E L S E V I E R Journal of Materials Processing Technology 58 (1996) 174 183

Journal of

Materials Processing Technology

Process design in multi-stage cold forging by the finite-element method

Jin-Hee Lee a Beom-Soo Kang a,*, Jung-Hwan Lee b ~' ERC,/or Net Shape and Die Manujacturmg, Pusan National University, Pusan 609-735, South Korea

b Korea Institute of Machineo' and Metals', Changwon, Kyungnam 641-010, South Korea

Received 6 December 1994

Industrial summary

In this work, a process sequence for multi-stage cold forging is designed with the rigid-plastic finite element method to form a constant-velocity joint (CVJ) housing with shaft. The material flow during the forming of a CVJ housing is axisymmetric until the final forging process for the forming of the ball grooves. The numerical approach in this study treats the deformation as an axisymmetric case. The main objective of the process-sequence design is to design preforms which satisfy the design criterion of a near-net-shape product requiring less machining after forming without any defects. It also included investigation of velocity distributions, effective strain distributions, and forging loads, which are useful information in process design. A systematic approach to process-sequence design is established using the finite-element method for the cold forging of the CVJ housing.

Keywor&': Process design; Cold forging; Finite-element method

1. Introduction

Near-net-shape or net-shape manufacturing is be- coming a trend in metal forming, especially in cold forging, resulting in savings in material, energy and machining requirements. Cold forging maintains strength, dimensional and surface-finish specifications. In practice, however, cold forging requires several pre- forming operations to transform an initial simple billet into a final complex product without defects. The design of a forging-process sequence involves the deter- mination of the number of preforms, and the determi- nation of the shapes and preform dimensions. The proper design of preforming operations to achieve an adequate material distribution is one of the most im- portant aspect in cold-forging processes. Traditionally, forging-sequence design is carried out using mainly empirical guidelines, experience and trial-and-error, which results in a long time for process development, and high cost of the products [1 3].

Computer-aided simulation techniques in metal forming before actual tryout may reduce the cost and time of process design. Many computer-aided ap- proaches based on approximate analysis and empiri- cally-established design rules have been published in the literature [4-9]. These techniques do not always

* Corresponding author.

Elsevier Science S.A. SSD1 0924-0136(95)02093-2

provide detailed information concerning the mechanics of the process. On the contrary the finite-element method has been proven to provide more accurate and detailed information, and is thus widely used for simu- lating and analyzing various metal-forming processes. Amongst various applications of the finite-element method in the metal-forming industry is practically one of the most important process-sequence design in multi- stage forming processes [10-19].

The production quantity of constant-velocity joints, which are indispensable for front-wheel-drive cars, has been increasing. The mass manufacturing of constant- velocity joints at an economical cost has thus become an important issue for production engineering. Con- stant-velocity joints are employed for torque transfer between the gear and the drive wheels, in which the steering and the suspension movements of the wheels must be followed simultaneously. A constant-velocity joint consists of a spider, an inner race and a housing with a shaft. Amongst the components, the production of the housing by machining is difficult because of its irregular shape. There are two methods for the mass production of housings, i.e., hot forging and cold forg- ing. The conventional hot-forging process requires sub- sequent machining operations involving an enormous number of man-hours. The cold-forging process, how- ever, makes it possible to produce net-shape housings without any machining after forming, and effects save

J.-H. Lee et al./Journal of Materials Processing Technology 58 (1996) 174 183 175

Frezvq

~ ~ upsetting backward V ~ -- ~extrusi°n , Annea in

initial forward ~ ~ deep backward bil let extrusion extrusion ironing

c losed die forging

Fig. 1. Suggested processes of cold forging to form a constant-veloc- ity-joint housing [19.23].

material of up to 40%. However, great efforts in design- ing a delicate process sequence are needed in cold forging of the net-shape housings [20-22].

In this study, the process sequence in the cold forging of a constant-velocity joint (CVJ) housing with a shaft has been investigated and designed using the rigid- plastic finite-element method. The cold forging process- sequence to form the CVJ housing consists of four operations: forward extrusion, closed-die forging, deep backward-extrusion, and ironing. Here the practical problems of the deformed shape of the cup opening, the slope angle, the press capacity, and surface cracking are considered, and a forging process-sequence is designed which can produce a net-shape housing without defects within a given press capacity. The information obtained from the finite-element simulation, including the shapes of preforms, effective strains, velocity fields, and die load, is utilized in designing the new process sequence.

