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Back tension value in the fine wire drawing process
Journal of Materials Processing Technology 80 – 81 (1998) 380 – 387
Back tension value in the fine wire drawing process A. Skołyszewski *, M. Pac´ko Department of Metal Forming, Faculty of Metallurgy and Materials Science, Akademia Go´rniczo-Hutnicza, Mickiewicza 30, PL-30 059 Krako´w, Poland
Abstract The production of fine and very fine wire of high-alloy steels realized through multi-stage drawing would be impossible with no back tension applied. The most favourable conditions of the drawing process occur when the back tension value is close to the critical back tension. The paper focuses on two problems. In the first part, based on the results of extensive laboratory tests for six grades of high-alloy steels, an attempt of finding the relationship between the critical back tension value and the mechanical properties of a material is presented. The generalized relation s0kr = s0kr (E), regardless of the material grade, is also discussed. The knowledge of that relationship allows, with no need to perform labour-consuming tests, quick determination of the value of critical back tension. In the second part, the results of industrial investigations on the optimization of the fine wire multi-stage slip drawing process are presented. The tests included variations of the back tension value in successive deformation stages as well as the measurements of the drawing force, metal pressure on the die and back tension. The aim was to decrease the wear of dies as well as to increase the stability of the drawing process. The results of industrial tests verified the relationships presented in the first part of the paper. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Critical back tension; Drawing stress; High-alloy steels; Mechanical properties; Multi-stage slip drawing; Wire drawing
1. Introduction In the period 1995 – 1997, the Department of Metal Forming of the University of Mining and Metallurgy, Krako´w, Poland and the Mikrohuta Plant, Baildon Steel Mill, Katowice, Poland performed extensive laboratory and industrial research on starting the production of fine and very fine wire having a round, flattened and complex profile of the cross-section. The material grades included alloy and high-alloy steels as well as special alloys. The results of part of these investigations were published previously [1 – 7] and presented at three international conferences [8 – 10]. During the discussion on the paper at the 6th International Conference ‘Metal Forming ’96’ in Krako´w [9], it was stated that the results of further research work would be presented at the 7th International Conference ‘Metal Forming ’98’. The present paper is the above mentioned publication. The results of investigations presented here have not been published until now and are the continuation of previous works [1–10].
* Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00116-2
The investigations focused on the estimation of the back tension value in the fine wire drawing processes. The multi-stage slip drawing process is optimum when the back tension value in each deformation stage is equal to or slightly greater than the critical back tension. The determination of the value of the stress (s0kr) or force (F0kr) of the critical back tension requires the performance of strenuous and complicated laboratory tests [3,9]. The question arises: is the value of s0kr related to any of the mechanical properties of the deformed material? If the answer is in the affirmative, the critical back tension value can be quickly determined from the result of a simple uniaxial tensile test. The knowledge of s0kr is the first step to the optimization of the multi-stage drawing process. The second step is the knowledge of the relationship between the number of coils of the wire on the drawing rings and the back tension value in each deformation stage. The present paper discusses the above mentioned two steps of optimization. Several grades of stainless steel (1H13, H17, 1H18N9), heat-resisting steel (H25N20S2, 0H23J5) and implant steel (00H17N14M2) were investigated. The chemical constitution of the above materials is presented in Table 1.
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Table 1 Chemical constitution (in %) of high-alloy steels being investigated
C Ni Mn Mo Si Cu P S Cr Ti N W V Al Zn
1H13 stainless steel
1H18N9 stainless steel
H17 stainless steel
0H23J5 heat-resisting steel
H25N20S2 heat-resisting steel
00H17N14M2 implant steel
0.12 0.46 0.36 0.07 0.32 0.18 0.027 0.023 12.75 — — 0.08 0.02 — —
0.12 9.0 2.0 0.3 0.8 0.2 0.04 0.025 18.0 0.2 — 0.3 0.15 — —
0.019 — 0.42 — 0.31 — 0.02 0.001 16.9 — — — — — —
0.02 0.4 0.49 — 0.75 0.06 0.035 0.01 23.2 0.025 0.014 — — 5.0 2.6
0.15 19.5 1.5 0.4 2.5 0.2 0.04 0.025 25.5 0.15 — 0.4 0.15 — —
0.02 13.5 1.5 2.25 0.5 0.2 0.04 0.02 17.1 0.2 0.16 0.4 0.16 — —
2. Back tension in the drawing process The probable distribution of metal pressure on the die during drawing without back tension is shown in Fig. 1. This has been confirmed by theoretical and experimental investigations [11]. In the zone of elastic deformation, which is a few micrometres thick, the pressure pN exceeds several times the value of the flow stress sp. This very unfavourable phenomenon is extremely dangerous during fine wire drawing. Application of a back tension value (s0) lower than the stress on the boundary between the elastic and plastic zones (slsp) results in a decrease of the pressure pN in the zone of elastic deformation. If the value of s0 reaches slsp, the elastic zone in the die disappears (elastic deformation is realized in tension at the stress s0 = slsp). The following relationships can be written for the elastic zone: s0 = 0 pN1 \5sp
(1)
s0 B slsp pN2 BpN1
(2)
s0 = slsp pN3 $sp
(3)
The value of the back tension stress equal to slsp is the critical back tension value: s0 = slsp =s0kr
(4)
Experimental determination of the critical back tension force F0kr (s0kr) was based on another definition of critical back tension. The critical back tension is defined as the limiting value of the back tension force F0, the application of which does not increase the value of the drawing force (Fcp), and causes the value of the force of metal pressure on the die (Fm) to decrease clearly (Fig. 2).
