the contact time at which every die segment comes into contact with the workpiece. The recorded boundary conditions are modified and then used to control the boundary node release during the inverse simulation in searching for the preform shape. Fig. 4 displays the reverse material flow process. To determine the proper position of the initial billet in the blocker die cavity, the final blocking for starting the inverse simulation has the same flash width on both the right and the left side. During the inverse simulation, two remeshing procedures were required due to mesh distortion. At the end of inverse simulation, the intermediate workpiece shape shown in Fig. 4(c) was obtained. Smoothing the boundary of the preform shape in Fig. 4(c) results in the busting shape shown in Fig. 5(a). Figs. 4(c) or 5(a) also shows the proper initial position of the busting in the blocker die cavity. To verify the effectiveness of the busting design obtained by the inverse deformation, the forward simulation of the blocking stage was completed. Fig. 5(a) shows the busting
Fig. 4. Material flow patterns during the backward simulation of the blocking stage.
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Fig. 5. Verification of the blocking stage with the reduced flash preform design.
shape and position designed by the inverse simulation and the blocker dies. When the blocking process is finished, the workpiece has very little flash and completely fills the dies with no evidence of surface defects, as shown in Fig. 5(c). The right and left-hand flash is of nearly the same volume. This resulted from the proper volume distribution achieved by the proper initial position of the busting in the blocker die cavity that corresponds to the volume requirements of the left and right die cavity. In comparison with the reference busting design, the width of both the left and right-hand flash was reduced considerably. The final shape in Fig. 5(c) also matched very closely with the initial shape for the inverse simulation in Fig. 4(a).
Fig. 6. Simulation of the busting stage using a round billet.
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Fig. 7. Verification of the blocking stage with the flattened round billet.
The busting shape for this section shown in Fig. 5(a) can be obtained very easily by flattening the round or square billet between two parallel dies. The important parameters in the flattening (busting) and the blocking stage are the busting height and its initial horizontal position in the blocker dies. Fig. 6 shows the material flow patterns in the busting stage using a round billet as the starting shape. The radius or diameter of the round billet is determined from the required blocking volume or plane strain section area. The flattened height is equal to the busting height shown in Fig. 5(a). Fig. 7 shows the material flow patterns for the blocking process
using the round billet. Fig. 7(a) illustrates the proper relative positioning of the blocker dies and the busting. When the upper die reaches the final position (Fig. 5(c)), the formed blocking has very little flash and completely fills the dies with no evidence of surface defects. The right and left-hand flash have nearly the same volume. This demonstrates that the use of the round billet can also achieve the production of a sound blocking. From experience, it is obvious that the busting obtained by flattening a square billet between two parallel dies can also produce the required blocking since its lateral bulge is typically smaller than that given by flattening the round billet. The die load–stroke curves in Fig. 8 indicate a reduced peak die load at the completion of the die stroke in the blocking stage for both the present design and round billet designs. The steep slope indicates simultaneous filling of the die recesses and formation of the flash. For the Caterpillar design, the load increases slowly with the die stroke. When the material touches the flash gutter inlets, the flash gutter, which is still relatively larger, provides a wider flow channel for the materials. The die stroke in which the peak load occurs is longer than that of the present design. So the original design needs more power input for completing the blocking stage than that of the present design. Fig. 9 illustrates the change in the maximum effective strain variance in the workpiece vs. the upper die stroke for three cases of track link blocking processes. The effective strain variance provides a measure of the uniformity of total deformation. In this case, a volume weighting is included to account for the variation in element size after deformation and is calculated from PN Vi ðei eave Þ Var ¼ i¼1PN i¼1 Vi
Fig. 8. Comparison of the load vs. stroke curves of the three preform designs.
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Fig. 9. Comparison of the effective strain variance of the three preform designs.
where Vi is the volume of the ith element and N the total number of elements, eave the average effective strain of all elements. It can be seen from Fig. 9 that the effective strain variance of the present preform design is much less than that of the original preform design. However, the analysis of the original design also includes the flash material that is eventually removed from the part. Fig. 10 gives a comparison of the busting shape and fixed position of the reduced flash preform design with the original preform design for a bushing bore cross-section. The commercial code ANTARES [17] which provides auto-meshing capability was used to analyze the resulting preform designs and verify the results given by the
PREFORMS forward simulations. For each ANTARES run, two die velocity profiles were used. The first schedule was a varying die velocity given for the mechanical press. This provided the strain rates and ram loads for the actual processing conditions. Runs were also done at a constant 10 in./s velocity to provide a comparison with the PREFORMS forward simulation results. The comparison of the results shows that a consistent result with respect to the workpiece shape and die fill is obtained from the ANTARES and PREFORMS simulations. The values of load, average effective strain, and average effective strain rate also compare very closely for the two simulation programs.
