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Process sequence design in cold forging to form a constant velocity joint housing
Int. J. Mach~ Tools Manufact. Vol. 34, No. 8, pp. 1133-1146. 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0890-6955/9457,00 + .00
Pergamon
0890--6955(93)E0015-W
PROCESS
SEQUENCE DESIGN IN COLD FORGING TO FORM A CONSTANT VELOCITY JOINT HOUSING BEOM-SOO KANGt a n d SHIRO KOBAYASHI:~
(Received September 1992; in final form November 1993) Abstract--A systematic approach to process sequence design is established by the finite element method for multi-operational cold forging to form a constant velocity joint housing. Both the loading simulation and the backward tracing by the rigid plastic finite element method provide useful information for designing new process sequences. The newly designed sequence has four forming operations and one annealing treatment, and can achieve net-shape manufacturing, while the conventional process sequence has five forming operations and two annealing treatments, and requires machining after forming. The refinement at the top surface of the product is made by applying the backward tracing scheme for the purpose of netshape manufacturing. This specific case can be considered for application of the method and for development of the sequence design methodology in general.
1. INTRODUCTION
THE FINITEELEMENTMETHODhas been widely used for simulating and analyzing various metal forming processes. One of the most practical applications of the finite element method to the metal forming industry is process sequence design in multi-stage forming processes. Design of the forming process involves the determination of number of preforms and the determination of the shapes and preform dimensions. The problem of process sequence design arises in many forming processes, such as forging, drawing, extrusion, rolling and sheet metal forming [1, 2]. The conventional approaches to the process sequence design have been empirical or based on approximate analysis and require extensive experience and expensive trial and error [3-7]. Several computeraided approaches have been proposed for preforms and sequence design for complex forging components [8-11]. One indispensable component of front-wheel drive compact cars is a constant velocity joint. The mass production of constant velocity joints at an economical cost has thus become an important issue for production engineering [12]. Constant velocity joints function to transmit the output power of the engine to the wheels. A constant velocity joint consists of a tulip shaft, a spider and a housing. The production of housings among the components by machining is difficult because of the irregular shape. There are two methods for mass production of the housing, hot forging and cold forging. The conventional hot forging process requires machining operations with an enormous number of man-hours. The cold forging process, however, makes it possible to produce net-shape housings without any machining after forming and saves 40% of materials. Even so, great effort in designing delicate process sequences is needed in the cold forging of net-shape housings. The process sequence design in cold forging of a constant velocity joint housing is investigated in this study by the rigid plastic finite element method. Here a forging
tDepartment of Aerospace Engineering, Pusan National University, Korea--Visiting Research Engineer, Department of Mechanical Engineering, University of California at Berkeley. ~:Professor Emeritus, Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, U.S.A. and 414 Sea View Drive, El Cerrito, CA 94530, U.S.A. 1133
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BEOM-SooKANGand SHIROKOBAYASHI unit : nun
,80.5
*55.0
I
(a) initialbillet
o I*27.5 ] (b) extrusion
(c) upsetting
(e) backwardextrusion 2
(f) ironing
%
1)backward extrusion 1
FIG. 1. Process description of five-operation cold forging to form a constant velocityjoint housing. process sequence with five operations, shown in Fig. 1, is designed to a new process sequence which can produce net-shape housings with minimum number of operations within a given press capacity. This study is an extension of the preform design using the rigid plastic finite element method and the backward tracing scheme, and one of the research series, "Process Sequence Design in Metal Forming". The rigid plastic finite element method has been used for process simulation, and the computational technique for the analysis of metal forming processes has been well established [13]. In the backward tracing procedure, the finite element method traces backward from the final specified configuration. The procedure has been applied to various problems in prior investigations. For the process sequence design, forward loading simulation and backward tracing by the use of the finite element method capabilities will be applied, which have proved to be powerful and effective for preform design in metal forming [14-20]. 2. PROCESS DESCRIPTION AND OBJECTIVE OF DESIGN An outline of the cold forging process for a constant velocity joint housing of axial symmetry is illustrated in Fig. 1 [21]. The first operation is forward extrusion with 75% area reduction, and the second operation is upsetting. Plastic instability may be involved in the upsetting operation if the forward extrusion is skipped. Fig. l(d) shows the third operation of backward extrusion, in which the maximum die load is critical to the fatigue life of punch owing to compression stresses. During this operation, the flow stress of the material becomes large and a great deal of compressive stress is applied to the tools. Thus it is essential to perform an appropriate heat treatment on the material so as to give it the degree of cold formability required
Process Sequence Design in Cold Forging
1135
for the processing operation. Another backward extrusion operation is shown in Fig l(e). Delicate design of the punch shape in the fourth operation is required to obtain dimensional accuracy of the final product. The shape of the punch used in the fourth operation, particularly the shape of the punch top, affects product functionality. The last operation involves ironing and bending, shown in Fig. l(f). The actual upper die consists of six radially segmented components around a central core, like the slices of an apple. Removal of the die from the final socket-shaped product is carried out by retracting the central core and collapsing the segments of the die inward. The objective of the study presented here is to design an appropriate reduced process sequence for the current five-operation process, with net-shape final products within die load capacity. A great deal of loading simulations by the rigid plastic finite element are carried out to obtain design information. Considerable remeshing work is expected during simulations since the process has multi-operations and deformation of the workpiece is complicated. Also the backward tracing scheme, in which the rigid plastic finite element method traces backward from the final specified configuration to a prior preforming configuration, will be applied to the final ironing and bending operation to obtain a preforming die configuration in the second backward extrusion. It is noted that the deformation mechanics involved in the final operation are not actually axisymmetric. This study, however, treats the deformation as an axisymmetric case since it has relatively small deviation from the actual case. The difference between axisymmetric and the actual process must be compensated in the final die design in industry. 3. METHOD OF APPROACH In the process sequence design for multi-stage forming operation, the forward loading simulations by the finite element method are performed mainly to obtain useful design information such as deformation characteristics, die load, and strain distribution. The rigid plastic finite element method for the analysis of metal forming processes has been well established, and the derivation and computation procedure for the rigid plastic finite element method are not repeated here. The information from backward tracing simulations as well as from forward loading simulations is essential for the refinement of product configuration. The backward tracing scheme will be applied to the final operation during this study of process sequence design. Similarly to forward simulation, the backward tracing method uses the finite element method. Backward tracing refers to the prediction of the part configuration at any stage in a deforming process, when the final part geometry and process conditions are given. The application of backward tracing is straightforward if the changes of the boundary conditions during a process are known. The boundary conditions are usually derived from the loading simulations of a trial preform, and modified slightly for backward tracing. This aspect of determining the boundary conditions during backward tracing is discussed in some detail in the later section. This multi-operational process involves complex plastic deformation during forming. Thus simulations by the finite element method have severe grid distortion for following the given process. In some cases, the simulation does not continue because of the negative Jacobian of four-node rectangular elements, and remeshing is essential for the study of process sequence design using the finite element method. The remeshing requires, in this study, reallocation of nodal points to avoid negative Jacobians and transfer of effective strain by linear interpolation. The material characteristic of the workpiece considered here is work-hardening, and the plastic deformation is influenced by the effective strain distribution of the workpiece. For remeshing, data such as coordinates of nodal points, strain distributions at the integration points of each element, die contact points, and force boundary conditions, are stored. New nodal points and connectivity matrices of elements are generated. The values of effective strain at integration points of each element are obtained by interpolation of the stored data, and die contact points and force boundary conditions are assigned in the new mesh system.
