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    Theoretical and experimental analysis of non-axisymmetrical deep drawing.pdf

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    Theoretical and experimental analysis of non-axisymmetrical deep drawing.pdf

    ELSEVIER Journal of Materials Processing Technology 54 1995 375-384 Join-hal d Materials Processing Technology Theoretical and experimental analysis of non-axisymmetrical deep drawing E. Ceretti*, C. Giardini, G. Maccarini Department of Mechanical Engineering, University of Brescia, Via Branze 40, 25123 Brescia, Italy Received 25 April 1994; accepted 12 October 1994 Industrial summary Deep drawing is one of the most common sheet-metal working processes and is used to make different items automotive components, household goods, gas bottles, etc. The theoretical studies on this process are mostly related to axisymmetrical bodies, i.e., bodies that are geometrically symmetrical with respect to any diameter, are symmetrically loaded and have symmetrical constraints. When items of a more complex shape have to be produced, the process and its optimisation depend only on the operators expertise. The present article reports a study made on non-symmetrical bodies. In particular, the effects are considered of some technological parameters, such as strain rate, type of lubricant, die-punch clearance and sheet-metal thickness, on drawing force and deformation, when producing mess tins. 1. Deep drawing Deep drawing is a plastic deformation process where the material is changed from a fiat to a concave element, through one or more steps. Deformation is obtained with the use of a die, a punch and a blank-holder. Material is forced by the punch into the die, so assuming the concave form \[1-3\]. The principal phases of drawing can be summarized as see Fig. 1 i a fiat circular bank, of diameter D, is positioned on the die; ii the blank-holder locks the external surface of the blank on the die whilst the punch is lowered down to the material; iii the punch comes into contact with the blank and the material is drawn inwards progressively, stretching towards the die profile the blank external diameter is reduced from D to D; iv when the operation is completed, and the piece has reached its final form, the punch and the blank-holder are raised. The thickness of the fiat circular blank remains equal to the original thickness only in the middle of the bottom, decreasing in the lateral regions because of the stretching * Corresponding author. of the material these are the zones where failures are most frequent. To outline the problems that are most significant and of practical interest in the industrial process of drawing, a piece that is actually produced is considered, namely the productive cycle of military mess tins. 2. The productive process Two different models of military mess tins are studied, characterized by being of 1 and 2 mm thickness see Fig. 2. The mess tins, made of Aluminium anticorodal, have a final height of 90 mm, the bottom is designed with the typical bean shape and the sides are slightly conical; they are obtained after three drawing passes, starting from a circular fiat blank of 220 mm diameter. In the first pass the drawing depth is about 80 mm and the base surface is greater than the final surface this is obviously necessary to avoid excessive straining of ma- terial that can lead to unavoidable fractures. In the second drawing pass the mess tin assumes its final height and there is the formation of a blank flange, which is necessary for the calibration of the height of the piece; the base surface is reduced; and the typical bean shape is formed. Strain distributions are more homo- geneous and the process is conducted without an excess- ively high drawing ratio. In the last pass the blank flange is upset and then folded, so as to obtain the final product. 0924-0136/95/09.50 1995 Elsevier Science S.A. All rights reserved SSDI 0924-01369401768-V 376 E. Ceretti et al./Journal of Materials Processing Technology 54 1995 375 384 D Fig. 1. The four steps of deep drawing. Fig. 2. The military mess tin considered. 3. The problem Deep drawing is one of the most complex plastic defor- mation operations because several parameters influence the productive process. Furthermore, especially for pieces with complex shapes, success depends on the oper- ators ability and the definition of correct technological parameters is obtained only after several experiments, so E. Ceretti et al./Journal of Materials Processing Technology 54 1995 375-384 377 2 3.2 5 8 20 40 80 120 170 250 0.5 Blank thicknese \[ram\] Internal reeietance of the material \[N/ram 2\] Aluminium ,heet 69 N/ram2 I 01 , I ; , i l ,. . . . I ; 0 ;t , . ; I 1;2 z5 Drawing diameter \[mm\] .... Fir,at, pa / ...... 5eared pae, I I Drawing \] force \[tons\] 4OO Fig. 3. Siebel and Oeheler diagram for the case considered. 