A new shape complexity factor

Journal of Materials Processing Technology 92±93 (1999) 439±443

A new shape complexity factor B. Tomov* University of Rousse, Faculty of Mechanical and Manufacturing Engineering, Rousse, Bulgaria

Abstract In conventional closed-die forging process design the engineer must determine the required number of stages, which for forging parts of revolution could be from one to three or even more for the most complicated shapes. Bearing in mind that the direct transforming of the billet to a ®nal forging shape is possible only in some very rare cases when mass M is very small (M < 0.5 kg), or the shape is extremely simple or both conditions occur: in every other case, there is an essential need to assess the shape complexity of the forging part. In the present paper is proposed a new shape complexity factor based on the comparison of the work done during the forging to the ®nal die impression when a rotationally symmetrical forging part is forged, with the work done for the forging of an imaged pancake with the same volume but with a height determined under the condition of equality of the volumes transformed. A very simple criterion is K1 > 'H, where K1 describes the amount of the transformed volume during two arbitrary stages of forging and 'H is the logarithmic height strain. The criterion is checked for some examples using FEM analysis for calculating the work done. It is found that the new shape complexity factor reduce the number of forging steps. # 1999 Elsevier Science S.A. All rights reserved. Keywords: Forging; Rotationally symmetrical forging parts; Shape complexity

1. Introduction The present state in forging technologies is characterised by an increasing development of computer science and engineering. A suf®cient number of computational techniques have been developed in the last years, offering to the engineer a useful tool when a close-die forging process is under investigation. 2. Experimental In conventional closed-die forging process design, the engineer must determine the required number of stages which, according to Fig. 1, could be from one to three or even more, depending upon the forging mass and shape. The direct transforming of the billet into a forging part (route A) is possible in the very rare cases when Mf is very small (Mf  0.5 kg) or the shape is extremely simple, or both conditions occurs. More often, routes B and C are applied. The question of whether the number of the intermediate stages will be one or two or even more doesn't have a de®nite and correct answer in the special literature until now.

*Tel.: +359-8244-7268; fax: +359-8245-5145.

The literature shape complexity factor ®rst mentioned in the literature [1] is the well-known von Spies ratio Sˆ

Mf ; M0f

(1)

where Mf is the mass of the forging part and M0f is the mass of the circumscribing ®gure, being only prismatic or cylindrical. The Spies factor doesn't offer any answer concerning the necessity of preforming and the only thing it affects is the amount of the machining allowances when a forging part is designed. Some instructions concerning the ratio hF/bF (Fig. 1) could be used as a shape-complexity factor. These instructions are de®ned by Bruchanov and Rebelscki [2] but regrettably, they are applicable only in an extremely small number of cases. It could be asserted that the ®rst real shape complexity factor was offered by Teterin at all [3] ST ˆ

P2F =AF 2RgF ; P2C =AC RC

(2)

where PF and AF are the perimeter and the area of the axial cross-section of the forging, PC and AC are the perimeter and area of the axial cross-section of a circumscribing cylinder, RgF is the distance from the axis of symmetry to the centre of gravity and RC is the radius of the circumscribing cylinder.

0924-0136/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 9 9 ) 0 0 1 6 7 - 3

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B. Tomov / Journal of Materials Processing Technology 92±93 (1999) 439±443

Fig. 2. An imaged forging part. Fig. 1. Sequence of the forging stages for an H - formed forging part.

For a multi-stage forming, the ®nishing shape complexity factor ST for the ®nishing operation is given by ST ˆ