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BEOM-Soo KANG and SHIRO KOBAYASHI
The final operation of ironing and bending involves three-dimensional metal flow in the actual process, and the plastic deformation is not axisymmetric. As mentioned in the previous section the socket-shaped product is formed by special dies with six segments around a core. Assuming that the difference between the actual process and the related axisymmetric case is relatively minor, we consider an axisymmetric problem with a socket-shaped product. The maximum die load in the final operation is similar to the value of the actual case, but the top configuration of the product is influenced by the problem modification. When applying this result to die design in industry, some design modification will be performed to compensate the difference between the actual process and the simulated process. Here the study considers an axisymmetric top configuration for the numerical analysis. The workpiece material considered is a mild steel, AISI 1018, whose work-hardening characteristic is given by -6/Y = (1.0 + 50.0E) °-e64
where the initial yield strength Y is 362 MPa (0.037 ton/mm2). The work-hardening characteristic is implemented in the finite element program. The backward tracing simulations also use the same work-hardening effect. In the backward tracing (t ~< to), at time t = to-j = to - At, eo-1 should satisfy the following condition.
The die-workpiece interface condition is characterized by the friction law of constant factor, usually used for bulk metal forming problems, namely, "r=mk
Here, "r is the frictional shear stress, m the friction factor, and k the shear flow stress. The friction factor for the cold forging in this study is assumed to be 0.1. 4. FEM SIMULATIONSOF THE CONVENTIONAL PROCESS The conventional process sequence to form a constant velocity joint housing, shown in Fig. 1, is a classical expert's solution. It is designed within die load capacity and for near-net-shape products. The process sequence consists of five operations, which are forward extrusion, upsetting, two operations of backward extrusion, and ironing with bending. These simulation results are shown in Figs 2-6. Two hundred and eighty nodes, and 247 four-node elements are used for simulation. The first operation shown in Fig. 2 is forward extrusion. The area reduction is 75%. As shown in the simulation results, remeshing at the die stroke of 64% is carried out since the original mesh has negative Jacobian near the outlet of the container. The remesh work makes it possible to complete the simulation of the extrusion with 75% area reduction. The deformation pattern is typical in forward extrusion. The front end of the extruded workpiece has a blunt shape as studied in Ref. [22]. The distribution of effective strain and grid distortion at the finishing stroke are shown in Fig. 2(c). The maximum die load is 580 ton. The second operation is upsetting, and is shown in Fig. 3. The workpiece extruded in the first operation prevents plastic buckling, and thus enables one to complete the upsetting operation. The ratio of maximum area increase is 2,14 in the upper cylindrical part. This operation is a preparation for the next operation, the first backward extrusion. The simulation is stopped at the maximum die load of 780 ton, at which the filling of the die cavity is almost complete. After the upsetting operation, an annealing heat treatment is performed in industry. The effect of annealing treatment on the workpiece is reflected as strain-free material in the simulation by the finite element method. Figure 4 shows the third operation, namely, the first backward extrusion. Since the
Process Sequence Design in Cold Forging
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¢
f
(a)
1_.
(b)
(c)
FIo. 2. The first operation of forward extrusion: (a) initial set-up; (b) remeshing at the stroke of 64%; and (c) grid distortion and effective strain distribution at the end of the operation.
(a)
(b)
FIG. 3. The second operation of upsetting.
workpiece is annealed before the operation, the upset workpiece is considered to be in a state of zero-strain at the start of simulation. The initial mesh, shown in Fig. 4(a), is slightly altered from the distorted mesh of the second upsetting in Fig. 3(b). The punch with a sharp blunt at the central part is used in industry for centering the workpiece and for stabilizing the start of the operation. The grid distortion at the stroke of 42% (Fig. 4(b)), has a negative Jacobian of an element near the convex punch. The remeshed grid is used to finish the simulation after 42% die stroke. The operation is a preprocess to the second backward extrusion. The grid distortion and effective strain distribution are shown in Fig. 4(c). The work-hardening effect due to plastic strain is severe around the punch. The maximum die load at the end of the operation is 327 ton. The grid distortion pattern during the fourth operation is shown in Fig. 5. Before performing this operation, the workpiece is annealed again to obtain sufficient forinability. The heat treatment is the second annealing of the whole process, and is critical to produce a near-net-shape product. Another remeshing is performed at the stroke of 97%, shown in Fig. 5(b). The shape of the punch used in this operation,
BEoM-SOo KANGand Smao KOBAYASHI
1138
1.0 0.6
(a)
(b)
(c)
FIG. 4. The third operation of backward extrusion: (a) initial set-up; (b) step for remeshing; and (c) final deformation.
(a)
(b)
(c)
Fl~. 5. The fourth operation of backward extrusion: (a) intial set-up; (b) remeshing at the stroke of 97%; and (c) final deformation.
(a)
(b)
FiG. 6. The last operation of ironing: (a) initial set-up; and (b) final deformation. particularly the shape of the punch top, affects product functionality. Consequently, the degree of freedom for modifying the punch shape is severely limited. Thus, an attempt is made to redesign only the base counter of the punch to produce net-shape products without machining after forming. The deformation pattern at completion of
Process Sequence Design in Cold Forging
800
800,-
800 I
600 t
max.die load = 327 ton
600-
600 -
{ 400
400
200
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max. die load = 780 ton
max. die load = 580 ton
1139
20
40
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200 I 80 i(J0
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(c) backward extrusion 1
(b) upsetting
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20
40
60
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40
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STROKE (%)
STROKE (%) (d) backward extrusion 2
(e) ironing
FIG. 7. Load-stroke curves for the conventional five-operation process.
the operation is shown in Fig. 5(c). Through the operation, the maximum die load is 380 ton. The last operation is an ironing with bending. This operation requires minor plastic deformation. To produce the socket-shaped product, a special set of die components is used for easy die removal from the workpiece after the operation. One type of special upper die set consists of six radial segments around a central core, similar to the slices of an apple. The ring-type lower die moves upward while the upper die set is fixed. Thus the whole workpiece deforms radially inward and upward. Thus this operation can be called an ironing with bending. The initial set-up is shown in Fig. 6(a), and the final deformed product in Fig. 6(b). The die load during the operation is relatively small compared with those of the previous four operations. The maximum die load is 78 ton at the stroke of 53%. The whole process sequence includes five operations of a forward extrusion, an upsetting, two backward extrusions, and an ironing with radial bending, and two heat treatments of annealing. In industry, two annealing treatments require high cost of labor, energy and production time. Thus the reduction of the number of forming operations and heat treatments is a key factor in designing a new process sequence. The load-stroke curves for the five operations are shown in Fig. 7. The maximum die load through the whole process is 780 ton in the second operation of upsetting. 5. A NEW PROCESS S E Q U E N C E
A better process sequence should have fewer numbers of processes including annealing treatments, and produce net-shape products. First, we have to decide how MTM 34:8-G
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BEOM-SOOKANGand SHmoKOBAYASH!
