A method of determining the response of elastohydrodynamic line contacts to low amplitude, sinusoidal variations in load is presented. It is shown that the load variations alter the Hertz width, cyclically increasing and reducing the effective entrainment velocity. This produces clearance variations in the inlet, which are transported through the conjunction altering the pressure distribution as they pass. The resulting pressure and clearance changes can be many times greater than when the load changes slowly. The results are used to determine the flexibility and damping of the conjunctions. These vary depending on the number of transported waves inside the contact. It is shown that a Maxwell model rather than the usual Voigt model is required to define the contact's behavior. While the Voigt model may be used at low frequencies, it has a damping coefficient that is not unique to the contact but depends on the total system stiffness.

References

1.
Hooke
,
C. J.
,
2003
, “
Dynamic Effects in EHL Contacts
,”
29th Leeds–Lyon Symposium on Tribology
, Leeds,
D.
Dowson
,
M.
Priest
,
G.
Dalmaz
, and
A. A.
Lubrecht
, eds.,
Elsevier
,
Amsterdam, The Netherlands
. Tribol. Res. Des. Eng. Syst., 41, pp.
69
78
.
2.
Morales-Espejel
,
G. E.
,
2008
, “
Central Film Thickness in Time-Varying Normal Approach of Rolling Elastohydrodynamically Lubricated Contacts
,”
Proc. Inst. Mech. Eng., Part C
,
222
(
7
), pp.
1271
1280
.
3.
Félix-Quiñonez
,
A.
, and
Morales-Espejel
,
G. E.
,
2010
, “
Film Thickness Fluctuations in Time-Varying Normal Loading of Rolling Elastohydrodynamically Lubricated Contacts
,”
Proc. Inst. Mech. Eng., Part C
,
224
(
12
), pp.
2559
2567
.
4.
Dareing
,
D. W.
, and
Johnson
,
K. L.
,
1975
, “
Fluid Film Damping of Rolling Contact Vibrations
,”
J. Mech. Eng. Sci.
,
17
(
4
), pp.
214
218
.
5.
Walford
,
T. L. H.
, and
Stone
,
B. J.
,
1980
, “
The Measurement of the Radial Stiffness of Rolling Element Bearings Under Oscillating Conditions
,”
J. Mech. Eng. Sci.
,
22
(
4
), pp.
175
181
.
6.
Walford
,
T. L. H.
, and
Stone
,
B. J.
,
1980
, “
Some Stiffness and Damping Characteristics of Angular Contact Bearings Under Oscillating Conditions
,”
2nd International Conference on Vibrations in Rotating Machinery, Cambridge, Mechanical Engineering Publications for the Institution of Mechanical Engineers
, London, pp.
157
162
, Paper No. C274/80.
7.
Walford
,
T. L. H.
, and
Stone
,
B. J.
,
1983
, “
The Sources of Damping in Rolling Element Bearings Under Oscillating Conditions
,”
Proc. Inst. Mech. Eng., Part C
,
197
(
4
), pp.
225
232
.
8.
Dietl
,
P.
,
Wensing
,
J.
, and
Nijen
,
G. C.
,
2000
, “
Rolling Bearing Damping for Dynamic Analysis of Multi-Body Systems-Experimental and Theoretical Results
,”
Proc. Inst. Mech. Eng., Part K
,
214
(1), pp.
33
43
.
9.
Lambert
,
R. J.
,
Pollard
,
A.
, and
Stone
,
B. J.
,
2006
, “
Some Characteristics of Rolling-Element Bearings Under Oscillating Conditions. Part 1: Theory and Rig Design
,”
Proc. Inst. Mech. Eng., Part K
,
220
(3), pp.
157
170
.
10.
Lambert
,
R. J.
,
Pollard
,
A.
, and
Stone
,
B. J.
,
2006
, “
Some Characteristics of Rolling Element Bearings Under Oscillating Conditions. Part 2: Experimental Results for Interference Fitted Taper-Roller Bearings
,”
Proc. Inst. Mech. Eng., Part K
,
220
(
3
), pp.
171
179
.
11.
Lambert
,
R. J.
,
Pollard
,
A.
, and
Stone
,
B. J.
,
2006
, “
Some Characteristics of Rolling-Element Bearings Under Oscillating Conditions. Part 3: Experimental Results for Clearance-Fitted Taper-Roller Bearings and Their Relevance to the Design of Spindles With High Dynamic Stiffness
,”
Proc. Inst. Mech. Eng., Part K
,
220
(3), pp.
181
190
.
12.
Ali
,
N. J.
, and
García
,
J. M.
,
2010
, “
Experimental Studies on the Dynamic Characteristics of Rolling Element Bearings
,”
Proc. Inst. Mech. Eng., Part J
,
224
(
7
), pp.
659
666
.
13.