2. Process description and modeling

Fig. 1 is a schematic drawing showing the suggested processes of cold forging for a CVJ housing with axial symmetry [19,23]. Process sequence I in Fig. 1 is a classical expert's solution [23]. The cylindrical billet is extruded forwards to form a shift in the first operation, and upset in the second operation. The head is com- pressed by closed-die forging to form a flange with a radius approaching the outer diameter of the cup. After

annealing, so as to give the preform the required degree of cold formability, the third operation of backward extrusion is performed. During the 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 another annealing heat-treatment on the preform (resulting from the third operation). The fourth operation is deep backward-extrusion. Pre- cise design of the punch and die shape is required in order to obtain the required dimensional accuracy of the final product. The part formed by the fourth opera- tion has a shape close to the finished product, but it is required to form the cup opening with the prescribed dimensional accuracy. Usually an ironing operation with axial bending is carried out as the last operation. The actual punch in the ironing operation consists of six radially-segmented components, 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 inwards.

Fig. 2 shows the simulation results by Kang and Kobayashi [19] to form a CVJ housing according to the expert's solution of case I in Fig. 1. The possibility of cold forging for this CVJ housing using a new process- sequence has been suggested. By combining the upset- ting with the backward-extrusion of case I, a new process sequence is obtained with four forming opera- tions and one annealing treatment, shown in Fig. 1 as case II.

In this study, a process sequence of multi-stage cold forging of a CVJ housing is designed by the rigid-plas- tic finite-element method according to case II.

The dimensions and configurations of the initial billet and the final cold-forged CVJ housing product are illustrated in Fig. 3.

The material flow during forging of the CVJ housing is axisymmetric before the deep backward-extrusion: the flow then becomes three-dimensional. As mentioned above, the socket-shaped product is formed by special dies with six segments around a core. Assuming that the difference between the actual three-dimensional pro- cess and the axisymmetric case is relatively minor, it is possible to consider the deformation of CVJ housing as

1 Fig. 2. Results of simulations of the conventional five-operation process [19].

176 J.-H. Lee et al . / Journal of Materials Processing Technology 58 (1996) 174 183

(Unit : m m )

I i

[

i q

I

I i

I

_ ~so.0

\ " - i oi

& (a) (b)

Fig. 3. Dimensions and configurations of the CVJ housing: (a) initial billet; (b) final product.

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 cup-opening configuration of the product is influenced by the mod- ification. When applying this result to die design in industry, slight design-modification will be performed to compensate for the difference between the actual process and the simulated process.

Although three-dimensional finite-element-based codes enable the modeling of large plastic deformation [24], three-dimensional modeling is still much too com- plicated and time consuming for industrial application. Considering an axisymmetric cup configuration, the simulations are performed with the two-dimensional rigid-plastic finite-element method that can give sound results for the material flow in the CVJ housing forging.

The fundamental of the rigid-plastic finite-element method and the mathematical formulation are well established and given in the literature [25,26]. The material used for the simulations is a mild steel, AISI 1018, with the following flow-stress behavior: ~ = 0.037(1.0 + 50.0g) T M tonne/mm 2 (1 tonne mm 2). The die-workpiece interface is characterized by the con- stant-factor friction law, usually used for bulk metal- forming problems: r = m k . Here, r is the frictional shear stress, m is the friction factor, and k is the shear flow stress.

The friction factor in this study is assumed to be 0.1 which is suitable for cold-forging processes. During the simulations the mesh is distorted severely, and thus should be remeshed to avoid negative Jacobians and to

assign new effective strains at the nodal points by linear interpolation. The press capacity is limited to 1000 tonne in respect of the actual press capacity in industry.

3. Simulation results and discussion

A process sequence for the multi-stage cold forging of a CVJ housing is simulated according to the process of case II in Fig. 1. The main objective of the process- sequence design in this study is to obtain intermediate preforms which produce a near-net-shape product. Also design conditions, such as the limit of the press capacity and the avoidance of surface cracking, should be sa- tisfied.

The first operation shown in Fig. 4 is forward extru- sion to form the shaft of the CVJ housing. The reduc- tion of area in the extrusion is 64% and the semi-cone angle of die is 35.5 ° . This extrusion is in preparation for the next operations. Figs. 4(a)-(c) show the initial mesh, the deformed grid distortion at punch stroke of 60%, and the final grid distortion with the effective strain distribution. The extrusion operation was stopped when the extruding part was of the same final dimensions as the shaft part of the CVJ housing.