to reduce the number of operations and heat treatments. The approach to net-shape manufacturing will be discussed later. Annealing is treated before each backward extrusion (the third and the fourth operations). Combining the two backward extrusion operations into one operation may be the simplest way of reducing the two heat treatments to one, and also may achieve reduction of one forming operation. The conventional process sequence, an expert's solution, however, has two distinct backward extrusions because of die load and nearnet-shape manufacturing. There seems to be a high possibility of achieving one backward extrusion operation, if it can produce fine and sound preform which will result in netshape manufacturing in the final ironing operation. For this purpose, the maximum die load of the operation should have enough margin of safety in view of the hydraulic press capacity of 1000 ton, and the plastic deformation involved in the backward extrusion should not be severe. Further, possibilities of combining upsetting with the first backward extrusion process and the second backward extrusion with the final ironing process can be considered. There is no possibility of combining the second backward extrusion with the ironing operation, since the two operations have very different deformation characteristics, and opposite directions of die movement. Considering a case of combining the upsetting operation with the first backward extrusion, two operations have similar metal flow during plastic deformation, and the same direction of die movement. It appears possible that upsetting with the backward extrusion may be carried out by designing a new punch. The punch shape should be in-between the two punch shapes of upsetting and backward extrusion, so that the same deformation effects such as upsetting and backward extrusion can be achieved. Based on the argument presented above, a new process sequence is designed and shown in Fig. 8 as a four-operation process. This process requires one heat treatment before backward extrusion. Thus the new process consists of four forming operations and one annealing treatment. The first operation, forward extrusion, in the new process is the same as in the conventional process sequence, and the deformed configuration after the first operation is shown in Fig. 8(b). Figure 8(c) shows a newly designed operation, which is called a closed die forging and combines upsetting with backward extrusion. The punch has a spherical shape at the center and fiat peripheral part for upsetting. The purpose of the sharp blunt at the center is to stabilize the initiation of deformation. The simulation of this process is shown in Fig. 9. Jacobian is negative near the spherical part of the punch at the stroke of 78%, and remeshing is necessary for complete simulation. The grid distortion and effective strain distribution are shown in Fig. 9(c). The maximum die load is 850 ton at the end of the operation. Since this is not a finishing operation, forging is not necessary for complete filling. A small cavity is shown at the intersection between the fiat part and the spherical part of the punch. The third operation in the new process sequence shown in Fig. 8(d) is a backward extrusion. Simulation of the process is shown in Fig. 10. The die set used in this operation is the same one as the fourth operation in the conventional process, and the deformation pattern is also very similar. The workpiece is assumed to be strain-free at the start of deformation because of the annealing. The remeshed grid pattern at the die stroke of 36% is in Fig. 10(b), and the final deformation is shown in Fig. 10(c). The maximum die load is 550 ton, which is larger than the value of the fourth operation in the conventional process by 170 ton, but well within the press capacity of 1000 tons. The results of simulation of the last operation are shown in Fig. 11. This operation is exactly the same as the last operation of the conventional process (Fig. 6), except that the workpiece configurations are slightly different. The load-stroke curves for each operation in the new process are shown in Fig. 12. There is no significant peak of die load. Now the process sequence with four forming operations and one heat treatment is established for production of a sound product within the capacity of the available press. However, the net-shape manufacturing of the final product of geometrically accurate shape still remains to be solved.
Process Sequence Design in Cold Forging
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unit : mm
f
(a) initial billet
(b) extrusion
(d)backward extrusion
°80.5
I~
(c)closed die forging(upsetting)
(e)ironing
Fro. 8. Process description of the new forming sequence.
-N
\
(a)
(b)
(c)
FIG. 9. The second operation of closed die forging in the new process.
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BEOM-SOo KANG and SHIRO KOBAYASHI
(a)
(b)
(c)
FI~. 10. The third operation of backward extrusion in the new process.
1.1
(a)
(b)
(c)
Fic. 11. The last operation of ironing with radial bending in the new process. 6. FINAL PROCESS SEQUENCE DESIGN USING THE BACKWARD TRACING SCHEME
For net-shape manufacturing the geometrical configuration of top surface in the final product, especially the slope angle shown by a solid line in Fig. 13, is required. In the conventional process, the required slope is obtained by machining after forming. The top surface configuration in the product formed by the new four-operation process is also shown in Fig. 13 by a dotted line, and the slope angle obtained is 16.1 ° while the angle in a real product after machining is 10.0°. In order to produce a final product with 10.0 ° slope on the top surface, it is necessary to design a proper preform before the final forming operation. The procedures of preform design to obtain an appropriate slope are as follows. First, a preform shape is obtained by applying the backward tracing scheme to the finishing operation, ironing with bending. Based on the preform shape, the shape of the punch in the third operation, backward extrusion, is redesigned. Loading simulations using the new punch shape in the backward extrusion and in the finishing operation are carried out to confirm the design result by backward tracing simulations. For the use of the backward tracing scheme, the top surface of the final product obtained in the new process (see Fig 11(c)) is modified to have a 10° slope as shown by the solid line in Fig. 13. This is achieved by changing corresponding nodal coordinates in the result of the new process, and thus, has the effect of adding a small amount of material. The effective strains at the nodal points are assigned the same values before modification. In the application of the backward tracing procedure to this problem, the boundary
Process Sequence Design in Cold Forging 1000
1000
max.die load= 580 ton
max. die load = 850 ton
750
750 0
O
5OO
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500 < O ,d
250 0 0
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20 40 60 80 100 STROKE (%) (a) extrusion
1000
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max.die load= 550 ton
max.die load= 110 ton
75O
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,..2
20 40 60 80 100 STROKE (%)
(b) closed die forging (upsetting)
750 r~ < ©
1143
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500
r~ <
250
500 25O
~ 1 1 l I 0 20 40 60 80 100 STROKE (%)
0 0
(c) backward extrusion
20 40 60 80 100 STROKE (%) (d) ironing
FIG. 12. Load-stroke curves for the new four-operation process.
0p16.1 o
02=10.0°
FIG. 13. Modified configuration (solid line) for the application of backward tracing (dotted line; the configuration before modification). c o n d i t i o n s a r e c o n t r o l l e d in s u c h a w a y t h a t t h e p r e f o r m s h a p e a f t e r c o m p l e t i o n o f b a c k w a r d t r a c i n g b e c o m e s t h e s a m e as t h e p r e f o r m b e f o r e m o d i f i c a t i o n e x c e p t t h e t o p s u r f a c e c o n f i g u r a t i o n . T h e s m a l l a m o u n t o f m a t e r i a l a d d e d to m a k e 10 ° t o p s u r f a c e s l o p e d o e s n o t a f f e c t t h e d e f o r m a t i o n o f t h e o t h e r p a r t , since t h e a d d e d m a t e r i a l d e f o r m s o n l y by r a d i a l b e n d i n g . T h e c o n t a c t n o d a l p o i n t s to t h e d i e s in b a c k w a r d
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BEOM-SOo KANG and SmRO KOBAYASHI
tracing should follow the boundary conditions obtained from forward loading simulations. These are shown in Fig. 14(a) and (b). Fig. 14(a) displays the contact angle to the die 1 according to the stroke of the die 2 during backward tracing simulation. During the loading simulation, die 1 is stationary and the die 2 moves upward. In backward tracing, die 2 moves downward, and the contact angle of the workpiece to die 1 decreases. The movement of die 2 can be indicated by the mean height of the die and contact area to the workpiece, as shown in Fig. 14(b). The boundary conditions during backward tracing are based on the results in the previous forward loading simulations. The backward tracing simulations for the last operation are shown in Fig. 15. The initial set-up for backward tracing is shown in Fig. 15(a), and the workpiece contour is modified according to that shown in Fig. 13. Figure 15(b) shows backward tracing simulation at 46% stroke of die 2. The preform finally derived from the backward tracing is given in Fig. 15(c). The preform shape and effective strain distribution are almost the same as those in the process, Fig. 10(c), except the configuration of top surface. The resulted configuration shows that the outward radial slope of the top surface is 12.2 ° and provides the punch shape in the third operation of backward extrusion.
