In the paper are presented elements of drawing theory and technology of the high mechanical strength wires, when the auger die is located in the maximum of the waves oscillation and it is activated on drawing direction. Force parameters are determined based on the theorem of total consumed power considering metal-tool friction Coulomb type. In order to form a stable system of stationary waves into processed wire there are used ultrasonic energy reflectors. The experiments are accomplished in laboratory on wires made of RUL 1V/ AISI 52100

Brian Tudor LANDKRAMMER

Dragoş Cristian ACHIŢEI

Mihai SUSAN

Roxana Gabriela ŞTEFANICĂ

Viorel ILIESCU

The Annals of “Dunarea de Jos” University of Galati Fascicle IX Metallurgy and Materials Science

Directory of Open Access Journals

FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
 
 
ELEMENTS OF DRAWING THEORY AND TECHNOLOGY  
OF THE HIGH MECHANICAL STRENGTH WIRES IN  
ULTRASONIC FIELD 
 
Viorel ILIESCU1, Mihai SUSAN2, Roxana Gabriela ŞTEFANICĂ2, 
Dragoş Cristian ACHIŢEI2, Brian Tudor LANDKRAMMER2 
1SC CABLERO SA Iaşi,  
2Gheorghe Asachi Technical University of Iaşi, Faculty of Material Science and Engineering 
email: mihaisusan@yahoo.com  
 
ABSTRACT 
 
In the paper are presented elements of drawing theory and technology of the 
high mechanical strength wires, when the auger die is located in the maximum of the 
waves oscillation and it is activated on drawing direction. Force parameters are 
determined based on the theorem of total consumed power considering metal-tool 
friction Coulomb type. In order to form a stable system of stationary waves into 
processed wire there are used ultrasonic energy reflectors. The experiments are 
accomplished in laboratory on wires made of RUL 1V/ AISI 52100. 
 
KEYWORDS: drawing, wire, ultrasonic field, force parameters, ultrasonic 
energy reflectors, mechanical characteristics of resistance and plasticity. 
 
1. Introduction 
 
The wires/metallic wires are generally obtained 
through cold drawing. The plastic deformation 
through cold drawing is accompanied by cold-
hardenings of cold-age hardening which complicates 
the plastic deformation for great reduction degrees of 
the section of the blank wire. The cold-hardening is 
much more obvious for metallic wires of high 
mechanical resistance. In the present paper is 
presented their processing in ultrasonic field 
“ultrasonic vibration drawing-UVD” or UVD 
technology, as an alternative to the classical 
technology (CT). 
The characterization of the UVD technology 
compared to the classical technology (CT) is realized 
on two objective directions such as: 
(i) the calculus of the force parameters; 
(ii) the efficiency of the UVD technology. 
 
 
2. The calculus of force parameters 
 
The calculus of force parameters is made taking 
into consideration the deformation zone of the 
material, the ball-shaped rate field and the Bernoulli 
type laminar flow, figure 1.  
 
 
Fig.1. The interior geometry of the auger die and the components of the rate  
in the deformation zone of the material [1]. 
 
