Journal of Materials Processing Technology 151 (2004) 105114

Study of the new floating-plug drawing process of thin-walled tubesK. Swiatkowski a,, R. Hatalak b

a AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Polandb FAG Poland, ul. Kosciuszki 19, 30-105 Cracow, Poland

Abstract

The tube drawing process has been in a common use for many years. Especially useful is the method of drawing with the floating-plugbecause it allows the manufacturing of very long tubes. For thin-walled small-sized tubes the drum-drawing process is very popular. Theadditional advantage of this process is the possibility of using a very high velocity of drawing and the ability to achieve a very highproductivity. This paper describes a new tool design which allows greater wall-thickness reductions and increases process stability. 2004 Elsevier B.V. All rights reserved.

Keywords: Tube drawing; Thin-walled; Floating-plug

1. Introduction

In the practice of the hot extrusion of input material usedduring the drawing process, the value of D/g (outer tubediameter/tube wall-thickness) is limited not only because ofthe conditions of the extrusion process but also because ofthe technological conditions of the welding process used fortube joining. Usually D/d < 13 and g 0.40.5 mm inputtubes are produced commonly by the extrusion process.

The drawing of tubes with D/d < 13 and wall-thicknessg 0.40.5 mm is a typical process commonly used andvery well elaborated from the theoretical and practical pointsof view. The scheme of such a process is presented in Fig. 1.

The manufacturing of tubes with D/g > 20 and awall-thickness of less than 0.4 mm is until now a veryserious practical problem and has not yet been solved theo-retically. The drawing methods actually used are based onthe simultaneous reduction in the wall-thickness and theouter tube diameter during deformation in the drawing die.Such a process is also applied to the drawing of thin-walledsmall-size tubes.

The theoretical methods of the designing of tube drawingprocess that are actually used are based on the strain andstress state analysis in the zone of deformation and on theanalysis of the phenomena observed during the real process.These methods are analysis of the floating-plug position inthe deformation zone [14], analysis of the U function [5],

Corresponding author.E-mail address: kaski@galaxy.uci.agh.edu.pl (K. Swiatkowski).

analysis of the differential equations of equilibrium [1,5,6],energetics [4,7] and redundant stress analysis [8,9].

The choice of the proper method depends on the a prioriassumed optimizing criterion, the practical importance ofthe problem being solved and the technical possibilities ofcalculation apparatus.

In each method limiting assumptions are introduced con-cerning the geometry of the deformation zone, the values ofunit pressures acting on characteristic regions of the tools,or the assumed position of the floating-plug in the deforma-tion zone.

Using a different analytical method, the different values ofthe basic technological process parameters can be obtainedas a final result.

Summarizing the results obtained by using different ana-lytical methods, it is possible to arrive at the following con-clusions. The method based on the analysis of floating-plugposition in the zone of deformation shown in Fig. 2 allowsthe defining of the extreme floating-plug position assumingthat the wall-thickness of the tube is constant in the sink-ing zone. Additionally, it is possible to define the extremerear-most plug position assuming the lack of friction be-tween the plug and the tube: such a situation does not existin the real process of tube deformation.

The method based on the minimum U function [5] en-ables the process stability be estimated assuming that thepressures acting on the cylindrical and the conical surfacesof the plug are identical and assuming that the value ofback-track of the plug can be less than that of its minimumvalue: such situation also does not exist in the real pro-cess. Making such assumptions it is possible to obtain the

0924-0136/$ see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2004.04.024

106 K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114

Fig. 1. Scheme of tube drawing with a floating-plug.

optimum value of the () difference, for which the pro-cess is most stable with regard to the ability of the plug toadapt to the equilibrium condition of the forces acting on itin the deformation zone. According to this method it is pos-sible to conclude that the values of the friction coefficient,the reduction in the tube area and the die angle influencethe process stability. In Fig. 3, the dependence of the Ufunction versus the () difference is presented.

In the case of the differential equations of equilibriummethod (Fig. 4) the only optimization criterion can be theminimization of the drawing force for the assumed input tubeand the final tube dimensions. In that case the plug oughtto be in the extreme fore-most position: such situation doesnot exist in the real process because the plug has to changeits position during deformation to adapt it to the equilibriumconditions.