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(b) FIG. 14. Boundary conditions during the backward tracing simulation: (a) contact angle to die 1; and (b) contact location and area to die 2.
Process Sequence Design in Cold Forging
(a)
(b)
1145
(c)
FIG. 15. Backward tracing simulation for ironing: (a) initiation of backward tracing; (b) 46% stroke of backward tracing; and (c) result of complete backward tracing.
10.5°
(a)
(b)
(c)
FIG. 16. Loading simulations of the backward extrusion and the ironing with bending in the finally designed process. (a) backward extrusion; (b) ironing and bending; and (c) configuration of the final product.
Since the deformed workpiece, Fig. 16(a), is based on the result of backward tracing, it is desirable to confirm that this preform results in the desired final product by performing loading simulation of the last operation. This loading simulation is shown in Fig. 16(b). The workpiece contour obtained here is displayed in Fig. 16(c) and shows a very close slope of the top surface to the required geometry. The resulted slope is 10.5 °, while the required slope is 10.0° after machining. A slight difference in slope angles can be compensated for with some minor trial in industry. Thus, the final process sequence design can be considered to be completed. 7. SUMMARY AND CONCLUDING REMARKS
The current five-operation cold forging process sequence is designed to a new process sequence. The newly designed sequence has four forming operations and one annealing treatment, and can achieve net-shape manufacturing, while the conventional process sequence has five forming operations and two annealing treatments, and requires machining after forming. The maximum die load involved in each operation is checked during the process sequence design. Based on the loading simulations of the conventional process sequence, some information useful in designing a new, improved process sequence is derived. An operation of closed die forging combined upsetting with backward extrusion is introduced as the second operation in the new process sequence, thus achieving removal of one annealing treatment in the conventional process. The refinement at the top surface of the product is made by applying the backward tracing scheme for the purpose of net-shape manufacturing. Based on the results of
1146
BEOM-Soo KANG and SHIRO KOBAYASHI
the backward tracing, new punch shape at the third operation of extrusion is designed. Finally, the loading simulations are carried out to confirm the design result based on the backward tracing procedure. A systematic approach to process sequence design is established by the finite element method for multi-operation cold forging to form a constant velocity joint housing. Both the loading simulation and the backward tracing by the rigid plastic finite element method provide useful information for designing a new process sequence. This specific case can be considered for application of the method and for development of the sequence design methodology in general. Future work of this investigation will be the actual application of the finally designed process sequence in industry. Further refinement of the die configurations and compensation of the approximation of three-dimensional deformation to axisymmetric metal flow must also be studied. Acknowledgements--The authors would like to thank the National Science Foundation for the grant DDM9101199 under which the present study was possible, and CRAY Research Inc. for the University Research and Development Grant Program which supported computation with a CRAY XM-P/25 supercomputer. The junior author would like to thank the Korea Science and Engineering Foundation for the grant 9230900-009-2. REFERENCES [1] S. KOBAYASHI,Plasticity and design in metal forming, Asia-Pacific Symposium on Advances in Engineering Plasticity and its Application, Hong Kong, December (1992). [2] B. S. KANG, Process sequence design in a heading process, J. Mater. Process. Technol. 27, 213-226 ( 1991 ). [3] G. D. LAHOTI, T. L. SUBRAMANIANand T. ALTAN, Development of computerized mathematical model for the hot/cold nosing of shells, Report ARSCD-CR-78019 to U.S. Army Research and Development Command, September (1978). [41 Y. MmARA and W. JOHNSON, Crop loss: front and back end deformation during slab and bloom rolling, Metallurgia Metal Forming 44, 332 (1977). [5] U. STAHLBERG,J-O. SODERBERGand A. WALLERO. Overlap at the back and front ends in slab ingot rolling, lnt.J.Mech.Sci.,23, 243-252 (1981). [6] V. GOPINArHAN, Optimum blank profile determination for rectangular deep drawing, Indian J. Technol. 15, 330-333 (1977). [7] H. GLOECKL and K. LANGE, Computer-aided design of blanks for deep drawing irregular-shaped components, Proc. l lth NAMRC, SME, p.243 (1983). [8] S. K. BISWAS and W. A. KNIGHT, Computer-aided design of axisymmetric hot forging processes, Proc. 15th Int. MTDR Conf. Birmingham, England, pp. 135-143, (1974). [9] N. AKGERMAN and T. ALTAN, Recent developments in computer-aided design of forging processes, SME Techn. Paper, no. 72-110, April (1972). [10] G. B. Yu and T. A. DEAN, A practical computer-aided approach to mould design for axisymmetric forging die cavities, Int. J. Mach. Tool Des. Res. 25, 1 (1985). [ll] K. LANGE and G. Du, A formal approach to designing forming sequences for cold forging, Proc. 17th NAMRC, SME, p. 17, (1989). [12] T. MAKI, Trends in forging technology in field of constant-velocity joint, JIDOSHA-GHUTSU (JSAE) 36, 898, (1982). [13] S. KOBAYASHI,S. I. OH and T. ALTAN, Metal Forming and the Finite Element Method, Oxford University Press, Oxford (1989). [14] J. J. PARK, N. REBELO and S. KOBAYASHI, A new approach to preform design in metal forming with the finite element method, Int. J. Mach. Tool Des. Res. 23, 71 (1983). [15] S. M. HWANG and S. KOBAYASHI,Preform design in plane-strain rolling by the finite element method, Int. J. Mach. Tool Des. Res, 24, 253 (1984). [16] S. M. HWANG and S. KORAYASHI, Preform design in disk forging, Int. J. Mach. Tool Des. Res. 26, 231-243 (1986). [17] S. M. HWANG and S. KOBAYASHI,Preform design in shell nosing at elevated temperatures, Int. J. Mach. Tools Manufact. 27, 1-14 (1987). [18] B. S. KANG, N. KIM and S. KOBAYASHI,Computer-aided preform design in forging of an airfoil section blade, Int. J. Mach. Tools Manufact. 30, 43-52 (1990). [19] N. KIM and S. KOBAYASHI, Preform design in H-shaped cross-sectional axisymmetric forging by the finite element method, Int. J. Mach. Tools Manufact. 30, 243 (1990). [20] B. S. KANG and S. KORAYASHI, Preform design in ring rolling by the three-dimensional finite element method, Int. J. Mach. Tools Manufact. 31, 139-151 (1991). [21 ] COMPANY,PROJECTTEAM OF IL-SHIN COLD FORGING, Cold forging process to form a C.V. joint housing, Summary Report, ll-Shin Cold Forging Company, Ltd., Changwon, Korea (1992). [22] B. S. KANG, B. M. KIM and J. C. CHOl, Preform design in extrusion by the finite element method and its confirmation, (accepted for publication J.Mater. Process. Technol. (1993).