The value of critical back tension is not a constant quantity. It depends on the strain-hardening state of the material (Fig. 3), the amount of deformation (Fig. 4), and the flow stress sp. The value of s0kr is slightly influenced also by the diameter of the drawn wire (dk), the drawing velocity (6c), and the coefficient of friction (m). This can be expressed as follows: s0kr = s0kr (sp, z, R0.2, dk, 6c, m)
(5)
The above relationship, known from previous research, was taken into consideration in subsequent works.
3. Critical back tension value During the tests conducted for fine and very fine wire drawing process [1–9], measurements allowing the determination of the force or the calculation of the stress of the critical back tension were performed. The drawing tests were performed with the following variable parameters: six steel grades diameter d0 = 1.6–0.2 mm unit reduction zi = 12–25% total reduction zc = 50–76% strain-hardening R0.2 = 350–2000 MPa drawing velocity 6c = 0.2–1.6 m s − 1 three sorts of liquid lubricants diamond dies with 2a=12° A significant number of s0kr values was obtained for a wide range of parameters influencing the critical back tension stress. This group of results was highly representative. The wires drawn according to each schedule were subjected to tensile testing using the INSTRON 4502 testing machine digitally controlled, with application of
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Fig. 1. Distribution of unit pressure over the length of the deformation zone.
s0kr = (4.3–4.9)× 10 − 4E
computer processing. The mechanical properties were determined: elastic limit (R0.05), yield strength (R0.2), tensile strength (Rm) and Young’s modulus (E). Their values were related to the critical back tension stress. As an example, such relations for 1H18N9 steel are given in Table 2. It can be concluded from the data presented in Table 2 that a strict relationship exists between the critical back tension value and Young’s modulus, regardless of the technological variant:
1H18N9
s0kr/E=(4.3–4.9)×10 − 4
Eqs. (7)–(12) clearly evidence the possibility of determination of the critical back tension stress value based on the value of Young’s modulus obtained from the uniaxial tensile test. For the investigated alloy steel grades, the generalized relationship can be formulated:
(6)
Substantial discrepancies occur when relating s0kr to the R0.2, Rm and R0.05 values. This was observed also for the remaining five grades of investigated steels. The relationships between s0kr and E are as follows:
H17
s0kr = (4.0–4.8)× 10 − 4E
1H13 0H23J5
(8)
s0kr = (4.3–5.2)× 10 − 4E s0kr = (4.1–4.6)× 10
H25N20S2
(9)
−4
E
s0kr = (4.7–5.1)× 10 − 4E
00H17N14M2
(7)
s0kr = (4.1–5.0)× 10 − 4E
s0kr = (4.0–5.2) · 10 − 4E
(10) (11) (12)
(13)
4. Force parameters in the multi-stage slip drawing process
Fig. 2. Variation of the drawing force (Fc) and the force of metal pressure on the die (Fm) as a function of the back tension force (F0).
The next stage of investigations was an attempt of optimization of the operation of a UDZWG 160/15 multi-stage drawing machine (Fig. 5) used for high-alloy steel fine wire drawing. The optimization consisted of finding the number of wire coils on the drawing ring which resulted in a back tension value close to the critical back tension in each deformation stage. This approach to the drawing process provides the most favourable distribution of forces, the lowest wear of expensive dies and high stability of the deformation process. It should be noted that the construction of the examined drawing machine (and every other one which could be applied) does not the value of the back tension to be changed continuously, as the possible number of wire coils (n) on the ring varies in a stepwise manner. In
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strain gauge B); Fm(sr) = (Fm1 + Fm2)/2 represents the average value of the drawing force without back tension (the Fm1 and Fm2 values measured by the same strain gauge in two successive passes); F0(sr) = dFm(sr) = Fm(sr) − Fm0 represents the average back tension value. The reading of appropriate values was always made from two successive measurements performed in succeeding stages. The investigations focused on two steel grades— 1H18N9 and H17. Three different deformation schedules and four variants of coiling (n=0.5, 1.5, 2.5 and 3.5) were applied. Due to limitations of space, only sample results are presented in this paper, allowing the illustration of the possibility of optimization of the multi-stage drawing process by applying a proper back tension value. A more extensive report from this research work will be presented elsewhere at a later date. The sample oscillogram of the recorded forces, allowing the determination of the value of the back
Fig. 3. Influence of strain-hardening on critical back tension variations for wires drawn with zc = 67.3% (zi = 17%, d0 = 1.4 mm, dk = 0.8 mm): (a) NH19; (b) 1H18N9; (c) H25N20S2.
