Elasto-plastic contact stresses between working cylinder and support cylinder of cold rolling using FEM are presented in this paper. Pressure and tractions resulted from the rolling process were obtained by using a calculus program and they were used as loads on a working cylinder

A. D. MAIMON

D. BOAZU

L. STOICESCU

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

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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2008, ISSN 1453 – 083X 
 
FO N D ATĂ
197 6
 
 
 
CONTRIBUTIONS IN THE DOMAIN OF THE CONTACT  
STRESSES BETWEEN CYLINDERS OF COLD ROLLING  
 
A.D. MAIMON1, D. BOAZU2, L. STOICESCU2
1ARCELOR – Mittal Steel Galati 
2“Dunărea de Jos” University of Galaţi 
email: dboazu@ugal.ro 
 
ABSTRACT 
 
Elasto-plastic contact stresses between working cylinder and support cylinder of 
cold rolling using FEM are presented in this paper. Pressure and tractions resulted 
from the rolling process were obtained by using a calculus program and they were 
used as loads on a working cylinder. 
 
KEYWORDS: cold rolling, elasto-plastic contact stresses, rolling process 
 
 
1. FEM model of contact between  
working cylinder (585mm) and support 
cylinder(1525mm) of cold rolling 
 
For the modelling process COSMOS/M version 
2.5 was used. The two cylinders were modelled using 
PLANE2D (plane strain) elements with 4 nodes and 
two degrees of freedom per node. 2D model is 
represented in Fig. 1. A zoom of fin mesh in the 
vicinity of contact between the two cylinders is 
presented in Fig. 3 and the mesh in loading zone (load 
is given by normal and tangential pressure from 
rolling process) is represented in Fig. 2. The whole 
model has 14517 nodes and 17101 elements.  
One node GAP elements (in 2D node-line contact 
elements) were used for transmission of stresses and 
deformations through contact zone.  
The two cylinders were considered supported by 
elastic elements whose rigidity is given by that of the 
rolling system. Working with GAP elements imposed 
an incremental loading and so the analysis is static 
but nonlinear.  
The contact between cylinders is a non-
conforming contact problem because the extension of 
contact zone is not known from the beginning. 
 
  
Fig. 1. FEM model between working cylinder and support cylinder of cold rolling. 
 
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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2008, ISSN 1453 – 083X 
 
FO N D ATĂ
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Fig. 2. Mesh in loading zone of working cylinder 
 
 
Fig. 3. Mesh in contact zone between the two cylinders 
 
 
2. Material model 
 
The elasto plastic behaviour of material (special 
steel) of the two cylinders was considered von Mises 
with isotropic hardening. Principal parameters of 
material model are: Young modulus E=2.1 104 
daN/mm2, Poisson ratio 0.3, yield stress 73 daN/mm2, 
and tangent modulus 20daN/mm2). 
 
3. Studied cases 
 
It was analyzed two cases with the 5 phases of 
sheet thickness reduction. (17.7%, 20.6%, 24.2%, 
20.8, 17.5%). In the first case the friction coefficient 
was considered μ=0.1 and in the second case friction 
coefficient was considered μ=0.075. The width of the 
sheet was considered 1250mm.  
The loading conditions for cold rolling were 
established according to reference [3]. 
For these analyzed cases the equivalent von Mises 
stress distribution and principal stresses are 
represented in Fig. 4-8 (μ=0.1) and Fig. 9-13 
(μ=0.075). The extension of contact zone is of 40mm. 
The contact stain extends to about 40 mm.  
The results of nonlinear analysis are given in 
Table 1 (Case 1 (μ=0.1)) and Table 2 (Case 1 
(μ=0.1))-von Mises stresses from contact zone  (σech 
∗ - for working cylinder) and (σech ∗∗ - for 
supporting cylinder) and principal stresses in the 
contact zone 
1 2 3
, ,σ σ σ . The stress state in the 
vicinity of contact is 3D.  In Tables 1 and 2 principal 
stresses 
1 2 3
σ σ σ< < are negative values and the 
biggest one 
3
σ is considered the contact stress 
(Hertzian pressure).  The equivalent von Mises stress 
was evaluated at a distance of 2 mm from contact 
effective zone, because in the contact zone the 
components of deviator tensor are unmeaningful.  
The influence of friction on loading and contact 
behaviour was considered by modifying friction 
coefficient   (μ=0.1 for dry friction) and (μ=0.075 for 
lubrification). 
The equivalent von Mises stress is calculated 
using the formula: 
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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2008, ISSN 1453 – 083X 
 
FO N D ATĂ
197 6
 
VON = {(1/2)[(σX - σY)2 + (σX - σZ)2 + (σY - σZ)2] 
+ 3(τ2XY + τ2XZ + τ2YZ)}(1/2)
Or by means of principal stresses:  
VON = {(1/2)[( σ1 - σ2)2 + (σ1 - σ3)2 + (σ2 - 
σ3)2]}(1/2)
 