Pergamon
0890--6955(93)E0015-W
PROCESS
SEQUENCE DESIGN IN COLD FORGING TO FORM A CONSTANT VELOCITY JOINT HOUSING BEOM-SOO KANGt a n d SHIRO KOBAYASHI:~
(Received September 1992; in final form November 1993) Abstract--A systematic approach to process sequence design is established by the finite element method for multi-operational cold forging to form a constant velocity joint housing. Both the loading simulation and the backward tracing by the rigid plastic finite element method provide useful information for designing new process sequences. The newly designed sequence has four forming operations and one annealing treatment, and can achieve net-shape manufacturing, while the conventional process sequence has five forming operations and two annealing treatments, and requires machining after forming. The refinement at the top surface of the product is made by applying the backward tracing scheme for the purpose of netshape manufacturing. This specific case can be considered for application of the method and for development of the sequence design methodology in general.
1. INTRODUCTION
THE FINITEELEMENTMETHODhas been widely used for simulating and analyzing various metal forming processes. One of the most practical applications of the finite element method to the metal forming industry is process sequence design in multi-stage forming processes. Design of the forming process involves the determination of number of preforms and the determination of the shapes and preform dimensions. The problem of process sequence design arises in many forming processes, such as forging, drawing, extrusion, rolling and sheet metal forming [1, 2]. The conventional approaches to the process sequence design have been empirical or based on approximate analysis and require extensive experience and expensive trial and error [3-7]. Several computeraided approaches have been proposed for preforms and sequence design for complex forging components [8-11]. One indispensable component of front-wheel drive compact cars is a constant velocity joint. The mass production of constant velocity joints at an economical cost has thus become an important issue for production engineering [12]. Constant velocity joints function to transmit the output power of the engine to the wheels. A constant velocity joint consists of a tulip shaft, a spider and a housing. The production of housings among the components by machining is difficult because of the irregular shape. There are two methods for mass production of the housing, hot forging and cold forging. The conventional hot forging process requires machining operations with an enormous number of man-hours. The cold forging process, however, makes it possible to produce net-shape housings without any machining after forming and saves 40% of materials. Even so, great effort in designing delicate process sequences is needed in the cold forging of net-shape housings. The process sequence design in cold forging of a constant velocity joint housing is investigated in this study by the rigid plastic finite element method. Here a forging
tDepartment of Aerospace Engineering, Pusan National University, Korea--Visiting Research Engineer, Department of Mechanical Engineering, University of California at Berkeley. ~:Professor Emeritus, Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, U.S.A. and 414 Sea View Drive, El Cerrito, CA 94530, U.S.A. 1133
1134
BEOM-SooKANGand SHIROKOBAYASHI unit : nun
,80.5
*55.0
I
(a) initialbillet
o I*27.5 ] (b) extrusion
(c) upsetting
(e) backwardextrusion 2
(f) ironing
%
1)backward extrusion 1
FIG. 1. Process description of five-operation cold forging to form a constant velocityjoint housing. process sequence with five operations, shown in Fig. 1, is designed to a new process sequence which can produce net-shape housings with minimum number of operations within a given press capacity. This study is an extension of the preform design using the rigid plastic finite element method and the backward tracing scheme, and one of the research series, "Process Sequence Design in Metal Forming". The rigid plastic finite element method has been used for process simulation, and the computational technique for the analysis of metal forming processes has been well established [13]. In the backward tracing procedure, the finite element method traces backward from the final specified configuration. The procedure has been applied to various problems in prior investigations. For the process sequence design, forward loading simulation and backward tracing by the use of the finite element method capabilities will be applied, which have proved to be powerful and effective for preform design in metal forming [14-20]. 2. PROCESS DESCRIPTION AND OBJECTIVE OF DESIGN An outline of the cold forging process for a constant velocity joint housing of axial symmetry is illustrated in Fig. 1 [21]. The first operation is forward extrusion with 75% area reduction, and the second operation is upsetting. Plastic instability may be involved in the upsetting operation if the forward extrusion is skipped. Fig. l(d) shows the third operation of backward extrusion, in which the maximum die load is critical to the fatigue life of punch owing to compression stresses. During this operation, the flow stress of the material becomes large and a great deal of compressive stress is applied to the tools. Thus it is essential to perform an appropriate heat treatment on the material so as to give it the degree of cold formability required
Process Sequence Design in Cold Forging
1135
for the processing operation. Another backward extrusion operation is shown in Fig l(e). Delicate design of the punch shape in the fourth operation is required to obtain dimensional accuracy of the final product. The shape of the punch used in the fourth operation, particularly the shape of the punch top, affects product functionality. The last operation involves ironing and bending, shown in Fig. l(f). The actual upper die consists of six radially segmented components around a central core, like the slices of an apple. Removal of the die from the final socket-shaped product is carried out by retracting the central core and collapsing the segments of the die inward. The objective of the study presented here is to design an appropriate reduced process sequence for the current five-operation process, with net-shape final products within die load capacity. A great deal of loading simulations by the rigid plastic finite element are carried out to obtain design information. Considerable remeshing work is expected during simulations since the process has multi-operations and deformation of the workpiece is complicated. Also the backward tracing scheme, in which the rigid plastic finite element method traces backward from the final specified configuration to a prior preforming configuration, will be applied to the final ironing and bending operation to obtain a preforming die configuration in the second backward extrusion. It is noted that the deformation mechanics involved in the final operation are not actually axisymmetric. This study, however, treats the deformation as an axisymmetric case since it has relatively small deviation from the actual case. The difference between axisymmetric and the actual process must be compensated in the final die design in industry. 3. METHOD OF APPROACH In the process sequence design for multi-stage forming operation, the forward loading simulations by the finite element method are performed mainly to obtain useful design information such as deformation characteristics, die load, and strain distribution. The rigid plastic finite element method for the analysis of metal forming processes has been well established, and the derivation and computation procedure for the rigid plastic finite element method are not repeated here. The information from backward tracing simulations as well as from forward loading simulations is essential for the refinement of product configuration. The backward tracing scheme will be applied to the final operation during this study of process sequence design. Similarly to forward simulation, the backward tracing method uses the finite element method. Backward tracing refers to the prediction of the part configuration at any stage in a deforming process, when the final part geometry and process conditions are given. The application of backward tracing is straightforward if the changes of the boundary conditions during a process are known. The boundary conditions are usually derived from the loading simulations of a trial preform, and modified slightly for backward tracing. This aspect of determining the boundary conditions during backward tracing is discussed in some detail in the later section. This multi-operational process involves complex plastic deformation during forming. Thus simulations by the finite element method have severe grid distortion for following the given process. In some cases, the simulation does not continue because of the negative Jacobian of four-node rectangular elements, and remeshing is essential for the study of process sequence design using the finite element method. The remeshing requires, in this study, reallocation of nodal points to avoid negative Jacobians and transfer of effective strain by linear interpolation. The material characteristic of the workpiece considered here is work-hardening, and the plastic deformation is influenced by the effective strain distribution of the workpiece. For remeshing, data such as coordinates of nodal points, strain distributions at the integration points of each element, die contact points, and force boundary conditions, are stored. New nodal points and connectivity matrices of elements are generated. The values of effective strain at integration points of each element are obtained by interpolation of the stored data, and die contact points and force boundary conditions are assigned in the new mesh system.
