In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

1.
Euler, M. L., 1762, “Remarques sur l’effect du frottement dans l’equilibre,” Me´m. Acad. Sci., Berlin, pp. 265–278.
2.
Grashof, B. G., 1883, Theoretische Maschinenlehre, Bd 2. Leopold Voss, Hamburg.
3.
Fawcett
,
J. N.
,
1981
, “
Chain and Belt Drives-A Review
,”
Shock Vib. Dig.
,
13
(
5
), pp.
5
12
.
4.
Johnson, K. L., 1985, Contact Mechanics, Chap. 8, Cambridge Univ. Press, London.
5.
Bechtel
,
S. E.
,
Vohra
,
S.
,
Jacob
,
K. I.
, and
Carlson
,
C. D.
,
2000
, “
The Stretching and Slipping of Belts and Fibers on Pulleys
,”
ASME J. Appl. Mech.
,
67
(
1
), pp.
197
206
.
6.
Firbank
,
T. C.
,
1970
, “
Mechanics of the Belt Drive
,”
Int. J. Mech. Sci.
,
12
, pp.
1053
1063
.
7.
Gerbert, G. G., 1991, “On Flat Belt Slip,” Vehicle Tribology, Tribology Series 16, Elsevier, Amsterdam, pp. 333–339.
8.
Gerbert
,
G. G.
,
1996
, “
Belt Slip-A Unified Approach
,”
ASME J. Mech. Des.
,
118
(
3
), pp.
432
438
.
9.
Townsend
,
W. T.
, and
Salisbury
,
J. K.
,
1988
, “
The Efficiency Limit of Belt and Cable Drives
,”
ASME J. Mech., Transm., Autom. Des.
,
110
, pp.
303
307
.
10.
Barker, C. R., Oliver, L. R., and Brieg, W. F., 1991, “Dynamic Analysis of Belt Drive Tension Forces During Rapid Engine Acceleration,” SAE Congress, Detroit, MI, Paper No. 910687, pp. 239–254.
11.
Hwang
,
S. J.
,
Perkins
,
N. C.
,
Ulsoy
,
A. G.
, and
Meckstroth
,
R. J.
,
1994
, “
Rotational Response and Slip Prediction of Serpentine Belt Drive Systems
,”
ASME J. Vibr. Acoust.
,
116
(
1
), pp.
71
78
.
12.
Beikmann
,
R. S.
,
Perkins
,
N. C.
, and
Ulsoy
,
A. G.
,
1996
, “
Free Vibration of Serpentine Belt Drive Systems
,”
ASME J. Vibr. Acoust.
,
118
(
3
), pp.
406
413
.
13.
Beikmann
,
R. S.
,
Perkins
,
N. C.
, and
Ulsoy
,
A. G.
,
1996
, “
Nonlinear Coupled Vibration Response of Serpentine Belt Drive Systems
,”
ASME J. Vibr. Acoust.
,
118
(
4
), pp.
567
574
.
14.
Beikmann
,
R. S.
,
Perkins
,
N. C.
, and
Ulsoy
,
A. G.
,
1997
, “
Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance
,”
ASME J. Mech. Des.
,
119
(
2
), pp.
162
168
.
15.
Leamy, M. J., Perkins, N. C., Barber, J. R., and Meckstroth, R. J., 1997, “The Influence of Tensioner Friction on Accessory Drive Dynamics,” 1997 SAE Noise and Vibration Conference and Expedition, Traverse City, MI, May, Paper No. 97NV103.
16.
Leamy
,
M. J.
, and
Perkins
,
N. C.
,
1998
, “
Nonlinear Periodic Response of Engine Accessory Drives with Dry Friction Tensioners
,”
ASME J. Vibr. Acoust.
,
120
(
4
), pp.
909
916
.
17.
Kraver
,
T. C.
,
Fan
,
G. W.
, and
Shah
,
J. J.
,
1996
, “
Complex Modal Analysis of a Flat Belt Pulley System with Belt Damping and Coulomb-Damped Tensioner
,”
ASME J. Mech. Des.
,
118
(
2
), pp.
306
311
.
18.
Leamy
,
M. J.
,
Barber
,
J. R.
, and
Perkins
,
N. C.
,
1998
, “
Distortion of a Harmonic Elastic Wave Reflected From a Dry Friction Support
,”
ASME J. Appl. Mech.
,
65
(
4
), pp.
851
857
.
19.
Leamy, M. J., Barber, J. R., and Perkins, N. C., 1998, “Dynamics of Belt/Pulley Frictional Contact,” Proc. of IUTAM Symp. on Unilateral Multibody Contacts, Munich, August, Kluwer Academic Press, pp. 277–286.
20.
Leamy, M. J., 1998, “The Influence of Dry Friction in the Dynamic Response of Accessory Belt Drive Systems,” Doctoral Dissertation, Univ. of Michigan.
21.
Oden
,
J. T.
, and
Martins
,
J. A. C.
,
1985
, “
Models and Computational Methods for Dynamic Friction Phenomena
,”
Comput. Methods Appl. Mech. Eng.
,
52
, pp.
527
634
.
22.
Makris
,
N.
, and
Constantinou
,
M. C.
,
1991
, “
Analysis of Motion Resisted by Friction, II: Velocity-Dependent Friction
,”
Mech. Struct. Mach.
,
19
(
4
), pp.
501
526
.
23.
Begley
,
C. J.
, and
Virgin
,
L. N.
,
1997
, “
A Detailed Study of the Low-Frequency Periodic Behavior of a Dry Friction Oscillator
,”
ASME J. Dyn. Syst., Meas., Control
,
119
(
3
), pp.
491
497
.
24.
Leamy
,
M. J.
, and
Wasfy
,
T.
,
2002
, “
Analysis of Belt-Drive Mechanics Using a Creep-Rate Dependent Friction Law
,”
ASME J. Appl. Mech.
,
69
(
6
), pp.
763
771
.
25.
Wasfy
,
T.
,
1996
, “
A Torsional Spring-Like Beam Element for the Dynamic Analysis of Flexible Multibody Systems
,”
Int. J. Numer. Methods Eng.
,
39
(
7
), pp.
1079
1096
.
26.
Wasfy
,
T.
, and
Noor
,
A. K.
,
1996
, “
Modeling and Sensitivity Analysis of Multibody Systems Using New Solid, Shell and Beam Elements
,”
Comput. Methods Appl. Mech. Eng.
,
138
(
1/4
), pp.
187
211
.
27.
Advanced Science and Automation Corp., 2000, Dynamic Interactions Simulator (DIS) User’s Manual Version 1.1.
You do not currently have access to this content.