The energetics method of calculation of the drawing pro-cess presented in Fig. 5 shows that the value of the plugback-track is influenced by the wall-thickness of the tube,the difference of the () angles and the wall-thicknessesD/g of the tube. From the analysis based on this method itis possible to conclude that the tool geometry should be dif-ferent for thin-walled tube drawing than for the drawing of

Fig. 3. Relationships between U function and the () difference [5].

Fig. 2. Plug positions in deformation zone: (a) extreme fore-most; (b)extreme rear-most.

tubes with the normal wall-thicknesses D/g. Fig. 6 con-firms the results of this theoretical analysis.

Analysis of the redundant strains method shows that theexistence of the defined level of redundant strains leads to thedistinct decreasing of the total deformation in one pass of theprocess. Also the level of internal stresses distinctly increase.For the proper realization of the drawing process the levelof redundant strains should be reduced to the minimum.

The redundant strain coefficient does not allow the predic-tion of the optimal process parameters but knowing its valueit is possible to estimate the correctness of process realiza-tion and tool selection. Decreasing the level of redundantstrains can be achieved by proper tool design. Particularly,the portion of sinking deformation in the total deformationof the tube should be minimized. The example of process pa-rameters influenced by the redundant strain coefficient valueis shown in Fig. 7.

K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114 107

Fig. 4. Segmentation of the deformation zone in tube drawing with a floating-plug.

Analysis of the actually applied analytical methods showsthat no one method takes into account all technological con-ditions and phenomenon taking place in the thin-walled realdrawing process with a floating-plug. In many cases assump-tions made a priori are dramatically different from thoseexisting under the real process conditions. Particularly, thespecifics of the thin-walled tube drawing process are nottaken into account in any known analytical method. Theonly method based on the redundant strains coefficient val-ues analysis points out the necessity of the application of aquite different tool geometry to the drawing of thin-walledtubes from that used for the drawing of tubes with the usualwall-thickness.

In actually applied methods, process optimization is basedon the minimization of the drawing force or drawing stressand on the analysis of equilibrium condition of forces actingon the floating-plug. Such analysis is carried out assuminga defined wall-thickness tube reduction and a defined reduc-tion in the tube outer diameter. As a main geometrical tool

Fig. 5. Scheme of the deformation zone with an isolated infinitesimalvolume element in tube drawing with floating-plug [5].

parameters the () difference and the value of back-trackn of the plug is under consideration. Process optimiza-tion is leading to the moment when the changes in both ofthese quantities will receive the minimum value of assumed

Fig. 6. Relationship between the relative plug back-track and the tubewall reduction for different wall-thicknesses and () values [2].

108 K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114

Fig. 7. Relationship between the redundant strain coefficient and theangle of the die for different () difference and total tube reductionc [9].

criterion for an a priori assumed input and final tube di-mensions. As a final effect of calculations carried out usingearly specified methods, the optimum value of the () dif-ference was found to be in the range of between 2 and 3.

The reality and the specifics of the thin-walled tube draw-ing process shows that for the proper realization of thisprocess it is necessary to use tools with a geometry whichdiffer from commonly used for tubes with D/d < 13 andg > 0.40.5 mm. Especially important is to obtain the valueof (), because carrying out the process with values of = 23 causes process instability.

In contemporary applied theoretical solutions the changein wall-thickness of the tube is not taken into account.

This parameteraccording to the results of practicalexperimentsinfluences seriously the course of the process.

Fig. 8. A scheme of a floating-plug tube drawing process with marked angle , describing the wall-thicknesses variation in the sinking zone, and diameterdr , describing the starting value of plug diameter before the tube wall deformation [10].

Taking into consideration this fact it is necessary to definethe real plug position n in the deformation zone and alsothe values of unit pressures, acting on the characteristicworking surfaces of the plug.

The aim of the paper is to elaborate a new analyticalmethod of thin-walled tube drawing process solution, takinginto account the above mentioned process parameters, untilnow not taken into consideration in the process solutions.

