Mechanical systems including conveyor belts, band saw blades, and power transmission belts are influenced by the lateral motion of the moving structure. This phenomenon was studied in the literature both using the theory of the continuous linear and nonlinear systems and following the multibody technique. The subject is studied by using the finite element method (FEM) validated with reference to the analytical models described in the literature. The contributions of the Coriolis forces, the negative stiffness linked to the transport speed, and the bending stiffness due to the transverse moment of inertia are discussed. The dynamic behavior of a prototypical belt transmission layout with two fixed pulleys and an automatic tensioner is then analyzed. The results show the effect of the transport speed on the reduction of the flexural natural frequencies of the mode shapes strictly related to the lateral motion of the belt span and evidence the design strategy that needs to be followed for a correct operation of the whole system.
Issue Section:
Research Papers
References
1.
Skutch
, R.
, 1897
, “Uber die Bewegungeines Gespannten Fadens (On the Motion of a Tensioned String)
,” Ann. Phys. Chem.
, 61
, pp. 190
–195
.2.
Sack
, R. A.
, 1954
, “Transverse Oscillations in Traveling Strings
,” Br. J. Appl. Phys.
, 5
, pp. 224
–226
.10.1088/0508-3443/5/6/3073.
Wickert
, J. A.
, and Mote
, C. D.
, 1988
, “Current Research on the Vibration and Stability of Axially-Moving Materials
,” Shock Vib. Dig.
, 20
(5
), pp. 3
–13
.10.1177/0583102488020005034.
Wickert
, J. A.
, and Mote
, C. D.
, 1988
, “On the Energetics of Axially Moving Continua
,” J. Acoust. Soc. Am.
, 85
(3
), pp. 1365
–1368
.10.1121/1.3974185.
Wickert
, J. A.
, and Mote
, C. D.
, 1990
, “Classical Vibration Analysis of Axially Moving Continua
,” ASME J. Appl. Mech.
, 57
, pp. 738
–744
.10.1115/1.28970856.
Wickert
, J. A.
, and Mote
, C. D.
, 1991
, “Response and Discretization Methods for Axially Moving Materials
,” ASME Appl. Mech. Rev.
, 44
(11
), pp. S279
–S284
.10.1115/1.31213657.
Wickert
, J. A.
, 1991
, “Travelling Load Response of an Axially Moving String
,” J. Sound Vib.
, 149
(2
), pp. 267
–284
.10.1016/0022-460X(91)90636-X8.
Wickert
, J. A.
, and Mote
, C. D.
, 1988
, “Linear Transverse Vibration of an Axially Moving String–Particle System
,” J. Acoust. Soc. Am.
, 84
(3
), pp. 963
–969
.10.1121/1.3966119.
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
, pp. 71
–78
.10.1115/1.293040010.
Beikmann
, R. S.
, Perkins
, N. C.
, and Ulsoy
, A. G.
, 1996
, “Free Vibration of Serpentine Belt Drive Systems
,” ASME J. Vibr. Acoust.
, 118
, pp. 406
–413
.10.1115/1.288819711.
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
, pp. 567
–574
.10.1115/1.288833612.
Zhang
, L.
, and Zu
, J. W.
, 1999
, “Modal Analysis of Serpentine Belt Drive System
,” J. Sound Vib.
, 222
(2
), pp. 259
–279
.10.1006/jsvi.1998.207813.
Zhang
, L.
, Zu
, J. W.
, and Hou
, Z.
, 2001
, “Complex Modal Analysis of Non-Self-Adjoint Hybrid Serpentine Belt Drive Systems
,” ASME J. Vibr. Acoust.
, 123
, pp. 150
–156
.10.1115/1.135669714.
Brake
, M. R.
, and Wickert
, J. A.
, 2010
, “Modal Analysis of Continuous Gyroscopic Second-Order System With Nonlinear Constraints
,” J. Sound Vib.
, 329
, pp. 893
–911
.10.1016/j.jsv.2009.10.00415.
Kong
, L.
, and Parker
, R. G.
, 2003
, “Equilibrium and Belt-Pulley Vibration Coupling in Serpentine Belt Drives
,” ASME J. Appl. Mech.
, 70
, pp. 739
–750
.10.1115/1.159847716.
Kong
, L.
, and Parker
, R. G.
, 2004
, “Coupled Belt-Pulley Vibration in Serpentine Drives With Belt Bending Stiffness
,” ASME J. Appl. Mech.
, 71
, pp. 109
–119
.10.1115/1.164106417.
Lin
, Y.
, DePauw
, T.
, and Jiang
, Y.
, 1997
, “Analysis of the Dynamic Effects of an Elastic Belt in a General Mechanical System
,” Proceedings of the 12th European ADAMS User's Conference
, Marburg, Germany, November 18–19, pp. 1
–9
.18.
Hashimoto
, Y.
, 2007
, “Finite Element Vibration Analysis of Axially Moving Belt
,” Trans. Jpn. Soc. Mech. Eng., Ser. C
, 73
, pp. 655
–660
.10.1299/kikaic.73.65519.
Amati
, N.
, Tonoli
, A.
, and Zenerino
, E.
, 2005
, “Dinamica Flessionale di Sistemi Continui Traslanti: Modellazione Agli Elementi Finiti (Flexural Dynamics of Continuum Translating Systems: Finite Element Modeling)
,” Proceedings of the 34th Convegno Nazionale AIAS
, Milano, Italy, September 14–17, pp. 1
–10
.20.
Zen
, G.
, and Muftu
, G.
, 2006
, “Stability of an Axially Accelerating String Subjected to Frictional Guiding Forces
,” J. Sound Vib.
, 289
, pp. 551
–576
.10.1016/j.jsv.2005.02.02621.
Przemieniecki
, J. S.
, 1968
, Theory of Matrix Structural Analysis
, McGraw-Hill
, New York
.22.
Genta
, G.
, 1999
, Vibration of Structures and Machines: Practical Aspects
, Springer
, New York
.23.
Belingardi
G.
, 1995
, Il Metodo Degli Elementi Finiti Nella Progettazione Meccanica (The Finite Elemet Method in Machine Design)
, Levrotto and Bella
, Torino
.24.
Genta
, G.
, and Tonoli
, A.
, 1996
, “A Harmonic Finite Element for the Analysis of Flexural, Torsional and Axial Rotordynamic Behaviour of Discs
,” J. Sound Vib.
, 196
, pp. 13
–43
.10.1006/jsvi.1996.046525.
Perkins
, N. C.
, and Mote
, C. D.
, 1986
, “Comments on the Curve Veering in Engineering Problems
,” J. Sound Vib.
, 106
, pp. 451
–463
.10.1016/0022-460X(86)90191-426.
Amati
, N.
, Tonoli
, A.
, and Zenerino
, E.
, 2006
, “Dynamic Modeling of Belt Drive Systems: Effects of the Shear Deformations
,” ASME J. Vibr. Acoust.
, 128
, pp. 555
–567
.10.1115/1.2202153Copyright © 2014 by ASME
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