A New Method to Design Blockers

A New Method to Design Blockers S.1. Oh (21,S. M. Yoon, Plastic Forming Laboratory,

Seoul National University Received on January 13,1994

Summary : This paper investigates a new method to design blocker geometry in rib-web type closed die forging. By examining various forging and blocker geometries, it was found that blocker geometry can be generated by eliminating high frequency mode from finisher geometry. In order to formalize the procedure, low pass filters, which can convert finisher to blocker geometry, are proposed. Also discrete Fourier transform is used for computational efficiency. The blocker geometry designed by the present method are compared with the one by an experienced designer. The blocker geometries are also validated by using FEM simulation. Present results shows that the frequency approach may offer a promising method to design blocker automatically. Keywords: metal forming, die design, digital filter

1. Introduction In forging operations, a billet of simple shape is deformed using dies to obtain an useful product, which usually has a more complex shape. When the shape of the final product is too complicated, intermediate shapes are often formed to ensure proper metal distribution and flow. Thus, the desired final shape of the part is obtained in a forging process by plastic deformation using successive dies. Accordingly, design of intermediate stages, also called blockers and preforms, is of critical importance for the success of forging processes, particularly for closed-die forging with flash. While simulation programs are gaining wider acceptance to evaluate completed designs, actual die design itself still remains predominantly manual. Determination of proper blocker configuration is a very difficult task, an art requiring skills achieved only through years of experience. Most of the time, die designers are forced to use trial and error (i.e. make a blocker die and try it), before they can achieve a satisfactory blocker design. As a result, extensive die try-outs' are necessary, and expensive productive machine capacity and man-hours are spent in developing the blocker dies. In the past, there had been several attemps to computerize or automate the blocker design by several investigators, [l-91 with marginal success. In the present paper, it is attempted to apply a new method in designing blocker. Considering the complexity and the variety of factors involved in designing blocker geometries, the present research work concentrates on a specific family of forgings, i.e. rib-web type forgings.

corner and fillet radii are larger in blocker, the cross sectional areas of the blocker and the finisher are almost the same. It is also observed that the volume is locally balanced as shown in the area f; and f j . Fig. 2 shows the suggested blocker shape when the height of the rib is larger than the twice of the rib width and the distance between t h e ribs are moderate. Here again we can observe the same trends as the ones we observed in Fig. 1 .

Fig.1 Preform shape for an H cross section with a large distanc between the ribs[l 11

2. Method of Approach 2.1

Preliminaries on Blocker Design

One of the most important aspects of impression- and closeddie forging is proper design of preforming operations and of blocker dies to achieve adequate metal distribution. Thus, in the finish forging operation, defect free metal flow and complete die filling can be achieved, and metal losses into the flash can be minimized. Even though there is no unique way of designing blocker for a given finisher shape, the qualitative principles of blocker design are well known. For example, some basic rules are given below[lO]: All corner and fillet radii of the blocker should be larger than those of the finisher. The area of each cross section along the length of the preform must be equal to the finish cross section augmented by the area necessary for flash. Practically, the dimensions of the preform should be larger than those of the finished part in the forging direction so that metal flow is mostly of the upsetting rather than the extrusion, etc. Fig. 1 shows a suggested blocker shape for an H cross section having a large distance between the ribs[ll]. From the Fig. 1, it can be observed that the blocker shape is "similar" to that of finisher except that blocker ribs are shorter, blocker webs are thicker,

Annals of the ClRP Vol. 43/1/1994

Fig.2 Suggested preform shape for H cross section with moderate rib distances[ll] From Figs. 1 and 2, it can be observed that the blocker geometries may be obtained through some kind of moving average of the finisher geometry. More formally, blocker shape may be obtained by expanding the finisher geometry in terms of Fourier series and eliminating the higher frequency terms. Elimination of the high frequency terms can be achieved by introducing low pass filters which are commonly used in signal processing. 2.2

Mathematical Foundations

It is well known that a function, f(x), which is defined in geometric domain, can be uniquely represented in frequency domain by the Fourier transform, Ffu),

where i = q

q . The

inverse transform is defined by

f(x) = j'?(u)exp(i2xux)du -_

(2)

For the computational convenience, we introduce the Discrete Fourier Transform(DFT)[12]. Given N complex numbers

245

N-l

(filj=,

, their N-point DFT is denoted by

[ f i ) where fi

is

defined by

fi =

N-1

f j exp(-i2njk / Nj

are shown in Fig. 4 and frequency profiles before and after filtering are shown in Fig. 5. From the filtered geometries shown in Fig. 4, following can be observed: The rectangular function is transformed to smoother shapes, which are more closer to ribs in blocker design.