2. Theoretical analysis of the tool geometry in thethin-walled tubes drawing process

2.1. Changes in the wall-thickness in the zone of tubesinking

In the practice of the thin-walled tube drawing process,each change in the tube wall-thickness seriously influencesthe process stability. For this reason, it is necessary to takeinto account the wall-thickness change in the zone of tubesinking. Qualitative wall-thickening in this zone is given inFig. 8 by the angle value.

The angle can be obtained from the equation:

= arc tan 2g sin 2g0 cos+D0 Dk 2g0 (1)

in which

g = gk g0 = g0(e 1) (2)and , according to the Smirnov-Aljaev and Gun proposal[11], is as follows:

= ln gkg0

=ln(D0/Dk)2(1+c tan ) 2(1 (g0/D0)) ln

(3(1 (2g0/D0))2

+(D0/Dk)2(1+c tan )/3(1 (2g0/D0))2 + 1)

2 (1+ c tan ) (1 (2g0/D0)) (3)

From this scheme of zone deformation the value of angle can be obtained.

K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114 109

It is necessary to take into consideration the wall-thicknesschanges in the sinking zone because in the practice ofthis process such angle changes are within the range of0.50.65 or 0.0090.011 rad for commonly used anglesof the die.

From the presented consideration it is possible to concludethat the tube-sinking zone exerts a substantial influence onthe wall-thickness changes. Shortening of the sinking zonecan substantially improve the process stabilitywhich isvery important in the case of thin-walled tube drawing witha floating-plug.

2.2. Floating-plug geometry

2.2.1. Angle of deformation of the conical part of the plug In contemporarily used analytical methods of the

thin-walled tube drawing process the () difference andback-track n of the plug have been taken into considera-tion as principal tool geometry parameters. Analyzing thedeformation conditions it is also necessary to take into ac-count the changes in wall-thickness in the sinking zone ofthe drawing process. Such changes are illustrated in Fig. 8.

The equilibrium condition of the forces acting on thefloating-plug in the deformation zone, which is very wellknown in [16], allows the obtaining of the equation for theangle of inclination of the conical part of the plug in theform:

tan = 1(1/) 4dk(lc + nr)pw/(d2r d2k)ps

(4)

where, pw and ps are the unit pressures acting, respec-tively, on the cylindrical and the conical working parts ofthe floating-plug.

As can seen, the angle depends on the values of pw andps, the friction coefficient and the diameter dr of the work-ing part of the plug taking part in the deformation process,and the diameter dk and the length lc of the cylindrical partof the die.

According to Eq. (4), the angle decreases with short-ening of the cylindrical part of the die lc. It is easy toconclude that a reduced lc value causes the () differ-ence to increase in the case when the angle is strictlydefined. Such situation is a very beneficial for the processin practice, because it makes it possible to run the pro-cess under more stable conditions. This remark is particu-larly essential in the case of the thin-walled tube drawingprocess.

The equation for the angle which fulfill the conditionmentioned above is as follows:

tan = dk tan dk + 2gk + 2nr tan (5)

According to the authors of paper [12], the value of suchdefined angle can be recognized as a max which allowsthe drawing process to operate in a stable manner.

2.2.2. Back-track n of the floating-plug in deformationzone

The equation of the minimal nmin and maximal nmax val-ues of back-track are very well known from [3,6,13], andare as follows:

nmin = gk tan 2 (6)

nmax = g0sin

gkc tan (7)Taking into account the value of angle, the equation forthe real plug position (back-track) nr is as follows:

nr = nmax (dr dk) sin (+ )2 sin (+ ) sin (8)

where

nmax = gk tan + (g0 +g (gk/cos)) cossin (+ ) (9)

The real value of back-track nr should be between theextremal n values:

nmax>nr nmin (10)

2.2.3. Real diameter dr of the floating-plugTaking into account the geometry of the deformation zone

it is possible to calculate the real value of the floating-plugdiameter using the equilibrium condition of forces acting onthe floating-plug. The final equation for the dr value is asfollows:

dr =d2k + R2

sin2(+ )sin2(+) + 2Rdk

sin(+ )sin(+) + 4R

(lcpc

pw+ nmax

)sin R sin(+ )

sin(+) (11)

where

R = 2dkpw(sin cos)ps (12)

Value obtained from Eq. (11) can be accepted as a minimalfloating-plug diameter taking part in the process of tubedeformation. The method of calculation is presented in [10].