this case it was equal to 0.5, 1.5, 2.5 and 3.5 circles of the ring. By applying properly constructed and graduated strain gauges, the force parameters of the drawing process were measured. This allowed the determination of the actual back tension value, according to the principle presented in Fig. 6. A and B (Fig. 6) designate the strain gauges; N− 1, N, N + 1 are the drawing stages in the multi-stage drawing machine (numbers of passes); Fm0 is the force of metal pressure on the die in the case of drawing with back tension (second die (N), first pass), strain gauge B; Fm1 is the force of metal pressure on the die without back tension (the force measured by the same strain gauge (B) which measures Fm0, using the same pass —first pass); Fm2 is the force of metal pressure on the die without back tension, measured in the first die (N) (the same strain gauge (B) which measures Fm0 and Fm1)—second pass; F0 =dFm =Fm1 − Fm0 represents the back tension value (strain gauge B, first pass —measurement of Fm1 and Fm0 by the same
Fig. 4. Variation of the critical back tension stress as a function of reduction (z); (a) CuNi11Pr alloy; (b) H17; (c) 1H18N9.
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Table 2 Relationships for the wire of 1H18N9 steel No.
d0 (mm)
dk (mm)
zi (%)
R0.2 (MPa)
Rm (MPa)
E (MPa)
s0kr (MPa)
s0kr/Rm
s0kr/R0.2
s0kr/E
1 2 3 4 5 6 6a 6b 6c 7 7a 7b 7c 8 9 10 11 12 13 14
1.600 1.600 1.600 0.474 1.273 0.696 0.696 0.696 0.696 1.397 1.397 1.397 1.397 0.327 1.060 0.877 0.576 0.528 0.230 0.248
1.507 1.450 1.397 0.434 1.160 0.632 0.632 0.632 0.632 1.273 1.273 1.273 1.273 0.298 0.963 0.799 0.528 0.474 0.202 0.230
12.4 18.8 24.7 16.2 16.9 17.5 17.5 17.5 17.5 17.0 17.0 17.0 17.0 16.9 17.5 17.0 16.0 19.4 22.8 14.0
596 632 746 1088 1096 961 960 988 949 954 964 972 942 1640 1390 1319 1020 1038 2015 1852
723 820 1074 1565 1522 1096 1090 1118 1084 1118 1123 1128 1100 1724 1693 1757 1355 1482 2089 1932
91 600 94 600 108 000 129 200 131 100 114 600 113 100 116 000 114 800 115 800 116 200 116 000 115 000 154 600 149 800 154 400 122 400 129 900 164 900 159 900
39.4 44.3 48.3 64.5 63.9 50.1 49.6 50.8 49.6 53.4 53.0 53.4 52.3 68.3 68.0 70.1 57.8 61.2 74.9 72.4
0.055 0.054 0.045 0.041 0.042 0.046 0.046 0.045 0.046 0.048 0.047 0.047 0.048 0.039 0.040 0.040 0.043 0.041 0.036 0.037
0.066 0.070 0.065 0.059 0.058 0.052 0.052 0.051 0.052 0.056 0.055 0.055 0.056 0.042 0.049 0.053 0.057 0.059 0.037 0.039
0.00043 0.00047 0.00045 0.00049 0.00049 0.00044 0.00044 0.00044 0.00043 0.00046 0.00046 0.00046 0.00045 0.00044 0.00045 0.00045 0.00047 0.00047 0.00045 0.00045
Fig. 5. Scheme of wire guiding and die positions in the UDZWG 160/15 drawing machine.
tension force in the fourth deformation stage, is shown in Fig. 7. Fig. 8 presents the values of the forces of metal pressure on the die (Fm(sr), Fm0) as well as back tension forces (F0, F0(sr)) for 1H18N9 steel (the variant with n= 1.5 and 6c = 0.5 m s − 1). The preliminary analysis of the results of investigations shown in Fig. 8 indicates significant differences in force loads in individual deformation stages at n = 1.5.
Fig. 6. Scheme of force measurement and principle of determination of back tension value (F0): A and B represent strain gauges.
