Friction and system models are fundamentally coupled. In fact, the success of models in predicting experimental results depends highly on the modeling of friction. This is true at the atomic scale where the nanoscale friction depends on a large set of parameters. This paper presents a novel nanoscale friction model based on the bristle interpretation of single asperity contact. This interpretation is adopted after a review of dynamic friction models representing stick-slip motion in macrotribology literature. The proposed model uses state variables and introduces a generalized bristle deflection. Jumping mechanisms are implemented in order to take into account the instantaneous jumps observed during 2D stick-slip phenomena. The model is dynamic and Lipchitz, which makes it suitable for future control implementation. Friction force microscope scans of a muscovite mica sample were conducted in order to determine numerical values of the different model parameters. The simulated and experimental results are then compared in order to show the efficacy of the proposed model.

1.
Berger
,
E.
, 2002, “
Friction Modeling for Dynamic System Simulation
,”
Appl. Mech. Rev.
0003-6900,
55
(
6
), pp.
535
577
.
2.
Bhushan
,
B.
, 1999,
Handbook of Micro/Nano Tribology
, 2nd ed.,
CRC
,
Boca Raton, FL
.
3.
Sasaki
,
N.
,
Kobayashi
,
K.
, and
Tsukada
,
M.
, 1996, “
Atomic-Scale Friction Image of Graphite in Atomic-Force Microscopy
,”
Phys. Rev. B
0163-1829,
54
, pp.
2138
2149
.
4.
Carpick
,
R. W.
,
Ogletree
,
D. F.
, and
Salmeron
,
M.
, 1997, “
Lateral Stiffness: A New Nanomechanical Measurement for the Determination of Shear Strengths With Friction Force Microscopy
,”
Appl. Phys. Lett.
0003-6951,
70
, pp.
1548
1550
.
5.
Carpick
,
R.
,
Flater
,
E.
,
Sridharan
,
K.
,
Ogletree
,
D.
, and
Salmeron
,
M.
, 2004, “
Atomic-Scale Friction and Its Connection to Fracture Mechanics
,”
J. Miner. Met. Mater. Soc.
,
56
(
10
), pp.
48
52
. 1047-4838
6.
Gnecco
,
E.
,
Bennewitz
,
R.
,
Gyalog
,
T.
, and
Meyer
,
E.
, 2001, “
Friction Experiments on the Nanometer Scale
,”
J. Phys. Condens. Matter
0953-8984,
13
, pp.
R619
R642
.
7.
Fujisawa
,
S.
,
Kishi
,
E.
,
Sugawara
,
Y.
, and
Morita
,
S.
, 1994, “
Two-Dimensionally Discrete Friction on the NaF(100) Surface With the Lattice Periodicity
,”
Nanotechnology
0957-4484,
5
, pp.
8
11
.
8.
Fujisawa
,
S.
,
Kishi
,
E.
,
Sugawara
,
Y.
, and
Morita
,
S.
, 1995, “
Load Dependence of Two Dimensional Atomic Scale Friction
,”
Phys. Rev. B
0163-1829,
52
(
7
), pp.
5302
5305
.
9.
Kerssemakers
,
J.
, and
Hosson
,
J. T. M. D.
, 1996, “
Influence of Spring Stiffness and Anisotropy on Stick-Slip Atomic Force Microscopy Imaging
,”
Appl. Phys. (Berlin)
0340-3793,
80
(
2
), pp.
623
631
.
10.
Morita
,
S.
,
Fujisawa
,
S.
, and
Sugawara
,
Y.
, 1996, “
Spatially Quantized Friction With a Lattice Periodicity
,”
Surf. Sci. Rep.
0167-5729,
23
, pp.
1
41
.
11.
Fujisawa
,
S.
,
Sugawara
,
Y.
,
Ito
,
S.
,
Mishima
,
S.
,
Okada
,
T.
, and
Morita
,
S.
, 1993, “
The Two-Dimensional Stick-Slip Phenomenon With Atomic Resolution
,”
Nanotechnology
0957-4484,
4
, pp.
138
142
.
12.
Fujisawa
,
S.
,
Kishi
,
E.
,
Sugawara
,
Y.
, and
Morita
,
S.
, 1995, “
Atomic Scale Friction Observed With a Two-Dimensional Frictional Force Microscope
,”
Phys. Rev. B
0163-1829,
51
, pp.
7849
7857
.
13.
Resch
,
R.
,
Bugacov
,
A.
,
Baur
,
C.
,
Koel
,
B.
,
Madhukar
,
A.
,
Requicha
,
A.
, and
Will
,
P.
, 1998, “
Manipulation of Nanoparticles Using Dynamic Force Microscopy: Simulation and Experiments
,”
Appl. Phys. A: Mater. Sci. Process.
0947-8396,
67
, pp.
265
271
.
14.
Decossas
,
S.
,
Mazen
,
F.
,
Baron
,
T.
,
Bremond
,
G.
, and
Souifi
,
A.
, 2003, “
Atomic Force Microscopy Nanomanipulation of Silicon Nanocrystals for Nanodevice Fabrication
,”
Nanotechnology
0957-4484,
14
, pp.