Fig. 10. Comparison of the busting shape and fixed position of the three preform designs (solid line: original design; dotted line: reduced flash design: (a) rectangular billet; (b) round billet).
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5. Discussion The above analysis shows that a sound track link asblocked without defects such as fold-over, excessive flash and dimensional inaccuracies can be produced using the busting designed by the inverse deformation and preform design methods. This success is achieved under the conditions of maintaining the exact busting shape and dimensions and its location in the blocker die cavity corresponding to the analysis. Strictly, this design provides the lower limit or minimum volume required for a successful forming operation. In practical production, incidental errors also affect the product quality. Therefore, for practical die design, the following should be taken into account to ensure the reliability of production: 1. The location of the workpiece in the die cavity is an important factor to achieve the proper volume distribution, especially for plane strain forging problems with multiple cavities. For the track link forging, if the same busting shape and the location in the blocker dies as those analyzed are achieved in practical forging, the required reduced flash blocking can be achieved with a complete die fill. In reality, positioning errors of the as-busted workpiece can occur in the blocker die cavity as the workpiece is held, fed and fixed by the manipulator in a continuous multi-stage forging process. Particularly, the stabilization and reliability of the positioning structure affect the position of the workpiece in the die cavity. The unstable location of the workpiece in the die cavity often causes the workpiece to move or roll and thereby cause deviations in location. This results in the unreasonable volume distribution of workpiece material and possibly causes underfill in one side. The busting cross-sectional area should be slightly increased if the location deviation of the busting in the blocker die cavities is considered. 2. The volume loss of the billet due to the scale resulting from the oxidizing during heating should also be considered and added to the initial billet volume. 3. This effort contributes only the preform design of the busting stage for the bushing bore cross-section. Typically, the last step in the reverse simulation is taken as the hot preform shape for the current stage. This provides the least complex die shape geometry (rectangular in this case) which is easier to produce and change if later adjustments to volume are required. In some instances, it may be desirable to form some of the features in the busting stage to support more stable positioning of the workpiece. Die design for this case is easily accomplished by taking the preform shape at an intermediate step near the end of the reverse simulation process. The increased cost of producing and maintaining a more complex die would have to be weighed against allowing a slightly greater flash volume tolerance. The analysis gives the volume (section area) requirements for the bushing sections. However, the billet stock (round or
square) typically has the same cross-sectional area and the final forging has different cross-sectional area along the length direction. Achievement of the proper cross-section area distribution in the length of the track link becomes a major concern. If this lengthwise distribution can be achieved, the material loss due to flash would be significantly reduced. Furthermore, the current blocker and finisher need not be changed when using the preform shapes provided. The information provided in this paper is limited only to one representative cross-section. When using this information for the design of the final three-dimensional buster die geometry, several other cross-sections along the length of the track link forging should be considered. However, the analysis and design of this representative cross-section indeed provide a useful reference for the final three-dimensional design. The preform designs of the other sections and the final three-dimensional buster die design will be introduced in subsequent papers.
6. Summary remarks This task utilizes the inverse die contact tracking method to design the preform shapes for a track link. This method invokes both forward and reverse finite element simulations. The procedure starts with the forward simulation of forging a candidate preform into the final forging shape. A record of the boundary condition changes is generated by identifying when a particular segment of the die makes contact with the workpiece surfaces in forward simulation. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill. The modified time sequence is finally used as the boundary condition control criterion for the inverse deformation simulation. This method does not depend on the mesh division of a workpiece and the number of boundary nodes. It can be used to design the preform shapes of forging processes including plane strain and axisymmetric deformation problems in which the deformation is severe and remeshing procedures are required. A method based on trial forward simulation to determine staging points is also presented. By using this preform design method, the material loss due to flash was reduced significantly. Additionally, the relatively simple busting shape can be obtained by flattening either a square or round billet to the required height at each section between parallel dies. The complete busting shape for the track link forging can be determined by consolidating preform designs of a limited number of cross-sections into a three-dimensional shape. The effectiveness of preform design is then verified via forward simulation prior to die manufacture. In this case, the analysis shows that for each section analyzed, a sound final forging without defects such as foldover, excessive flash and dimensional inaccuracies can be produced using the designed busting shape. This paper gives important parameters for improving the design of the buster dies including the billet section volume, the flattening
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height, and the fixed position of the busting in the blocker die cavity.