5. Optimization of the operation of drawing machines During the performance of the industrial tests, the drawing machine was stopped and the specimens were taken from the wire after each pass. The values of Young’s modulus were determined from uniaxial tensile testing (example for 1H18N9 steel—Fig. 9). Subsequently, using Eq. (7) determined previously, the values of the critical back tension stress were calculated (Table 3). The multi-stage slip drawing process is optimum when the back tension values are close to s0kr (Table 3). Critical back tension values which were obtained during the drawing tests of 1H18N9 steel, with different numbers of coils (n), are presented in Fig. 10. The comparison of s0kr values (Table 3) with the recorded back tension values s0 (Fig. 10) allows the conclusion that each of the industrial variants produced falls far short of the optimum conditions. In order to optimize the drawing machine working conditions, the number of wire coils on individual rings has to be different. The most favourable conditions for the drawing process of 1H18N9 steel were achieved with the number of coils given in Table 4.
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Fig. 7. Sample oscillogram of force variations recorded in the third and fourth deformation stages during drawing of wire of 1H18N9 steel (number of coils on rings no. 3 and 4: n= 1.5). Table 4 The number of wire coils on the drawing rings for 1H18N9 steel No. of pass
1
2
3
4
5
6
7
8
9
10
11
12
13
14
No. of coils
1.5
0.5
0.5
2.5
2.5
1.5
2.5
0.5
2.5
1.5
2.5
2.5
2.5
1.5
Fig. 8. The values of the forces of metal pressure on the die and back tension forces: 1H18N9 steel, the variant with n =0.5 and 1.5, 6c = 0.5 m s − 1.
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Fig. 10. Back tension stress values recorded during industrial investigations of the process of multi-stage drawing of the wire of 1H18N9 steel.
Fig. 9. Variation of Young’s modulus of the wire of 1H18N9 steel.
The number of coils given above did not fully correspond to the optimum condition s0 $s0kr. It is impossible to achieve optimum conditions considering the stepwise number of wire coils as well as various drawing ring diameters, which results from the construction of the drawing machine. The conditions obtained should be recognized as the most favourable ones. The fact of achieving such conditions is confirmed by the results of the distribution of the strength reserve coefficient g =sc/sp obtained for the individual passes designed (Fig. 11). Over almost the whole range of the process, the value of the g coefficient is close to the optimum value (gopt =0.4 – 0.7). 6. Conclusions The results of the extensive laboratory and industrial investigations concerning the process of multi-stage Table 3 Critical back tension stress for 1H18N9 steel No. of pass
Di (mm) E (MPa)
s0kr min (MPa)
s0kr max (MPa)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.750 0.696 0.632 0.576 0.528 0.474 0.434 0.395 0.362 0.327 0.298 0.267 0.248 0.230 0.202
39.1 47.3 49.8 51.5 52.4 55.4 55.4 56.2 59.0 61.5 63.2 64.0 66.7 70.3 71.1
44.6 53.9 56.7 58.6 59.7 63.1 63.2 64.0 67.3 70.1 72.0 73.0 76.0 80.1 81.0
91 000 109 900 115 700 119 700 121 800 128 800 128 900 130 600 137 300 143 000 146 900 148 900 155 200 163 500 165 400
Fig. 11. The values of the strength reserve coefficient (g = sc/sp) in individual passes, with the number of wire coils given in Table 4; for 1H18N9 steel.
drawing of fine and very fine wire of high-alloy steels allow the following observations and conclusions to be formulated: Regardless of the material grade, the strain-hardening state, as well as the drawing process conditions (unit and total reduction, drawing velocity, coefficient of friction), the s0kr/E ratio takes values in the range (4.0–5.2) · 10 − 4 for the materials examined. It can be concluded that for any unknown process conditions, based on the results of the uniaxial tensile test, the approximate value of the critical back tension stress can be determined. The knowledge of the s0kr value allows the optimization of the fine wire multi-stage drawing process, considering the force parameters, tool wear and stability of the operation of the drawing machine.
Acknowledgements The financial support of the Polish Committee for Scientific Research (Grant No. 7T08B-064-96C/3200) is gratefully acknowledged.
A. Skołyszewski, M. Pac´ko / Journal of Materials Processing Technology 80–81 (1998) 380–387
References [1] A. Skołyszewski, J. Luksza, Z. Zawila, M. Sko´ra, Hutnik — Wiad. Hutnicze 62 (9) (1995) 346–353. [2] L. Sadok, A. Skołyszewski, J. Luksza, Hutnik—Wiad. Hutnicze 62 (11) (1995) 479 – 484. [3] A. Skołyszewski, L. Sadok, J. Luksza, Wire Ind. 63 (747) (1996) 279 – 284. [4] L. Sadok, A. Skołyszewski, J. Szczepanski, W. Zachariasz, Metall. Foundry Eng. 22 (1) (1996) 33–40. [5] J. Luksza, A. Skołyszewski, R. Scha¨ffer, Arch. Metall. 41 (1996) 237 – 250. [6] F. Witek, A. Skołyszewski, R. Oleksiak, Hutnik—Wiad. Hut-
.