The maximum extrusion load is 270 tonne, which is within the press capacity of 1000 tonne. High effective strains appear in the outside part of the extruded shaft, whilst the workpiece in the container virtually does not deform.

The simulation of the second operation is shown in Fig. 5, which is called a closed-die forging, and com- bines upsetting with the backward extrusion of the conventional process sequence (see case I in Fig. 1).

Due to negative Jacobians resulting from severe mesh distortion near to the part contacting with the punch, two remeshings are required to complete the simulation up to the die-filling stage. The number of nodes and elements decrease slightly for each remeshing because a coarser mesh is used in the shaft part. Fig. 5(a) shows the preform after forward extrusion and the grid distor- tion at a punch stroke of 88% whilst Fig. 5(b) shows the grid distortion and the effective-strain distribution at the end of the second operation. The maximum forging load is 850 tonne: it is possible to reduce the forging load by controlling the punch stroke in the closed-die forging. Thus, the punch stroke at the finish- ing step lies within the available press capacity. Since this second operation is not a finishing operation and does not influence significantly the shape of the final product, complete filling is not required: A small cavity appears at the corner between the flat part and spheri- cal part of the punch. The preform obtained from the second operation is assumed to be satisfactory as preparation for the next operation. The preform is called Preform PCDF, having the dimensions shown in

J.-H. Lee et al./ Journal of Materutls Processing Technology 58 (1996) 174 183 177

_d- -t_

Die s e m i - a n g l e : 35.50 R e d u c t i o n of a r e a : 64%

(a ) (b) (e)

Fig. 4. Simulation of forward extrusion: (a) initial billet; (b) stroke of 60%; and (c) final deformation and effective-strain distribution.

Fig. 5(c). The high value of effective strain near to the punch tip reflects severe plastic deformation, as shown in Fig. 5(b). In the next operation of deep backward-extrusion, mainly the upper part of Y-shaped Preform PCDF deforms. Complete filling in this opera- tion can cause the final forging load exceeding the press capacity so that the upsetting operation is stopped before complete filling. It is necessary that the preform be annealed to obtain sufficient formability prior to deep backward-extrusion. Since the annealing treat- ment of the workpiece means a strain-free state in simulation using the finite-element method, Preform PCDF is considered to be in the state of zero-strain at the start of the next simulation. Remeshing is carried out again for simulation of the next operation (see Fig. 5(c)).

Fig. 6 shows the die configuration designed for the following deep backward-extrusion process, hereinafter the process being referred to as backward extrusion.

In this operation, the dies are designed carefully, since the backward-extrusion process affects, directly, the precision forming of the final product. In order to obtain the net-shape final product, the preform from the backward extrusion should be formed soundly and precisely before being used in the last operation, an ironing process.

Fig. 7 shows the dies for ironing which is conducted by covering the male die of ball groove shape with the workpiece and having the female die extrude the outer rim of the workpiece upwards with bending.

When investigating the effects of the preform shape derived from the backward extrusion on the forming of

the final product, it would be helpful to be able to obtain some knowledge of the metal flow involved in the backward extrusion. Simulations are conducted us- ing the trial dies with punch I and die I, as shown in Fig. 6(a). The simulation results of the backward extru- sion and the last operation of ironing process appear in Figs. 8(a) and (b), respectively.

The left side of Fig. 8(c) displays the velocity field of the preform (Preform PDBE-I) after the third opera- tion, and the right side of the figure describes the final product, with dimensions, after the ironing operation. As shown in Fig. 8(b), the top surface of the cup opening in the final product is not in close contact with the punch after ironing, which indicates that sound and precise forming at the top surface is not achieved. The undesirable forming at the top surface can be assumed to occur for the reason that an excessive amount of material deforms radially outside at the top part in the backward extrusion, as shown in the right side of Fig. 8(a). During the ironing operation, the thickness of the cup bottom becomes less than that of Preform PDBE-I. The dimensions in Fig. 8(c) differ from those of the real product of the CVJ housing (see Fig. 3(b)). The slope angle of the cup opening in the simulation is 33 ° , whilst the angle in the real product is 25 ° .

The most stringent forging operation amongst all the operations is the third operation. Surface cracks may appear in the forming material near to the cup bottom along the direction of the circumference. Fig. 9 shows the relationship between the crack generation during forging and the thickness of the cup bottom in the case of CVJ forming with carbon steel [22].

