Journal of Materials Processing Technology 145 (2004) 7–13

Effect of interstand tension on roll load, torque and workpiece

deformation in the rod rolling process
Laila S. Bayoumi a , Youngseog Lee b,∗
a Department of Mechanical Design and Production, Cairo University, Cairo, Egypt
b Plate and Rod Research Group, POSCO Technical Research Laboratories, P.O. Box 36, Pohang, South Korea
Received 7 June 2002; received in revised form 8 November 2002; accepted 11 March 2003

Abstract

The effect of interstand tension, resulting from the increase in relative rolling velocity in successive stands of continuous rolling with a
round–oval–round sequence, on the roll load, rolling torque and workpiece deformation has been investigated. For this purpose, a simplified
analytical approach has been formulated and validated by comparison with available experimental results. Based on this approach, a limiting
value was determined for the increase in the ratio of relative rolling velocity between stands.
When this limiting value is reached, the state of stress in the workpiece within the roll gap changes to a uniaxial state of stress that
can lead to the loss of the ability of the work rolls to grip the workpiece and consequently these changes might make the rolling process
unstable. The results have also shown that the roll load decreases with increasing interstand tension while the torque increases with an
increase in back tension and decreases with an increase in front tension. The reduction in the outgoing maximum width of the workpiece
as a result of interstand tension is linearly related to the increase in the ratio of relative rolling velocity between stands.
© 2003 Elsevier B.V. All rights reserved.

Keywords: Metal hot working; Rod rolling; Interstand tension; Limiting interstand rolling velocity increase ratio

1. Introduction pass rolling sequence. An attempt is then made to relate the

change in interstand tension to a condition in which the vari-
The round–oval–round sequence is the most commonly ation of interstand tension causes a change in the state of
used roll pass for the production of rounds in the interme- stress components of the workpiece within the roll gap such
diate and finishing stands of present continuous bar and rod that the stress component in the direction of rolling becomes
rolling mills. It has the merits of simple groove geometry, dominant in relation to the other stress components. Such a
uniform deformation, good surface quality free from folds, state of stress can lead to loss of the ability of the work rolls
and easy design. Several studies have been carried out to to grip the workpiece due to the loss of pressure and make
update the empirical and semi-empirical approaches in the the rolling process unstable.
analysis of rod (or bar) rolling [1–3]. There have also been The approach is based on assuming homogeneous defor-
efforts to design the roll pass and predict the roll load and mation through the workpiece height and width and uniform
rolling torque by applying analytical method [4], the finite rolling velocity across the workpiece profile. The work-
element method [5–7] and by regression based on exten- piece material is considered to be isotropic, rigid–plastic
sive experimental data [8]. These studies, however, have not and incompressible. At any cross section, the flow stress of
given much attention to assessing the effect of interstand ten- the material is obtained by substituting the effective strain
sion, as a function of relative velocity in successive stands, and effective strain rate into the material constitutive law
on the roll load, rolling torque and workpiece deformation. at the prevailing rolling temperature. This approach has
In the present work a simplified analytical approach is then been applied to the four-pass rolling sequence where
proposed to study the effect of interstand tension, as a func- experimental data is available [1]. Finally, we have carried
tion of relative velocity in successive stands, on the roll load, out a numerical simulation to predict the limitation of the
roll pressure and rolling torque for the round–oval–round increase in the interstand rolling velocity in the next stands
and demonstrated its effect on the interstand tensile force,
∗ Corresponding author. Tel.: +82-54-220-6058; fax: +82-54-220-6911. roll force and rolling torque as a function of the increases
E-mail address: pc554162@posco.co.kr (Y. Lee). in the ratio of interstand rolling velocity.

0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0924-0136(03)00581-8
8 L.S. Bayoumi, Y. Lee / Journal of Materials Processing Technology 145 (2004) 7–13

Nomenclature
A workpiece cross sectional area
F interstand tension
G roll gap
Lr roll-bite length
Ls distance between two successive
stands
M roll torque
n roll velocity (rpm)
N rolling power
P roll load
Re effective roll radius
Ri inner roll radius
R0 maximum roll radius
vx , vy , vz workpiece velocity components
V1 , V2 entry and exit pass velocity
2b projected width of workpiece–roll
groove contact
2h workpiece height
2w workpiece maximum width

Greek letters
λ interstand velocity increase ratio
σ1, σ2 back and front axial stress
ω roll angular velocity