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nicze 62 (12) (1995) 517 – 523. [7] A. Skołyszewski, F. Witek, M. Ruminski, Hutnik — Wiad. Hutnicze 63 (1) (1996) 13 – 18. [8] J. Luksza, A. Skołyszewski, M. Ruminski, Proc. II Semina´rio de Trefilac¸a˜o de Arames, Barras e Tubos de Materiais Ferrosos e Na˜o-Ferrosos, Sa˜o Paulo, Brazil, 7 – 8 Nov. 1995, Brazilian Association for Metallurgy and Materials, Sao Paulo, 1995, pp. 111 – 125. [9] A. Skołyszewski, J. Luksza, M. Palko, J. Mater. Process. Technol. 60 (1996) 155 – 160. [10] J. Luksza, A. Skołyszewski, M. Ruminski, Politechnika Czestochowska, Konferencje 7, Wydawnictwo Pol. Czestochowskiej, Czestochowa, 1996, pp. 95 – 104. [11] L. Sadok, M. Pac´ko, M. Pietrzyk, Steel Res. 6 (1988) 275–278.
Back tension value in the fine wire drawing process A. Skołyszewski *, M. Pac´ko Department of Metal Forming, Faculty of Metallurgy and Materials Science, Akademia Go´rniczo-Hutnicza, Mickiewicza 30, PL-30 059 Krako´w, Poland
Abstract The production of fine and very fine wire of high-alloy steels realized through multi-stage drawing would be impossible with no back tension applied. The most favourable conditions of the drawing process occur when the back tension value is close to the critical back tension. The paper focuses on two problems. In the first part, based on the results of extensive laboratory tests for six grades of high-alloy steels, an attempt of finding the relationship between the critical back tension value and the mechanical properties of a material is presented. The generalized relation s0kr = s0kr (E), regardless of the material grade, is also discussed. The knowledge of that relationship allows, with no need to perform labour-consuming tests, quick determination of the value of critical back tension. In the second part, the results of industrial investigations on the optimization of the fine wire multi-stage slip drawing process are presented. The tests included variations of the back tension value in successive deformation stages as well as the measurements of the drawing force, metal pressure on the die and back tension. The aim was to decrease the wear of dies as well as to increase the stability of the drawing process. The results of industrial tests verified the relationships presented in the first part of the paper. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Critical back tension; Drawing stress; High-alloy steels; Mechanical properties; Multi-stage slip drawing; Wire drawing
1. Introduction In the period 1995 – 1997, the Department of Metal Forming of the University of Mining and Metallurgy, Krako´w, Poland and the Mikrohuta Plant, Baildon Steel Mill, Katowice, Poland performed extensive laboratory and industrial research on starting the production of fine and very fine wire having a round, flattened and complex profile of the cross-section. The material grades included alloy and high-alloy steels as well as special alloys. The results of part of these investigations were published previously [1 – 7] and presented at three international conferences [8 – 10]. During the discussion on the paper at the 6th International Conference ‘Metal Forming ’96’ in Krako´w [9], it was stated that the results of further research work would be presented at the 7th International Conference ‘Metal Forming ’98’. The present paper is the above mentioned publication. The results of investigations presented here have not been published until now and are the continuation of previous works [1–10].
* Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00116-2
The investigations focused on the estimation of the back tension value in the fine wire drawing processes. The multi-stage slip drawing process is optimum when the back tension value in each deformation stage is equal to or slightly greater than the critical back tension. The determination of the value of the stress (s0kr) or force (F0kr) of the critical back tension requires the performance of strenuous and complicated laboratory tests [3,9]. The question arises: is the value of s0kr related to any of the mechanical properties of the deformed material? If the answer is in the affirmative, the critical back tension value can be quickly determined from the result of a simple uniaxial tensile test. The knowledge of s0kr is the first step to the optimization of the multi-stage drawing process. The second step is the knowledge of the relationship between the number of coils of the wire on the drawing rings and the back tension value in each deformation stage. The present paper discusses the above mentioned two steps of optimization. Several grades of stainless steel (1H13, H17, 1H18N9), heat-resisting steel (H25N20S2, 0H23J5) and implant steel (00H17N14M2) were investigated. The chemical constitution of the above materials is presented in Table 1.
