Abstract

The current work investigates the influence of real lubricant density–pressure behavior on the dynamic response of elastohydrodynamic lubricated conjunctions. Such a response is often based on a nonrealistic universal equation of state, despite longstanding evidence of its lack of support by measurements. A finite element framework is employed to investigate the damping and stiffness characteristics of line contact elastohydrodynamic (EHD) lubricating films, subject to a harmonic loading. Both the equivalent stiffness and damping coefficients of lubricating films are found to increase with the base applied external load and its amplitude of oscillation. They decrease however with increasing mean entrainment speed and load oscillation frequency. That is, they both increase as lubricant films get thinner. By comparison with the real density–pressure response of a highly compressible silicon oil, the universal equation of state is shown to underestimate the lubricant film’s stiffness and damping characteristics. The relative deviations in equivalent damping and stiffness coefficients can reach up to about 12% and 25%, respectively. Therefore, realistic lubricant characteristics should always be considered. In particular, the use of the universal equation of state should not be taken for granted, as is customary in the elastohydrodynamic lubrication (EHL) literature. Lubricant density–pressure response is not of a secondary nature when it comes to predicting the dynamic performance characteristics of EHL conjunctions.

References

1.
Wijnant
,
Y. H.
,
Venner
,
C. H.
,
Larsson
,
R.
, and
Eriksson
,
P.
,
1999
, “
Effects of Structural Vibrations on the Film Thickness in an EHL Circular Contact
,”
ASME J. Tribol.
,
121
(
2
), pp.
259
264
.
2.
Nonato
,
F.
, and
Cavalca
,
K. L.
,
2010
, “
On the Non-Linear Dynamic Behavior of Elastohydrodynamic Lubricated Point Contact
,”
J. Sound Vib.
,
329
(
22
), pp.
4656
4671
.
3.
Nonato
,
F.
, and
Cavalca
,
K. L.
,
2014
, “
An Approach for Including the Stiffness and Damping of Elastohydrodynamic Point Contacts in Deep Groove Ball Bearing Equilibrium Models
,”
J. Sound Vib.
,
333
(
25
), pp.
6960
6978
.
4.
Qin
,
W.
,
Chao
,
J.
, and
Duan
,
L.
,
2015
, “
Study on Stiffness of Elastohydrodynamic Line Contact
,”
Mech. Mach. Theory
,
86
(
4
), pp.
36
47
.
5.
Zhang
,
Y.
,
Liu
,
H.
,
Zhu
,
C.
,
Liu
,
M.
, and
Song
,
C.
,
2016
, “
Oil Film Stiffness and Damping in an Elastohydrodynamic Lubrication Line Contact-Vibration
,”
J. Mech. Sci. Technol.
,
30
(
7
), pp.
3031
3039
.
6.
Tsuha
,
N. A. H.
,
Nonato
,
F.
, and
Cavalca
,
K. L.
,
2017
, “
Formulation of a Reduced Order Model for the Stiffness on Elastohydrodynamic Line Contacts Applied to Cam-Follower Mechanism
,”
Mech. Mach. Theory
,
113
(
7
), pp.
22
39
.
7.
Fang
,
C.
,
Zhu
,
A.
,
Zhou
,
W.
,
Peng
,
Y.
, and
Meng
,
X.
,
2022
, “
On the Stiffness and Damping Characteristics of Line Contacts Under Transient Elastohydrodynamic Lubrication
,”
Lubricants
,
10
(
73
), pp.
1
14
.
8.
Zhou
,
C.
,
Xiao
,
Z.
,
Chen
,
S.
, and
Han
,
X.
,
2017
, “
Normal and Tangential Oil Film Stiffness of Modified Spur Gear With Non-Newtonian Elastohydrodynamic Lubrication
,”
Tribol. Int.
,
109
(
5
), pp.
319
327
.
9.
Zhou
,
C.
, and
Xiao
,
Z.
,
2018
, “
Stiffness and Damping Models for the Oil Film in Line Contact Elastohydrodynamic Lubrication and Applications in the Gear Drive
,”
Appl. Math. Modell.
,
61
(
9
), pp.
634
649
.
10.
Xiao
,
Z.
,