178 J.-H. Lee et al./Journal of Materials Processing Technology 58 (I996) 174 183

( U n i t : r a m )

2 2! '5

1.51 2.0

2 (

~,o

P r e f o r m PCDF

~95.0

~40.0

(~) (b) (e)

Fig. 5. Simulation of closed-die forging: (a) initial set-up and stroke of 88%; (b) final deformation and effective-strain distribution; and (c) dimensions of Preform PCDF.

( U n i t : m m )

(a ) (b ) (c )

PUNCII I PUNCll II PUNCH III

"-.j/N/A ~, "1 '5.

DIE I DIE II

Fig. 6. Dimensions and configurations of the dies for deep backward-extrusion.

J.-H. Lee et al./Journal of Materials" Processing Technology 58 (1996) 174-183

(Unit : m m )

]

DI E

11:3R ]~ 1 . ~ ¢ a 6 . 0

Before i ron ing

PUNCII

~- 2~ DIE

F During i ron ing

Fig. 7. Dimension and configuration of the dies for the ironing process.

The value calculated by the dimensions in Fig. 8(c) is plotted as point A in Fig. 9, indicated to be inside the danger zone where surface cracks may occur. This is caused by a large amount of deformation being concen- trated in the cup-bottom area of the forging. Based on the simulation results, the preform derived from the backward extrusion influences the final product signifi- cantly. Especially, the control of the material flow near to the cup opening affects the configuration of the final product critically. In order to obtain the same dimen- sions of the cup bottom and the same slope angle, and to fill the undeformed part near to the cup opening, the

179

75.0

70.0

65.0

+~ 60.0

" 55,0 Q)

O >~ 50.0

0.0 0.0

DANGER ZONE aJ C /

/

/ SAFE ZONE / / / /

l/ lo'.o 1 .o 14'.o Bot tom t h i c k n e s s ( r a m )

16.0

Fig. 9. Forming limit for surface cracks in the inner surface near to the cup bottom [22].

height and corner radius of the punch are reduced compared to those of punch I. The newly designed punch is shown in Fig. 6(b) and is called punch II, based on the previous discussion.

Fig. 10 shows the simulation results using the die set of punch II and die I, the third operation being shown in Fig. 10(a), and the last ironing operation in Fig. 10(b). Also, Fig. 10(c) shows the velocity field of the preform (Preform PDBE-II) formed in the third opera- tion and the dimensions of the final product formed in the last operation.

For the case using Preform PDBE-II, the amount of material flow into the top part is reduced in comparison with the case of Preform PDBE-I. The deformation of

(Unit : ram)

undes i rab le fo rma t ion

• i

(a) (b) (c)

Fig. 8. Simulations of deep backward-extrusion using the dies in Fig. 6(a) and the ironing process.

180 J.-H. Lee et al./Journal of Materials Processing Technology 58 (1996) 174-183

(Unit : ram)

Preform _ 3 o ' ~

(a) (b) (c)

Fig. 10. Simulations of deep backward-extrusion using the dies in Fig. 6(b) and the ironing process.

the inward cup opening is almost complete and the configuration of the final product in Fig. 10(c) is far more desirable than the final configuration using Pre- form PDBE-I: however, it still does not satisfy the dimensions of the cup bottom thickness and slope angle of the CVJ housing. A surface crack does not appear in the forming material, the latter being represented by point B in Fig. 9.

An attempt has been made to redesign the dies to produce net-shape products without machining after forming. Fig. 6(c) shows the finally-designed die set consisting of punch III and die II for deep backward- extrusion, the design of the die set reflecting the simula- tion results in Fig. 10.

The left side of Fig. l l (a) shows the simulation results of the third operation using the die set in Fig. 6(c), where the backward extrusion is carried out up to

the stage when the inside punch is filled completely. Three stages of the last operation of ironing are shown in the right side of Fig. l l(a) (c).

As shown in the right side of Fig. 1 l(c), there is no undeforming part, but the final dimensions are not the same as those of the product in Fig. 3(b). The slope angle of the cup opening is 29 ° , which is larger than the desired angle, but no surface cracks occur near to the cup bottom: point C in Fig. 9. The maximum die load in the backward extrusion is 1500 tonne at the final stage with completion, which will be shown later in Fig. 15(c). Because the available press capacity is 1000 tonne, the process should be modified to reduce the maximum die load. The present preform does not de- form satisfactorily with respect to all of the final crite- ria. The dimensions of the final product, however, are similar to those of the real product. Thus, a slight

(Unit : mm)

(a) (b) (c)

Fig. 11. Simulations of deep backward-extrusion using the dies in Fig. 6(c) and the ironing process where the punch stroke is 100%.

