A mathematical programming solution based on finite element method is used to analyze wall slip of viscoplastic lubrication in a metal-rolling inlet zone. Slip velocity can be directly obtained by parametric quadratic programming without an iterative process between the oil film pressure and the slip velocity. It is found that wall slip causes the oil film thickness to decrease dramatically. The initial limiting shear strength and proportional constant of the viscoplastic lubricant have a larger effect on the oil film pressure than the rolling speed. The nonsensitivity of oil film thickness to the rolling speed is a great particular advantage to metal-rolling processing.

1.
Wilson
,
W. R. D.
, and
Aggarwal
,
B. B.
, 1978, “
A Plastohydrodynamic Inlet Zone Analysis for a Viscoplastic Lubrication
,”
Wear
0043-1648,
7
, pp.
119
132
.
2.
Wilson
,
W. R. D.
, and
Huang
,
X. B.
, 1989, “
Viscoplastic Behavior of a Silicone Oil in a Metalforming Inlet Zone
,”
ASME J. Tribol.
0742-4787,
111
, pp.
585
590
.
3.
Wilson
,
W. R. D.
, 1997, “
Tribology in Cold Metal Forming
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
119
, pp.
695
698
.
4.
Hatzikiriakos
,
S. G.
, and
Dealy
,
J. M.
, 1991, “
Wall Slip of Molten High Density Polyethylene I—Sliding Plate Rheometer Studies
,”
J. Rheol.
0148-6055,
35
, pp.
497
523
.
5.
Pit
,
R.
,
Hervet
,
H.
, and
Leger
,
L.
, 1999, “
Friction and Slip of a Simple Liquid at a Solid Surface
,”
Tribol. Lett.
1023-8883,
7
, pp.
147
152
.
6.
Kaneta
,
N.
, et al.
, 1990, “
Observation of Wall Slip in Elastophydrodynamic Lubrication
,”
ASME J. Tribol.
0742-4787,
112
, pp.
447
584
.
7.
Ehret
,
P.
,
Dowson
,
D.
, and
Taylor
,
C. N.
, 1999, “
Transient EHL Solutions with Interfacial Slip
,”
ASME J. Tribol.
0742-4787,
121
, pp.
703
710
.
8.
Jacobson
,
B. O.
, and
Hamrock
,
B. J.
, 1984, “
Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication of Rectangular Contacts
,”
ASME J. Lubr. Technol.
0022-2305,
106
, pp.
275
282
.
9.
Bair
,
S.
, and
Winer
,
W. O.
, 1979, “
Shear Strength Measurements of Lubricants at High Pressure
,”
ASME J. Lubr. Technol.
0022-2305,
101
, pp.
251
256
.
10.
Bair
,
S.
, and
Winer
,
W. O.
, 1990, “
The Shear Stress Rheology of Liquid Lubricants at Pressure of 2to200MPa
,”
ASME J. Tribol.
0742-4787,
112
, pp.
246
252
.
11.
Strozzi
,
A.
, 1975, “
Formation of Three Lubrication Problems in Terms of Complementarity
,”
Wear
0043-1648,
104
, pp.
103
119
.
12.
Wu
,
C. W.
, et al.
, 1992, “
Parametric Variational Principle for Viscoplastic Lubrication Model
,”
ASME J. Tribol.
0742-4787,
113
, pp.
731
735
.
13.
Zhong
,
W. X.
, and
Wu
,
C. W.
, 1992, “
Elastic-Plastic Contacts Using Parametric Quadratic Programming
,”
Numerical Methods in Contact Problems
,
M. H.
Aliabadi
and
C. A.
Brebbia
, eds.,
Computational Mechanics Publication and Elsevier Applied Science
, Chap. 9, pp.
305
356
.
14.
Huebner
,
K. H.
, 1975,
The Finite Element Method for Engineers
,
Wiley
, New York.
15.
Murch
,
L. E.
, and
Wilson
,
W. R. D.
, 1975, “
A Thermal Elastohydrodynamic Inlet Zone Analysis
,”
ASME J. Lubr. Technol.
0022-2305,
97
, pp.
212
216
.
16.
Wilson
,
W. R. D.
, and
Murch
,
L. E.
, 1976, “
A Refined Model for the Hydrodynamic Lubrication of Strip Rolling
,”
ASME J. Lubr. Technol.
0022-2305,
98
, pp.
426
432
.
17.
Christensen
,
H.
, 1969, “
Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces
,”
Proc. Inst. Mech. Eng.
0020-3483,
184
(
1
), pp.
1013
1025
.
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