 
Table 1 
Case 1 (μ=0.1) σech ∗ [daN/mm2] σech ∗∗ [daN/mm2] 
σ1,max
[daN/mm2] 
σ2,max
[daN/mm2] 
σ3,max
[daN/mm2] 
Phase A1 72.95 72.95 79.95 117.97 150.91 
Phase A2 73 73 150.4 178.9 215.5 
Phase A3 73 73 156.068 184.79 230.258 
Phase A4 72.99 72.99 130.989 146.134 200.24 
Phase A5 73.563 73.563 253.754 289.142 330.84 
Table 2 
Case 1 (μ=0.075) σech ∗ [daN/mm2] σech ∗∗ [daN/mm2] 
σ1,max
[daN/mm2] 
σ2,max
[daN/mm2] 
σ3,max
[daN/mm2] 
Phase F_A1 72.953 72.953 73.389 108.123 136.507 
Phase F_A2 72.890 72.890 81.960 118.186 153.887 
Phase F_A3 73.044 73.044 141.576 172.475 217.362 
Phase F_A4 72.937 72.937 105.476 129.328 169.797 
Phase F_A5 73.036 73.036 167.813 197.075 241.869 
 
  
Fig. 4a. Case 1 (μ=0.1) Phase A1  
von Mises stress 
Fig.4b. Case 1 (μ=0.1) Phase A1  
principal stress σ3 
  
Fig. 5a. Case 1 (μ=0.1) Phase A2  
von Mises stress 
Fig. 5b. Case 1 (μ=0.1) Phase A2 
 principal stress σ3 
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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2008, ISSN 1453 – 083X 
 
FO N D ATĂ
197 6
 
  
Fig. 6a. Case 1 (μ=0.1) Phase A3  
von Mises stress 
Fig. 6b. Case 1 (μ=0.1) Phase A3  
principal stress σ3 
  
Fig. 7a. Case 1 (μ=0.1) Phase A4  
principal stress σ3 
Fig. 7b. Case 1 (μ=0.1) Phase A4  
principal stress σ3 
 
 
Fig. 8a. Case 1 (μ=0.1) Phase A5 
 principal stress σ3 
Fig. 8b. Case 1 (μ=0.1) Phase A5 
 principal stress σ3 
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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2008, ISSN 1453 – 083X 
 
FO N D ATĂ
197 6
 
 
 
Fig. 9a. Case 2 (μ=0.075) Phase F_A1 
principal stress σ3 
Fig. 9b. Case 2 (μ=0.075) Phase F_A1 
principal stress σ3 
 
 
Fig. 10a. Case 2 (μ=0.075) Phase F_A2  
principal stress σ3 
Fig. 10b. Case 2 (μ=0.075) Phase F_A2  
principal stress σ3 
  
Fig. 11a. Case 2 (μ=0.075) Phase F_A3  
principal stress σ3 
Fig. 11b. Case 2 (μ=0.075) Phase F_A3  
principal stress σ3 
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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2008, ISSN 1453 – 083X 
 
FO N D ATĂ
197 6
 
  
Fig. 12a. Case 2 (μ=0.075) Phase F_A4  
principal stress σ3 
Fig. 12b.Case 2 (μ=0.075) Phase F_A4  
principal stress σ3 
  
Fig. 13a. Case 2 (μ=0.075) Phase F_A4  
principal stress σ3 
Fig. 13b. Case 2 (μ=0.075) Phase F_A4  
principal stress σ3 
  
 
4. Conclusions 
 
From Fig. 14 one can observe that contact 
stresses are bigger when the rolling process is not 
lubrificated.  
 
Fig. 14. 
 
 
For all loading cases there are important plastic 
zones of elliptic shape. In the worst loading case 
(Case 1 (μ=0.1) Phase A5 - see table 1) this elliptic 
region is determined by the two semiaxes of 30mm 
and 25mm; the eccentricity of this plastic zone in 
respect  to  vertical axis of  the two cylinders  is about 
40mm.  
 
References 
 
[1]. Bern A., 1990, Le laminage a froid, Symposium franco-
roumain, Galati. 
[2]. Poloukhine V., 1977, Simulation mathematique et calcul sur 
ordinateur des laminoirs a toles, Edition MIR, Moscou,. 
[3]. Stoicescu L., Gavrilescu I., Boazu D., 1995, Algoritm şi 
program pentru modelarea laminării la rece, Asociaţia oamenilor 
de ştiinţă, filiala Galaţi, Departamentul de Inginerie Tehnologică şi 
Deformare Plastică, tom 21, octombrie 1995, pg. 123-128. 
 
 
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Contributions in the Domain of the Contact Stresses Between Cylinders of Cold Rolling

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Contributions in the Domain of the Contact Stresses Between Cylinders of Cold Rolling

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