References [1] C.R. Boer, N. Rebelo, H. Pydgted, G. Schroder, Process Modeling of Metal Forming and Thermo-mechanical Treatment, Springer, Berlin, 1985. [2] E.M. Mielnik, Metalworking Science and Engineering, McGrawHill, New York, 1991. [3] S. Kobayashi, S.I. Oh, T. Altan, Metal Forming and the Finite Element Method, Oxford University Press, New York, 1989. [4] B.L. Jenkins, S.I. Oh, T. Altan, Investigation of defect formulation in a 3-station closed die forging operation, Ann. CIRP 38 (1989) 243–252. [5] J.C. Nagtegal, N. Rebelo, On the development of a general purpose finite element program for analysis of forming processes, Int. J. Numer. Meth. Eng. 25 (1988) 113–124. [6] Y.C. Shiau, S. Kobayashi, Three-dimensional finite element analysis of open-die forging, Int. J. Numer. Meth. Eng. 25 (1988) 67–78. [7] A. Raikar, I. Haque, J. Jackson, An empirically based computeraided design procedure for closed die forgings, J. Appl. Metalworking 4 (1987) 306–316.
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[8] G.B. Yu, T.A. Dean, A practical computer-aided approach to mould design for axisymmetric forging die cavities, Int. J. Mach. Tool Design Res. 25 (1985) 1–13. [9] S.H. Choi, T.A. Dean, Computer aided design of die block layouts, Int. J. Mach. Tools Manuf. 27 (1987) 91–103. [10] N. Kim, S. Kobayashi, Preform design in H-shaped cross section axisymmetric forging by finite element method, Int. J. Mach. Tools Manuf. 30 (1990) 243–268. [11] B.S. Kang, N. Kim, S. Kobayashi, Computer-aided preform design in forging of an airfoil section blade, Int. J. Mach. Tools Manuf. 30 (1990) 43–52. [12] B.S. Kang, S. Kobayashi, Preform design in rolling processes by the three dimensional finite element method, Int. J. Mach. Tools Manuf. 31 (1991) 139–151. [13] S.S. Lanka, R. Srinivasan, R.V. Grandhi, A design approach for intermediate die shapes in plane strain forgings, J. Mater. Shaping Technol. 9 (1991) 193–206. [14] C.S. Han, R.V. Grandhi, R. Srinivasan, Optimum design of forging die shapes using nonlinear finite element analysis, AIAA J. 31 (1993) 774–781. [15] G. Zhao, E. Wright, R.V. Grandhi, Forging preform design with shape complexity control in simulating backward deformation, Int. J. Mach. Tools Manuf. 35 (1995) 1225–1239. [16] G. Zhao, E. Wright, R.V. Grandhi, Computer aided preform design in forging using the inverse die contact tracking method, Int. J. Mach. Tools Manuf. 36 (1996) 755–769. [17] UES Inc., ANTARES Primer Manual, Dayton, OH, Version 4.0, 1995.