1136
BEOM-Soo KANG and SHIRO KOBAYASHI
The final operation of ironing and bending involves three-dimensional metal flow in the actual process, and the plastic deformation is not axisymmetric. As mentioned in the previous section the socket-shaped product is formed by special dies with six segments around a core. Assuming that the difference between the actual process and the related axisymmetric case is relatively minor, we consider an axisymmetric problem with a socket-shaped product. The maximum die load in the final operation is similar to the value of the actual case, but the top configuration of the product is influenced by the problem modification. When applying this result to die design in industry, some design modification will be performed to compensate the difference between the actual process and the simulated process. Here the study considers an axisymmetric top configuration for the numerical analysis. The workpiece material considered is a mild steel, AISI 1018, whose work-hardening characteristic is given by -6/Y = (1.0 + 50.0E) °-e64
where the initial yield strength Y is 362 MPa (0.037 ton/mm2). The work-hardening characteristic is implemented in the finite element program. The backward tracing simulations also use the same work-hardening effect. In the backward tracing (t ~< to), at time t = to-j = to - At, eo-1 should satisfy the following condition.
The die-workpiece interface condition is characterized by the friction law of constant factor, usually used for bulk metal forming problems, namely, "r=mk
Here, "r is the frictional shear stress, m the friction factor, and k the shear flow stress. The friction factor for the cold forging in this study is assumed to be 0.1. 4. FEM SIMULATIONSOF THE CONVENTIONAL PROCESS The conventional process sequence to form a constant velocity joint housing, shown in Fig. 1, is a classical expert's solution. It is designed within die load capacity and for near-net-shape products. The process sequence consists of five operations, which are forward extrusion, upsetting, two operations of backward extrusion, and ironing with bending. These simulation results are shown in Figs 2-6. Two hundred and eighty nodes, and 247 four-node elements are used for simulation. The first operation shown in Fig. 2 is forward extrusion. The area reduction is 75%. As shown in the simulation results, remeshing at the die stroke of 64% is carried out since the original mesh has negative Jacobian near the outlet of the container. The remesh work makes it possible to complete the simulation of the extrusion with 75% area reduction. The deformation pattern is typical in forward extrusion. The front end of the extruded workpiece has a blunt shape as studied in Ref. [22]. The distribution of effective strain and grid distortion at the finishing stroke are shown in Fig. 2(c). The maximum die load is 580 ton. The second operation is upsetting, and is shown in Fig. 3. The workpiece extruded in the first operation prevents plastic buckling, and thus enables one to complete the upsetting operation. The ratio of maximum area increase is 2,14 in the upper cylindrical part. This operation is a preparation for the next operation, the first backward extrusion. The simulation is stopped at the maximum die load of 780 ton, at which the filling of the die cavity is almost complete. After the upsetting operation, an annealing heat treatment is performed in industry. The effect of annealing treatment on the workpiece is reflected as strain-free material in the simulation by the finite element method. Figure 4 shows the third operation, namely, the first backward extrusion. Since the
Process Sequence Design in Cold Forging
1137
¢
f
(a)
1_.
(b)
(c)
FIo. 2. The first operation of forward extrusion: (a) initial set-up; (b) remeshing at the stroke of 64%; and (c) grid distortion and effective strain distribution at the end of the operation.
(a)
(b)
FIG. 3. The second operation of upsetting.
workpiece is annealed before the operation, the upset workpiece is considered to be in a state of zero-strain at the start of simulation. The initial mesh, shown in Fig. 4(a), is slightly altered from the distorted mesh of the second upsetting in Fig. 3(b). The punch with a sharp blunt at the central part is used in industry for centering the workpiece and for stabilizing the start of the operation. The grid distortion at the stroke of 42% (Fig. 4(b)), has a negative Jacobian of an element near the convex punch. The remeshed grid is used to finish the simulation after 42% die stroke. The operation is a preprocess to the second backward extrusion. The grid distortion and effective strain distribution are shown in Fig. 4(c). The work-hardening effect due to plastic strain is severe around the punch. The maximum die load at the end of the operation is 327 ton. The grid distortion pattern during the fourth operation is shown in Fig. 5. Before performing this operation, the workpiece is annealed again to obtain sufficient forinability. The heat treatment is the second annealing of the whole process, and is critical to produce a near-net-shape product. Another remeshing is performed at the stroke of 97%, shown in Fig. 5(b). The shape of the punch used in this operation,
BEoM-SOo KANGand Smao KOBAYASHI
1138
1.0 0.6
(a)
(b)
(c)
FIG. 4. The third operation of backward extrusion: (a) initial set-up; (b) step for remeshing; and (c) final deformation.
(a)
(b)
(c)
Fl~. 5. The fourth operation of backward extrusion: (a) intial set-up; (b) remeshing at the stroke of 97%; and (c) final deformation.
(a)
(b)
FiG. 6. The last operation of ironing: (a) initial set-up; and (b) final deformation. particularly the shape of the punch top, affects product functionality. Consequently, the degree of freedom for modifying the punch shape is severely limited. Thus, an attempt is made to redesign only the base counter of the punch to produce net-shape products without machining after forming. The deformation pattern at completion of
Process Sequence Design in Cold Forging
800
800,-
800 I
600 t
max.die load = 327 ton
600-
600 -
{ 400
400
200
200
ff 0
/
max. die load = 780 ton
max. die load = 580 ton
1139
20
40
60
80 100
y
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20
I
I
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60
400
200 I 80 i(J0
800 max. die load = 380 ton 600
800 r ] 600
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(c) backward extrusion 1
(b) upsetting
(a) extrusion
0
STROKE (%)
STROKE (%)
STROKE (%)
oV I
max. die load = 78 ton
0
400 ~-
"~ 400 < 200 0 0
20
40
60
80 100
0
20
40
60
80 100
STROKE (%)
STROKE (%) (d) backward extrusion 2
(e) ironing
FIG. 7. Load-stroke curves for the conventional five-operation process.
the operation is shown in Fig. 5(c). Through the operation, the maximum die load is 380 ton. The last operation is an ironing with bending. This operation requires minor plastic deformation. To produce the socket-shaped product, a special set of die components is used for easy die removal from the workpiece after the operation. One type of special upper die set consists of six radial segments around a central core, similar to the slices of an apple. The ring-type lower die moves upward while the upper die set is fixed. Thus the whole workpiece deforms radially inward and upward. Thus this operation can be called an ironing with bending. The initial set-up is shown in Fig. 6(a), and the final deformed product in Fig. 6(b). The die load during the operation is relatively small compared with those of the previous four operations. The maximum die load is 78 ton at the stroke of 53%. The whole process sequence includes five operations of a forward extrusion, an upsetting, two backward extrusions, and an ironing with radial bending, and two heat treatments of annealing. In industry, two annealing treatments require high cost of labor, energy and production time. Thus the reduction of the number of forming operations and heat treatments is a key factor in designing a new process sequence. The load-stroke curves for the five operations are shown in Fig. 7. The maximum die load through the whole process is 780 ton in the second operation of upsetting. 5. A NEW PROCESS S E Q U E N C E
A better process sequence should have fewer numbers of processes including annealing treatments, and produce net-shape products. First, we have to decide how MTM 34:8-G
1140
BEOM-SOOKANGand SHmoKOBAYASH!
