A new solution method for the oblique elastic impact of similar spheres with Coulomb friction is presented. The solution uses approximations of the shear stress distributions at each time step during impact. These distributions are solved from analytical formulations and are able to account for both full sliding and partial-slip scenarios that may both be present for this problem due to inclusion of tangential compliance and friction effects. Comparison to previous continuum models in the literature shows very good agreement for the contact force wave forms obtained. The major advantage of this method is the drastic reduction in computation time required compared to previous solutions.

1.
Chatterjee
,
A.
, 1997, “
Rigid Body Collisions: Some General Considerations, New Collision Laws, and Some Experimental Data
,” Ph.D. thesis, Cornell University, Ithaca.
2.
Stronge
,
W. J.
, 2000,
Impact Mechanics
,
Cambridge University Press
,
Cambridge
.
3.
Mindlin
,
R. D.
, 1949, “
Compliance of Elastic Bodies in Contact
,”
ASME J. Appl. Mech.
0021-8936,
16
, pp.
259
268
.
4.
Gonthier
,
Y.
,
McPhee
,
J.
,
Lange
,
C.
, and
Piedboeuf
,
J.-C.
, 2004, “
A Regularized Contact Model With Asymmetric Damping and Dwell-Time Dependent Friction
,”
Multibody Syst. Dyn.
1384-5640,
11
, pp.
209
233
.
5.
Gilardi
,
G.
, and
Sharf
,
I.
, 2002, “
Literature Survey of Contact Dynamics Modeling
,”
Mech. Mach. Theory
0094-114X,
37
, pp.
1213
1239
.
6.
Maw
,
N.
,
Barber
,
J. R.
, and
Fawcett
,
J. N.
, 1976, “
The Oblique Impact of Elastic Spheres
,”
Wear
0043-1648,
38
, pp.
101
114
.
7.
Thornton
,
C.
, and
Yin
,
K. K.
, 1991, “
Impact of Elastic Spheres With and Without Adhesion
,”
Powder Technol.
0032-5910,
65
, pp.
153
166
.
8.
Mindlin
,
R. D.
, and
Deresiewicz
,
H.
, 1953, “
Elastic Spheres in Contact Under Varying Oblique Forces
,”
ASME J. Appl. Mech.
0021-8936,
20
, pp.
327
344
.
9.
Jaeger
,
J.
, 1992, “
Elastic Impact With Friction
,” Ph.D. thesis, Delft University, Delft.
10.
Zharii
,
O. Y.
, 1996, “
An Exact Solution of a Time-Dependent Frictional Contact Problem for Two Elastic Spheres
,”
Int. J. Eng. Sci.
0020-7225,
34
, pp.
537
548
.
11.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
,
Cambridge
.
12.
Walpole
,
R. E.
, and
Myers
,
R. H.
, 1993,
Probability and Statistics for Engineers and Scientists
, 5th ed.,
Prentice-Hall
,
Englewood Cliffs, NJ
, p.
434
.
13.
Maw
,
N.
,
Barber
,
J. R.
, and
Fawcett
,
J. N.
, 1981, “
The Role of Elastic Tangential Compliance in Oblique Impact
,”
ASME J. Lubr. Technol.
0022-2305,
103
, pp.
74
80
.
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