-  58  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
2.1. The rate field at wire drawing 
The hypotheses of plastic deformation are: the 
metallic material is incompressible, the auger die is a 
rigid body and the metal deformation occurs 
according to Von Mises flow condition, the Coulomb 
type metal-tool contact friction, on the oscillating 
system only longitudinal elastic waves are acting in 
stationary regime and the deformation process is 
isothermal, [1, 2]. 
In the areas (I) and (III) the rate is uniform and 
has only axial components with the values v0 and vtr 
existing the interdependency relationship: 
2
01tr0 )R/R(vv =             (1) 
The area of plastic deformation (II) is bounded 
by two spherical surfaces; G1 of radius rf and G2 of 
radius r0 and by a conic surface G3 (defined by the 
taper opening of the auger die 2α). In this area the rate 
is oriented towards the cone’s tip, 0, having 
cylindrical symmetry. In spherical coordinates (r, θ, 
φ) the components of the displacement rate are 
determined as displacement derivatives as a function 
of time ϕθ
..
r
.
uandu,u . The components of the 
deformation rate are determined as derivatives of the 
deformation degree as a function of time and are 
presented in [2]. 
The components of displacement rate in (II) 
zone are: 
⎪⎩
⎪
⎨
⎧
==
θ⋅−==
ϕ 0uu
)r/(cosrvvu
.
0
.
2
0
2
ftrr
.
          (2) 
Along the G1 and G2 limits, the normal 
components of the rate are continuous; however rate 
discontinuities occur at parallel positions to these 
limits: 
- for G1: θ⋅=Δ sinvv tr1  
- for G2: θ⋅=Δ sinvv 02                          (3) 
It appears rate discontinuities both on the conic 
surface G3 and on cylindrical surface G4 since the 
auger die is a rigid body: 
- for G3: )r/(cosrvv 20
2
ftr3 α⋅=Δ  
- for G4: tr4 vv =Δ             (4)  
Under these circumstances, the volumetric rate 
.
V of metal flow through any surface bounded by the 
conical tubular channel defined by dθ ise identical to 
the rate of metal flow through the elementary tube 
defined by dR. Therefore, in zone (III): 
θ⋅θ⋅θ⋅⋅π=
=⋅⋅π=
θ⋅θ⋅=θ⋅=
dcossinv2
vdRR2V
;dcosrdR;sinrR
tr
tr3
.
ff
                          (5) 
In zone (II):
.
r2
.
udrsinr2V ⋅θ⋅⋅θ⋅π−=             (6) 
From the congruency of the two volumetric 
rates it results: 
)r/(cosrvu 20
2
ftrr
.
θ⋅−=            (7) 
 
2.2. The consumed power through drawing 
According to the theorem of the total consumed 
power it can be written the congruency: 
SG
.
def
.
tot
.
WWW +=            (8) 
The necessary power for plastic deformation by 
drawing has the expression: 
UVD2
1trnec
.
RvW σ⋅⋅⋅π=            (9) 
UVDσ  - should balance the total consumption of 
power. 
2.2.1. The consumed power for the proper 
plastic deformation 
It can be noticed from figure 1 that in the areas 
(I) and (III) it is not produced the plastic deformation 
of the metal. 
The plastic deformation of the metal occurs only 
in the area (II). 
Owing to the axial-cylindrical symmetry as a 
function of φ, equation system becomes: 
( )
⎪
⎪
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎪
⎪
⎨
⎧
=ε=ε
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
θ∂∂⋅=ε
=ε
=ε
∂∂=ε
ϕθϕ
θ
ϕϕ
θθ
0
ur21
r/u
r/u
r/u
r
..
r
.
r
.
r
..
r
..
r
.
rr
.
         (10) 
Considering the rate field equations given by 
relationship (4) the deformation rates become: 
    
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎨
⎧
==
⋅⋅=
⋅=−=−=
0
)/(sin)2/1(
)/(cos222
..
3
0
2.
.
3
0
2..
ϕθϕ
θ
ϕϕθθ
εε
θε
θεεε
r
ftrr
ftrrr
rrv
rrv
(11) 
So that the consumed power for proper deformation 
has the expression: 
dV))(2/1()3/2(W
V
ji
.
ij
.
cdef
.
⋅ε⋅ε⋅σ= ∫          (12) 
or 
∫
∫
⋅−⋅⋅⋅=
=⋅+⋅=
V
ftrr
V
ftrcdef
dVrrv
dVrrvW
θσ
θθσ
232
2232.
sin)12/11(1)/1(2
sin)4/1(cos3)/1()3/2(
             (13) 
-  59  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
 
where: 
drdrrdV ⋅⋅⋅⋅= θθπ sin2         (14) 
Replacing dV into relationship (15) it is obtained the 
new relationship for def
.
W : 
 
∫∫ ∫
α
=θ
α
=θ =
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
θ⋅θ⋅θ⋅−⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅⋅⋅πσ=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅θ⋅θ⋅−⋅⋅⋅πσ=
0
2
f
02
ftrc
0
r
rr
22
ftrcdef
.
dsinsin
12
111
r
r
lnrv4
r
drsinsin
12
111rv4W
0
f
                 (15) 
After integration it results the expression: 
)r/rln(]
sin)12/11(1cos)12/11((
12/111ln
12/11
)12/11(1sin)12/11(1cos1[rv2W f0
2
.
22
ftrcdef ⋅
α⋅−+α⋅
+
⋅
−
+α−α−⋅⋅πσ=   (16) 
Taking into consideration the fact that: 
10f0 R/Rr/r =  and )sin/1(Rr 1f α=  
It results: 
.
10
2
1trcdef )R/Rln()(fRv2W ⋅α⋅⋅⋅πσ=             (17) 
where: 
α⋅−+α⋅
+
⋅
⋅
+α−α−α=α
2
22
sin)12/11(1cos)12/11(
12/111ln
1211
1sin)12/11(1cos1)[sin2/1()(f                   (18) 
 