Subscripts
i stand (pass) number
r along roll-bite length
s along interstand length
1 at roll-bite entry Fig. 1. Workpiece profile geometry: (a) oval pass; (b) round pass.
2 at roll-bite exit

piece are separated. Lr represents the length of the roll-bite

Lr = 2Ri (h1 − h2 ), (1)
2. Problem formulation
where Ri is the roll inner root radius. The section height 2h
2.1. Roll-bite geometry at any distance x from entry is given by

Referring to Figs. 1 and 2, Cartesian coordinates x, y, z are Lr x2

h = h1 − x+ . (2)
chosen to be the directions of workpiece length, height and Ri 2Ri
width, respectively, with the origin of axes at the midpoint
The section maximum width 2w is approximated to have a
of the entry plane. The x–y and x–z planes are planes of
parabolic distribution along the roll-bite length given by
symmetry. 2h1 , 2h2 , 2h are the cross section heights, 2w1 ,
2w2 , 2w are the cross section widths and A1 , A2 , A are the x x2
cross section areas at entry, exit and any cross section along w = w1 − 2(w1 − w2 ) + (w1 − w2 ) 2 , (3)
Lr Lr
the roll-bite length, respectively. It is assumed that the entry
and exit profiles are already known. which satisfies the boundary conditions of w = w1 at x = 0,
Fig. 3 shows the experimentally obtained projected area of w = w2 and dw/dx = 0 at x = Lr . The projected area
contact between workpiece and roll groove surface, for oval of the workpiece–roll contact surface on the x–z plane is
and round passes, respectively. These were acquired by the approximated to a semi-elliptic shape of a width 2b2 at exit
emergency stop of the pilot rod rolling mill and the detail of and 2b at any section distance x from entry expressed as
this experiment is described in Ref. [9]. The white line dis- 
tinguishes the portion in contact. Here, Cx and –Cx are points 2x x2
b = b2 − 2, (4)
on the abscissa where the roll groove and deformed work- Lr Lr
 L.S. Bayoumi, Y. Lee / Journal of Materials Processing Technology 145 (2004) 7–13 9

Fig. 2. Roll-bite geometry.

which satisfies the boundary conditions of b = 0 at x = 0,

b = b2 and db/dx = 0 at x = Lr .

2.2. Velocity, strain and strain rate components

2.2.1. Along roll-bite length Fig. 3. Shape of projected contact area of workpiece deformed inside of
The workpiece enters the roll-bite with a velocity V1 |i = roll groove and its geometric designation when a specimen with 60 mm
diameter is rolled: (a) oval pass; (b) round pass. The pass sequence is
V2 |i · A2 |i /A1 |i and exits the roll-bite with a velocity V2 = described in Ref. [9].
ωRe , where i represents the stand (pass) number. ω is the
angular velocity of the rolls and Re is the effective roll radius
obtained from the maximum roll radius R0 , roll gap G and the
workpiece exit maximum width 2w2 and exit cross sectional across the workpiece cross section and that the cross section
area A2 as of the workpiece is rectangular
  V2 h2 w2
A2 vx = . (6)
Re = R0 − 0.5 −G . (5) hw
2w2
For homogeneous deformation of the workpiece in the direc-
Eq. (5) works only when the exit cross sectional shape
tions of height and width the respective strain components
is rectangular. Eq. (5) is based on equivalent rectangular
are given by
approximation method that transforms the non-rectangular    
cross section into a rectilinear one of a width equal to the h w
εy = ln , εz = ln , (7)
maximum width of the cross section while net cross sec- h1 w1
tional area is maintained the same [1]. The approximation
method is explained in detail in Ref. [10]. and from the constant volume condition
To calculate the axial velocity component of the work- εx = −(εy + εz ). (8)
piece cross section, the equivalent rectangle approximation
method was again employed using the maximum width Neglecting the shear strain components, the effective strain
equivalence. At any cross section at a distance of x from is obtained as
entry, the axial velocity component vx is obtained from the 
constant volume flow condition assuming vx to be uniform ε̄r = 23 (ε2x + ε2y + ε2z ). (9)
10 L.S. Bayoumi, Y. Lee / Journal of Materials Processing Technology 145 (2004) 7–13

The strain rate components are obtained by differentiating the material constitutive law at the rolling temperature. Since
the strain components with respect to time the state of stress along the interstand length is uniaxial then
the stresses σ 1 and σ 2 are the flow stresses of the workpiece
vx ∂h vx ∂w
ε̇y = , ε̇z = , ε̇x = −(ε̇y + ε̇z ), along the interstand length at the entry to and the exit from
h ∂x w ∂x the roll-bite of the pass. The back and front tensile forces
 for the pass are obtained from the relations F1 = A1 σ1 and
ε̄˙ r = 3 (ε̇x
2 2
+ ε̇2y + ε̇2z ). (10) F2 = A2 σ2 .

