Spin in frictional rolling contact can cause significant stress, which is the key to understanding and predicting the wear and fatigue behavior of contact components, such as wheels, rails, and rolling bearings. The lateral creep force arising from spin influences the kinematics of a wheelset and thus of vehicles. The solution that is currently employed in the field of elasticity and continuum statics was developed by Kalker and uses a boundary element method (BEM). In this paper, a new approach based on Lagrangian explicit finite element (FE) analysis is employed. This approach is able to consider arbitrary geometric profiles of rails and wheels, complex material behavior and dynamic effects, and some other factors. The new approach is demonstrated using a three-dimensional (3D) model of a wheel with a coned profile rolling along a quarter cylinder and can be easily adapted to apply to wheels and rails of arbitrary profiles. The 3D FE model is configured with elastic material properties and is used to obtain both normal and tangential solutions. The results are compared with those of the Hertz theory and the Kalker's model. The 3D FE model is then configured with elastoplastic material properties to study the spin-rolling contact with plasticity. The continuum dynamics phenomenon is captured by the FE model, which enhances the ability of the model to mimic reality. This improvement considerably extends the applicability of the FE model. The model can be applied to fatigue and wear analyses at gauge corners or rails as well as to deep groove bearings, where a large geometrical spin is present and plastic deformation may be of importance.

References

References
1.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
2.
Johnson
,
K. L.
,
1958
, “
The Effect of Spin Upon the Rolling Motion of an Elastic Sphere on a Plane
,”
ASME J. Appl. Mech.
,
25
(
3
), pp.
332
338
.
3.
Kalker
,
J. J.
,
1990
,
Three-Dimensional Elastic Bodies in Rolling Contact
,
Kluwer Academic Publishers
,
Dordrecht
.10.1007/978-94-015-7889-9
4.
Li
,
Z.
, and
Kalker
,
J. J.
,
1998
, “
Simulation of Severe Wheel–Rail Wear
,”
Proceedings of the 6th International Conference on Computer Aided Design, Manufacture and Operation in the Railway and Other Advanced Mass Transit Systems
, Lisbon, Portugal, Sept. 2–4, Computational Mechanics Publications, Southampton, UK, pp.
393
402
.
5.
Dollevoet
,
R.
,
Li
,
Z.
, and
Arias-Cuevas
,
O.
,
2010
, “
A Method for the Prediction of Head Checking Initiation Location and Orientation Under Operational Loading Conditions
,”
Proc. Inst. Mech. Eng., Part F
,
224
(
5
), pp.
369
374
.10.1243/09544097JRRT368
6.
Burgelman
,
N.
,
Li
,
Z.
, and
Dollevoet
,
R.
,
2014
, “
A New Rolling Contact Method Applied to Conformal Contact and the Train–Turnout Interaction
,”
Wear
,
321
, pp.
94
105
.10.1016/j.wear.2014.10.008
7.
Carbone
,
G.
, and
Putignano
,
C.
,
2013
, “
A Novel Methodology to Predict Sliding and Rolling Friction of Viscoelastic Materials: Theory and Experiments
,”
J. Mech. Phys. Solids
,
61
(
8
), pp.
1822
1834
.10.1016/j.jmps.2013.03.005
8.
Chaise
,
T.
, and
Nélias
,
D.
,
2011
, “
Contact Pressure and Residual Strain in 3D Elasto-Plastic Rolling Contact for a Circular or Elliptical Point Contact
,”
ASME J. Tribol.
,
133
(
4
), p.
041402
.10.1115/1.4004878
9.
Padovan
,
J.
,
1987
, “
Finite Element Analysis of Steady and Transiently Moving/Rolling Nonlinear Viscoelastic Structure—I. Theory
,”
Comput. Struct.
,
27
(
2
), pp.
249
257
.10.1016/0045-7949(87)90093-9
10.
Yukio
,
N.
, and
Padovan
,
J.
,
1987
, “
Finite Element Analysis of Steady and Transiently Moving/Rolling Nonlinear Viscoelastic Structure—III. Impact/Contact Simulations
,”
Comput. Struct.
,
27
(
2
), pp.
275
286
.10.1016/0045-7949(87)90095-2
11.
Oden
,
J.
, and
Lin
,
T.
,
1986
, “
On the General Rolling Contact Problem for Finite Deformations of a Viscoelastic Cylinder
,”
Comput. Methods Appl. Mech. Eng.
,
57
(
3
), pp.
297
367
.10.1016/0045-7825(86)90143-X
12.
Nackenhorst
,
U.
,
2004
, “
The ALE-Formulation of Bodies in Rolling Contact: Theoretical Foundations and Finite Element Approach
,”
Comput. Methods Appl. Mech. Eng.
,
193
(
39
), pp.
4299
4322
.10.1016/j.cma.2004.01.033
13.
Ziefle
,
M.
, and
Nackenhorst
,
U.
,
2008
, “
Numerical Techniques for Rolling Rubber Wheels: Treatment of Inelastic Material Properties and Frictional Contact
,”
Comput. Mech.
,
42
(
3
), pp.
337
356
.10.1007/s00466-008-0243-9
14.
Li
,
Z.
,
Zhao
,
X.
,
Dollevoet
,
R.
, and
Molodova
,
M.
,
2008
, “
Differential Wear and Plastic Deformation as Causes of Squat at Track Local Stiffness Change Combined With Other Track Short Defects
,”
Veh. Syst. Dyn.
,
46
(
Suppl. 1
), pp.
237
246
.10.1080/00423110801935855
15.
Zhao
,
X.
, and
Li
,
Z.
,
2011
, “
The Solution of Frictional Wheel–Rail Rolling Contact With a 3D Transient Finite Element Model: Validation and Error Analysis
,”
Wear
,
271
(
1–2
), pp.
