The column continuity equation is used in formulating a modified Reynolds equation for elastohydrodynamic lubrication of elliptical contacts. A finite element method (FEM), here the Galerkin weighting method with isoparametric Q9 elements, is used to discretize the weak form of the Reynolds equation. In addition to the nodal pressures and the offset film thickness, the locations of the two-dimensional irregular free boundary are explicitly solved for by simultaneously forcing the essential and the natural Reynolds boundary conditions. Newton-Raphson’s iterations with a user-friendly yet efficient meshless scheme (i.e., automatic meshing-remeshing) are finally applied to solve these equations. A decoupled circular non-Newtonian fluid model is adapted in a way to illustrate the implementation of this new solution method. Extensive results will be given in Part II.

1.
Bisset
E. J.
, and
Glander
D. W.
,
1988
, “
A Highly Accurate Approach That Resolves the Pressure Spike of Elastohydrodynamic Lubrication
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
110
, pp.
241
246
.
2.
Hamrock, B. J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill.
3.
Hamrock
B. J.
, and
Dowson
D.
,
1976
, “
Isothermal Elastohydrodynamic Lubrication of Point Contacts, Part I—Theoretical Formulation
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
98
, No.
2
, pp.
223
229
.
4.
Houpert
L. G.
, and
Hamrock
B. J.
,
1986
, “
Fast Approach for Calculating Film Thickness and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
108
, pp.
441
420
.
5.
Hsiao, H. S., 1992, “Modeling and Analysis of Elastohydrodynamic Lubrication of Line Contacts Considering Thermal and Non-Newtonian Effects,” Dissertation, The Ohio State University.
6.
Hsiao
H. S.
, and
Hamrock
B. J.
,
1992
, “
A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
114
, No.
3
, pp.
540
552
.
7.
Kostreva
M. M.
,
1984
, “
Elasto-hydrodynamic Lubrication; A Nonlinear Complementarity Problem
,”
International Journal for Numerical Methods in Fluids
, Vol.
4
, pp.
377
397
.
8.
Lee
R. T.
, and
Hamrock
B. J.
,
1989
, “
Squeeze and Entraining Motion in Nonconformal Line Contacts, Part II—Elastohydrodynamic Lubrication
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
111
, pp.
8
16
.
9.
Lubrecht, A. A., 1987, “The Numerical Solution of the Elastohydrodynamically Lubricated Line- and Point Contact Problem Using Multigrid Techniques,” Ph.D. Thesis, Twente University, The Netherlands.
10.
Lubrecht, A. A., Dwyer-Joyce, R. S., and loannides, E., 1992, “Analysis of the Influence of Indentation on Contact Life,” Proceedings of the 18th Leeds-Lyon Symposium on Tribology, Lyon, France, pp. 173–181.
11.
Lubrecht
A. A.
,
ten Napel
W. E.
, and
Bosma
R.
,
1986
, “
Multigrid, An Alternative Method for Calculating Film Thickness and Pressure Profiles in Elastohydrodynamically Lubricated Line Contacts
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
108
, pp.
551
556
.
12.
Lubrecht
A. A.
,
ten Napel
W. E.
, and
Bosma
R.
,
1987
, “
Multigrid, An Alternative Method of Solution for Two-Dimensional Elastohydrodynamically Lubricated Point Contact Calculations
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
109
, pp.
437
443
.
13.
Lubrecht
A. A.
,
Venner
C. H.
,
ten Napel
W. E.
, and
Bosma
R.
,
1988
, “
Film Thickness Calculations in Elastohydrodynamically Lubricated Circular Contacts Using a Multigrid Method
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
110
, pp.
503
507
.
14.
Nijenbaning
G.
,
Venner
C. H.
, and
Moes
H.
,
1994
, “
Film Thickness in Elastohydrodynamically Lubricated Elliptic Contacts
,”
Wear
, Vol.
176
, pp.
217
229
.
15.
Oh
K. P.
,
1984
, “
The Numerical Solution of Dynamically Loaded Elastohydrodynamic Contact as a Nonlinear Complementarity Problem
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
106
, pp.
88
95
.
16.
Oh
K. P.
, and
Rhode
S. M.
,
1977
, “
Numerical Solution of the Point Contact Problem Using the Finite Element Method
,”
International Journal for Numerical Methods in Engineering
, Vol.
11
, pp.
1507
1518
.
17.
Reddy, J. N., 1993, An Introduction to the Finite Element Method, 2nd. Ed., McGraw-Hill.
18.
Rhode
S. M.
, and
Oh
K. P.
,
1975
, “
A Unified Treatment of Thick and Thin Film Elastohydrodynamic Problems by Using Higher Order Element Methods
,”
Proceedings Royal Society of London, Series A
, Vol.
343
, pp.
315
331
.
19.
Shieh, J. A., 1992, “Film Collapse in Elastohydrodynamic Lubrication,” Dissertation, The Ohio State University.
20.
Taylor
C.
, and
O’Callaghan
J. F.
,
1972
, “
A Numerical Solution of the Elastohydrodynamic Lubrication Problem Using Finite Elements
,”
Journal of Mechanical Engineering Science
, Vol.
14
, No.
4
, pp.
229
237
.
21.
Venner, C. H., 1991, “Multilevel Solution of the EHL Line and Point Contact Problems,” Ph.D. Thesis, Twente University, The Netherlands.
This content is only available via PDF.
You do not currently have access to this content.