1.6 2.5 4 6.5 10 the efficiency of the operation is, in general, not good. For these reasons the present study, which concerns indus- trial production, aims to identify the influence on the deep-drawing operation of parameters such as the strain rate, the lubricant type, the clearance between die and punch and the thickness of the metal sheet \[4-8\]. The scope of the research is to define, if possible, a relationship between these technological variables and the geometry of the die and the final piece, and to deter- mine some general rules for facilitating non-axisymmetri- cal drawing operations. 4. Methods for the evaluation of the drawing force and deformation The theoretical studies for the evaluation of the draw- ing force are related to the determination of the stresses acting on the different sections of the piece \[1-3\]. This method is easy to apply with axisymmetrical solids indeed, in these cases, the different sections over which the stresses act are defined quickly. From an analysis of the stress can be obtained by the total drawing tension, rt which enables the calculation of the theoretical force V t psot, where p is the drawn perimeter and s is the initial thick- ness of the metal sheet. This force depends on the resistance of the material to deformation, on the piece diameter, on the blank dia- meter and on the blank thickness. The drawing force increases suddenly at the beginning of the drawing phase, reaching its greatest value when the punch has penetrated to a level equal to the sum of the fillet radius of the die and the punch. For rectangular or similarly shaped pieces, calculation of the drawing force can be realised by means of graphics, 378 E. Ceretti et al./Journal of Materials Processing Technology 54 1995 375 384 for example using the Siebel and Oheler nomogramme \[9-11\]. This nomogramme, Fig. 3, is related to the draw- ing ratio/ D/d, where D is the original blank diameter and d would be the punch diameter if it were circular i.e. with the same surface area. From the nomogramme, if/ is known, it is possible to determine the mean internal resistance to deformation as a function of the type of material worked proceeding horizontally to the left the line related to the thickness of the drawn piece can be matched. Then going down verti- cally the line related to the punch diameter d can be matched; now proceeding horizontally to the right the vertical line of the drawing ratio/ can be found, this point giving the value of the drawing force necessary. This value has to be multiplied by a coefficient c which is a function of the punch diameter d \[9-11\]. In addition, it is neces- sary to consider another force component, due to folding. Ff 0.4aosp, where ao is the internal resistence of the material under deformation. Deformation can be studied with simulative tests through which, in a laboratory, different deformation conditions characterising materials under industrial deep-drawing conditions can be reproduced. These methods are unable to describe complex deep drawing; thus other solutions such as the anisotropy test and the limit curve of deformation are used. These tests can determine parameters that explain the effective attitude of the material to be deformed. Using the limit-curve-of-deformation method gives the possibility of evaluating material exploitation by the cal- culation of maximum and minimum strain. To obtain this, a grid, made of small circles of diameter d, is traced on the metal sheet. These circles, because of deep drawing, are changed into curves approximating ellipses, the deformation value at a point being obtained by measuring the major and the minor ellipse axis a-d b-d max d Emin d ....................... \[ Pressure i i ........ CII Pressure ........ , With this method the severity of drawing can be evalu- ated and modified die geometry determined. The conventional systems for tracing the grid on the metal sheet are photogravure and chemical attack. 5. Experimental tests Experimental deep-drawing tests were realised on 60 specimens of 1 and 2 mm thickness. The two groups, each of 30 pieces, were divided into 6 lots of 5 pieces to investigate strain rate and lubrication effects. The draw- ing tests were conducted varying i the speed So min 16 mm/s; somed 28 mm/s; somax 40 mm/s; ii the lubricant teflon; animal fat diluted with mineral oil; and iii the blank thickness 1 mm; 2 mm. For the execution of the tests an oleodynamic semi- automatic press with one rod was used, having the following technical features i variable closing force 15-170 tonnes; ii a die dis- placement of 800mm; and iii variable blank-holder closing force 15-115 tonnes. The analysis concerns the first two deep-drawing phases the third pass has only the function of upsetting and folding the flange. A precise and continuous study of the drawing force was obtained by furnishing the press with a measuring system characterized by a data acquisi- tion card, mounted on a personal computer, by a posi- tion transducer and by two pressure transducers see Fig. 4. The collected data are shown on a PC video and then converted into the