2.2.4. Length lt of the cylindrical part of the floating-plugThe minimal length lt can be assumed as the sum of the

maximal value of floating-plug back-track in the deforma-tion zone and the length of the cylindrical part of the die.

From the equilibrium condition of the forces acting onthe floating-plug it is possible to calculate the length lc ofthe cylindrical part of the die:

lc = 14ps

pw

(d2rdk dk

)(1 c tan

) nr (13)

It is possible to calculate the minimal value of a cylindricalpart of the floating-plug assuming in Eq. (13) the minimal

110 K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114

value of floating-plug back-track in the deformation zone.The final equation is as follows:

lt = nmax + 14ps

pw

(d2rdk dk

)(1 c tan

) gk tan 2

(14)In the equation presented, pw is the value of unit pressureacting on the cylindrical surface of the floating-plug in theworking zone; ps on the conical surface, and pc on the cylin-drical surface in calibrating zone of the plug.

To determine the values of unit pressures, the method ofequilibrium differential equations of an infinitesimal elementof a tube in the particular zones of the deformation fieldwas used [1,3,4]. Knowing the values of stresses x actingin each zone, the unit pressures in any zone can be obtainedaccording to the following equation [10]:

pouX = f(SX) Xcosx 1 sin x (15)

pinX = f(SX) Xcosx + 2 sin x (16)

where pouX is the current unit pressure on the working sur-face of the die, and pinX the current unit pressure on theworking surface of the plug.

As can be seen, the values of the unit pressures influencethe value of dr and nr, and vice versa the values of the unitpressures in the deformation zone depend on the values ofdr and nr. The values are incoherent but the equation maybe solved by iteration: the values are determined when suc-cessive iterations are adequately close. Using FEM analysissuch method was presented in [10,14] for calculations ofunit pressures pw, ps and pc as well as the real plug positionnr, and the real dr value.

Also, knowing the values of stresses x acting in eachdeformation zone, it is possible to obtain the total drawingstresses c according to [10]:

c =[E + (f(SE) 2E)(1+ (1/2))1+ (Dk1/dk2)

]

e(1+(Dk1/dk2))2dk lc/dkgk+g2k (f(SE) 2E)(1+ (1/2))

1+ (Dk1/dk2) (17)

where E is the stress acting in the E cross-section of the tube(Fig. 4), SE is the cross-section area E of the tube (Fig. 4).

3. Material, experimental procedure and results

Drawing tests were carried out for verification of the re-sults of calculations performed for tubes made of CuZn37brass and OF-Cu copper.

The nominal dimensions of the tubes were as follows:initial diameter D0 = 18 mm and initial wall-thicknessesg0 = 0.80 and 0.60 mm.

Table 1Mechanical properties of the initial tubes

Material Mechanicalproperties

Tube dimensions

18.0 0.60 mm 18.0 0.80 mmCuZn37 Rm (MPa) 402.6 6.77 379.2 2.65

R0.2 (MPa) 204.0 10.72 177.6 2.78A100 (%) 43.8 1.76 45.5 0.40

OF-Cu Rm (MPa) 234.6 1.32 235.5 3.46R0.2 (MPa) 53.5 1.58 49.9 5.17A100 (%) 40.9 0.81 32.8 1.24

The tubes were drawn to the final dimensions: final di-ameter Dk = 16.0 mm and final wall-thicknesses gk = 0.60and 0.50 mm.

The mechanical properties of the initial tubes are shownin Table 1.

The tubes were drawn using tools with various geometryof dies with the following angles and lengths lc of die cal-ibrating zone: = 1920 (0.3374 rad), lc = 2.25 mm; =1900 (0.3316 rad), lc = 4.25 mm; = 1530 (0.2705 rad),lc = 2.00 mm; = 1530 (0.2705 rad), lc = 4.25 mm; alsowith plugs with the following angles : 10 (0.1745 rad),12 (0.2094 rad), 14 (0.2443 rad), 16 (0.2793 rad) and 18(0.3142 rad).