1272
1278
.
15.
Decossas
,
S.
,
Patrone
,
L.
,
Bonnot
,
A.
,
Comin
,
F.
,
Derivaz
,
M.
,
Barski
,
A.
, and
Chevrier
,
J.
, 2003, “
Nanomanipulation by Atomic Force Microscopy of Carbon Nanotubes on a Nanostructured Surface
,”
Surf. Sci.
0039-6028,
543
, pp.
57
62
.
16.
Ammi
,
M.
, and
Ferreira
,
A.
, 2004, “
Path Planning of an AFM-Based Nanomanipulator Using Virtual Force Reflection
,”
Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems
, Sendai, Japan, pp.
577
582
.
17.
Du
,
E.
,
Cui
,
H.
, and
Zhu
,
Z.
, 2006, “
Review of Nanomanipulators for Nanomanufacturing
,”
Int. J. Nanomanufacturing
,
1
, pp.
83
104
.
18.
Tafazzoli
,
A.
, and
Sitti
,
M.
, 2004, “
Dynamic Behavior and Simulation of Nanoparticle During Nanoprobe-Based Positioning
,”
Proceedings of the ASME International Mechanical Engineering Congress
, Anaheim, CA, pp.
1
8
.
19.
Zhou
,
Q.
,
Kallio
,
P.
,
Arai
,
F.
,
Fukuda
,
T.
, and
Koivoc
,
H. N.
, 1999, “
A Model for Operating Spherical Micro Objects
,”
Proceedings of the International Symposium on Micromechatronics and Human Science
, Nagoya, Japan, pp.
79
85
.
20.
Rifai
,
K. E.
,
Rifai
,
O. E.
, and
Youcef-Toumi
,
K.
, 2005, “
Modeling and Control of AFM Based Nano-Manipulation Systems
,”
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
, Barcelona, Spain, pp.
157
162
.
21.
Gnecco
,
E.
,
Bennewitz
,
R.
,
Gyalog
,
T.
,
Loppacher
,
C.
,
Bammerlin
,
M.
,
Meyer
,
E.
, and
Guntherodt
,
H. -J.
, 2000, “
Velocity Dependence of Atomic Friction
,”
Phys. Rev. Lett.
0031-9007,
84
, pp.
1172
1175
.
22.
Hoshi
,
Y.
,
Kawagishi
,
T.
, and
Kawakatsu
,
H.
, 2000, “
Velocity Dependence and Limitations of Friction Force Microscopy of Mica and Graphite
,”
Jpn. J. Appl. Phys.
0021-4922,
39
, pp.
3804
3807
.
23.
Carlson
,
J. M.
, and
Batista
,
A. A.
, 1996, “
Constitutive Relation for the Friction Between Lubricated Surfaces
,”
Phys. Rev. E
1063-651X,
53
(
4
), pp.
4153
4165
.
24.
Persson
,
B. N. J.
, 2000,
Sliding Friction
,
Springer
,
New York
.
25.
Bliman
,
P. A.
, and
Sorine
,
M.
, 1991, “
Friction Modelling by Hysteresis Operators. Application to Dahl, Stiction and Stribeck Effects
,”
Proceedings of the Conference “Models of Hysteresis
,” Trento, Italy, pp.
10
19
.
26.
Bliman
,
P. A.
, and
Sorine
,
M.
, 1993, “
A System-Theoretic Approach of Systems With Hysteresis. Application to Friction Modeling and Compensation
,”
Proceedings of the Second European Control Conference
, Groningen, The Netherlands, pp.
1844
1849
.
27.
Dahl
,
P.
, 1976, “
Solid Friction Damping of Mechanical Vibrations
,”
AIAA J.
0001-1452,
14
(
12
), pp.
1675
1682
.
28.
Haessig
,
D. A.
, Jr.
, and
Friedland
,
B.
, 1991, “
On the Modeling and Simulation of Friction
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
113
, pp.
354
362
.
29.
de Wit
,
C.
,
Olsson
,
H.
,
Astrom
,
K. J.
, and
Lischinsky
,
P.
, 1995, “
A New Model for Control of Systems With Friction
,”
IEEE Trans. Automatom. Control.
,
40
(
3
), pp.
419
425
. 0018-9286
30.
Velenis
,
E.
,
Tsiotras
,
P.
, and
de Wit
,
C. C.
, 2002, “
Extension of the LuGre Dynamic Tire Friction Model to 2D Motion
,”
Proceedings of the 10th IEEE Mediterranean Conference on Control and Automation
, Lisbon, Portugal.
31.
Stark
,
R. W.
,
Schitter
,
G.
, and
Stemmer
,
A.
, 2003, “
Tuning the Interaction Forces in Tapping Mode Atomic Force Microscopy
,”
Phys. Rev. B
0163-1829,
68
(
8
), pp.
085401
.
32.
Lou
,
J.
, and
Kim
,
K. -S.
, 2008, “
Effects of Interfaces on Nano-Friction of Vertically Aligned Multi-Walled Carbon Nanotube Arrays
,”
Mater. Sci. Eng., A
0921-5093,
483–484
, pp.
664
667
.
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