n smaller angles f(α) tend to unity and the relationship  
(19) becomes: 
)R/Rln(Rv2W 101trcdef
.
⋅⋅⋅πσ=           (19) 
The latest relationship is considered to be the 
definition of the ideal power for a uniform rate field: 
.
0
2
ftrr )r/r(vvu −==          (20) 
 
2.2.2. The lost power caused to the rate 
discontinuities 
As it is noticed in figure 1 the G1 and G2 
surfaces are surfaces of rate discontinuities. The metal 
discharge is the same no matter if is calculated with 
relationships that describe the rate field to the right or 
to the left of these surfaces.  
The condition of metal flow continuity requires 
the normal components of the rate, derived from each 
of the rate field on these surfaces, to be equivalent. So 
that, for the G1 surface, the normal component to the 
left has the expression: 
θ⋅= cosvu tr
.
r                          (21) 
Analogous by the axial component of the rate vtr 
of the zone (III), normal on the G1 surface is equal 
with αcos⋅trv . 
The tangential components are no longer equal, 
the difference is known also as rate discontinuity. 
Based on Von Mises flowing criterion, the 
power consumed along the G1 and G2 surfaces has the 
expression: 
1 2
1 2 1 2
.
2 2
SG ,G 1 2 tr f c
G G G G 0
W v dS v dS v dS 4 v r ( / 3) sin d
α
θ=
= τ ⋅Δ ⋅ = τ ⋅Δ ⋅ + τ ⋅Δ ⋅ = π ⋅ ⋅ σ θ ⋅ θ∫ ∫ ∫ ∫             (22) 
after integration 21
.
GSGW  becomes: 
]ctg)sin/[(Rv)3/2()cossin(rv)3/2(W 221trc
2
ftrcGSG
.
21 α−αα⋅⋅π⋅σ=α⋅α−α⋅⋅π⋅σ=     (23) 
 
2.2.3. The consumed power caused by 
friction losses 
The power losses caused by metal-tool friction 
are consumed at the level of G3 and G4 surfaces. 
Along the conical portion, bounded by G3 
surface (figure 1), the rate discontinuity is given by 
the relationship: 
α⋅=α=Δ cos)R/R(vcos)r/r(vv 201tr
2
0
2
ftr3 (24) 
 
and the contact surface element is: 
)sin/dR(R2dS απ=           (25) 
Up to the cylindrical surface G4 the rate 
discontinuity is trvv =Δ 4 . 
Taking into consideration the expression given 
by Sach’s relationship for σr [3]: 
]1)R/R[ln( 210cr −σ=σ                        (26) 
It results the expressions for the friction losses: 
)/ln()]/ln(1[2 1010
2
13
.
3
3 RRRRctgRvdSvW ctr
UVD
G
SG ⋅−⋅⋅⋅⋅=⋅Δ⋅= ∫ σαμπτ     and: 
-  60  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
.
1
2
14 ))(/(24
UVD
ctr
UVD
SG RlRvdSvW σσμπτ −⋅⋅⋅⋅=⋅Δ⋅=                    (27) 
 
In relationships (27) and (28) the friction factor 
μUVD is determined with the relationship [3]: 
)
v
varccos21(
0
trCTUVD
π
−μ=μ          (28) 
with 0,1v/v 0tr ≤ . 
The drawing stress (σUVD) is determined with  
relationship (32). 
 
2.2.4. The drawing stress and force 
From the made power balance it results for the 
classical technology, the following drawing stress 
(noted σCT): 
 
)]R/l(21/[]}R/l)R/Rln()]R/Rln(1(ctg[2]ctg)sin/[(3/2)R/Rln()(f2{ 1
CT
11o10
CT2
10c
CT μ++⋅−αμ+α−αα+⋅ασ=σ   (29) 
 
Coincidently the drawing force (FCT) has the 
expression: 
CT2
1
CT
1
CT D
4
1SF σ⋅⋅π⋅=σ⋅=          (30) 
 
