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Research Papers

Effect of Flat Belt Thickness on Steady-State Belt Stresses and Slip

[+] Author and Article Information
Tamer M. Wasfy

Mem. ASME
Purdue School of Engineering &
Technology at IUPUI,
723 W Michigan Street,
SL 260G,
Indianapolis, IN 46202-5160
e-mail: twasfy@iupui.edu

Cagkan Yildiz

Purdue School of Engineering &
Technology at IUPUI,
723 W Michigan Street,
SL 260G,
Indianapolis, IN 46202-5160
e-mail: cyildiz@iupui.edu

Hatem M. Wasfy

Mem. ASME
Advanced Science and Automation Corp.,
28 Research Drive,
Suite F,
Hampton, VA 23666
e-mail: hatem@ascience.com

Jeanne M. Peters

Advanced Science and Automation Corp.,
28 Research Drive,
Suite F,
Hampton, VA 23666
e-mail: jeanne.peters@ascience.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 2, 2015; final manuscript received December 10, 2015; published online February 3, 2016. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 11(5), 051005 (Feb 03, 2016) (13 pages) Paper No: CND-15-1149; doi: 10.1115/1.4032383 History: Received June 02, 2015; Revised December 10, 2015

A necessary condition for high-fidelity dynamic simulation of belt-drives is to accurately predict the belt stresses, pulley angular velocities, belt slip, and belt-drive energy efficiency. In previous papers, those quantities were predicted using thin shell, beam, or truss elements along with a Coulomb friction model. However, flat rubber belts have a finite thickness and the reinforcements are typically located near the top surface of the belt. In this paper, the effect of the belt thickness on the aforementioned response quantities is studied using a two-pulley belt-drive. The belt rubber matrix is modeled using three-dimensional brick elements. Belt reinforcements are modeled using one-dimensional truss elements at the top surface of the belt. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure.

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References

Euler, M. L. , 1762, “ Remarques sur l'effect du frottement dans l'equilibre,” Mem. Acad. Sci., pp. 265–278.
Grashof, B. G. , 1883, Theoretische Maschinenlehre, Bd. Theorie der getriebe und der mechanischen messinstrumente, Vol. 2, Leopold Voss, Hamburg.
Fawcett, J. N. , 1981, “ Chain and Belt Drives—A Review,” Shock Vib. Dig., 13(5), pp. 5–12. [CrossRef]
Johnson, K. L. , 1985, Contact Mechanics, Cambridge University Press, London, Chap. 8.
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. [CrossRef]
Townsend, W. T. , and Salisbury, J. K. , 1988, “ The Efficiency Limit of Belt and Cable Drives,” ASME J. Mech., Transm., Autom. Des., 110(3), pp. 303–307. [CrossRef]
Leamy, M. J. , and Wasfy, T. M. , 2002, “ Analysis of Belt-Drive Mechanics Using a Creep-Rate Dependent Friction Law,” ASME J. Appl. Mech., 69(6), pp. 763–771. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Leamy, M. J. , and Wasfy, T. M. , 2001, “ Dynamic Finite Element Modeling of Belt-Drives,” 18th Biennial Conference on Mechanical Vibration and Noise, ASME International DETC, Pittsburgh, PA.
Leamy, M. J. , and Wasfy, T. M. , 2002, “ Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives,” ASME J. Dyn. Syst., Meas., Control, 124(4), pp. 575–581. [CrossRef]
Pietra, L. D. , and Timpone, F. , 2013, “ Tension in a Flat Belt Transmission: Experimental Investigation,” Mech. Mach. Theory, 70, pp. 129–156. [CrossRef]
Leamy, M. J. , and Wasfy, T. M. , 2001, “ Dynamic Finite Element Modeling of Belt-Drives Including One-Way Clutches,” ASME International Mechanical Engineering Congress and Exposition, New York, NY.
Meckstroth, R. J. , Wasfy, T. M. , and Leamy, M. J. , 2004, “ Finite Element Study of Dynamic Response of Serpentine Belt-Drives With Isolator Clutches,” CAD/CAM/CAE Technology and Design Tools, SAE International, Detroit, MI.
Wasfy, T. M. , and Leamy, M. J. , 2002, “ Effect of Bending on the Dynamic and Steady-State Responses of Belt-Drives,” 27th Biennial Mechanisms and Robotics Conference, ASME International DETC, Montreal, Canada.
Wasfy, T. M. , 2003, “ Asperity Spring Friction Model With Application to Belt-Drives,” ASME Paper No. DETC2003-48343.
Leamy, M. J. , Meckstroth, R. J. , and Wasfy, T. M. , 2004, “ Finite Element Study of Belt-Drive Frictional Contact Under Harmonic Excitation,” CAD/CAM/CAE Technology and Design Tools, SAE International, Detroit, MI.
Leamy, M. J. , and Wasfy, T. M. , 2005, “ Time-Accurate Finite Element Modeling of the Transient, Steady-State, and Frequency Responses of Serpentine and Timing Belt-Drives,” Int. J. Veh. Des., 39(3), pp. 272–297. [CrossRef]
Wasfy, T. M. , Leamy, M. J. , and Meckstroth, R. J. , 2004, “ Prediction of System Natural Frequencies Using an Explicit Finite Element Code With Application to Belt-Drives,” ASME Paper No. DETC2004-57117.
Firbank, T. C. , 1970, “ Mechanics of the Belt Drive,” Int. J. Mech. Sci., 12(12), pp. 1053–1063. [CrossRef]
Gerbert, G. G. , 1991, “ On Flat Belt Slip,” Vehicle Tribology (Tribology Series 16), Elsevier, Amsterdam, pp. 333–339.
Gerbert, G. G. , 1996, “ Belt Slip—A Unified Approach,” ASME J. Mech. Des., 118(3), pp. 432–438. [CrossRef]
Alciatore, D. G. , and Traver, A. E. , 1995, “ Multipulley Belt Drive Mechanics: Creep Theory vs Shear Theory,” ASME J. Mech. Des., 117(4), pp. 506–511. [CrossRef]
Kong, L. , and Parker, R. G. , 2005, “ Microslip Friction in Flat Belt Drives,” J. Mech. Eng. Sci., 219(10), pp. 1097–1106. [CrossRef]
Kim, D. , Leamy, M. J. , and Ferri, A. , 2009, “ Dynamic Modeling of Flat-Belt Drives Using the Elastic-Perfectly Plastic Friction Law,” ASME Paper No. DETC2009-87296.
Kerkkanen, K. S. , Garcia-Vallejo, D. , and Mikkola, A. M. , 2006, “ Modeling of Belt-Drives Using Large Deformation Finite Element Formulation,” Nonlinear Dyn., 43(3), pp. 239–256. [CrossRef]
Cepon, G. , Manin, L. , and Boltezar, M. , 2011, “ Validation of a Flexible Multibody Belt-Drive Model,” J. Mech. Eng., 57, pp. 539–546. [CrossRef]
Chen, W.-H. , and Shien, C.-J. , 2003, “ On Angular Speed Loss Analysis of Flat Belt Transmission System by Finite Element Method,” Int. J. Comput. Eng. Sci., 4(1), pp. 1–18. [CrossRef]
Wasfy, T. M. , Wasfy, H. M. , and Peters, J. M. , 2013, “ Prediction of the Normal and Tangential Friction forces for Thick Flat Belts Using an Explicit Finite Element Code,” ASME Paper No. DETC2013-13714.
Yildiz, C. , Wasfy, T. M. , Wasfy, H. M. , and Peters, J. M. , 2015, “ Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives,” ASME Paper No. DETC 2015-47147.
Wasfy, T. M. , 2004, “ Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation,” ASME Paper No. DETC2004-57352.
Wasfy, T. M. , 2001, “ Lumped-Parameters Brick Element for Modeling Shell Flexible Multibody Systems,” 18th Biennial Conference on Mechanical Vibration and Noise, ASME International DETC, Pittsburgh, PA.
Wasfy, T. M. , 2003, “ Edge Projected Planar Rectangular Element for Modeling Flexible Multibody Systems,” ASME, Paper No. DETC2003-48351.
Wasfy, T. M. , and O'Kins, J. , 2009, “ Finite Element Modeling of the Dynamic Response of Tracked Vehicles,” ASME Paper No. DETC 2009-86563.
DIS (Dynamic Interactions Simulator), 2015, “ Advanced Science and Automation Corp.,” http://www.ascience.com/ScProducts.htm