to reduce the number of operations and heat treatments. The approach to net-shape manufacturing will be discussed later. Annealing is treated before each backward extrusion (the third and the fourth operations). Combining the two backward extrusion operations into one operation may be the simplest way of reducing the two heat treatments to one, and also may achieve reduction of one forming operation. The conventional process sequence, an expert's solution, however, has two distinct backward extrusions because of die load and nearnet-shape manufacturing. There seems to be a high possibility of achieving one backward extrusion operation, if it can produce fine and sound preform which will result in netshape manufacturing in the final ironing operation. For this purpose, the maximum die load of the operation should have enough margin of safety in view of the hydraulic press capacity of 1000 ton, and the plastic deformation involved in the backward extrusion should not be severe. Further, possibilities of combining upsetting with the first backward extrusion process and the second backward extrusion with the final ironing process can be considered. There is no possibility of combining the second backward extrusion with the ironing operation, since the two operations have very different deformation characteristics, and opposite directions of die movement. Considering a case of combining the upsetting operation with the first backward extrusion, two operations have similar metal flow during plastic deformation, and the same direction of die movement. It appears possible that upsetting with the backward extrusion may be carried out by designing a new punch. The punch shape should be in-between the two punch shapes of upsetting and backward extrusion, so that the same deformation effects such as upsetting and backward extrusion can be achieved. Based on the argument presented above, a new process sequence is designed and shown in Fig. 8 as a four-operation process. This process requires one heat treatment before backward extrusion. Thus the new process consists of four forming operations and one annealing treatment. The first operation, forward extrusion, in the new process is the same as in the conventional process sequence, and the deformed configuration after the first operation is shown in Fig. 8(b). Figure 8(c) shows a newly designed operation, which is called a closed die forging and combines upsetting with backward extrusion. The punch has a spherical shape at the center and fiat peripheral part for upsetting. The purpose of the sharp blunt at the center is to stabilize the initiation of deformation. The simulation of this process is shown in Fig. 9. Jacobian is negative near the spherical part of the punch at the stroke of 78%, and remeshing is necessary for complete simulation. The grid distortion and effective strain distribution are shown in Fig. 9(c). The maximum die load is 850 ton at the end of the operation. Since this is not a finishing operation, forging is not necessary for complete filling. A small cavity is shown at the intersection between the fiat part and the spherical part of the punch. The third operation in the new process sequence shown in Fig. 8(d) is a backward extrusion. Simulation of the process is shown in Fig. 10. The die set used in this operation is the same one as the fourth operation in the conventional process, and the deformation pattern is also very similar. The workpiece is assumed to be strain-free at the start of deformation because of the annealing. The remeshed grid pattern at the die stroke of 36% is in Fig. 10(b), and the final deformation is shown in Fig. 10(c). The maximum die load is 550 ton, which is larger than the value of the fourth operation in the conventional process by 170 ton, but well within the press capacity of 1000 tons. The results of simulation of the last operation are shown in Fig. 11. This operation is exactly the same as the last operation of the conventional process (Fig. 6), except that the workpiece configurations are slightly different. The load-stroke curves for each operation in the new process are shown in Fig. 12. There is no significant peak of die load. Now the process sequence with four forming operations and one heat treatment is established for production of a sound product within the capacity of the available press. However, the net-shape manufacturing of the final product of geometrically accurate shape still remains to be solved.
Process Sequence Design in Cold Forging
1141
unit : mm
f
(a) initial billet
(b) extrusion
(d)backward extrusion
°80.5
I~
(c)closed die forging(upsetting)
(e)ironing
Fro. 8. Process description of the new forming sequence.
-N
\
(a)
(b)
(c)
FIG. 9. The second operation of closed die forging in the new process.
1142
BEOM-SOo KANG and SHIRO KOBAYASHI
(a)
(b)
(c)
FI~. 10. The third operation of backward extrusion in the new process.
1.1
(a)
(b)
(c)
Fic. 11. The last operation of ironing with radial bending in the new process. 6. FINAL PROCESS SEQUENCE DESIGN USING THE BACKWARD TRACING SCHEME
For net-shape manufacturing the geometrical configuration of top surface in the final product, especially the slope angle shown by a solid line in Fig. 13, is required. In the conventional process, the required slope is obtained by machining after forming. The top surface configuration in the product formed by the new four-operation process is also shown in Fig. 13 by a dotted line, and the slope angle obtained is 16.1 ° while the angle in a real product after machining is 10.0°. In order to produce a final product with 10.0 ° slope on the top surface, it is necessary to design a proper preform before the final forming operation. The procedures of preform design to obtain an appropriate slope are as follows. First, a preform shape is obtained by applying the backward tracing scheme to the finishing operation, ironing with bending. Based on the preform shape, the shape of the punch in the third operation, backward extrusion, is redesigned. Loading simulations using the new punch shape in the backward extrusion and in the finishing operation are carried out to confirm the design result by backward tracing simulations. For the use of the backward tracing scheme, the top surface of the final product obtained in the new process (see Fig 11(c)) is modified to have a 10° slope as shown by the solid line in Fig. 13. This is achieved by changing corresponding nodal coordinates in the result of the new process, and thus, has the effect of adding a small amount of material. The effective strains at the nodal points are assigned the same values before modification. In the application of the backward tracing procedure to this problem, the boundary
Process Sequence Design in Cold Forging 1000
1000
max.die load= 580 ton
max. die load = 850 ton
750
750 0
O
5OO
S
500 < O ,d
250 0 0
250 0 0
20 40 60 80 100 STROKE (%) (a) extrusion
1000
1000
max.die load= 550 ton
max.die load= 110 ton
75O
Q
,..2
20 40 60 80 100 STROKE (%)
(b) closed die forging (upsetting)
750 r~ < ©
1143
o
500
r~ <
250
500 25O
~ 1 1 l I 0 20 40 60 80 100 STROKE (%)
0 0
(c) backward extrusion
20 40 60 80 100 STROKE (%) (d) ironing
FIG. 12. Load-stroke curves for the new four-operation process.
0p16.1 o
02=10.0°
FIG. 13. Modified configuration (solid line) for the application of backward tracing (dotted line; the configuration before modification). c o n d i t i o n s a r e c o n t r o l l e d in s u c h a w a y t h a t t h e p r e f o r m s h a p e a f t e r c o m p l e t i o n o f b a c k w a r d t r a c i n g b e c o m e s t h e s a m e as t h e p r e f o r m b e f o r e m o d i f i c a t i o n e x c e p t t h e t o p s u r f a c e c o n f i g u r a t i o n . T h e s m a l l a m o u n t o f m a t e r i a l a d d e d to m a k e 10 ° t o p s u r f a c e s l o p e d o e s n o t a f f e c t t h e d e f o r m a t i o n o f t h e o t h e r p a r t , since t h e a d d e d m a t e r i a l d e f o r m s o n l y by r a d i a l b e n d i n g . T h e c o n t a c t n o d a l p o i n t s to t h e d i e s in b a c k w a r d
1144
BEOM-SOo KANG and SmRO KOBAYASHI
tracing should follow the boundary conditions obtained from forward loading simulations. These are shown in Fig. 14(a) and (b). Fig. 14(a) displays the contact angle to the die 1 according to the stroke of the die 2 during backward tracing simulation. During the loading simulation, die 1 is stationary and the die 2 moves upward. In backward tracing, die 2 moves downward, and the contact angle of the workpiece to die 1 decreases. The movement of die 2 can be indicated by the mean height of the die and contact area to the workpiece, as shown in Fig. 14(b). The boundary conditions during backward tracing are based on the results in the previous forward loading simulations. The backward tracing simulations for the last operation are shown in Fig. 15. The initial set-up for backward tracing is shown in Fig. 15(a), and the workpiece contour is modified according to that shown in Fig. 13. Figure 15(b) shows backward tracing simulation at 46% stroke of die 2. The preform finally derived from the backward tracing is given in Fig. 15(c). The preform shape and effective strain distribution are almost the same as those in the process, Fig. 10(c), except the configuration of top surface. The resulted configuration shows that the outward radial slope of the top surface is 12.2 ° and provides the punch shape in the third operation of backward extrusion.
