Friction is an important part of many dynamic systems, and, as a result, a good model of friction is necessary for simulating and controlling these systems. A new friction model, designed primarily for optimal control and real-time dynamic applications, is presented in this paper. This new model defines friction as a continuous function of velocity and captures the main velocity-dependent characteristics of friction: the Stribeck effect and viscous friction. Additional phenomena of friction such as microdisplacement and the time dependence of friction were not modeled due to the increased complexity of the model, leading to reduced performance of real-time simulations or optimizations. Unlike several current friction models, this model is C1 continuous and differentiable, which is desirable for optimal control applications, sensitivity analysis, and multibody dynamic analysis and simulation. To simplify parameter identification, the proposed model was designed to use a minimum number of parameters, all with physical meaning and readily visible on a force–velocity curve, rather than generic shape parameters. A simulation using the proposed model demonstrates that the model avoids any discontinuities in force at initial impact and the transition from slipping to sticking.

References

References
1.
Berger
,
E. J.
,
2002
, “
Friction Modeling for Dynamic System Simulation
,”
ASME Appl. Mech. Rev.
,
55
(
6
), pp.
535
577
.
2.
Gilardi
,
G.
, and
Sharf
,
I.
,
2002
, “
Literature Survey of Contact Dynamics Modelling
,”
Mech. Mach. Theory
,
37
(
10
), pp.
1213
1239
.
3.
Zmitrowicz
,
A.
,
2010
, “
Contact Stresses: A Short Survey of Models and Methods of Computations
,”
Arch. Appl. Mech.
,
80
(
12
), pp.
1407
1428
.
4.
Seth
,
A.
, and
Pandy
,
M. G.
,
2007
, “
A Neuromusculoskeletal Tracking Method for Estimating Individual Muscle Forces in Human Movement
,”
J. Biomech.
,
40
(
2
), pp.
356
366
.
5.
Banerjee
,
J. M.
, and
McPhee
,
J.
,
2014
, “
Graph-Theoretic Sensitivity Analysis of Multibody Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
4
), p.
041009
.
6.
Uchida
,
T. K.
,
Sherman
,
M. A.
, and
Delp
,
S. L.
,
2015
, “
Making a Meaningful Impact: Modelling Simultaneous Frictional Collisions in Spatial Multibody Systems
,”
Proc. R. Soc. A
,
471
(
2177
), p.
20140859
.
7.
Fleischmann
,
J.
,
Serban
,
R.
,
Negrut
,
D.
, and
Jayakumar
,
P.
,
2016
, “
On the Importance of Displacement History in Soft-Body Contact Models
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
4
), p.
044502
.
8.
Liang
,
J.
,
Fillmore
,
S.
, and
Ma
,
O.
,
2012
, “
An Extended Bristle Friction Force Model With Experimental Validation
,”
Mech. Mach. Theory
,
56
, pp.
123
137
.
9.
Gonthier
,
Y.
,
McPhee
,
J.
,
Lange
,
C.
, and
Piedbœuf
,
J.-C.
,
2004
, “
A Regularized Contact Model With Asymmetric Damping and Dwell-Time Dependent Friction
,”
Multibody Syst. Dyn.
,
11
(
3
), pp.
209
233
.
10.
Andersson
,
S.
,
Söderberg
,
A.
, and
Björklund
,
S.
,
2007
, “
Friction Models for Sliding Dry, Boundary and Mixed Lubricated Contacts
,”
Tribol. Int.
,
40
(
4
), pp.
580
587
.
11.
de Wit
,
C. C.
,
Olsson
,
H.
,
Aström
,
K. J.
, and
Lischinsky
,
P.
,
1995
, “
A New Model for Control of Systems With Friction
,”
IEEE Trans. Autom. Control
,
40
(
3
), pp.
419
425
.
12.
Hunt
,
K. H.
, and
Crossley
,
F. R. E.
,
1975
, “
Coefficient of Restitution Interpreted as Damping in Vibroimpact
,”
ASME J. Appl. Mech.
,
42
(
2
), pp.
440
445
.
13.
Gonthier
,
Y.
,
McPhee
,
J.
,
Lange
,
C.
, and
Piedbœuf
,
J.-C.
,
2005
,
A Contact Modeling Method Based on Volumetric Properties
,”
ASME
Paper No. DETC2005-84610.
14.
“HuntCrossleyForce Class Reference,” Last accessed Nov. 20, 2015, https://simtk.org/api_docs/simbody/latest/classSimTK_1_1HuntCrossleyForce.html
15.
Specker
,
T.
,
Buchholz
,
M.
, and
Dietmayer
,
K.
,
2014
, “
A New Approach of Dynamic Friction Modelling for Simulation and Observation
,”
19th World Congress of the International Federation of Automatic Control
, Cape Town, South Africa, Aug. 24–29, pp.
4523
4528
.
16.
Rabinowicz
,
E.
,
1956
, “
Stick and Slip
,”
Sci. Am.
,
194
(
5
), pp.
109
118
.
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