For the UVD technology the drawing stress (σUVD) 
has the expression: 
UVD
1
0
UVD
11010
2
10c
UVD
R
R
1
2]R/l)R/Rln())]R/Rln(1(ctg[]ctg)sin/[(3/2)R/Rln()(f2{
μ+
μ
⋅+⋅−α+α−αα+⋅ασ=σ              (31) 
 
The drawing force for the UVD technology is 
determined with the relationship: 
UVDUVD DF σπ ⋅= 214
1           (32) 
3. Experimental procedure 
  
The experiments were performed on a classical 
hydraulically actuated drawing bench able to develop 
a drawing force of 12·104 N and an active stroke of 
1,5 m. the assembly of the oscillating system has been 
fastened on the resistance frame of the bench by 
means of the nodal flange.  
 
The principle scheme of the experimental 
installation, used for wire drawing in ultrasonic field 
is illustrated in fig. 2, [4]. 
 
Fig.2. Principle scheme of the experimental installation used for wire drawing in ultrasonic field, 
according to UVD technology: 1 – supply bloc; 2 – polarization bloc; 3 – ultrasonic generator type 
UZG 2-4M; 4, 13 – reflectors of ultrasonic energy (pressure rolls); 5 – raw wire; 6 – magnetostrictive 
transducer; 7 – conical concentrator; 8 – nodal flange; 9 – frame of the classical drawing device; 10 
– guide for ultrasonic waves; 11 – die; 12 – processed wire; A – amplitude of die’s oscillations;  B – 
wave oscillation in processed wire; ——— progressive wire; ------- regressive wave, [4,5]. 
-  61  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
The UZG 2-4M type ultrasonic generator, with a 
power of 2000 W and resonance frequency f = 
17,5·103 Hz, works in conjunction with the PMS 15A-
18 type oscillating system, which comprises a 
magnetostrictive transducer and a conical wave 
concentrator made from titanium based alloy. At the 
right side of the conical concentrator a guiding device 
core and convergent conical inner geometry with semi 
angle conicity α = 8° and cylindrical calibration zone. 
As drawing lubricant soap powder was used in a 
mixture with 10-15% fine lime powder and 12-15% 
tale powder. The assembly of the oscillating system is 
dimensioned as a multiple of λ/2, where λ = c / f  - is 
the ultrasonic wave length determined by the 
ultrasonic propagation rate (c) in the metallic wire and 
resonance frequency (f). 
The ultra-acoustic energy reflectors (pressure 
rolls) play the role to limit the action of ultrasonic 
energy upon well defined portions of both raw and 
processed wire, from AISI 52100 ( RUL IV / STAS 
11250) ball bearing steel.  
Raw wire had initial diameter D0 = 4,6·10-3 m 
and the chemical composition : Fe - 1.2C - 0.4Mn – 
0.3Si – 0.5Cr – 0.02S – 0.02P - 0.08Mo – 0.2Ni – 
0.2Cu (wt%). The wire was processed by single stage 
drawing to the final diameter D1 = 4.22·10-3 m. 
The mechanical characteristics of resistance 
(yield stress, Rp0.2, and tensile strength, Rm) and 
plasticity (ultimate strain, A5), were determined, for 
both raw and drawn wires, by tensile tests performed, 
according to EN 10002-1/1995, with a strain rate of 
3.33·10-4 m/sec, on MTS 810.24 tensile testing 
machine. 
 
4. Experimental results and discussion 
 
In the case of classical technology (CT), the 
experimental average value of the drawing force was 
determined as NF CTex 1370= . With this value, the 
experimental values were calculated for the drawing 
stress, MPaCTex 98=σ , by means of means of 
relationship (32) and for the friction coefficient 
026.0CTμ , by means of Sach’s relationship given in 
[3]. The effects of ultrasonic oscillation amplitude on 
both technological parameters and efficiency of UVD 
technology are summarized in table 1. 
 