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Table 1 Chemical constitution (in %) of high-alloy steels being investigated
C Ni Mn Mo Si Cu P S Cr Ti N W V Al Zn
1H13 stainless steel
1H18N9 stainless steel
H17 stainless steel
0H23J5 heat-resisting steel
H25N20S2 heat-resisting steel
00H17N14M2 implant steel
0.12 0.46 0.36 0.07 0.32 0.18 0.027 0.023 12.75 — — 0.08 0.02 — —
0.12 9.0 2.0 0.3 0.8 0.2 0.04 0.025 18.0 0.2 — 0.3 0.15 — —
0.019 — 0.42 — 0.31 — 0.02 0.001 16.9 — — — — — —
0.02 0.4 0.49 — 0.75 0.06 0.035 0.01 23.2 0.025 0.014 — — 5.0 2.6
0.15 19.5 1.5 0.4 2.5 0.2 0.04 0.025 25.5 0.15 — 0.4 0.15 — —
0.02 13.5 1.5 2.25 0.5 0.2 0.04 0.02 17.1 0.2 0.16 0.4 0.16 — —
2. Back tension in the drawing process The probable distribution of metal pressure on the die during drawing without back tension is shown in Fig. 1. This has been confirmed by theoretical and experimental investigations [11]. In the zone of elastic deformation, which is a few micrometres thick, the pressure pN exceeds several times the value of the flow stress sp. This very unfavourable phenomenon is extremely dangerous during fine wire drawing. Application of a back tension value (s0) lower than the stress on the boundary between the elastic and plastic zones (slsp) results in a decrease of the pressure pN in the zone of elastic deformation. If the value of s0 reaches slsp, the elastic zone in the die disappears (elastic deformation is realized in tension at the stress s0 = slsp). The following relationships can be written for the elastic zone: s0 = 0 pN1 \5sp
(1)
s0 B slsp pN2 BpN1
(2)
s0 = slsp pN3 $sp
(3)
The value of the back tension stress equal to slsp is the critical back tension value: s0 = slsp =s0kr
(4)
Experimental determination of the critical back tension force F0kr (s0kr) was based on another definition of critical back tension. The critical back tension is defined as the limiting value of the back tension force F0, the application of which does not increase the value of the drawing force (Fcp), and causes the value of the force of metal pressure on the die (Fm) to decrease clearly (Fig. 2).
The value of critical back tension is not a constant quantity. It depends on the strain-hardening state of the material (Fig. 3), the amount of deformation (Fig. 4), and the flow stress sp. The value of s0kr is slightly influenced also by the diameter of the drawn wire (dk), the drawing velocity (6c), and the coefficient of friction (m). This can be expressed as follows: s0kr = s0kr (sp, z, R0.2, dk, 6c, m)
(5)
The above relationship, known from previous research, was taken into consideration in subsequent works.
3. Critical back tension value During the tests conducted for fine and very fine wire drawing process [1–9], measurements allowing the determination of the force or the calculation of the stress of the critical back tension were performed. The drawing tests were performed with the following variable parameters: six steel grades diameter d0 = 1.6–0.2 mm unit reduction zi = 12–25% total reduction zc = 50–76% strain-hardening R0.2 = 350–2000 MPa drawing velocity 6c = 0.2–1.6 m s − 1 three sorts of liquid lubricants diamond dies with 2a=12° A significant number of s0kr values was obtained for a wide range of parameters influencing the critical back tension stress. This group of results was highly representative. The wires drawn according to each schedule were subjected to tensile testing using the INSTRON 4502 testing machine digitally controlled, with application of
382
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Fig. 1. Distribution of unit pressure over the length of the deformation zone.
s0kr = (4.3–4.9)× 10 − 4E
computer processing. The mechanical properties were determined: elastic limit (R0.05), yield strength (R0.2), tensile strength (Rm) and Young’s modulus (E). Their values were related to the critical back tension stress. As an example, such relations for 1H18N9 steel are given in Table 2. It can be concluded from the data presented in Table 2 that a strict relationship exists between the critical back tension value and Young’s modulus, regardless of the technological variant:
1H18N9
s0kr/E=(4.3–4.9)×10 − 4
Eqs. (7)–(12) clearly evidence the possibility of determination of the critical back tension stress value based on the value of Young’s modulus obtained from the uniaxial tensile test. For the investigated alloy steel grades, the generalized relationship can be formulated:
(6)
Substantial discrepancies occur when relating s0kr to the R0.2, Rm and R0.05 values. This was observed also for the remaining five grades of investigated steels. The relationships between s0kr and E are as follows:
H17
s0kr = (4.0–4.8)× 10 − 4E
1H13 0H23J5
(8)
s0kr = (4.3–5.2)× 10 − 4E s0kr = (4.1–4.6)× 10
H25N20S2
(9)
−4
E
s0kr = (4.7–5.1)× 10 − 4E
00H17N14M2
(7)
s0kr = (4.1–5.0)× 10 − 4E
s0kr = (4.0–5.2) · 10 − 4E
(10) (11) (12)
(13)
4. Force parameters in the multi-stage slip drawing process
Fig. 2. Variation of the drawing force (Fc) and the force of metal pressure on the die (Fm) as a function of the back tension force (F0).