135
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90
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_~ 45 O=contac* ,e
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0
q
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1 80
100
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125
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~3 2
75
~
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(b) FIG. 14. Boundary conditions during the backward tracing simulation: (a) contact angle to die 1; and (b) contact location and area to die 2.
Process Sequence Design in Cold Forging
(a)
(b)
1145
(c)
FIG. 15. Backward tracing simulation for ironing: (a) initiation of backward tracing; (b) 46% stroke of backward tracing; and (c) result of complete backward tracing.
10.5°
(a)
(b)
(c)
FIG. 16. Loading simulations of the backward extrusion and the ironing with bending in the finally designed process. (a) backward extrusion; (b) ironing and bending; and (c) configuration of the final product.
Since the deformed workpiece, Fig. 16(a), is based on the result of backward tracing, it is desirable to confirm that this preform results in the desired final product by performing loading simulation of the last operation. This loading simulation is shown in Fig. 16(b). The workpiece contour obtained here is displayed in Fig. 16(c) and shows a very close slope of the top surface to the required geometry. The resulted slope is 10.5 °, while the required slope is 10.0° after machining. A slight difference in slope angles can be compensated for with some minor trial in industry. Thus, the final process sequence design can be considered to be completed. 7. SUMMARY AND CONCLUDING REMARKS
The current five-operation cold forging process sequence is designed to a new process sequence. The newly designed sequence has four forming operations and one annealing treatment, and can achieve net-shape manufacturing, while the conventional process sequence has five forming operations and two annealing treatments, and requires machining after forming. The maximum die load involved in each operation is checked during the process sequence design. Based on the loading simulations of the conventional process sequence, some information useful in designing a new, improved process sequence is derived. An operation of closed die forging combined upsetting with backward extrusion is introduced as the second operation in the new process sequence, thus achieving removal of one annealing treatment in the conventional process. The refinement at the top surface of the product is made by applying the backward tracing scheme for the purpose of net-shape manufacturing. Based on the results of
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BEOM-Soo KANG and SHIRO KOBAYASHI
the backward tracing, new punch shape at the third operation of extrusion is designed. Finally, the loading simulations are carried out to confirm the design result based on the backward tracing procedure. A systematic approach to process sequence design is established by the finite element method for multi-operation cold forging to form a constant velocity joint housing. Both the loading simulation and the backward tracing by the rigid plastic finite element method provide useful information for designing a new process sequence. This specific case can be considered for application of the method and for development of the sequence design methodology in general. Future work of this investigation will be the actual application of the finally designed process sequence in industry. Further refinement of the die configurations and compensation of the approximation of three-dimensional deformation to axisymmetric metal flow must also be studied. Acknowledgements--The authors would like to thank the National Science Foundation for the grant DDM9101199 under which the present study was possible, and CRAY Research Inc. for the University Research and Development Grant Program which supported computation with a CRAY XM-P/25 supercomputer. The junior author would like to thank the Korea Science and Engineering Foundation for the grant 9230900-009-2. REFERENCES [1] S. KOBAYASHI,Plasticity and design in metal forming, Asia-Pacific Symposium on Advances in Engineering Plasticity and its Application, Hong Kong, December (1992). [2] B. S. KANG, Process sequence design in a heading process, J. Mater. Process. Technol. 27, 213-226 ( 1991 ). [3] G. D. LAHOTI, T. L. SUBRAMANIANand T. ALTAN, Development of computerized mathematical model for the hot/cold nosing of shells, Report ARSCD-CR-78019 to U.S. Army Research and Development Command, September (1978). [41 Y. MmARA and W. JOHNSON, Crop loss: front and back end deformation during slab and bloom rolling, Metallurgia Metal Forming 44, 332 (1977). [5] U. STAHLBERG,J-O. SODERBERGand A. WALLERO. Overlap at the back and front ends in slab ingot rolling, lnt.J.Mech.Sci.,23, 243-252 (1981). [6] V. GOPINArHAN, Optimum blank profile determination for rectangular deep drawing, Indian J. Technol. 15, 330-333 (1977). [7] H. GLOECKL and K. LANGE, Computer-aided design of blanks for deep drawing irregular-shaped components, Proc. l lth NAMRC, SME, p.243 (1983). [8] S. K. BISWAS and W. A. KNIGHT, Computer-aided design of axisymmetric hot forging processes, Proc. 15th Int. MTDR Conf. Birmingham, England, pp. 135-143, (1974). [9] N. AKGERMAN and T. ALTAN, Recent developments in computer-aided design of forging processes, SME Techn. Paper, no. 72-110, April (1972). [10] G. B. Yu and T. A. DEAN, A practical computer-aided approach to mould design for axisymmetric forging die cavities, Int. J. Mach. Tool Des. Res. 25, 1 (1985). [ll] K. LANGE and G. Du, A formal approach to designing forming sequences for cold forging, Proc. 17th NAMRC, SME, p. 17, (1989). [12] T. MAKI, Trends in forging technology in field of constant-velocity joint, JIDOSHA-GHUTSU (JSAE) 36, 898, (1982). [13] S. KOBAYASHI,S. I. OH and T. ALTAN, Metal Forming and the Finite Element Method, Oxford University Press, Oxford (1989). [14] J. J. PARK, N. REBELO and S. KOBAYASHI, A new approach to preform design in metal forming with the finite element method, Int. J. Mach. Tool Des. Res. 23, 71 (1983). [15] S. M. HWANG and S. KOBAYASHI,Preform design in plane-strain rolling by the finite element method, Int. J. Mach. Tool Des. Res, 24, 253 (1984). [16] S. M. HWANG and S. KORAYASHI, Preform design in disk forging, Int. J. Mach. Tool Des. Res. 26, 231-243 (1986). [17] S. M. HWANG and S. KOBAYASHI,Preform design in shell nosing at elevated temperatures, Int. J. Mach. Tools Manufact. 27, 1-14 (1987). [18] B. S. KANG, N. KIM and S. KOBAYASHI,Computer-aided preform design in forging of an airfoil section blade, Int. J. Mach. Tools Manufact. 30, 43-52 (1990). [19] N. KIM and S. KOBAYASHI, Preform design in H-shaped cross-sectional axisymmetric forging by the finite element method, Int. J. Mach. Tools Manufact. 30, 243 (1990). [20] B. S. KANG and S. KORAYASHI, Preform design in ring rolling by the three-dimensional finite element method, Int. J. Mach. Tools Manufact. 31, 139-151 (1991). [21 ] COMPANY,PROJECTTEAM OF IL-SHIN COLD FORGING, Cold forging process to form a C.V. joint housing, Summary Report, ll-Shin Cold Forging Company, Ltd., Changwon, Korea (1992). [22] B. S. KANG, B. M. KIM and J. C. CHOl, Preform design in extrusion by the finite element method and its confirmation, (accepted for publication J.Mater. Process. Technol. (1993).