The drawing tests were carried out using a chain draw-bench with a maximum drawing force of 40 kN and at adrawing speed of 4 m/min. Trefil 1780 lubricant was used tolubricate the working surfaces of the drawing dies and theplugs.

The calculations were performed for tubes made ofCuZn37 brass and OF-Cu copper, for which experimentaltests of drawing on a floating-plug were carried out. Theobtained results were compared with the results of calcula-tions enabled the values of the real plug diameters dr to beobtained, at which the contact of the tube under deformationwith the working surface of the plug began.

The results of the calculated values of the real nr for exper-iments in which stable runs of the process were observed arepresented in Figs. 912. The value of nr is only theoretical,

Fig. 9. The real plug position nr vs. the () difference, for = 0.2705 rad, lc = 2.00 mm [15].

K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114 111

Fig. 10. The real plug position nr vs. the () difference,for = 0.2705 rad, lc = 4.25 mm [15].

Fig. 11. The real plug position nr vs. the () difference, for = 0.3374 rad, lc = 2.25 mm [15].

but it must be between nmin and nmax, according to Eqs. (6)and (7).

The range of the stable run of the process for the samevalues of wall reduction is very narrow for greater values oflc, and it is equal to the () difference applied in the prac-tice of this process: (0.0523 rad or 3 and 0.0873 rad or 5);(Figs. 10 and 12). For smaller values of lc this range increasesdistinctly (0.0232 rad or 120 and 0.1280 rad, 720), as itis possible to observe in Fig. 11. The increasing die angle also influences the (), increasing the difference range

Fig. 12. The real plug position nr vs. the () difference, for = 0.3316 rad, lc = 4.25 mm [15].

Fig. 13. Plug starting diameter dr vs. plug angle , for = 0.3374 rad,lc = 2.25 mm and = 0.3316 rad, lc = 4.25 mm (D0 = 18 mm,g0 = 0.6 mm) [12].

Fig. 14. Plug starting diameter dr vs. plug angle , for = 0.3374 rad,lc = 2.25 mm and = 0.3316 rad, lc = 4.25 mm (D0 = 18 mm,g0 = 0.8 mm) [12].

(Figs. 9 and 11). It is easy to conclude that the values of realplug position nr increase with decreasing () difference.

The results of calculations of the plug diameter dr val-ues versus the plug geometry (angle ) for tubes made ofCuZn37 brass are shown in Figs. 1317 [12].

Fig. 15. Plug starting diameter dr vs. plug angle , for = 0.2705 rad,lc = 2.0 mm and = 0.3316 rad, lc = 4.25 mm (D0 = 18 mm,g0 = 0.6 mm) [12].

112 K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114

Fig. 16. Plug starting diameter dr vs. plug angle , for = 0.2705 rad,lc = 2.0 mm and = 0.3316 rad, lc = 4.25 mm (D0 = 18 mm,g0 = 0.8 mm) [12].

Fig. 17. The difference between the drawing die angle and the plugangle vs. the drawing die angle , which satisfies the stable drawingcondition [12].

The value of the real tube diameter dr determine the sizeof the sinking zone of the tube on the conical part of thedie. These figures also illustrate the calculated plug angles, determining the stable metal flow conditions for the de-formed tube in the direction of the geometrical center of adrawing die.

Comparison of the results of total drawing stress ccalculations with an experimental data obtained for tubesmade of OF-Cu copper and CuZn37 brass is shown inFigs. 1821.

4. Analysis of results

The dependence of the real plug position nr in the de-formation zone as a function of the () difference in theprocess for tubes made of copper and brass are presented inFigs. 912. In Figs. 9 and 10 their dependence for a constantvalue of the angle of the conical part of the plug and dif-ferent length of cylindrical part of the die lc is shown. In alldiagrams the limiting positions nmax and nmin are plotted.

Fig. 18. The relationship between calculated drawing stresses c as wellas an experimental drawing stresses rz and the plug angle for dies = 15.5 (0.2705 rad), lc = 2.00 mm, and = 15.5 (0.2705 rad),lc = 4.25 mm. Tube material OF-Cu copper [14].

