A model has been developed for simulating hydrodynamic lubrication in cold rolling. Both Roelands’ and Barus’ viscosity-pressure relations have been applied. Thermal effects regarding heat development caused by plastic deformation as well as work hardening have been included. Furthermore, elastic deformation of the surfaces has fully been incorporated in the model, i.e., elastic deformation of both the strip and the rolls. The governing equations have been solved numerically throughout the entire contact i.e. inlet, work and outlet zone using a very dense grid. Multigrid techniques have been used to solve the equations. It will be shown here that roll flattening has a significant effect on film thickness. However, elastic deformation of the strip material in the inlet region even has a more pronounced effect on film thickness and thus on several process conditions. Furthermore, it is shown that the choice of the viscosity-pressure parameter is limited. Higher values of this parameter cause excessive shear stresses on the strip surface.

Issue Section:
Research Papers
Topics:
Cold rolling, Deformation, Strips, Film thickness, Pressure, Viscosity, Heat, Lubrication, Shear stress, Temperature effects, Work hardening
1.
Atkins
A. G.
,
1970
, “
Hydrodynamic Lubrication in Cold Rolling
,”
Int. J. Mech. Sci.
, Vol.
16
, pp.
1
–
19
.
2.
Barus
C.
,
1893
, “
Isothermals, Isopiestics and Isometrics Relative to Viscosity
,”
Am. J. of Science
, Vol.
45
, pp.
87
–
96
.
3.
Bedi
D. S.
, and
Hillier
M. J.
,
1967
, “
Hydrodynamic Model for Cold Strip Rolling
,”
Proc. I. Mech. E.
, Vol.
182
, pp.
153
–
160
.
4.
Brandt, A., 1984, “Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics,” G.M.D., St. Augustin 1, Germany. Available as G.M.D.-Study No. 85, from G.M.D.-FIT, Postfach 1240, D-5205, St. Augustin 1, Germany.
5.
Brandt
A.
, and
Lubrecht
A. A.
,
1990
, “
Multilevel Matrix Multiplication and Fast Solution of Integral Equations
,”
J. of Comp. Physics
, Vol.
90
, No.
2
, pp.
348
–
370
.
6.
Cheng, H. S., 1966, “Plastohydrodynamic Lubrication,” Friction and Lubrication in Metal Processing, ASME, New York, pp. 69–80.
7.
Dow
T. A.
,
Kannel
J. W.
, and
Bupara
S. S.
,
1975
, “
A Hydrodynamic Lubrication Theory for Strip Rolling Including Thermal Effects
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
97
, No.
1
, pp.
4
–
13
.
8.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, England.
9.
Ka´rma´n, Th. Von, 1925, “Contribution to the Theory of Rolling,” original title: “Beitrag zur Theorie des Walzvorganges,” Vortra¨ege der Dresdener Tagung, Band 5, Heft 2.
10.
Lin
J. F.
, and
Jone
R. C.
,
1992
, “
Analyses of Thermal Hydrodynamic Lubrication in High Speed Rolling. Part I: The Effect of the Roller’s Elastic Deformation
,”
Tribology International
, Vol.
25
, No.
5
, pp.
329
–
339
.
11.
Lin
J. F.
, and
Horng
J. H.
,
1992
, “
Analyses of Thermal Hydrodynamic Lubrication in High Speed Rolling. Part II: The Effect of non-Newtonian Viscosity Models
,”
Tribology International
, Vol.
25
, No.
5
, pp.
341
–
349
.
12.
Lugt, P. M., 1992, “Lubrication in Cold Rolling, Numerical Simulation Using Multigrid Techniques,” Ph.D. thesis. University of Twente, Enschede, The Netherlands, ISBN 90-9005313-1.
13.
Lugt
P. M.
,
Wemekamp
A. W.
,
ten Napel
W. E.
,
van Liempt
P.
, and
Otten
J. B.
,
1993
, “
Lubrication in Cold Rolling, Elasto-Plasto-Hydrodynamic Lubrication of Smooth Surfaces
,”
Wear
, Vol.
166
, pp.
203
–
214
.
14.
Petrusevich
A. I.
,
1951
, “
Fundamental Conclusions from the Contact-Hydrodynamic Theory of Lubrication
,”
Izu. Akad. Nauk. SSSR.
(OTN), Vol.
2
, p.
209
209
.
15.
Reid
J. v.
, and
Schey
J. A.
,
1978
, “
Full Film Lubrication in Aluminum Strip Rolling
,”
Tr. ASLE
, Vol.
21
, pp.
191
–
200
.
16.
Roelands, C. J. A., 1966, “Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils,” Ph.D. thesis, Technische Hogeschool Delft, The Netherlands (V.R.B., Groningen, The Netherlands.)
17.
Sheu, S., 1985, “Mixed Lubrication in Bulk Metal Forming Processes,” Ph.D. thesis. Northwestern University, Evanston, IL.
18.
Schey, J. A., 1984, “Tribology in Metalworking; Friction, Lubrication and Wear,” American Society for Metals, ISBN: 0-87170-155-3.
19.
Sutcliffe, M. P. F., 1989, “Friction and Lubrication in Metal Rolling,” Ph.D. thesis, Cambridge University, Cambridge, England.
20.
Tsao
Y. H.
, and
Sargent
L. B.
,
1975
, “
A Mixed Lubrication Model for Cold Rolling of Metals
,”
Tr. A.S.L.E.
, Vol.
20
, pp.
55
–
63
.
21.
Venner
C. H.
,
Lubrecht
A. A.
, and
ten Napel
W. E.
,
1991
, “
Numerical Simulation of the Overrolling of a Surface Feature in a EHL Line Contact
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
113
, pp.
777
–
783
.
22.
Wilson, W. R. D., and Walowit, J. A., 1971, “An Isothermal Hydrodynamic Lubrication Theory for Strip Rolling with Front and Back Tension,” Tribology Convention 1971, I. Mech. E., C86/71, pp. 164–172.
23.
Wilson
W. R. D.
, and
Mahdavian
S. M.
,
1974
, “
A Thermal Reynolds Equation and its Application in the Analysis of Plasto-Hydrodynamic Inlet Zones
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
96
, No.
4
, pp.
572
–
578
.
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