2.2.2. Along interstand length 2.4. Roll load, rolling torque and power
The workpiece emerges from the roll-bite with a veloc-
ity V2 |i which is assumed to increase along the interstand The roll load P and rolling torque M are, respectively,
length Ls to reach the entry of the next stand at a veloc-  Lr
ity V1 |i = (1 + λ)V2 |i+1 , where λ is the ratio of velocity P = −2 σy b dx, (15)
increase through the interstand length and i stands for
0
 Lr
pass number. The state of stress in the workpiece along
M = −4 σy b(Lr − x) dx + Re (F1 − F2 ). (16)
the interstand length is a uniaxial tension so that the strain 0
components between the stands are expressed as
The rolling power N is obtained as
εx = ε̄s = λ. (11) MV2
N= . (17)
The strains in Eq. (11) are small and they range from 0 Re
to 0.06. For such small values of strains, the engineering
and logarithmic strains are almost the same. The strain rate 2.5. Workpiece dimensions
components between i and i + 1 stands are thus obtained as
It is assumed that the workpiece dimensions are already
λV2
ε̇x = ε̄˙ s = , ε̇y + ε̇z = −0.5ε̇x . (12) known in the case of no back and front tensions. An increase
Ls in the exit velocity V2 by a ratio of λ along the interstand
The workpiece cross sectional area at the entry of the next distance will reduce the cross sectional area of the work-
stand is A1 |i+1 = A2 |i /(1 + λ). piece at entry to the next pass by 1/(1 + λ) which leads to a
decrease in the cross sectional area at the exit of the pass by
2.3. Stresses the same ratio. Since the exit workpiece height is determined
by the roll groove height, which is maintained unchanged,
2.3.1. Along roll-bite length the reduction in area will reduce only the workpiece maxi-
The flow stress is obtained by substituting the effective mum width 2w2 to become equal to 2w2 /(1 + λ).
strain and effective strain rate, from Eqs. (9) and (10) into
the material constitutive law at the rolling temperature. The
deviatoric stress components σx , σy and σz are obtained from 3. Limiting velocity increase ratio
Levy–Mises flow rule
2σ̄ 2σ̄ 2σ̄ If one of the stands is disturbed by a change in rolling
σx = ε̇x , σy = ε̇y , σz = ε̇z . (13) velocity, it also immediately affects the interstand tensions
3ε̄˙ r 3ε̄˙ r 3ε̄˙ r
and workpiece width (spread) as well as the roll force and
The mean stress σ m is obtained from the stress component rolling torque at the preceding and the following stands. This
σ x as σm = σx − σx . σ x is expressed by a parabolic relation implies that there will be changes in the state of stress in the
along the roll-bite length as workpiece within the roll gap such that the rolling process
x x2 might become unstable. Such changes in the state of stress
σx = σ1 − 2(σ1 − σ2 ) + (σ1 − σ2 ) 2 , (14) can be assessed in terms of the velocity increase ratio in the
Lr Lr
next stands.
where σ 1 and σ 2 are the back and front tensile stresses for It might be deduced that there will be a limiting value
the pass to be obtained from the stresses along the interstand for the velocity increase ratio λmax to avoid rolling becomes
length as shown below. The stress components in the y and unstable. This will occur when the back tension σ 1 becomes
z directions are given by σy = σy + σm and σz = σz + σm , equal to the flow stress at entry to the roll-bite. In such a
respectively. Note that if σ1 = σ2 = 0 then σ x will be equal case there is no stress discontinuity between the interstand
to zero. length and the entry plane so that the flow stress of the
workpiece becomes equal to σ x at entry to the roll-bite. This
2.3.2. Along interstand length means that the other two stress components σ y and σ z vanish
The flow stress is obtained by substituting the effective which leads to loss of workpiece grip and the rolling process
strain and effective strain rate from Eqs. (11) and (12) into becomes unstable.
 L.S. Bayoumi, Y. Lee / Journal of Materials Processing Technology 145 (2004) 7–13 11