(3)

Areas under the filtered functions are preserved and area is locally balanced. This is another important features in blocker design.

j=O

for all integers k=O,kl,k2 ,...,N12. The inversion of DFT is defined by

1.250

1 N-1

, , CFkexp(i2xjklN)

(4)

f.=-

1.000

k=O

for j=O, 1,....,N-1. If N = 2 R , where R is an integer, then DFT can be evaluated very efficiently. This procedure is called the Fast Fourier Transform(FFT). Assuming that the Fourier transform given in eq. (1) can be approximated by R U )=

W

-a

2 .E

<

.?SO

.so0

,250

R12

,000

j-*12f ( x ) e x p ( - j 2 7 w d r

(5) where n is a sufficiently large number, the Fourier transform can be represented in terms of DFT by

Frequency

Fig. 3 Low pass filters with various cut-off frequencies

i

1.500

for k=O,fl,k2,

r)

.... Here function g(x) is defined by

g ( x ) = ( f ( Q / 2 ) +f ( - R / 2 ) ) / 2

for

f(x-Q

01x < R / 2 x=R/2 R/2
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If [Gk) is DFT of [gj}, then, by periodicity, eq. (6) can be rewritten by

N

k Q F(n) =m G

for

k=O. 1,...,

F (-k + j - ) =51m G ~ - k

for

k=l, ....., TN- l .

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As it was mentioned before, low pass filter is needed. Low pass filter, as its name suggests, passes the low frequency signals unchanged and suppresses the high frequency. Filter function, H(u), is given in frequency domain. If the Fourier transform of f(x) is F(u), then the filtered function of f(x) is given by

I--F(u)H(u)exp(i2lcux)du

H , ( u ) = [ 0 . 5 + 0 . 5 ~ 0 ~ 2 n ~ ]-n0,. 5 1 ~ 1 0 . 5(9) where n = 20 was chosen. Note that the expression in the square parenthesis is the hanning filter. Cut off frequency of the low pass filter can be reduced by introducing a filter by function, H( u,a),

1+a,

for a
fc=

2n

In order to show the effect of filtering on a geometric shape, consider a rec(x) function which is defined by for 1.121, rec(x) = 1 for lxI>1 rec(x) = 0 Three filter functions, H(u,0.5), H(u,0.125), H(u,0.0625), which are shown in Fig. 3, are used. rec(x) and the filtered functions

246

LA

E 0.0

.100.0

(8)

There are various different low pass filters. In the present investigation, we use a monotonic smooth filter which is expressed by

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1

-c

00

for

4.000

Fig. 4 Geometry changes due to filtering by various cut-off frequencies

2.3 Filter Functions

H ( w )= HA;) H(u,a) = 0

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X-axis

J 0.bO

0.01

Oh2

0.b3

0.b4

0.bS

Frequency

Fig. 5 Frequency spectrum before and after filtering

3. Results and Discussions 3.1 Generation of Blocker Geometry

Fig. 6 shows a cross section of a complex three dimensional forgings and blocker sections, one for aluminum and the other for titanium designed by an experienced designer. The geometry of the forging cross section can be represented by coordinates of corner points and corner radii as given in Table 1.

Our immediate goal is to reproduce these blocker geometries by using the filtering method. For this purpose, the low pass filters given in eq. (10) with various cut-off frequencies are used. In order to apply FFT technique, x domain was chosen as - 1 0 1 . 6 1 x 1 1 0 1 . 6 which is sufficiently large enough to include forging and blocker cross sections. The x domain then was divided into N=1024 segments. The forging cross section was digitized at x , = 2 . 1 0 1 . 6 j l N , j = O , + l , ...,f N / 2 - 1 . It was sufficient to include upper half of the forging cross section due to symmetry. Fig. 7 shows the filtered geometries of the forging cross section when filters, H(u,0.089), H(u,O.l29), and H(u,0.198), are used. From Fig. 7, following can be observed: As the cut-off frequency decreases, rib is transformed to

smoother shape where the boundary between the rib and web becomes less distinct. Volume/area of the rib is redistributed while total volume is preserved.

Fig. 9 shows the final blocker geometries designed by the present method. It may be mentioned that the conventionally designed blocker has added volume of about 25 percent since the cross section is near the end of the forging.

r

3.2 Validation of Blocker Geometry

J

In order to validate the blocker geometry, three forging operations are simulated by using FEM software DEFORM[l3]. The three forging operations are simulated for this purpose. In the first case, forging was done without blocker with an initial rectangular shape preform with 61 mm width and 67.8 mm height. Due to symmetry, it is sufficient to include one quarter of the cross section. It is assumed that the forging material was aluminum with its flow stress represented by Ti=66.8k0.105MPa and that forging is done isothermally under plane strain condition. In the simulation, friction factor m=0.3 is assumed at the interface between the workpiece and die. Fig. 10 shows the predicted flownet at the end of the forging operation. The flownet was generated from the original pattern of 10x10 rectangular grid. As can be seen from Fig. 10, forging was done successfully without blocker. It may be reminded, however, that the original three dimensional forging reauires a blocker.

