Research Papers

Belt-Drive Mechanics: Friction in the Absence of Sliding

[+] Author and Article Information
Yingdan Wu

George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: yingdanwu@gatech.edu

Michael J. Leamy

George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: michael.leamy@me.gatech.edu

Michael Varenberg

George W. Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: varenberg@gatech.edu

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received April 26, 2019; final manuscript received May 31, 2019; published online June 27, 2019. Assoc. Editor: Jizhou Song.

J. Appl. Mech 86(10), 101001 (Jun 27, 2019) (9 pages) Paper No: JAM-19-1209; doi: 10.1115/1.4044019 History: Received April 26, 2019; Accepted May 31, 2019

Recent studies have shown that steady and unsteady operation of a belt drive may exhibit regimes absent of sliding at the belt–pulley interface, where instead detachment waves serve to relax stress in the so-called “slip” arc. To explore this finding further, herein we present an experimental and theoretical investigation into frictional mechanics in a simple belt drive system. To estimate friction experimentally, we perform a stress analysis based on spatio-temporal measurements of the belt tension, traction, and contact area evolution. Subsequently, we develop a model taking into account both bulk and surface hysteretic losses to explain the experimental observations. Our results show that the shear strain at the belt–pulley interface differs significantly between the driver and the driven pulleys, resulting in much larger mechanical losses in the driver case. The shear strain drops at the transition from the adhesion to the slip arc, and, in contrast to accepted theories, the slip arc contributes little to nothing to the power transmission. Our model reveals that the contact area evolution correlates to the shear traction changes and that viscoelastic shear and stretching dominate in the belt rolling friction. A significant contribution of detachment waves to the energy dissipation explains the higher mechanical losses observed in the driver case.

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Euler, M. L., 1762, “Remarques sur l’effect du frottement dans l’equilibre,” Mem. Acad. Sci., 18, pp. 265–278.
Grashof, F., 1890, Theoretische Maschinenlehre, L. Voss, Leipzig, Germany.
Firbank, T., 1970, “Mechanics of the Belt Drive,” Int. J. Mech. Sci., 12(12), pp. 1053–1063. [CrossRef]
Kong, L., and Parker, R. G., 2005, “Steady Mechanics of Belt-Pulley Systems,” ASME J. Appl. Mech., 72(1), pp. 25–34. [CrossRef]
Bechtel, S., Vohra, S., Jacob, K., and Carlson, C., 2000, “The Stretching and Slipping of Belts and Fibers on Pulleys,” ASME J. Appl. Mech., 67(1), pp. 197–206. [CrossRef]
Rubin, M., 2000, “An Exact Solution for Steady Motion of an Extensible Belt in Multipulley Belt Drive Systems,” ASME J. Mech. Des., 122(3), pp. 311–316. [CrossRef]
Gerbert, G., 1991, “On Flat Belt Slip,” Vehicle Tribol., 16, pp. 333–339. [CrossRef]
Sorge, F., 2007, “Shear Compliance and Self-Weight Effects on Traction Belt Mechanics,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci., 221(12), pp. 1717–1728. [CrossRef]
Alciatore, D., and Traver, A., 1995, “Multipulley Belt Drive Mechanics: Creep Theory versus 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,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci., 219(10), pp. 1097–1106. [CrossRef]
Leamy, M., and Wasfy, T., 2002, “Analysis of Belt-Driven Mechanics Using a Creep-Rate-Dependent Friction Law,” ASME J. Appl. Mech., 69(6), pp. 763–771. [CrossRef]
Leamy, M. J., 2005, “On a Perturbation Method for the Analysis of Unsteady Belt-Drive Operation,” ASME J. Appl. Mech., 72(4), pp. 570–580. [CrossRef]
Čepon, G., and Boltežar, M., 2009, “Dynamics of a Belt-Drive System Using a Linear Complementarity Problem for the Belt–Pulley Contact Description,” J. Sound Vib., 319(3–5), pp. 1019–1035. [CrossRef]
De Almeida, A., and Greenberg, S., 1995, “Technology Assessment: Energy-Efficient Belt Transmissions,” Energy Build., 22(3), pp. 245–253. [CrossRef]
Chen, T., Lee, D., and Sung, C.-K., 1998, “An Experimental Study on Transmission Efficiency of a Rubber V-Belt CVT,” Mech. Mach. Theory, 33(4), pp. 351–363. [CrossRef]
Silva, C. A., Manin, L., Rinaldi, R. G., Remond, D., Besnier, E., and Andrianoely, M.-A., 2018, “Modeling of Power Losses in Poly-V Belt Transmissions: Hysteresis Phenomena (Enhanced Analysis),” Mech. Mach. Theory, 121, pp. 373–397. [CrossRef]
Schallamach, A., 1971, “How Does Rubber Slide?,” Wear, 17(4), pp. 301–312. [CrossRef]
Barquins, M., and Courtel, R., 1975, “Rubber Friction and the Rheology of Viscoelastic Contact,” Wear, 32(2), pp. 133–150. [CrossRef]
Rubio, M. A., and Galeano, J., 1994, “Stick-Slip Dynamics in the Relaxation of Stresses in a Continuous Elastic Medium,” Phys. Rev. E, 50(2), p. 1000. [CrossRef]
Yamaguchi, T., Ohmata, S., and Doi, M., 2009, “Regular to Chaotic Transition of Stick–Slip Motion in Sliding Friction of an Adhesive Gel-Sheet,” J. Phys.: Condens. Matter, 21(20), p. 205105. [CrossRef] [PubMed]
Fukahori, Y., Gabriel, P., and Busfield, J. J. C., 2010, “How Does Rubber Truly Slide Between Schallamach Waves and Stick-Slip Motion?,” Wear, 269(11–12), pp. 854–866. [CrossRef]
Wu, Y., Leamy, M. J., and Varenberg, M., 2018, “Schallamach Waves in Rolling: Belt Drives,” Tribol. Int., 119, pp. 354–358. [CrossRef]
Wu, Y., Varenberg, M., and Leamy, M. J., 2019, “Schallamach Wave-Induced Instabilities in a Belt-Drive System,” ASME J. Appl. Mech., 86(3), p. 031002. [CrossRef]
Varenberg, M., and Varenberg, A., 2012, “Table Tennis Rubber: Tribological Characterization,” Tribol. Lett., 47(1), pp. 51–56. [CrossRef]
Folch, A., 2016, Introduction to bioMEMS, CRC Press, Boca Raton, FL.
Mark, J. E., 2009, Polymer Data Handbook, Oxford University Press, New York.
Della Pietra, L., and Timpone, F., 2013, “Tension in a Flat Belt Transmission: Experimental Investigation,” Mech. Mach. Theory, 70, pp. 129–156. [CrossRef]
He, B., Chen, W., and Wang, Q. J., 2008, “Surface Texture Effect on Friction of a Microtextured Poly (Dimethylsiloxane)(PDMS),” Tribol. Lett., 31(3), p. 187. [CrossRef]
Meyers, M. A., and Chawla, K. K., 2008, Mechanical Behavior of Materials, Cambridge University Press, Cambridge, UK.
Lin, I.-K., Ou, K.-S., Liao, Y.-M., Liu, Y., Chen, K.-S., and Zhang, X., 2009, “Viscoelastic Characterization and Modeling of Polymer Transducers for Biological Applications,” J. Microelectromech. Syst., 18(5), pp. 1087–1099. [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,” Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Portland, OR, Aug. 4–7, p. V07AT10A070.
Greenwood, J., 2004, “The Theory of Viscoelastic Crack Propagation and Healing,” J. Phys. D: Appl. Phys., 37(18), p. 2557. [CrossRef]
Emerson, J. A., OToole, E., Zamora, D., and Poon, B., 1998, Comparison of Three Work of Adhesion Measurements, Sandia National Labs., Albuquerque, NM.
Varenberg, M., and Gorb, S. N., 2009, “Hexagonal Surface Micropattern for Dry and Wet Friction,” Adv. Mater., 21(4), pp. 483–486. [CrossRef]
Kligerman, Y., and Varenberg, M., 2014, “Elimination of Stick-Slip Motion in Sliding of Split or Rough Surface,” Tribol. Lett., 53(2), pp. 395–399. [CrossRef]