Table 1
Pass data and theoretical roll loads compared with experimental loads
Pass no. 1 2 3 4
Pass shape Oval Round Oval Round
Entry bar section (2h1 /2w1 ) 29.5/29.5 43/14.8 20.1/20.1 30.1/10.4
Exit bar section (2h2 /2w2 ) 14.8/43 20.1/20.1 10.4/30.1 14.2/14.2
Entry section area, A1 (mm2 ) 638.5 424.5 316.8 208.4
Exit section area, A2 (mm2 ) 424.5 316.8 208.4 159.1
Roll root radius, Ri (mm) 132.6 129.75 134.8 135.4
Effective radius, Re (mm) 133.95 131.1 135.6 136.75
Exit contact width, 2b2 (mm) 35.1 19.1 23.7 12.2
Roll velocity (rpm) 78 105 154 198.5
Exit velocity, V2 (m/s) 1.088 1.458 2.216 2.903
Roll load, Pth /Pexp (kN) 170/168 98/97 102/113 74/73

4. Results and discussion Passes 1 and 2 are chosen to study the effect of inter-
stand tension on the interstand tensile force, roll load, rolling
In order to validate the proposed theory the above analy- torque and the rolling condition at which rolling of the work-
sis is applied to a case of experimental hot rolling of 0.18% piece tends to become unstable. In order to carry out the
plain carbon steel bars at 1050 ◦ C in a four-pass rod rolling study it is necessary first to determine the limiting velocity
sequence without interstand tensions [1]. The flow stress of increase ratio λmax between the two stands. This is obtained
the workpiece material is characterized by Shida’s constitu- by equating the back tension σ 1 to the flow stress upon en-
tive equation [11] as try to the roll-bite. Table 2 shows the results obtained for
˙ 0.126 λmax assuming different values of Ls , from 500 to 1500 mm,
σ̄ = 140[1.65(ε̄)0.4 − ε̄](ε̄) (18)
which indicates that λmax increases with the increase in Ls .
Table 1 shows the pass data and the results of theoretical
roll loads compared with those obtained from experiments
for the case of rolling without interstand tension. Table 2
Values of limiting velocity increase ratio λmax at different interstand
The good agreement between the theoretical and experi-
lengths, Ls between passes 1 and 2
mental values of the roll loads in Table 1 indicates that the
proposed theory can be applied successfully to analyze the Ls (mm)
oval–round (or round–oval) rolling sequence. The theoreti- 500 750 1000 1250 1500
cal roll pressure distribution along the roll-bite length for the
λmax 0.063 0.070 0.076 0.081 0.086
four passes, without interstand tension, is shown in Fig. 4.

Fig. 4. Pressure distribution along the roll-bite length with no interstand Fig. 5. Relation between interstand tensile force, F and velocity increase
tensions. ratio, λ at different interstand lengths, Ls .
12 L.S. Bayoumi, Y. Lee / Journal of Materials Processing Technology 145 (2004) 7–13

Fig. 6. Variation of roll load, P with velocity increase ratio, λ for different Fig. 8. Pressure distribution along the roll-bite length in pass 1 due to
interstand lengths, Ls . front tension.

The effect of interstand tension is studied by keeping the

is subjected to front tension, the torque decreases with the
roll velocity of pass 1 unchanged and increasing the roll
increase of λ and increases with the increase of Ls , while
velocity of pass 2 by different values of velocity increase
in pass 2, which is subjected to back tension the torque in-
ratios λ < λmax and assuming two values for Ls = 500 and
creases with the increase of λ and decreases with the increase
1500 mm. The study investigates the effect of λ and Ls on
of Ls . The effect of interstand length on the roll load and
the interstand tensile force F, roll load P and rolling torque
rolling torque is small. The roll pressure distribution along
M as shown in Figs. 5–7, respectively.
the roll-bite length as a result of front tension for pass 1 and
The results show that the interstand tensile force F in-
back tension for pass 2 for different values of λ < λmax and
creases with the increase of λ and decreases with the in-
an interstand distance of 500 mm is shown in Figs. 8 and 9,
crease of Ls . The roll load P decreases with the increase of
respectively.
λ and increases with the increase of Ls . In pass 1, which

Fig. 7. Variation of rolling torque, M with velocity increase ratio, λ for Fig. 9. Pressure distribution along the roll-bite length in pass 2 due to
different interstand lengths, Ls . back tension.
 L.S. Bayoumi, Y. Lee / Journal of Materials Processing Technology 145 (2004) 7–13 13

5. Concluding remarks References

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