Die cavity design of near flashless forging process using FEM-based backward simulation Guoqun Zhaoa,*, Guangchun Wanga, Ramana V. Grandhib a
College of Materials Science and Engineering, Shandong University of Technology, Jinan, Shandong 250061, PR China b Department of Materials and Mechanical Engineering, Wright State University, Dayton, OH 45435, USA Received 26 September 1999
Abstract Preform design in forging processes is an important aspect for improving the forging quality and decreasing the production cost. Forward and backward simulations of the forging process based on rigid visco-plastic finite element methods (FEMs) can directly provide a preform shape from the final forged shape at a given stage. The objective of this effort is to reduce the material lost as flash by the design of an improved busting operation for a track link forging. This paper uses the FEM-based inverse die contact tracking method to design the preform shapes for a representative plane-strain cross section of the track link blocker forging. This procedure establishes a record of the boundary condition time sequence via forward simulation, using a candidate preform, into the final forged shape. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill to satisfy the requirement of material utilization and forging quality. The modified boundary condition sequence is then applied to control die/node separation during the backward deformation simulation. The backward simulation for the section analyzed provided the blocker preform shape from which the buster dies can be designed. The preform for the section is then evaluated by forward FEM simulation and compared with the results from the original busting operation. Performance measures for the comparison includes die fill, flash size, strain variance, frictional power and die load. Use of round billet stock was also investigated for producing the required preform shape. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Die cavity design; Finite element method; Backward simulation
1. Introduction The forged track link with its significantly complex shape provides an interesting challenge for the design of the manufacturing processes. The links are produced in large quantities so that process improvements can provide significant economic pay-off. In view of the current production methods, there are usually two ways to produce this forging. One is nonisothermal die forging using a mechanical press in multiple main stages of forging including flattening, blocking and finishing. The other is a roll forging process where the forming die cavities are sunk into the cylindrical surface of forming rolls. Because of the geometrical complexity of the track link forging, the current material utilization ratio is relatively low. A large amount of flash extruded in the forming process must be trimmed away and discarded. Therefore, reduction of the flash volume becomes a major concern in increasing the material utilization ratio and lowering the production cost. For the track link forged on a mechanical press, the initial billet form starts as rectangular steel melts with rounded *
Corresponding author.
corners or round steel bar. The track link is forged in a 40 000 kN mechanical press. An upsetting operation flattens the billet in the first station. In the second stage, a blocking operation provides the majority of the deformation to form the features of the track link prior to the finishing or third station operation. In the finishing operation, the majority of the material located in the link pin and bushing bores and shoe bolt access recesses is pushed away for later punch-out. The fourth station is the trimming process for flash removal. Currently, a large amount of flash extruded in the blocking operation must be trimmed away and discarded in the fourth station. The objective of this project is to support process improvement efforts through the reduction of the flash volume produced in the blocking stage. The goal is to achieve this objective through the selection and design of a progressive preforming operation. Currently, the press is limited to four stations and knock-out pins for workpiece removal are not available at the current busting station. Therefore, a preforming operation will be designed to replace the existing busting operation with further constraints on geometric complexity to accommodate manual
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removal of the workpiece. In considering the cost and convenience of production, it is not desirable to add an additional forging stage. An additional forging stage would increase die costs and require major capital investment in press equipment. Therefore, the ideal process improvement is to redesign the initial billet size and busting dies and maintain the same forging stage sequence. A proper die design can be derived from the preform shapes developed using isothermal backward tracing finite element methods (FEMs). Although the cross-section of the link varies throughout the length, a three-dimensional problem can be simplified into a series of two-dimensional problems according to the geometric and deformation features of the track link by modeling several sections along the link considered as plane strain deformation processes. To evaluate the utility of the backward deformation simulation method for preform design, the bushing bore cross-section is selected as the representative section for the backward and forward simulation.
2. FEM analysis and backward simulation Process modeling for computer simulation has been a major concern in the modern material forming industry. In the past, a number of approximate methods of analysis have been developed and applied to various forming processes. The methods most well known are the slab method, the slipline field method, the visco-plasticity method, upper bound techniques and upper bound elemental techniques [1,2]. These methods have been useful in predicting forming loads, overall geometry changes of the deformed workpiece, material flow, and in determining approximate optimum process conditions. However, accurate determination of the effects of various process parameters on the material flow became possible only when the FEM was developed for the analysis of material forming processes. Since then, the FEM has been found to be widely used in the simulation of material forming process [3–6]. With proper die design, very complex product geometry can be realized. However, production of high quality forgings typically requires one or more preforming operations or stages before the finishing die can produce the final shape. Conventional design methods draw upon the designer’s experience and empirical rules to determine the required number of intermediate stages, the preform or intermediate shapes, the billet dimensions and the process conditions for a given final product shape and material. Many hours of valuable engineering time can be spent in a build-and-try cycle before a workable process is achieved. Therefore, design optimization in these areas would provide great benefit. Computer aided design and manufacturing and FEMs are now available to assist the experienced designer. Raikar et al. [7] gave an empirically based computer aided design procedure for closed-die forgings. Yu and Dean [8] developed a practical computer aided approach to mould design for axisymmetric forging die cavities. Choi and Dean