STF ; STP

(2a)

where STF is the shape complexity factor (SCF) of the forged part of STP is the SCF for the preform shape. It is evident that if the forged shape is simply a cylinder then the SCF is unity. As the SCF becomes larger for a given ®nal forging shape, this will indicate the need for a preforming stage to protect the ®nal die cavity and to avoid a defective forging. The Teterin SCF has been used successfully in pre-form forging, designed with shape complexity control in simulating backward deformation using FEM analysis [4]. The evident shortcomings of the above-mentioned SCF are the lack of a speculative conclusion describing SCF by p2/A and Rg/RC and at the same time it is of sophisticated form such that mistakes, may occur. Remembering that the pre-forming stages allow booth decreasing of the die-wear and improving of the ®lling of the ®nal die cavity, the work done during forging is the only objective criterion helping to estimate the necessity of preforming stages. In the present paper the SCF of a forging part will be de®ned calculating the work done for plastic deformation. Consider the forging part depicted in Fig. 2. The work done is calculated after Tomlenov [5]:   SF (3) WF ˆ  Vm ln ‡ Vad S0 In Eq. (3),  is equal to  (KM, T, v) is the equivalent plastic stress, as a function of Km (the type of forged material), T (the temperature of forging) and v (the deformation velocity), Vm is the volume of the middle unchangeable part of the forging, Vad is equal to SiHi is the added volume or deformed volume, SF is the ®nal normal cross-sectional area of the forging part in the parting plane and S0 is the normal cross-section of the billet.

It is reasonable to assess the shape complexity of a given forging with the amount of work done. Eq. (3) will be transformed if written in terms of Vad ˆ K1 V0 ;

K1 ˆ

Vad V0

(4)

where V0 is the volume of the forging part (not including the amount of ¯ash). For a given forging part and where forging conditions  and V0 are constant WF ˆ

WF ˆ …1 ÿ K1 †'A ‡ K1 V0

(5)

It is easy to notice that the greater are K1 and 'A is equal to ln…S1 =SF †, the greater is the relative work WF*, which coincides with the general forging routine. The relationship WF* is equal to WF*('A) for K1 equal to constant is depicted in Fig. 3. In fact, cases where 'A is equal to 1 and K1 is equal to 1 are impossible, bearing in mind that every forging stage is due to one stroke of the machine, and Vad is always only a part of the volume forged.

Fig. 3. W* as a function of 'A for different values of K1.

B. Tomov / Journal of Materials Processing Technology 92±93 (1999) 439±443

441

Therefore, inequality Eq. (10) will be reduced to …1 ÿ K1 †ln

1 ‡ K1 ÿ 'H > 0 1 ÿ …2=5†=DF

or K1 > ' H

(11)

because ln Fig. 4. Scheme of the forging part for Fig. 2, showing the transformed volumes.

Coming back to Fig. 2 in the schematic form seen in Fig. 4, it will be useful to introduce the meaning of the ideal preform (IP) for which volume V0 is equal to the volume of the forging part but not allowing for the ¯ash. It is very easy to prove that its height is P  P  Ai Ai hi (6) ‡ hA ˆ hm7 1 ÿ AF AF in Eq. (6) hA is the average height of the ideal pancake satisfying the conditions Vp ˆ V0 X X VS ˆ Vad

(7)

where Vs is one of the volumes `squeezed' from IP and transformed into Vad-added volume. Now compare the work done ®rst when a simple perform forging (A1, H1) is transforming into a ®nal forging Eq. (5) and second when the same preform forging is transformed into an IP i.e. WF ˆ …1 ÿ K1 †'A ‡ K1 WF ˆ V0

It occurs that the greater is the diameter of the `pancake' after the ®rst step of forging, the lesser is the necessity of a preforming stage 2 (see Fig. 1). Now consider more carefully the sample in Fig. 2Eq. (3). The volume shown within brackets is in fact the one transformed during the deformation volume. In principle the work done for the deformation of a symmetrical forging part with known geometry, according to Fig. 5, is equal to 2 3 Zr2 4hA …r2 ÿ r1 †2Rg1 ÿ f …r†dr2Rg2 5 (12) WF ˆ 4 r1

where Rg1 and RRg2 are the radii of the centres of the areas r …r2 ÿ r1 †hA and r21 f(r)dr. Obviously Rg1 ˆ