related physical variables. The results obtained, in terms of drawing force, are presented in the Figs. 5a-c. These graphs reveal that the minimum drawing force is achieved at the mean strain rate, equal to 28 ram/s, for the other two speeds an increment of about 10 in the drawing force being obtained. The analysis of the influence of the lubricant has shown that the use of teflon films, compared with the use of animal fat, reduces the force necessary for the operation by 10-12. A.D.C. I Personal I Convertr Computer I Power supply I unit Fig. 4. Schematics of the acquisition chain. E. Ceretti et al./Journal of Materials Processing Technology 54 1995 375-384 379 5pcd 16 mm/5ec 12 240 10 ............................................................................................................................................. 200 120 “e I 6 2 .................................................... L ................................................................................... Forc _.au..J. .. ii ................ ....... .. L-_ ..... . ,.,,,.;_._..__.._._. ““ “11 .......................................... 40 0 3 6 9 12 15 rime e T c 2 mm blank thickness, teflon film “tons“ refers to Metric tonnes. It is found that the influence of the die-punch clear- thickness is doubled, the force should double. The experi- ante is related to the friction forces acting between the mental evidence shows an increment in the drawing blank and the die. The relationship between drawing force, of more than 10, over the expected data; this is force and blank thickness is theoretically linear if the due to the greater energy dissipation in die-piece 380 E. Ceretti et al./Journal of Materials Processing Technology 54 1995 375-384 12 10 6 2 12 10 6 2 Speed 16 mrn/sec ii iiiiiiiiiiiiiiiiiiiiii iiiiiiiiiiiii iiii ................ i ............................................ iiiiiiiii 0 3 6 9 12 Time fl 1.8; c 1.05. Fs o Ft Fs Fs o 2.67 tonnes FEX ----- 3 tonnes blank thickness l mm E. Ceretti el al./.hmrmd of Materials Iroces,in,,, Technology 54 1995 375-384 381 12 10 6 “ 4 2 Speed 16 rnrn/sec iiiiiiiiiiiiiiii IIIIIIIIIIIIIIIII ................ i ............................... .. 240 0 3 6 9 12 15 Time feeC 1 2OO ,-g le, o 120 E t3 3 8O .- t 40 12 lO o 2 Speed 28 rnm/sec iiiiiiiiiiiiiiiii iiiiiiill iiiiiiiiiiiii; ........................ .............................. iiii11115 0 6 8 4 Time feec\] 240 2OO T leo 120 3 10 40 Speed 4.0 mm/ec 12 2,10 Fs-o 5.32 tonnes FEX 6 tonnes blank thickness 2 mm The experimental results match the theoretical results, the calculated difference being only 3 A complete evaluation of the influence of the technolo- gical parameters also includes the study of deformation, using the limit curve of deformation described above. Because the commonly used methods of photogravure and of chemical attack are very expensive and the grid 10 ............................................................................................................................................ 200 18 ......... ,o ........ i ............ iil;iiiiiiil, iiiiiiiiiiiiiiiiiiiii t i 20 40 60 80 Position L L i 0 20 40 60 80 Position ang 0 I -4P-ang 45 I aO I --N- ang 125 -e--- ang 180 ----ang 0 \] ---n--ang 45 I ang 90 / --- ang 125\[ --o-- ang 180J \[--4--ang 0 I --B--ang 45 \[ ---- ang 90 I --N-- ang 125 --o- ang 180 0.9 0.8 0.7 0.6 0.5 o.4 E 0.3 0.2 0.1 0 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 6 1 0.9 0.8 0.7 “ o.6 0.5 0.4 0.3 0.2 0.1 0 .............. ...................... ........................... i ............................ I I I 20 40 60 80 Position ii iii i ..................... i ......................... i .............................. ......................... , i 0 20 40 60 80 Position ......................................... i ...................... i ................. 20 40 60 80 Position ---e--ang 0 l --m-- ang 45 I --- ang 90 / --- ang 125 --o-- ang 180 * ang 0 -- ang 45 ang 90 M ang 125 o ang 180 ang 0 1 -II--ang 45 / ---ang 90 \[ ang 125 / ---o-- ang 180J Fig. 7b. Deformation measured along the different directions 2 mm blank thickness, animal fat. Fig. 7c. Deformation measured along the different directions 2 mm blank thickness, teflon films. The study of the influence of the blank thickness has shown that the deformation varies according to the measuring points Fig. 7a-c. The mess tins with 1 mm thickness are more deformed than the 2 mm tins at the bottom, whilst the 2 mm tins are more deformed on the sides than are the thinner tins. This phenomenon is due to the greater availability of material at the bottom of the 2 mm tins, whilst on the sides there is a reduction of the die-punch clearance which results in an increase of blank straining The strain rate has no significant influence on the deformation 6. Conclusions The aim of the present experimental tests was to ana- lyse the influence of technological parameters on the deep drawing of complex-shaped pieces, involving s

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