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Fig. 1

The experimental apparatus: (a) schematic and (b) system as built

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Fig. 2

(a) Deformed and (b) undeformed tick marks created on the belt sidewalls for shear strain measurements

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Fig. 3

Young's modulus of PDMS measured as a function of strain rate at room temperature

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Fig. 4

Instantaneous shear strain (solid line), stretching strain (dashed line), and the contact status (black area denotes contact) at the belt–pulley interface for (a) the driver and (b) the driven cases

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Fig. 5

The visualization (a) and the distribution (b) of the negative shear strain at the middle layer of the belt at the entry zone

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Fig. 6

Comparison between the measurement of the shear strain at belt–pulley interface and the prediction by Firbank model for both the (a) driver and (b) driven pulleys. The borders between the adhesion and slip arcs are represented by the change from a shaded to a nonshaded region for the belt shear theory and by the maxima in the shear distribution curves for the experimental data.

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Fig. 7

Free body diagrams of the belt segment in contact with (a) the driver and (b) the driven pulleys. FTT and FTS represent tension (normal) forces, FST and FSS represent shear forces, and MT and MS represent moments at the tight and slack spans of the belt, and tn and tt represent normal and tangential (shear) traction at the belt/pulley interface.

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Fig. 8

Plots of shear strain, stretching strain, and contact area at the belt interface at several time frames as well as the correlation of corresponding tension difference, shear traction, and contact ratio for both the (a) driver and (b) driven pulleys

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Fig. 9

Energy dissipated by a viscoelastic material under cyclic loading

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Fig. 10

Schematic of the bending strain of a certain segment of the belt in contact with the pulley

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Fig. 11

Storage modulus E′ and loss modulus E″ of PDMS obtained as a function of frequency at room temperature (redrawn from Ref. [30])

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Fig. 12

Moments applied to the belt wrapped over (a) the driver and (b) the driven pulleys

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Fig. 13

Comparison between the experimental and computational results for the evolution of the moments acting on the belt in the driver and driven cases. Solid squares for both pulleys denote the specific frames extracted for the detailed plots shown in Fig. 12.



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