[9] studied the computer aided design of die block layouts that is an interactive computer program as part of a complete CAD/CAM package for forging hammer die design. Park et al. [10] developed the backward tracing method for preform design using the rigid visco-plastic FEM. Kim and coworkers [11] also applied the FEM backward tracing scheme for the design of preform shapes for an H-shaped cross-section axisymmetric forging problem. Kang and Kobayashi [12] established systematic approaches for the preform design in forging of an airfoil section blade as a twodimensional plane strain problem using the FEM-based back-tracing scheme. Kang et al. [13] have applied this preform design method in three-dimensional ring rolling processes. Han et al. [14] applied optimization techniques in the backward tracing method. Zhao et al. established a node detachment criterion for the inverse deformation and preform design based on minimizing the forging shape complexity factor [15] and gave an inverse die contact tracking method for the preform design in forging processes [16]. Both forward and backward simulation require a converged velocity field in the entire workpiece, but the backward deformation simulation needs an additional geometric adjustment procedure to ensure that the desired forging shape is achieved from the new preform shape. To ensure a correct backward tracing path, the geometry of any backward step must be based on the nodal velocity solution given by the forward simulation of the same step. This velocity field is found in an iterative manner where an initial estimate of preform node coordinates is based on the forward velocity solution of the previous forward step. Fig. 1 gives the schematic illustration of the backward deformation simulation method. The relative error norm of node coordinates is used to determine the convergence of the geometric iteration. Node velocities are found through the solution of the non-linear system of equations after applying the appropriate boundary conditions. Typically, these equations are solved iteratively using the Newton–Raphson method. The primary steps of the backward deformation simulation process shown in Fig. 1 are summarized as follows: 1. The final product geometry, finisher dies and processing conditions are used to establish the initial finite element model for the inverse deformation simulation. 2. The boundary conditions are determined for the current incremental time step. This is done by applying a predefined criterion for detaching nodes from the dies. The type of criteria used will determine the ultimate suitability of the preform shape for the particular forging process. 3. A backward step is taken to update the workpiece geometry and die position based on the velocity field from the previous backward step. This backward step is then verified by completing a forward step in conventional fashion where the updated node velocity field is found by solving the non-linear finite element system of equations using the Newton–Raphson method.
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Fig. 1. Schematic illustration of the backward deformation simulation method (vd : die velocity, X: workpiece geometry, x: coordinates of boundary node).
4. Step 3 is repeated in an iterative manner until the geometry provided by the forward step matches the geometry at the start of the prior backward step. When the geometry comparison is sufficiently close, the current backward step is taken using the last updated velocity field. 5. The inverse simulation progresses by completing steps 3 and 4 at each time step and is usually terminated when only one node remains in contact with each die.
3. Preform design method The configuration of the final forging die cavity is usually designed according to the required shape of hot forging. Similarly, the configuration of the preforming die cavity can also be designed from the preforming shapes. Therefore, the design of the intermediate die shapes can be derived from the final forging shape if there is a methodology for designing a preform shape from a given final shape. During forward simulation, nodal boundary conditions of non-steady material forming processes constantly change as die filling progresses. The manner in which the nodes make contact with or separate from the die is dictated by the given die shape and the form of the workpiece at the previous simulation time step. For the backward tracing simulation, the final die shape is known but the shape of the preceding stage is unknown, and so there is no predetermined manner in which nodes will separate from the dies. Due to the irreversibility of the forging process, the backward tracing path is not unique and any number of preform shapes can be found by changing the sequence in which boundary nodes separate from the dies. In order to obtain optimum preform design, the proper criteria for controlling the boundary conditions must be established in some way before backward tracing can be done. The inverse die contact tracking method developed by Zhao et al. [16] was selected for this