Fig. 19. The relationship between calculated drawing stresses c as well asan experimental drawing stresses rz and the plug angle for dies = 19(0.3316 rad), lc = 2.25 mm and = 19.2 (0.34 rad), lc = 4.25 mm. Tubematerial OF-Cu copper [14].

Fig. 20. The relationship between calculated drawing stresses c aswell as an experimental drawing stresses rz and the plug angle fordies = 15.5 (0.2705 rad) lc = 2.00 mm, and = 15.5 (0.2705 rad)lc = 4.25 mm. Tube material CuZn37 brass [14].

K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114 113

Fig. 21. The relationship between calculated drawing stresses c as well asan experimental drawing stresses rz and the plug angle for dies = 19(0.3316 rad) lc = 2.25 mm, and = 19.2 (0.3374 rad) lc = 4.25 mm.Tube material CuZn37 brass [14].Experiments show that the real position of the plug nr islocated between its limiting positions, and that its vale in-creases with increasing () difference. It is found fromobtained experimental data that the range of the () val-ues increases with the reduction of lc. Particularly, duringthe drawing of tubes made of CuZn37 brass, the values ofnr are much greater than during the drawing tubes made ofOF-Cu copper.

For smaller values of lc, the difference between the nrvalues for the drawing of copper and brass is more distinct.For dies having a longer calibrating part lc such differencedecays, but for greater die angles , smaller values of nr havebeen observed. This means that the process is less stable andthat the zone of tube sinking is greater.

Figs. 1316 illustrate the dependence between the realplug position nr and the calculated plug angles , which de-termines the stable flow condition for the deformed tube inthe direction of the geometrical center of a drawing die. Thecalculated values of the plug angles determining the re-quired metal flow are close to those practically applied min-imal values enabling stability of the drawing process [12].

All of the relationships presented show clearly that in-creasing angle causes the nr value to increase. This meansthat the tube-sinking zone decreases.

Shortening the calibrating part of die lc also causes alsonr to increase, as can be seen in Figs. 912. From this rela-tionships it is easy to conclude that a stable process occurswhen the main deformation is placed on the wall-thicknessreduction during the drawing of thin-walled tubes.

Increasing of the angle causes a () difference in-crease as is shown in Fig. 17.

In Figs. 1821, the relationships between the calculatedvalues of total drawing stress c, its real values rz obtainedfrom measuring experiments and the angle of the plug,are presented. The drawing of tubes made of copper andbrass was carried out using drawing dies with diversifiedgeometry ( and lc).

Comparison of the results of calculations and experimentsshows that the correlation in the nature of the curves is very

good. This tendency is the same for both copper and brassthin-walled tubes.

The relationships obtained confirm the influence of thetool geometry on the course of drawing process observed inthe earlier experiments.

Particularly, it is possible to conclude from these diagramsthat increase in the plug angle causes a decrease of thevalue of total drawing stress; both calculated c and mea-sured rz.

From the diagrams it is also seen that for greater lengthsof the calibrating part of the die lc the calculated values ofdrawing stress c are smaller than the real rz. For smallvalues of lc, a greater compatibility between the computedand the measured results is observed.

On the basis of the results in preliminary calculations, it ispossible to increase the stability of the thin-walled drawingprocess by using a () difference that is greater than thatwhich is actually employed in practice. Also, the zone ofcalibration of the tube lc on the cylindrical part of the plugcan be smaller.

5. Conclusions

Theoretical analysis of the thin-walled drawing process inwhich the variation of the wall-thickness in the zone of tubesinking and the real position of the plug in the deformationzone are taken into consideration has indicated that it ispossible to run a stable process using a () differencegreater than that actually employed in practice.

The results of calculation of drawing stresses accordingto the proposed methodology in which the real geometry ofthe deformation zone is taken into consideration, have beenconfirmed by the results of experiments. This means that it ispossible to apply this method to the analysis of thin-walledtube drawing with a floating-plug.

The results demonstrate that the range of angles of theconical part of the plug, , possible to apply in practice dis-tinctly depends on the reduction in the tube wall-thickness.

Shortening of the length of the calibrating part of thedie, lc, causes the enlargement of the range of the ()difference in which the drawing process is stable.