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d

1-

Ib)

Fig. 6 Cross section of a forging with conventionally designed blocker (a) Aluminum, (b) Titanium Table 1. Geometry of Finisher (mm)

r

j

-1 2

X -53.34 j -50.23 ' ~

I

Y j 0.00 I 37.53

R 1 0.00

\ a

Fig. 8 Comparison of the conventional blocker (A) and filtered curve (B)

The transformed curve with fiier function, H(u,O.l29), is compared with the blocker designed by the experienced designer in Fig. 8. From Fig. 8, it can be seen that two curves matched reasonably well within the range of finisher definition (PI-P range), with minor differences. The predicted blocker rib has sharper tip radius than the one conventionally designed. Also the slope at the inflection point near the inside surface of the rib is higher in the case of the conventional design. 76.20

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Fig. 7 Geometry changes due to filtering with various cut-off frequencies In the range outside of the finisher definition (P-Q range), there are consider-able differences between the predicted and the conventionally designed. From the conventionally designed blocker, it is observed that the one for titanium the outside surface of the rib has the same draft as that of the finisher. For aluminum blocker, curved slope was given as shown in Fig. 6. In order to finalize the blocker designed by filtering, additional tasks are performed as following: The height of the predicted curve was adjusted to make the blocker volume 6-7 percent more than the finisher volume. The outside of the rib was adjusted according to the convention used in traditional desian. That is. for titanium. the outside of the rib was adjustei so that the draft angle becomes the same as that of finisher and for aluminum, side surface was adjusted accordingly.

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Fig. 9 Blocker geometries designed by filtering method. Top : Aluminum, Bottom: Titanium In the second case, the blocker forging was done with the conventionally designed blocker die from the same initial preform shape used in the first simulation. After the flash was trimmed, the blocker shape was used for finisher forging operation. The predicted flownet at the end of the blocking and finishing operations are shown in Fig. 11. Comparing the result with that of the first case, it can be seen that the deformation near the die-workpiece interface requires less redundant work when a blocker is used. In the third case, simulation was performed using the blocker

247

designed by the filtering method. Fig. 12 shows the flownet at the end of the finishing operations. From Fig. 12. it is seen that the flow pattern of the third simulation is almost identical to that of the second simulation. This result was expected because the blocker shapes used for the second and the third simulations are almost identical. It is noted that the present investigation did not attempt to improve the blocker design over the conventional one. Rather, goal is to find a computerized method to design blocker. Considering our goal, it can be said that the present method was successful in generating blocker.

26.0

40.0

60.0

30.0

X-axis

Fig. 12 Predicted flownet at the end of finishing operation with blocker generated by the filtering method

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4. Concluding Remarks

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Fig. 10 Predicted flow net when no blocker is used

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In this paper, a new method is presented to design blockers automatically for rip-web type closed die forging processes. It seems that the proposed method is quite promising in automating blocker design for certain types of forgings. Actual blocker design procedure may be far more complex than the simple rib-web type forgings discussed in this paper. The present investigation is still preliminary and more work is needed in the future. It may be mentioned, however, that the present method seems to be especially attractive in designing blockers of three dimensional rib-web type forgings due to computational efficiency of the FFT procedure. Work is under way to apply the present method to three dimensional forgings.

5. References

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-

z

>r.

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X-axis Fig. 11 Predicted flownet at the end of blocking and finishing operations when the conventional blocker is used

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1 . Subramanian, T. L., et. al., 1977, Apolication of ComouterAided Desian and Manufacturina to Precision Isothermal Foraina of Titanium Allovs, Tech. Report AFML-TR-77-108, Air Force Material Labs. 2. Yu, G. B. and Dean, T. A., 1985, A Practical ComputerAided Approach to Mould Design for Axisymmetric Forging Die Cavities, Int. J. M.T.D.R.. 25:l-13 3. Bruchanow,. A. N. and Rebelski, A. W., 1955, Gesenkschmieden und Warmoressw, Veb Verlag Technik, Berlin 4. Biswas, S. K. and Knight, W., 1976, Towards an Integrated Design and Production System for Hot Forging Dies, Proc. 3rd Int. Conf. on Production Research (Amherst) 5. Chamouard, A., 1964, Estampaae et Dun o 4 Paris, 1 6. Hwang, S. M. and Kobayashi, S., 1984, Preform Design in Plane-Strain Rolling by the Finite Element Method, Int. J. Machine Tool Des. Res., 24:253 7. Hwang, S. M. and Kobayashi, S. 1986, Preform Design in Disk Forging, Int. J. MachineTool Des. Res., 26:231 8. Vemuri, K. R., Oh, S. I . , and Altan, T., 1989, BID - A Knowledge-Based System to Automate Blocker Design, Int. J. Machine Tools Manufact., 29:505 9. Vemuri, K. R., 1986, A Knowledae-based ADDrOaCh tQ Automate Geometric nesian with Aoolication to Desian Blockers in the Foraina Process, Ph.D. Dissertation, The Ohio State Universitv 10. Altan, T., Oh, S.,. and Gegel, H., 1983, Metal Formina Fundamentals and ApDlicatia, ASM 1 1 . Altan, T., et. al., 1973, Foraina Eauioment. Materials. and Practices, MCIC, Air Force Materials Laboratory 12. Walker, J. S., 1991, Fast Fourier Transforms, CPS Press 13. S. 1. Oh, et. al., 1991, Capabilities and applications of FEM code DEFORM: The perspective of the developer. J. Mat. . . Proc. Tech. 27:25