The next stage of investigations was an attempt of optimization of the operation of a UDZWG 160/15 multi-stage drawing machine (Fig. 5) used for high-alloy steel fine wire drawing. The optimization consisted of finding the number of wire coils on the drawing ring which resulted in a back tension value close to the critical back tension in each deformation stage. This approach to the drawing process provides the most favourable distribution of forces, the lowest wear of expensive dies and high stability of the deformation process. It should be noted that the construction of the examined drawing machine (and every other one which could be applied) does not the value of the back tension to be changed continuously, as the possible number of wire coils (n) on the ring varies in a stepwise manner. In
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strain gauge B); Fm(sr) = (Fm1 + Fm2)/2 represents the average value of the drawing force without back tension (the Fm1 and Fm2 values measured by the same strain gauge in two successive passes); F0(sr) = dFm(sr) = Fm(sr) − Fm0 represents the average back tension value. The reading of appropriate values was always made from two successive measurements performed in succeeding stages. The investigations focused on two steel grades— 1H18N9 and H17. Three different deformation schedules and four variants of coiling (n=0.5, 1.5, 2.5 and 3.5) were applied. Due to limitations of space, only sample results are presented in this paper, allowing the illustration of the possibility of optimization of the multi-stage drawing process by applying a proper back tension value. A more extensive report from this research work will be presented elsewhere at a later date. The sample oscillogram of the recorded forces, allowing the determination of the value of the back
Fig. 3. Influence of strain-hardening on critical back tension variations for wires drawn with zc = 67.3% (zi = 17%, d0 = 1.4 mm, dk = 0.8 mm): (a) NH19; (b) 1H18N9; (c) H25N20S2.
this case it was equal to 0.5, 1.5, 2.5 and 3.5 circles of the ring. By applying properly constructed and graduated strain gauges, the force parameters of the drawing process were measured. This allowed the determination of the actual back tension value, according to the principle presented in Fig. 6. A and B (Fig. 6) designate the strain gauges; N− 1, N, N + 1 are the drawing stages in the multi-stage drawing machine (numbers of passes); Fm0 is the force of metal pressure on the die in the case of drawing with back tension (second die (N), first pass), strain gauge B; Fm1 is the force of metal pressure on the die without back tension (the force measured by the same strain gauge (B) which measures Fm0, using the same pass —first pass); Fm2 is the force of metal pressure on the die without back tension, measured in the first die (N) (the same strain gauge (B) which measures Fm0 and Fm1)—second pass; F0 =dFm =Fm1 − Fm0 represents the back tension value (strain gauge B, first pass —measurement of Fm1 and Fm0 by the same
Fig. 4. Variation of the critical back tension stress as a function of reduction (z); (a) CuNi11Pr alloy; (b) H17; (c) 1H18N9.
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Table 2 Relationships for the wire of 1H18N9 steel No.
d0 (mm)
dk (mm)
zi (%)
R0.2 (MPa)
Rm (MPa)
E (MPa)
s0kr (MPa)
s0kr/Rm
s0kr/R0.2
s0kr/E
1 2 3 4 5 6 6a 6b 6c 7 7a 7b 7c 8 9 10 11 12 13 14
1.600 1.600 1.600 0.474 1.273 0.696 0.696 0.696 0.696 1.397 1.397 1.397 1.397 0.327 1.060 0.877 0.576 0.528 0.230 0.248
1.507 1.450 1.397 0.434 1.160 0.632 0.632 0.632 0.632 1.273 1.273 1.273 1.273 0.298 0.963 0.799 0.528 0.474 0.202 0.230
12.4 18.8 24.7 16.2 16.9 17.5 17.5 17.5 17.5 17.0 17.0 17.0 17.0 16.9 17.5 17.0 16.0 19.4 22.8 14.0
596 632 746 1088 1096 961 960 988 949 954 964 972 942 1640 1390 1319 1020 1038 2015 1852
723 820 1074 1565 1522 1096 1090 1118 1084 1118 1123 1128 1100 1724 1693 1757 1355 1482 2089 1932
91 600 94 600 108 000 129 200 131 100 114 600 113 100 116 000 114 800 115 800 116 200 116 000 115 000 154 600 149 800 154 400 122 400 129 900 164 900 159 900
39.4 44.3 48.3 64.5 63.9 50.1 49.6 50.8 49.6 53.4 53.0 53.4 52.3 68.3 68.0 70.1 57.8 61.2 74.9 72.4
0.055 0.054 0.045 0.041 0.042 0.046 0.046 0.045 0.046 0.048 0.047 0.047 0.048 0.039 0.040 0.040 0.043 0.041 0.036 0.037
0.066 0.070 0.065 0.059 0.058 0.052 0.052 0.051 0.052 0.056 0.055 0.055 0.056 0.042 0.049 0.053 0.057 0.059 0.037 0.039
0.00043 0.00047 0.00045 0.00049 0.00049 0.00044 0.00044 0.00044 0.00043 0.00046 0.00046 0.00046 0.00045 0.00044 0.00045 0.00045 0.00047 0.00047 0.00045 0.00045
Fig. 5. Scheme of wire guiding and die positions in the UDZWG 160/15 drawing machine.
tension force in the fourth deformation stage, is shown in Fig. 7. Fig. 8 presents the values of the forces of metal pressure on the die (Fm(sr), Fm0) as well as back tension forces (F0, F0(sr)) for 1H18N9 steel (the variant with n= 1.5 and 6c = 0.5 m s − 1). The preliminary analysis of the results of investigations shown in Fig. 8 indicates significant differences in force loads in individual deformation stages at n = 1.5.