project. A finite element code called PREFORMS (PReform Engineering using FOrward and Reverse Modeling Simulation) was developed and used for this project. The inverse die contact tracking method utilizes both the forward and inverse finite element simulations to design the preform shapes in forging processes. The procedure starts with the forward simulation of a candidate preform into the final forging shape or, in this case, the shape of the blocker. During the forward simulation, a record of the boundary condition changes is produced by identifying when a particular location on the die surface makes contact with the workpiece surfaces. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill to satisfy the requirement of material utilization and forging quality. The modified boundary conditions are finally used as the boundary condition control criterion for the inverse deformation simulation. The method can be used to design the preform shapes for forging processes in which the deformation is severe and remeshing procedures are required. As a part of the pre-processing tasks, all die surfaces are divided into a number of straight line or arc segments. During the forward simulation with a trial preform, the time at which each die segment comes into contact with the deforming body is calculated and recorded. In this way, it is not necessary to retain the original mesh division or the same position of the workpiece of the boundary nodes. If a die segment were to repeatedly separate and make contact with the workpiece, the last moment of segment contact is used for the record. To adequately reflect the change of the boundary condition using the contact time of the die segments, the length of each die segment should be less than the minimum side length of the workpiece boundary elements. With this die segment spacing, some segments that are between workpiece surface nodes will never make contact with a boundary node. The contact time for these central die segments is determined through linear interpolation using the contact times of the two
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nearest adjacent die segments as the end data points. This provides a continuous time sequence record for the segments that touch the workpiece between the nodes. The boundary condition sequence derived directly from the trial forward simulation must be modified according to the die fill state and material flow characteristics if the trial preform does not satisfy the design objectives. The extent of the modification depends on how close the selected trial preform is to the desired shape. Several guidelines were developed and used for modifying the boundary conditions [16]. During inverse simulation, if a die segment is scheduled to separate from the workpiece in the current step according to the modified record, then the boundary nodes that lie in this die segment will be detached from the die. The last die segments which come into contact with the deforming workpiece during trial forward simulation become the first die segments to break away from the dies during inverse simulation. All the die segments except the initial contact segments will become free at the completion of the inverse simulation. The intermediate workpiece shape at the completion of inverse simulation is typically selected for the preform shape.
4. Preform design in track link forging The cross-section (bushing bore) of the blocker dies and the original busting or preform shapes are shown in Fig. 2. A non-strain hardening material having the constitutive relation 0:145 s ¼ Y0 e_ with Y0 ¼ 4:93 kpsi (28.21 MN/m2) was recommended. A constant shear friction factor of 0.3 was assumed between the workpiece and the dies. The velocity of the upper die was assumed as a constant 10 in./s (254 mm/s) for
Fig. 2. Bushing bore cross-sectional shapes of the blocker dies and busting of the original design.
design purposes, while the lower die was held stationary. The design objective is to determine the buster die or the busting shape which will produce a sound blocking forging free of fold-over defects, underfill and with as little extrusion of flash as possible over the whole blocking process. Fig. 3 shows the material flow patterns in forward simulation of the blocking stage using the original preform shape. Because the two lateral cavities are shallow, they are easily filled with the closure of the upper and lower die. When the upper die moves to the position shown in Fig. 3(b), the two cavities are nearly completely filled and the material begins to be extruded into the flash gutters. Further closure of the dies only results in the movement of material to the two lateral flash gutters. This material flow pattern causes the forging load to increase abruptly. This load, combined with the excessive sliding velocity between the workpiece and dies near the flash gutter inlets, also causes the die surface at the flash gutter inlets to be worn severely.
Fig. 3. Material flow patterns in the forward simulation of the blocking stage using the original preform design.
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When the upper die moves down to the required position at a flash height shown in Fig. 3(c), the blocking stage is finished. At this point, the flash volume for this plane strain section is nearly one-third of the initial section volume. All of this material is trimmed away and discarded after forging, and so the waste is considerable. In addition, Fig. 3(c) illustrates that the volume of the left flash is larger than that of the right flash. This indicates the need for repositioning the billet further to the right at the start of the blocking stage. Analysis of the improved design should also provide the initial billet position within the blocker die cavity to ensure an even material distribution. During this trial forward simulation, both the upper die and lower die are divided into a series of die segments for recording the contact time at which every die segment comes into contact with the workpiece. The recorded boundary conditions are modified and then used to control the boundary node release during the inverse simulation in searching for the preform shape. Fig. 4 displays the reverse material flow process. To determine the proper position of the initial billet in the blocker die cavity, the final blocking for starting the inverse simulation has the same flash width on both the right and the left side. During the inverse simulation, two remeshing procedures were required due to mesh distortion. At the end of inverse simulation, the intermediate workpiece shape shown in Fig. 4(c) was obtained. Smoothing the boundary of the preform shape in Fig. 4(c) results in the busting shape shown in Fig. 5(a). Figs. 4(c) or 5(a) also shows the proper initial position of the busting in the blocker die cavity. To verify the effectiveness of the busting design obtained by the inverse deformation, the forward simulation of the blocking stage was completed. Fig. 5(a) shows the busting
Fig. 4. Material flow patterns during the backward simulation of the blocking stage.
