A two degrees-of-freedom (2DOFs) single mass-on-belt model is employed to study friction-induced instability due to mode-coupling. Three springs, one representing contact stiffness, the second providing lateral stiffness, and the third providing coupling between tangential and vertical directions, are employed. In the model, mass contact and separation are permitted. Therefore, nonlinearity stems from discontinuity due to dependence of friction force on relative mass-belt velocity and separation of mass-belt contact during oscillation. Eigenvalue analysis is carried out to determine the onset of instability. Within the unstable region, four possible phases that include slip, stick, separation, and overshoot are found as possible modes of oscillation. Piecewise analytical solution is found for each phase of mass motion. Then, numerical analyses are used to investigate the effect of three parameters related to belt velocity, friction coefficient, and normal load on the mass response. It is found that the mass will always experience stick-slip, separation, or both. When separation occurs, mass can overtake the belt causing additional nonlinearity due to friction force reversal. For a given coefficient of friction, the minimum normal load to prevent separation is found proportional to the belt velocity.

References

1.
Berger
,
E.
,
2002
, “
Friction Modeling for Dynamic System Simulation
,”
ASME Appl. Mech. Rev.
,
55
(
6
), pp.
535
577
.
2.
Ibrahim
,
R. A.
,
1994
, “
Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part I: Mechanics of Contact and Friction
,”
ASME Appl. Mech. Rev.
,
47
(
7
), pp.
209
226
.
3.
Ibrahim
,
R. A.
,
1994
, “
Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling
,”
ASME Appl. Mech. Rev.
,
47
(
7
), pp.
227
253
.
4.
Sarker
,
M.
,
Rideout
,
D. G.
, and
Butt
,
S. D.
,
2017
, “
Dynamic Model for Longitudinal and Torsional Motions of a Horizontal Oilwell Drillstring With Wellbore Stick-Slip Friction
,”
J. Pet. Sci. Eng.
,
150
, pp.
272
287
.
5.
Sinou
,
J.-J.
,
Thouverez
,
F.
, and
Jezequel
,
L.
,
2003
, “
Analysis of Friction and Instability by the Centre Manifold Theory for a Non-Linear Sprag-Slip Model
,”
J. Sound Vib.
,
265
(
3
), pp.
527
559
.
6.
Spurr
,
R. T.
,
1961
, “
A Theory of Brake Squeal
,”
Proc. Automob. Div., Inst. Mech. Eng.
,
15
(
1
), pp.
33
52
.
7.
Hetzler
,
H.
,
Schwarzer
,
D.
, and
Seemann
,
W.
,
2007
, “
Analytical Investigation of Steady-State Stability and Hopf-Bifurcations Occurring in Sliding Friction Oscillators With Application to Low-Frequency Disc Brake Noise
,”
Commun. Nonlinear Sci. Numer. Simul.
,
12
(
1
), pp.
83
99
.
8.
Le Rouzic
,
J.
,
Le Bot
,
A.
,
Perret-Liaudet
,
J.
,
Guibert
,
M.
,
Rusanov
,
A.
,
Douminge
,
L.
,
Bretagnol
,
F.
, and
Mazuyer
,
D.
,
2013
, “
Friction-Induced Vibration by Stribeck's Law: Application to Wiper Blade Squeal Noise
,”
Tribol. Lett.
,
49
(
3
), pp.
563
572
.
9.
Niknam
,
A.
, and
Farhang
,
K.
,
2018
, “
Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction
,”
ASME J. Vib. Acoust.
,
140
(
6
), p.
061017
.
10.
Juel
,
J.
, and
Fidlin
,
A.
,
2003
, “
Analytical Approximations for Stick—Slip Vibration Amplitudes
,”
Int. J. Nonlinear Mech.
,
38
(3), pp.
389
403
.
11.
Hoffmann
,
N.
,
Fischer
,
M.
,
Allgaier
,
R.
, and
Gaul
,
L.
,
2002
, “
A Minimal Model for Studying Properties of the Mode-Coupling Type Instability in Friction Induced Oscillations
,”
Mech. Res. Commun.
,
29
(
4
), pp.
197
205
.
12.
Sinou
,
J. J.
, and
Jézéquel
,
L.
,
2007
, “
Mode Coupling Instability in Friction-Induced Vibrations and Its Dependency on System Parameters Including Damping
,”
Eur. J. Mech., A/Solids
,
26
(
1
), pp.
106
122
.
13.
Kang
,
J.
,
Krousgrill
,
C. M.
, and
Sadeghi
,
F.
,
2009
, “
Oscillation Pattern of Stick-Slip Vibrations
,”
Int. J. Non-Linear Mech.
,
44
(
7
), pp.
820
828
.
14.
Popp
,
K.
,
2005
, “
Modelling and Control of Friction-Induced Vibrations
,”
Math. Comput. Modell. Dyn. Syst.
,
11
(
3
), pp.
345
369
.
15.
Hoffmann
,
N.
,
Bieser
,
S.
, and
Gaul
,
L.
,
2004
, “
Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems
,”
Tech. Mech.
,
24
(
3–4
), pp.
185
197
.http://www.uni-magdeburg.de/ifme/zeitschrift_tm/2004_Heft3_4/Hoffmann.pdf
16.
Hoffmann
,
N.
, and
Gaul
,
L.
,
2003
, “
Effects of Damping on Mode-Coupling Instability in Friction Induced Oscillations
,”
Z. Angew. Math. Mech.
,
83
(
8
), pp.
524
534
.
17.
Li
,
Z.
,
Ouyang
,
H.
, and
Guan
,
Z.
,
2016
, “
Nonlinear Friction-Induced Vibration of a Slider–Belt System
,”
ASME J. Vib. Acoust.
,
138
(
4
), p.
041006
.
18.
Verhulst, F., 2006,
Nonlinear Differential Equations and Dynamical Systems
, Springer Science & Business Media, Berlin.
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