The results obtained from theoretical calculations andfrom practical experiments allow the proposal to use a toolgeometry that is different from that actually employed. Inpractice, the new tool provides the minimization of the zoneof tube sinking, increases the wall-thickness reduction andassures a more stable performance of the drawing process.Particularly, the new tool has a smaller length of calibratingzone of the die, lc, and greater range of the () difference.

References

[1] M.B. Bisk, W.W. Svejkin, Volocenie trub na samoustanavlivajuscejsjaopravke, Metallurgia, Moskva, 1963.

114 K. Swiatkowski, R. Hatalak / Journal of Materials Processing Technology 151 (2004) 105114

[2] L. Sadok, M. Pietrzyk, Analiza pracy korka swobodnego w ob-szarze odksztalcenia (Analysis of floating-plug position in deforma-tion zone), Hutnik 2 (1981) 6265 (in Polish).

[3] A.N. Bramley, A.N.D.J. Smith, Tube drawing with a floating-plug,Met. Technol. 7 (1976) 322331.

[4] I.L. Perlin, M.Z. Ermanok, Teoria volocenia, Izd. Metallurgia,Moskva, 1971.

[5] J. Luksza, L. Sadok, Wybrane zagadnienia z ciagarstwa, AGH,Krakw, 1986.

[6] B. Avitzur, Drawing of Precision Tubes by the Floating-plug Tech-nique, Lehigh University, Bethlehem, 1975.

[7] L. Sadok, J. Kazanecki, M. Mucha, Energetyczny model procesuciagnienia na korku swobodnym (Energetic model of the floating-plugdrawing process), Hutnik 1 (1981) 2025 (in Polish).

[8] T.Z. Blazynski, Redundant deformation in some tube-forming pro-cesses, ZN AGH, Metalurgia i Odlewnictwo 3 (1977) 445460.

[9] A. Skolyszewski, L. Sadok, Redundant strain in the process of tubedrawing with a floating-plug, ZN AGH, Metalurgia i Odlewnictwo4 (1981) 431440.

[10] R. Hatalak, PhD Thesis, Faculty of Non-Ferrous Metals, Universityof Mining and Metallurgy, Cracow, Poland, 1998 (in Polish).

[11] G.A. Smirnov-Aljaev, G.Ja. Gun, Priblizennyj metod resenia obe-mnych stacionarnych zadac vjazkoplasticeskogo tecenia, Izv. vuzovCernaja Metallurgia Moskva Metallurgizdat 9 (1960) 6267.

[12] R. Hatalak, K. Swiatkowski, The direction of metal flow as a cri-terion of a floating-plug geometry design in the tube drawing pro-cess, in: M. Pietrzyk, J. Kusiak, J. Majta, P. Hartley, I. Pillinger(Eds.), Proceedings of the Eighth International Conference on MetalForming (Metal Forming 2000), Cracow, Poland, 37 Septem-ber 2000, A.A. Balkema, Rotterdam, Brookfield, 2000, pp. 605608.

[13] R. Hatalak, W. Kazana, Kryteria doboru trzpieni swobodnych dociagnienia rur drobnowymiarowych (Criterion of floating-plugs se-lection for drawing of small-sized tubes), Rudy i Metale Niezelazne37 (2) (1992) 4447 (in Polish).

[14] R. Hatalak, K. Swiatkowski, The wall deformation and the diameterreduction in the process of tube drawing with a floating-plug, Arch.Metall. 47 (3) (2002) 275285.

[15] R. Hatalak, K. Swiatkowski, Zakres stabilnego ciagnienia rurcienkosciennych na trzpieniu swobodnym (Range of a stablethin-walled tube drawing with a floating-plug), Rudy i Metale Nieze-lazne 43 (10) (1998) 479481 (in Polish).

Study of the new floating-plug drawing process of thin-walled tubesIntroductionTheoretical analysis of the tool geometry in the thin-walled tubes drawing processChanges in the wall-thickness in the zone of tube sinkingFloating-plug geometryAngle of deformation of the conical part of the plug betaBack-track "n" of the floating-plug in deformation zoneReal diameter dr of the floating-plugLength lt of the cylindrical part of the floating-plug

Material, experimental procedure and resultsAnalysis of resultsConclusionsReferences