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Fig. 5. Verification of the blocking stage with the reduced flash preform design.
shape and position designed by the inverse simulation and the blocker dies. When the blocking process is finished, the workpiece has very little flash and completely fills the dies with no evidence of surface defects, as shown in Fig. 5(c). The right and left-hand flash is of nearly the same volume. This resulted from the proper volume distribution achieved by the proper initial position of the busting in the blocker die cavity that corresponds to the volume requirements of the left and right die cavity. In comparison with the reference busting design, the width of both the left and right-hand flash was reduced considerably. The final shape in Fig. 5(c) also matched very closely with the initial shape for the inverse simulation in Fig. 4(a).
Fig. 6. Simulation of the busting stage using a round billet.
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Fig. 7. Verification of the blocking stage with the flattened round billet.
The busting shape for this section shown in Fig. 5(a) can be obtained very easily by flattening the round or square billet between two parallel dies. The important parameters in the flattening (busting) and the blocking stage are the busting height and its initial horizontal position in the blocker dies. Fig. 6 shows the material flow patterns in the busting stage using a round billet as the starting shape. The radius or diameter of the round billet is determined from the required blocking volume or plane strain section area. The flattened height is equal to the busting height shown in Fig. 5(a). Fig. 7 shows the material flow patterns for the blocking process
using the round billet. Fig. 7(a) illustrates the proper relative positioning of the blocker dies and the busting. When the upper die reaches the final position (Fig. 5(c)), the formed blocking has very little flash and completely fills the dies with no evidence of surface defects. The right and left-hand flash have nearly the same volume. This demonstrates that the use of the round billet can also achieve the production of a sound blocking. From experience, it is obvious that the busting obtained by flattening a square billet between two parallel dies can also produce the required blocking since its lateral bulge is typically smaller than that given by flattening the round billet. The die load–stroke curves in Fig. 8 indicate a reduced peak die load at the completion of the die stroke in the blocking stage for both the present design and round billet designs. The steep slope indicates simultaneous filling of the die recesses and formation of the flash. For the Caterpillar design, the load increases slowly with the die stroke. When the material touches the flash gutter inlets, the flash gutter, which is still relatively larger, provides a wider flow channel for the materials. The die stroke in which the peak load occurs is longer than that of the present design. So the original design needs more power input for completing the blocking stage than that of the present design. Fig. 9 illustrates the change in the maximum effective strain variance in the workpiece vs. the upper die stroke for three cases of track link blocking processes. The effective strain variance provides a measure of the uniformity of total deformation. In this case, a volume weighting is included to account for the variation in element size after deformation and is calculated from PN Vi ðei eave Þ Var ¼ i¼1PN i¼1 Vi
Fig. 8. Comparison of the load vs. stroke curves of the three preform designs.
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Fig. 9. Comparison of the effective strain variance of the three preform designs.
where Vi is the volume of the ith element and N the total number of elements, eave the average effective strain of all elements. It can be seen from Fig. 9 that the effective strain variance of the present preform design is much less than that of the original preform design. However, the analysis of the original design also includes the flash material that is eventually removed from the part. Fig. 10 gives a comparison of the busting shape and fixed position of the reduced flash preform design with the original preform design for a bushing bore cross-section. The commercial code ANTARES [17] which provides auto-meshing capability was used to analyze the resulting preform designs and verify the results given by the
PREFORMS forward simulations. For each ANTARES run, two die velocity profiles were used. The first schedule was a varying die velocity given for the mechanical press. This provided the strain rates and ram loads for the actual processing conditions. Runs were also done at a constant 10 in./s velocity to provide a comparison with the PREFORMS forward simulation results. The comparison of the results shows that a consistent result with respect to the workpiece shape and die fill is obtained from the ANTARES and PREFORMS simulations. The values of load, average effective strain, and average effective strain rate also compare very closely for the two simulation programs.