• u n l i l l e d

eavity

ro,orm =:

J.-H. Lee et al./Journal of Materials Processing Technology 58 (1996) 174-183 181

(a) (b) (e)

Fig. 12. As for Fig. 11, but for a punch stroke of 95%.

modification of the preform is made to keep the maxi- mum die load during backward extrusion below 1000 tonne and to obtain dimensions identical to those of the real product. In comparison with the real product in Fig. 3(c), it is necessary to increase the cup bottom thickness by 0.9 mm and to decrease the amount of material which contributes to the formation of the slope angle. For these purposes, the simulation of back- ward extrusion is stopped at the stage when the punch stroke is less than 100%, and the derived preform is used for the ironing process. The dies in Fig. 6(c) are used without modification during deep backward-extru- sion. It is possible to maintain the forging load within the press capacity because the load increases rapidly near the end stroke.

Fig. 12 shows the simulation of backward extrusion to a punch stroke of 95%, the darkened area in Fig. 12(c) indicating an unfilled cavity of very small volume.

The ironing operation is carried out using the preform (Preform PDBE-III) in Fig. 12(c), as shown in Fig. 13. Fig. 14(a) shows the velocity field and the effective- strain distribution after deep backward-extrusion, and Fig. 14(b) the dimensions and the effective-strain distri- bution of the final product.

As shown in the shape and velocity field of Preform PDBE-III, the material flow towards the outside of the cup opening is smaller than that in the previous cases. The maximum effective strain occurs near to the cup bottom, as displayed in Fig. 14(a). Therefore, it is known that should a surface crack occur, it will be located near to the cup bottom. Also, an undeformed part does not appear near to the cup opening, and the cup bottom thickness remains unchanged during the ironing process. The outside surface of the cup is deformed mainly by the ring-typed die in the ironing process. The dimensions of the final product in Fig.

(a) (b) (c)

Fig. 13. Simulation of the ironing process using Preform PDBE-III.

L,

182 J.-H. Lee et al. ,/'Journal of Materials Processing Teehnology 58 (1996) 174 183

(Unit : mm)

Preform PDBE-III

0.2

~'~ 0.~

¢i

0.8 o.

I

(a) (b)

Fig. 14. Showing: (a) distributions of effective strains for Preform PDBE-III; and (b) the final product.

500

400

o 300

< C~ 200

I00

%

1800

~ 120C

ooc

4OO

1000

0 o o i ~

60b [

~ 4 0 0

2oo / / / ~ /

' ' o' co ' o ' ' o' ' 20 40 6 100 20 40 6 80 100

STROKE(%) STROKE(Z) (~) (b)

500 [

400F

~o~ 3o0

200

, 0 0

o 2o 40 60 8o l oo 20 40 60 8o 1o0

STZ~OKE(~) STROKE(%) (c) (d)

Fig. 15. Load-stroke curves for the four-operation process: (a) extrusion; (b) closed-die forging; (c) deep backward-extrusion using the dies in Fig. 6(c); and (d) ironing.

14(b) are almost the same as those of the real product of the CVJ housing. The slope angle obtained in 25 °, which can be considered as almost the same as that in the real product. Also, a surface crack does not occur, as indicated by point D in Fig. 9.

The load-s t roke curves during the four operations for the cold forging of the CVJ housing are displayed in Fig. 15.

Point B in Fig. 15(c) is the maximum load of 980 tonne for backward extrusion when the punch stroke is

95%. The criterion for press capacity is thus satisfied throughout all of the forming operations.

4. Conclusions

A process sequence for the multi-stage cold forging of a CVJ housing with a shaft has been designed by the rigid-plastic finite-element method. The cold-forging process sequence to form the CVJ housing consists of the four operations of forward extrusion, closed-die forging, deep backward-extrusion, and ironing.

This study can be concluded with the following re- marks.

1. A better process sequence to form a CVJ housing has been designed by the rigid-plastic finite-element method, solving actual problems such as the precise deformed shape of the cup opening, the slope angle, the press capacity, and surface cracking.

2. The information obtained from the finite-element simulation, including the shapes of preforms, the effec- tive strains, the velocity fields, and the die load, is useful in designing a new process sequence.

3. A systematic approach to process-sequence design has been established using the finite-element method for multi-stage cold forging to form a constant-velocity- joint housing. This specific case can be considered as an example of the application of the method and for development of the sequence-design methodology in general.

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