Figures

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Fig. 1

Cross section of a flat belt and pulley

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Fig. 2

Belt model used in Ref. [29] (left). Brick elements are used to model the belt rubber and truss elements on the top belt surface (shown as black lines) are used to model the cords (right).

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Fig. 3

Twenty-four rigid body and deformation modes of a spatial eight-node brick element[32]

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Fig. 4

Subelements of the eight-node lumped-parameters brick element [32]

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Fig. 5

Contact surface and contact node

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Fig. 6

Asperity-based physical interpretation of friction

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Fig. 7

Asperity spring friction model [16]. Ft is the tangential friction force, Fn is the normal force, μk is the kinetic friction coefficient, and vrt is the relative tangential velocity between the two points in contact.

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Fig. 8

Two-pulley belt-drive model showing the slip and stick arcs on the driver and driven pulleys for the zero thickness belt. ω is the input angular velocity of the driver pulley and T is the applied opposing torque on the driven pulley.

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Fig. 9

Prescribed angular velocity of the driver pulley. The nominal driver pulley angular velocity is 120 rad/s.

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Fig. 10

Time-history of the driver and driven pulleys angular velocities as a function of belt thickness

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Fig. 11

Angular velocity ratio (driven/driver) as a function of the belt thickness

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Fig. 12

Time-history of the driver applied torque and driven pulley opposing torque as a function of belt thickness

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Fig. 13

Belt-drive energy efficiency (output power/input power) as a function of the belt thickness

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Fig. 14

Time-history of the midspan low and high tension belt-spans' tension as a function of belt thickness

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Fig. 15

Driver pulley tangential contact stress and rubber shear stress as a function of the belt rubber thickness

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Fig. 16

Driven pulley tangential contact stress and rubber shear stress as a function of the belt rubber thickness

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Fig. 17

Physical explanation of the negative initial belt shear on the driver pulley

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Fig. 18

Belt rubber shear stress over the normalized belt length as a function of belt rubber thickness

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Fig. 19

Driver pulley normal contact stress and rubber normal stress as a function of the belt rubber thickness

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Fig. 20

Driven pulley normal contact stress and rubber normal stress as a function of the belt rubber thickness

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Fig. 21

Driver and driven pulleys reinforcements tension force over the pulleys as a function of the belt rubber thickness

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Fig. 22

Reinforcements tension force over the belt length as a function of the belt rubber thickness

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Fig. 23

Steady-state experimental strain at the top belt surface versus time for a two-pulley belt-drive obtained in Ref. [12] for a belt with a 0.75 mm traction layer thickness

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Fig. 24

Belt rubber axial stress over the belt length as a function of the belt rubber thickness

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Fig. 25

Belt rubber lateral stress over the belt length as a function of the belt rubber thickness

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