444
452
.10.1016/j.wear.2010.10.007
16.
Li
,
Z.
,
Dollevoet
,
R.
,
Molodova
,
M.
, and
Zhao
,
X.
,
2011
, “
Squat Growth—Some Observations and the Validation of Numerical Predictions
,”
Wear
,
271
(
1–2
), pp.
148
157
.10.1016/j.wear.2010.10.051
17.
Pletz
,
M.
,
Daves
,
W.
, and
Ossberger
,
H.
,
2012
, “
A Wheel Set/Crossing Model Regarding Impact, Sliding and Deformation—Explicit Finite Element Approach
,”
Wear
,
294–295
, pp.
446
456
.10.1016/j.wear.2012.07.033
18.
Zhao
,
X.
,
Li
,
Z.
, and
Liu
,
J.
,
2011
, “
Wheel–Rail Impact and the Dynamic Forces at Discrete Supports of Rails in the Presence of Singular Rail Surface Defects
,”
Proc. Inst. Mech. Eng., Part F
,
226
(
2
), pp.
124
139
.10.1177/0954409711413975
19.
Belytschko
,
T.
,
Liu
,
W. K.
,
Moran
,
B.
, and
Elkhodary
,
K.
,
2000
,
Nonlinear Finite Elements for Continua and Structures
,
Wiley
,
Chichester, New York
.
20.
Zhong
,
Z.-H.
,
1993
,
Finite Element Procedures for Contact–Impact Problems
,
Oxford University Press
,
Oxford, London
.
21.
Bathe
,
K.
,
1982
,
Finite Element Procedures in Engineering Analysis
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
22.
Johnson
,
W.
,
1983
,
Impact Strength of Materials
,
Edward Arnold
,
London, UK
.
23.
Courant
,
R.
,
Friedrichs
,
K.
, and
Lewy
,
H.
,
1967
, “
On the Partial Difference Equations of Mathematical Physics
,”
IBM J. Res. Dev.
,
11
(
2
), pp.
215
234
.10.1147/rd.112.0215
24.
Hallquist
,
J.
,
Goudreau
,
G.
, and
Benson
,
D.
,
1985
, “
Sliding Interfaces With Contact–Impact in Large-Scale Lagrangian Computations
,”
Comput. Methods Appl. Mech. Eng.
,
51
(
1
), pp.
107
137
.10.1016/0045-7825(85)90030-1
25.
Benson
,
D. J.
, and
Hallquist
,
J. O.
,
1990
, “
A Single Surface Contact Algorithm for the Post-Buckling Analysis of Shell Structures
,”
Comput. Methods Appl. Mech. Eng.
,
78
(
2
), pp.
141
163
.10.1016/0045-7825(90)90098-7
26.
Taylor
,
L.
, and
Flanagan
,
D.
,
1989
, “
Pronto 3D: A Three-Dimensional Transient Solid Dynamics Program
,” Sandia National Laboratories, Albuquerque, NM, Technical Report No. SAND 87-1912.
27.
Hertz
,
H.
,
1882
, “
Über Die Berührung Fester Elastischer Körper
,”
J. Reine Angew. Math.
,
1882
(
92
), pp.
156
171
.10.1515/crll.1882.92.156
28.
Wernitz
,
W.
,
1962
, “
Friction at Hertzian Contact With Combined Roll and Twist
,”
Rolling Contact Phenomena
,
J. B.
Bidwell
, ed.,
Elsevier
,
New York
, pp.
132
156
.
29.
Johnson
,
K. L.
,
1962
, “
Tangential Traction and Microslip in Rolling Contact
,”
Rolling Contact Phenomena
,
J. R.
Bidwell
, ed.,
Elsevier
,
Amsterdam
, pp.
6
28
.
30.
Rońda
,
J.
,
Mahrenholtz
,
O.
,
Bogacz
,
R.
, and
Brzozowski
,
M.
,
1986
, “
The Rolling Contact Problem for an Elastic–Plastic Strip and a Rigid Roller
,”
Mech. Res. Commun.
,
13
(
3
), pp.
119
132
.10.1016/0093-6413(86)90053-4
31.
Bower
,
A. F.
, and
Johnson
,
K. L.
,
1989
, “
The Influence of Strain Hardening on Cumulative Plastic Deformation in Rolling and Sliding Line Contact
,”
J. Mech. Phys. Solids
,
37
(
4
), pp.
471
493
.10.1016/0022-5096(89)90025-2
32.
Kapoor
,
A.
,
Morales-Espejel
,
G.
, and
Olver
,
A.
,
2002
, “
A Shakedown Analysis of Simple Spur Gears
,”
Tribol. Trans.
,
45
(
1
), pp.
103
109
.10.1080/10402000208982527
33.
Ekberg
,
A.
, and
Kabo
,
E.
,
2005
, “
Fatigue of Railway Wheels and Rails Under Rolling Contact and Thermal Loading—An Overview
,”
Wear
,
258
(
7–8
), pp.
1288
1300
.10.1016/j.wear.2004.03.039
34.
Hua
,
L.
,
Deng
,
S.
,
Han
,
X.
, and
Huang
,
S.
,
2013
, “
Effect of Material Defects on Crack Initiation Under Rolling Contact Fatigue in a Bearing Ring
,”
Tribol. Int.
,
66
, pp.
315
323
.10.1016/j.triboint.2013.06.008
35.
Ahlström
,
J.
, and
Karlsson
,
B.
,
2005
, “
Fatigue Behaviour of Rail Steel—A Comparison Between Strain and Stress Controlled Loading
,”
Wear
,
258
(
7
), pp.
1187
1193
.10.1016/j.wear.2004.03.030
You do not currently have access to this content.