Numerical simulations are used to study the transient behavior of a four degree-of-freedom, rotational piecewise linear system. This study focuses on the impact between bodies in a system with backlash as a result of a sudden step input and the associated transient response. The subsequent single sided impacts and double sided impacts are studied as a function of the amplitude of the step input and the size of the backlash. Transitions have been observed between double sided impact regions and single sided impact regions, which agree with earlier findings. However, in this paper a more complete overview of the boundaries is given. The severity of the impacts is quantified with the peak-to-peak acceleration of the impacting bodies. The increase in the size of step input increases the severity of the impacts. However, the increase in backlash size leads to an extremum in impact severity. This is a possible explanation for seeming contradictions in literature.

1.
Gilardi
,
G.
, and
Sharf
,
I.
, 1983, “
Literature Survey of Contact Dynamics Modeling
,”
J. Sound Vib.
0022-460X,
90
(
1
), pp.
129
155
.
2.
Glocker
,
C.
, 2001, “
On Frictionless Impact Models in Rigid-Body Systems
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
359
, pp.
2385
2404
.
3.
Besselink
,
B.
,
Shukla
,
A.
,
Fey
,
R. H. B.
, and
Nijmeijer
,
H.
, 2007, “
Classification of Periodic Solutions in a Single Degree-of-Freedom System With Backlash
,” ASME Paper No. DETC2007-34236.
4.
Gerdes
,
J.
, and
Kumar
,
V.
, 1995, “
An Impact Model of Mechanical Backlash for Control System Analysis
,”
Proceedings of the American Control Conference
, Seattle, WA, Vol.
5
, pp.
3311
3315
.
5.
Wagg
,
D. J.
, 2006, “
Multiple Non-Smooth Events in Multi-Degree-of-Freedom Vibro-Impact Systems
,”
Nonlinear Dyn.
0924-090X,
43
(
1–2
), pp.
137
148
.
6.
Gurm
,
J. S.
,
Chen
,
W. J.
,
Keyvanmanesh
,
A.
,
Abe
,
T.
,
Crowther
,
A. R.
, and
Singh
,
R.
, 2007, “
Transient Clunk Response of a Driveline System: Laboratory Experiments and Analytical Studies
,” SAE Paper No. 2007-01-2233.
7.
Krenz
,
R. A.
, 1985, “
Vehicle Response to Throttle Tip-In/Tip-Out
,” SAE Paper No. 850967, pp.
45
52
.
8.
Budd
,
C.
, and
Dux
,
F.
, 1994, “
Chattering and Related Behavior in Impact Oscillators
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
347
, pp.
365
389
.
9.
Crowther
,
A. R.
,
Janello
,
C.
, and
Singh
,
R.
, 2007, “
Quantification of Clearance-Induced Impulsive Sources in a Torsional System
,”
J. Sound Vib.
0022-460X,
307
(
3–5
), pp.
428
451
.
You do not currently have access to this content.