…r2 ÿ r1 † 2

therefore,

2

4hA …r2 ÿ r1 †2 ÿ 2Rg2 WF ˆ 4

Zr2

3 f …r†dr 5

(13)

r1

or else At Rgt WF ˆ 4

(14)

where At is the `transformed' area and Rgt is its weights centrum radius. Now a more common equation can be written criteria Eq. (11), calculating K1 and 'H for an arbitrary forging part with rotational symmetry. It is easy

and  WIP ˆ

1  0: 1 ÿ …2=5†=DF

WIP ˆ 'A ' A V0

where A1 ˆ ln '

SF : S0

(8)

If …1 ÿ K1 †'A ‡ K1 > 'A1

(9)

or …1 ÿ K1 †'A ‡ K1 ÿ 'H > 0

(10)

then a preforming different from a pancake is necessary. According to the general forging routine, the diameter of the preforming after the step (see Fig. 1.) is less than the forging diameter by only 2/5 mm, hence, D1 ˆ DF ÿ …2=5†.

Fig. 5. Scheme of calculating of the amount of transformed volumes for an arbitrary forging part.

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B. Tomov / Journal of Materials Processing Technology 92±93 (1999) 439±443

Fig. 6. Sample of a forging part [7] forging directly from a workpiece of dimensions ù118 mm  170 mm: (a) the forging part; (b) the final distortion of the horizontal grid; and (c) the work done.

Fig. 7. The some forging part as shown in Fig. 6(a), forget after preforming according to Fig. 7(a): (a) the preforming cavity; (b) the moment of flash building; (c) the work done.

B. Tomov / Journal of Materials Processing Technology 92±93 (1999) 439±443

443

(FEM), known as Quantor [6], some calculations have been done in order to check the reliability of the criterion proposed. Not dwelling upon details, only two examples will be discussed here. The ®rst one is from [7], shown in Fig. 6. and Fig. 7. The K1 > 'H criterion required the preforming cavity that is shown in Fig. 7(a). The most important result here is that there is no contradiction between expectation (decreasing of the work done after preforming) and calculation. The second example is based on the results given in [4]. The results are really worthy, but applying Teterin's SCF, it occurs the forging process is in three stages, including pro®le upsetting, and blocker and ®nishing impressions, whilst, using K1 > 'H only one preforming shape (cavity) is suf®cient, as is depicted in Fig. 8. 3. Conclusions 1. A new criterion allowing the assessment of the shape complexity of a forging part of revolution is described. The criterion (SCF) is applicable both for primary assessment and for the assessment of the intermediate shapes calculated using the FEM. 2. The SCF acts more severely than Teterin's criterion, making some of intermediate shapes not necessary, which is highly desirable, for it allows both increasing of the forging efficiency due to a smaller number of die cavities, and for the same reason, decreasing of the diecosts. Fig. 8. The forging shapes described in [4]. According to the K1 > 'H criterion the second shape (after blocking) is not necessary.

to show that At Rgt AF RF 2Rg;F AF : hA ˆ R2F K1 ˆ

(15) (16)

In Eqs. (15) and (16) A1 and AF are the cross-sectional areas of the forging part (AF) and pre-forging (A1), and hA is the height of the IP. Thus, 'H is equal to 'H ˆ ln

h1 : hA

(17)

Using a program, based on the ®nite-element method

References [1] O. Kinzle, K.V. Spies, Werkstattstechnik und Maschinenban 47 (1957) 176 (in German). [2] A. Brukanov, V. Rebelsky, Hot Closed-Die Forging, Moscow, GNTIML (1962) (in Russian). [3] G.L. Teterin et al., Kuznechno-Shtanmpovochnoe proizvodstvo 7 (1966) 6±9 (in Russian). [4] G. Zhao, E. Wright, R.V. Grandhi, Int. J. Mach. Tools Manuf. 35(9) (1995) 1225±1239. [5] A.D. Tomlenov, Theory of plastic deformation of metals, Moscow, Mashinostroenie (1972) (in Russian). [6] N. Bila N. et al., Finite-element simulation and computer aided design of forging technology with From-3D system, International Conference on Metal Forging Simulation in Industry, 28±30 September 1994, Baden-Baden, Germany. [7] Form-2D, Finite Element System for Simulating and Analysis of Forming Processes (Version 2.11), User's Guide, Moscow (1995).