Fig. 6. Scheme of force measurement and principle of determination of back tension value (F0): A and B represent strain gauges.
5. Optimization of the operation of drawing machines During the performance of the industrial tests, the drawing machine was stopped and the specimens were taken from the wire after each pass. The values of Young’s modulus were determined from uniaxial tensile testing (example for 1H18N9 steel—Fig. 9). Subsequently, using Eq. (7) determined previously, the values of the critical back tension stress were calculated (Table 3). The multi-stage slip drawing process is optimum when the back tension values are close to s0kr (Table 3). Critical back tension values which were obtained during the drawing tests of 1H18N9 steel, with different numbers of coils (n), are presented in Fig. 10. The comparison of s0kr values (Table 3) with the recorded back tension values s0 (Fig. 10) allows the conclusion that each of the industrial variants produced falls far short of the optimum conditions. In order to optimize the drawing machine working conditions, the number of wire coils on individual rings has to be different. The most favourable conditions for the drawing process of 1H18N9 steel were achieved with the number of coils given in Table 4.
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Fig. 7. Sample oscillogram of force variations recorded in the third and fourth deformation stages during drawing of wire of 1H18N9 steel (number of coils on rings no. 3 and 4: n= 1.5). Table 4 The number of wire coils on the drawing rings for 1H18N9 steel No. of pass
1
2
3
4
5
6
7
8
9
10
11
12
13
14
No. of coils
1.5
0.5
0.5
2.5
2.5
1.5
2.5
0.5
2.5
1.5
2.5
2.5
2.5
1.5
Fig. 8. The values of the forces of metal pressure on the die and back tension forces: 1H18N9 steel, the variant with n =0.5 and 1.5, 6c = 0.5 m s − 1.
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Fig. 10. Back tension stress values recorded during industrial investigations of the process of multi-stage drawing of the wire of 1H18N9 steel.
Fig. 9. Variation of Young’s modulus of the wire of 1H18N9 steel.
The number of coils given above did not fully correspond to the optimum condition s0 $s0kr. It is impossible to achieve optimum conditions considering the stepwise number of wire coils as well as various drawing ring diameters, which results from the construction of the drawing machine. The conditions obtained should be recognized as the most favourable ones. The fact of achieving such conditions is confirmed by the results of the distribution of the strength reserve coefficient g =sc/sp obtained for the individual passes designed (Fig. 11). Over almost the whole range of the process, the value of the g coefficient is close to the optimum value (gopt =0.4 – 0.7). 6. Conclusions The results of the extensive laboratory and industrial investigations concerning the process of multi-stage Table 3 Critical back tension stress for 1H18N9 steel No. of pass
Di (mm) E (MPa)
s0kr min (MPa)
s0kr max (MPa)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.750 0.696 0.632 0.576 0.528 0.474 0.434 0.395 0.362 0.327 0.298 0.267 0.248 0.230 0.202
39.1 47.3 49.8 51.5 52.4 55.4 55.4 56.2 59.0 61.5 63.2 64.0 66.7 70.3 71.1
44.6 53.9 56.7 58.6 59.7 63.1 63.2 64.0 67.3 70.1 72.0 73.0 76.0 80.1 81.0
91 000 109 900 115 700 119 700 121 800 128 800 128 900 130 600 137 300 143 000 146 900 148 900 155 200 163 500 165 400
Fig. 11. The values of the strength reserve coefficient (g = sc/sp) in individual passes, with the number of wire coils given in Table 4; for 1H18N9 steel.
drawing of fine and very fine wire of high-alloy steels allow the following observations and conclusions to be formulated: Regardless of the material grade, the strain-hardening state, as well as the drawing process conditions (unit and total reduction, drawing velocity, coefficient of friction), the s0kr/E ratio takes values in the range (4.0–5.2) · 10 − 4 for the materials examined. It can be concluded that for any unknown process conditions, based on the results of the uniaxial tensile test, the approximate value of the critical back tension stress can be determined. The knowledge of the s0kr value allows the optimization of the fine wire multi-stage drawing process, considering the force parameters, tool wear and stability of the operation of the drawing machine.
Acknowledgements The financial support of the Polish Committee for Scientific Research (Grant No. 7T08B-064-96C/3200) is gratefully acknowledged.
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