Wijnant
,
Y. H.
, and
Venner
,
C. H.
,
1997
, “
Analysis of an EHL Circular Contact Incorporating Rolling Element Vibration
,”
Elastohydrodynamics—96, 23rd Leeds-Lyon Symposium on Tribology
,
D.
Dowson
,
C. M.
Taylor
,
T. H. C.
Childs
,
G.
Dalmaz
,
Y.
Berthier
,
L.
Flamand
,
J. M.
Georges
, and
A. A.
Lubrecht
, eds., pp.
445
456
.
14.
Wijnant
,
Y. H.
,
1998
, “
Contact Dynamics in the Field of Elastohydrodynamic Lubrication
,” Ph.D. thesis, University of Twente, Enschede, The Netherlands.
15.
Sarangi
,
M.
,
Majumdar
,
B. C.
, and
Sekhar
,
A. S.
,
2004
, “
Stiffness and Damping Characteristics of Lubricated Ball Bearings Considering the Surface Roughness Effect. Part 1: Theoretical Formulation
,”
Proc. Inst. Mech. Eng., Part J
,
218
(
6
), pp.
529
538
.
16.
Sarangi
,
M.
,
Majumdar
,
B. C.
, and
Sekhar
,
A. S.
,
2004
, “
Stiffness and Damping Characteristics of Lubricated Ball Bearings Considering the Surface Roughness Effect. Part 2: Numerical Results and Application
,”
Proc. Inst. Mech. Eng., Part J
,
218
(
6
), pp.
539
547
.
17.
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
.
18.
Zhang
,
Y. Y.
,
Wang
,
X. L.
, and
Yan
,
X. L.
,
2013
, “
Dynamic Behaviors of the Elastohydrodynamic Lubricated Contact for Rolling Bearings
,”
ASME J. Tribol.
,
135
(2), p.
021501
.
19.
Hooke
,
C. J.
,
1999
, “
The Behaviour of Low Amplitude Surface Roughness Under Line Contacts
,”
Proc. Inst. Mech. Eng., Part J
,
213
(
4
), pp.
275
286
.
20.
Hooke
,
C. J.
, and
Venner
,
C. H.
,
2000
, “
Surface Roughness Attenuation in Line and Point Contacts
,”
Proc. Inst. Mech. Eng., J
,
214
(
5
), pp.
439
444
.
21.
Hooke
,
C. J.
, and
Li
,
K. Y.
,
2006
, “
Rapid Calculation of the Pressures and Clearances in Rough EHL Contacts: Part 1—Analysis
,”
Proc. Inst. Mech. Eng., Part C
,
220
(
6
), pp.
901
914
.
22.
Hooke
,
C. J.
, and
Li
,
K. Y.
,
2006
, “
Rapid Calculation of the Pressures and Clearances in Rough EHL Contacts: Part 2—Application
,”
Proc. Inst. Mech. Eng., Part C
,
220
(
6
), pp.
915
926
.
23.
Hooke
,
C. J.
,
Li
,
K. Y.
, and
Morales-Espejel
,
G. E.
,
2007
, “
Rapid Calculation of the Pressures and Clearances in Rough, Rolling-Sliding Elastohydrodynamically Lubricated Contacts: Part 1—Low-Amplitude, Sinusoidal Roughness
,”
Proc. Inst. Mech. Eng., Part C
,
221
(
5
), pp.
535
550
.
24.
Hooke
,
C. J.
,
Li
,
K. Y.
, and
Morales-Espejel
,
G.
,
2007
, “
Rapid Calculation of the Pressures and Clearances in Rough, Rolling-Sliding Elastohydrodynamically Lubricated Contacts: Part 2—General, Non-Sinusoidal Roughness
,”
Proc. Inst. Mech. Eng., Part C
,
221
(
5
), pp.
551
564
.
25.
Hooke
,
C. J.
,
1998
, “
Surface Roughness Modification in Elastohydrodynamic Contacts Operating in the Elastic Piezoviscous Regime
,”
Proc. Inst. Mech. Eng., Part C
,
212
(
2
), pp.
145
162
.
26.
Hooke
,
C. J.
,
1999
, “
The Behaviour of Heavily Loaded Line Contacts With Transverse Roughness
,”
Proc. Inst. Mech. Eng., Part C
,
213
(
4
), pp.
309
320
.
27.
Lubrecht
,
A. A.
, and
Venner
,
C. H.
,
1999
, “
Elastohydrodynamic Lubrication of Rough Surfaces
,”
Proc. Inst. Mech. Eng., Part J
,
213
(
5
), pp.
397
403
.
28.
Polonsky
,
I. A.
, and
Keer
,
L. M.
,
1999
, “
A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques
,”
Wear
,
231
(
2
), pp.
206
219
.
29.
Derby
,
B.
,
Hills
,
D.
, and
Ruiz
,
C.
,
1992
,
Materials for Engineering
,
Longman Scientific and Technical
,
Harlow, UK
, pp.
188
189
.
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