Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of which are based on the Boussinesq–Cerruti solution. This paper presents a new approach, which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without engendering any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor (ψ), which accounts for the normal load. The expression ψ is derived from the Hetényi correction process, and the resulting displacements show an enhanced correspondence with validation finite element method models; with an imposed fluctuating pressure, the maximum edge displacement error was −21.90% for a shear load correction (Poisson coefficient ν=0.3), and introducing the ψ factor reduced the deviation to −9.55%, while for ν of 0.15, the maximum error was −11.30%, which was reduced to +0.60% with the ψ factor. This study introduces the factor ψ in a 3D elastic contact algorithm. The resulting calculation scheme is then able to simulate any point or line contact problems. Compared with coincident ends and sharp edge contact validation values, the model shows high conformity levels.

References

References
1.
Poon
,
C. Y.
, and
Sayles
,
R. S.
, 1994, “
Numerical Contact Model of a Smooth Ball on an Anisotropic Rough Surface
,”
ASME J. Tribol.
,
116
(
2
), pp.
194
201
.
2.
Tian
,
X.
, and
Bushan
,
B.
, 1996, “
A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle
,”
ASME J. Tribol.
,
118
(
1
), pp.
33
42
.
3.
Wilner
,
K.
, 2008, “
Fully Coupled Frictional Contact Using Elastic Halfspace
,”
ASME J. Tribol.
,
130
(
3
), p.
031405
.
4.
Chen
,
W. W.
, and
Wang
,
Q. J.
, 2009, “
A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material and Roughness
,”
ASME J. Tribol.
,
131
(
2
), pp.
1
8
.
5.
Liu
,
S.
, and
Hua
,
D. Y.
, 2009, “
Three-Dimensional Semiperiodic Line Contact-Periodic in Contact Length Direction
,”
ASME J. Tribol.
,
131
(
2
), p.
021408
.
6.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
, Chap. 5.
7.
Ahmadi
,
N.
,
Keer
,
L. M.
, and
Mura
,
T.
, 1983, “
Non-Hertzian Contact Stress Analysis for an Elastic Half Space-Normal and Sliding Contact
,”
Int. J. Solids Struct.
,
19
(
4
), pp.
357
373
.
8.
Yang
,
J.
, and
Komvopoulos
,
K.
, 2005, “
Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space
,”
ASME J. Tribol.
,
127
(
2
), pp.
325
330
.
9.
Bachtar
,
F.
,
Chen
,
X.
, and
Hisada
,
T.
, 2006, “
Finite Element Contact Analysis of the Hip Joint
,”
Med. Biol. Eng. Comput.
,
44
(
8
), pp.
643
651
.
10.
Sahoo
,
P.
, and
Ghosh
,
N.
, 2007, “
Finite Element Contact Analysis of Fractal Surfaces
,”
J. Phys. D: Appl. Phys.
,
40
(
14
), pp.
4245
4252
.
11.
Wang
,
Z.-J.
,
Wang
,
W.-Z.
,
Wang
,
H.
,
Zhu
,
D.
, and
Hu
,
Y.-Z.
, 2010, “
Partial Slip Contact Analysis Three-Dimensional Elastic Layered Half Space
,”
ASME J. Tribol.
,
132
(
2
), p.
021403
.
12.
Wang
,
F.
, and
Keer
,
L. M.
, 2005, “
Numerical Simulation for Three Dimensional Elastic-Plastic Contact With Hardening Behavior
,”
ASME J. Tribol.
,
127
(
3
), pp.
494
502
.
13.
Hetényi
,
M.
, 1960, “
A Method of Solution for the Elastic Quarter-Plane
,”
ASME J. Appl. Mech.
,
82
(
2
), pp.
289
296
.
14.
Hetényi
,
M.
, 1970, “
A General Solution for the Elastic Quarter Space
,”
ASME J. Appl. Mech.
,
37
(
1
), pp.
70
76
.
15.
Keer
,
L. M.
,
Lee
,
J. C.
, and
Mura
,
T.
, 1983, “
Hetényi’s Elastic Quarter Space Problem Revisited
,”
Int. J. Solids Struct.
,
19
(
6
), pp.
497
508
.
16.
Hartnett
,
M. J.
, 1980, “
A General Numerical Solution for Elastic Body Contact Problems
,”
Solid Contact and Lubrication
,
H. S.
Cheng
and
L. M.
Keer
, eds.,
ASME
,
New York
, Vol.
39
, pp.
51
66
.
17.
Li
,
J.
, and
Berger
,
E. J.
, 2001, “
A Boussinesq-Cerruti Solution Set for Constant and Linear Distribution of Normal and Tangential Load Over a Triangular Area
,”
J. Elast.
,
63
(
2
), pp.
137
151
.
18.
Li
,
J.
, and
Berger
,
E. J.
, 2003, “
A Semi-Analytical Approach to Three-Dimensional Normal Contact Problems With Friction
,”
Comput. Mech.
,
30
(
4
), pp.
310
322
.
19.
Love
,
A. E. H.
, 1929, “
The Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary
,”
Philos. Trans. R. Soc. London, Ser. A
,
228
, pp.
377
420
.
20.
de Mul
,
J. M.
,
Kalker
,
J. J.
, and
Fredriksson
,
B.
, 1986, “
The Contact Between Arbitrarily Curved Bodies of Finite Dimensions
,”
ASME J. Tribol.
,
108
(
1
), pp.
140
148
.
21.
Guilbault
,
R.
,
Gosselin
,
C.
, and
Cloutier
,
L.
, 2005, “
Express Model for Load Sharing and Stress Analysis in Helical Gears
,”
ASME J. Mech. Des.
,
127
(
6
), pp.
1161
1172
.
22.
Guilbault
,
R.
, 2010, “
A Fast Correction for Traction-Free Surface of Elastic Quarter-Space
,”
Third International Conference on Tribology and Design
,
M.
Hadfield
,
J.
Seabra
, and
C. A.
Brebia
, eds.,
WIT Press
,
Southampton, UK
, pp.
37
48
.
You do not currently have access to this content.