Fig. 10. Comparison of the busting shape and fixed position of the three preform designs (solid line: original design; dotted line: reduced flash design: (a) rectangular billet; (b) round billet).
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5. Discussion The above analysis shows that a sound track link asblocked without defects such as fold-over, excessive flash and dimensional inaccuracies can be produced using the busting designed by the inverse deformation and preform design methods. This success is achieved under the conditions of maintaining the exact busting shape and dimensions and its location in the blocker die cavity corresponding to the analysis. Strictly, this design provides the lower limit or minimum volume required for a successful forming operation. In practical production, incidental errors also affect the product quality. Therefore, for practical die design, the following should be taken into account to ensure the reliability of production: 1. The location of the workpiece in the die cavity is an important factor to achieve the proper volume distribution, especially for plane strain forging problems with multiple cavities. For the track link forging, if the same busting shape and the location in the blocker dies as those analyzed are achieved in practical forging, the required reduced flash blocking can be achieved with a complete die fill. In reality, positioning errors of the as-busted workpiece can occur in the blocker die cavity as the workpiece is held, fed and fixed by the manipulator in a continuous multi-stage forging process. Particularly, the stabilization and reliability of the positioning structure affect the position of the workpiece in the die cavity. The unstable location of the workpiece in the die cavity often causes the workpiece to move or roll and thereby cause deviations in location. This results in the unreasonable volume distribution of workpiece material and possibly causes underfill in one side. The busting cross-sectional area should be slightly increased if the location deviation of the busting in the blocker die cavities is considered. 2. The volume loss of the billet due to the scale resulting from the oxidizing during heating should also be considered and added to the initial billet volume. 3. This effort contributes only the preform design of the busting stage for the bushing bore cross-section. Typically, the last step in the reverse simulation is taken as the hot preform shape for the current stage. This provides the least complex die shape geometry (rectangular in this case) which is easier to produce and change if later adjustments to volume are required. In some instances, it may be desirable to form some of the features in the busting stage to support more stable positioning of the workpiece. Die design for this case is easily accomplished by taking the preform shape at an intermediate step near the end of the reverse simulation process. The increased cost of producing and maintaining a more complex die would have to be weighed against allowing a slightly greater flash volume tolerance. The analysis gives the volume (section area) requirements for the bushing sections. However, the billet stock (round or
square) typically has the same cross-sectional area and the final forging has different cross-sectional area along the length direction. Achievement of the proper cross-section area distribution in the length of the track link becomes a major concern. If this lengthwise distribution can be achieved, the material loss due to flash would be significantly reduced. Furthermore, the current blocker and finisher need not be changed when using the preform shapes provided. The information provided in this paper is limited only to one representative cross-section. When using this information for the design of the final three-dimensional buster die geometry, several other cross-sections along the length of the track link forging should be considered. However, the analysis and design of this representative cross-section indeed provide a useful reference for the final three-dimensional design. The preform designs of the other sections and the final three-dimensional buster die design will be introduced in subsequent papers.
6. Summary remarks This task utilizes the inverse die contact tracking method to design the preform shapes for a track link. This method invokes both forward and reverse finite element simulations. The procedure starts with the forward simulation of forging a candidate preform into the final forging shape. A record of the boundary condition changes is generated by identifying when a particular segment of the die makes contact with the workpiece surfaces in forward simulation. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill. The modified time sequence is finally used as the boundary condition control criterion for the inverse deformation simulation. This method does not depend on the mesh division of a workpiece and the number of boundary nodes. It can be used to design the preform shapes of forging processes including plane strain and axisymmetric deformation problems in which the deformation is severe and remeshing procedures are required. A method based on trial forward simulation to determine staging points is also presented. By using this preform design method, the material loss due to flash was reduced significantly. Additionally, the relatively simple busting shape can be obtained by flattening either a square or round billet to the required height at each section between parallel dies. The complete busting shape for the track link forging can be determined by consolidating preform designs of a limited number of cross-sections into a three-dimensional shape. The effectiveness of preform design is then verified via forward simulation prior to die manufacture. In this case, the analysis shows that for each section analyzed, a sound final forging without defects such as foldover, excessive flash and dimensional inaccuracies can be produced using the designed busting shape. This paper gives important parameters for improving the design of the buster dies including the billet section volume, the flattening
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height, and the fixed position of the busting in the blocker die cavity.
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