Zhou
,
C.
,
Chen
,
S.
, and
Li
,
Z.
,
2019
, “
Effects of Oil Film Stiffness and Damping on Spur Gear Dynamics
,”
Nonlinear Dyn.
,
96
(
1
), pp.
145
159
.
11.
Wiegert
,
B.
,
Hetzler
,
H.
, and
Seemann
,
W.
,
2013
, “
A Simplified Elastohydrodynamic Contact Model Capturing the Nonlinear Vibration Behaviour
,”
Tribol. Int.
,
59
(
3
), pp.
79
89
.
12.
Dowson
,
D.
, and
Higginson
,
G. R.
,
1959
, “
A Numerical Solution of the Elastohydrodynamic Problem
,”
J. Mech. Eng. Sci.
,
1
(
1
), pp.
6
15
.
13.
Kleinschmidt
,
R. V.
,
Bradbury
,
D.
, and
Mark
,
M.
,
1953
,
Viscosity and Density of Over Forty Lubricating Fluids of Known Composition at Pressures to 150,000 psi and Temperatures to 425 F
,
ASME
,
New York
.
14.
Hirschfelder
,
J. O.
,
Curtiss
,
C. F.
, and
Bird
,
R. B.
,
1954
,
Molecular Theory of Gases and Liquids
,
Wiley
,
New York
.
15.
Bair
,
S.
,
2019
, “
The Rheological Assumptions of Classical EHL: What Went Wrong?
,”
Tribol. Int.
,
131
(
3
), pp.
45
50
.
16.
Venner
,
C. H.
, and
Bos
,
J.
,
1994
, “
Effects of Lubricant Compressibility on the Film Thickness in EHL Line and Circular Contacts
,”
Wear
,
173
(
1–2
), pp.
151
165
.
17.
Habchi
,
W.
, and
Bair
,
S.
,
2013
, “
Quantitative Compressibility Effects in Thermal Elastohydrodynamic Circular Contacts
,”
ASME J. Tribol.
,
135
(
1
), p.
011502
.
18.
Issa
,
J. S.
, and
Habchi
,
W.
,
2020
, “
Influence of Realistic Lubricant Density-Pressure Dependence on the Stiffness of Elastohydrodynamic Lubricated Contacts
,”
ASME J. Tribol.
,
142
(
3
), p.
031601
.
19.
Habchi
,
W.
, and
Bair
,
S.
,
2019
, “
Is Viscoelasticity of Any Relevance to Quantitative EHL Friction Predictions
,”
Tribol. Int.
,
135
(
7
), pp.
96
103
.
20.
Habchi
,
W.
, and
Vergne
,
P.
,
2015
, “
On the Compressive Heating/Cooling Mechanism in Thermal Elastohydrodynamic Lubricated Contacts
,”
Tribol. Int.
,
88
(
8
), pp.
143
152
.
21.
Reynolds
,
O.
,
1886
, “
On the Theory of the Lubrication and Its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,”
Philos. Trans. R. Soc. London
,
177
(
1
), pp.
157
234
.
22.
Roelands
,
C. J. A.
,
1966
, “
Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils
,”
Ph.D. thesis
,
Technische Hogeschool Delft
,
Delft, The Netherlands
.
23.
Habchi
,
W.
,
Eyheramendy
,
D.
,
Vergne
,
P.
, and
Morales-Espejel
,
G. E.
,
2008
, “
A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem
,”
ASME J. Tribol.
,
130
(
2
), p.
021501
.
24.
Habchi
,
W.
,
2018
,
Finite Element Modeling of Elastohydrodynamic Lubrication Problems
,
Wiley
,
Chichester, UK
.
25.
Raisin
,
J.
,
Fillot
,
N.
,
Dureisseix
,
D.
,
Vergne
,
P.
, and
Lacour
,
V.
,
2015
, “
Characteristic Times in Transient Thermal Elastohydrodynamic Line Contacts
,”
Tribol. Int.
,
82
(
2
), pp.
472
483
.
26.
Habchi
,
W.
, and
Issa
,
J. S.
,
2017
, “
An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems
,”
ASME J. Tribol.
,
139
(
5
), p.
051501
.
27.
Deuflhard
,
P.
,
2004
,
Newton Methods for Nonlinear Problems, Affine Invariance and Adaptive Algorithms
,
Springer
,
Germany
.
28.
Wu
,
S. R.
,
1986
, “
A Penalty Formulation and Numerical Approximation of the Reynolds-Hertz Problem of Elastohydrodynamic Lubrication
,”
Int. J. Eng. Sci.
,
24
(
6
), pp.
1001
1013
.
29.
Habchi
,
W.
,
2019
, “
A Schur-Complement Model-Order-Reduction Technique for the Finite Element Solution of Transient Elastohydrodynamic Lubrication Problems
,”
Adv. Eng. Softw.
,
127
(
1
), pp.
28
37
.
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