Table 1. Effects of ultrasonic amplitude on bloth the technological parameters and the efficiency 
of the UVD technology in case of processing AISI 52100 ball bearing steel wires 
 
Technological parameters UVD efficiency Ultrasonic 
oscillation amplitude 
at UVD technology 
−
vtr vv /  
- 
UVDμ  
- 
UVD
anF  
[N] 
UVD
exF  
[N] 
FΔ  
[%] 
5 · 10-6 m 0.54 0.0062 1259 1250 8.75 
15 · 10-6 m 0.18 0.0044 1205 1184 13.57 
20 · 10-6 m 0.13 0.0030 1179 1147 16.27 
 
Based on the value of the friction coefficient for 
classical technology, 026.0=CTμ , in column 3 the 
friction coefficients at UVD technology , UVDμ , were 
calculated as a function of relative deformation 
rates
−
vtr vv / , by means of relationship (28). As 
compared to classical technology (CT) values at least 
four times lower were obviously obtained for UVD 
technology.  
The values of the analytical drawing force at 
UVD technology, UVDanF , were calculated in column 4 
with relationship (32), based on the analytical 
drawing stress at UVD technology , UVDanσ  determined 
with (31), where l is length of the calibration zone of 
the die. Column 5 lists the experimental values with 
the analytical ones.  
Finally, the efficiency of the UVD technology 
compared to CT was determined in column 6 with 
relationship: ( )[ ]CTexUVDex FFF −⋅=Δ 1100 .  
It is obvious that this highest efficiency was 
obtained for the ultrasonic oscillation amplitude A = 
20 · 10-6 m, which gives the lowest relative 
deformation rate, in agreement with our previous 
observations [4, 5]. 
The tensile – strain curves, determined as 
average values of five tests performed on raw 
(annealed) wires, on wires drawn with CT and on the 
three sets of wires processed by UVD are illustrated 
in fig. 3. 
On one hand, in case of CT, designated by 0 
oscillation amplitude, the drawn wires were obviously 
work hardened as compared to raw (annealed) wires.  
On the other hand, it is noticeable that, with the 
increase of ultrasonic oscillation amplitude, the 
decrease of intensity of the work hardening 
phenomenon in ultrasonically  drawn wires occurs, 
which causes low mechanical characteristics of 
resistance and higher plasticity as shown in table 2. 
-  62  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
 
Fig.3. Influence of the oscillation amplitude of ultrasonic at UVD technology on the tensile stress-
strain curves of processed wires. 
 
Table 2. Yield stress, (Rp0.2), tensile strength, (Rm) and ultimate strain, (A5) of the curves from fig.3 
0 5 15 20 A, 10-6 m raw wire CT UVD 
Rp0.2 [ MPa] 332 401 370 349 327 
Rm [MPa] 650 746 711 685 667 
A5 [%] 9.15 7.87 8.01 8.38 8.46 
 
5. Conclusions 
 
Based on a rate field with spherical distribution, 
a relationship was established for the drawing force 
for the metal wires and the analytical values were in 
very good agreement with the experimental ones, 
determined at UVD processing of AISI 52100 (RUL 
IV/ STAS 11250) ball bearing steel wires. 
With increasing ultrasonic oscillation amplitude 
applied to the die, from 5 to 20 · 10-6 m, progressive 
decreases were obtained for both the drawing force, 
from 1250 to 1147 N, and the friction coefficient, 
from 0.0062 to 0.003. As compared to classical 
technology, efficiency higher that 16% were obtained 
for UVD technology. By tensile tests it was 
emphasised that UVD technology not only allows 
lower drawing forces but also reduces the works 
hardening level – a phenomenon which is always 
present in classical technology – causing increases of 
ultimate strain from 7.87% at CT to 8.46%. 
 
 
References 
 
[1]. Susan, M. - Trefilarea sârmelor de oţel. Editura CERMI, Iaşi, 
2008. 
[2]. Cazimirovici, E. ş.a. - Teoria şi tehnologia deformării plastice 
prin tragere, Editura Tehnică, Bucureşti, 1990. 
[3]. Susan, M., s.a. - On the drawing in ultrasonic field of metallic 
wires high mechanical resistance. Journal of Optoelectronic and 
Advanced Materials, 7(2), Aprilie, pp. 637-645, 2005 
[4]. *** Contract CNCSIS  - tip A, GR 63 – 23.05.2006. 
[5]. *** Contract CNCSIS  - tip A, GR 80 – 23.05.2007. 
 
-  63  -


Elements of Drawing Theory and Technology of the High Mechanical Strength Wires in Ultrasonic Field

https://www.gup.ugal.ro/ugaljournals/index.php/mms/article/download/3068/2751

Elements of Drawing Theory and Technology of the High Mechanical Strength Wires in Ultrasonic Field

Abstract

Similar works

Full text

Available Versions

Directory of Open Access Journals