Research Papers

Hysteretic Rubber Friction: Application of Persson's Theories to Grosch's Experimental Results

[+] Author and Article Information
E. Fina

Department of Mechanical Engineering Sciences,
Faculty of Engineering and Physical Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: e.fina@surrey.ac.uk

P. Gruber

Department of Mechanical Engineering Sciences,
Faculty of Engineering and Physical Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: p.gruber@surrey.ac.uk

R. S. Sharp

Department of Mechanical Engineering Sciences,
Faculty of Engineering and Physical Sciences,
University of Surrey,
Guildford GU2 7XH, UK
e-mail: robinsharp37@talktalk.net

In the original models from Persson, the Young's modulus E(ω) is used instead of the shear modulus G(ω). E(ω) is replaced here by G(ω) using: E(ω) = 2G(ω) (1 + ν).

In this paper the Poisson's ratio is assumed to be constant with the varying frequency and equal to 0.5.

This is the compound shear stiffness in static condition.

The composition is 27% styrene and 73% butadiene.

There is a doubt about which temperature Grosch adopts to fit the loss modulus; in Ref. [2] the fitting temperature is indicated as 3 °C in Table 1 and as 0 °C in Table 2. This uncertainty is very small and can be assumed to have negligible effect on the final results.

In [2] Grosch uses a reference temperature Tref of 3 °C for styrene-butadiene compound instead of 20 °C (see Table 1 in Ref. [2]).

AMES laser texture scanner, model 9200.

The macrowavelength λ0 = 2π/q0, where q0 is the macrowavenumber (Fig. 5).

This is the upper half of the surface's profile, situated above the mean profile height.

See Table 3 in Ref. [2].

1The wavenumber is the equivalent of radian frequency in the distance domain (q = 2π/λ).

Contributed by the Applied Mechanics of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 3, 2014; final manuscript received September 26, 2014; accepted manuscript posted October 2, 2014; published online October 14, 2014. Assoc. Editor: Taher Saif.

J. Appl. Mech 81(12), 121001 (Oct 14, 2014) (6 pages) Paper No: JAM-14-1350; doi: 10.1115/1.4028722 History: Received August 03, 2014; Revised September 26, 2014; Accepted October 02, 2014

This paper revisits Grosch's work on rubber friction with Persson's contact theory. Persson's model is implemented to replicate Grosch's experiments on silicon carbide paper and compute the physical mechanism that Grosch identified as one of the main contributors to rubber friction: deformation friction. Grosch did not provide all rubber compound and surface characteristics required for the simulation work and, in order to obtain a full data set, the missing properties were adapted from literature sources and from measurements. The simulation results show that the deformation contribution is modeled correctly by Persson's model in terms of peak magnitude and sliding velocity at which the peak is located. On the contrary, poor correlation is found for the shape of the deformation friction master curve.

Copyright © 2014 by ASME
Topics: Friction , Rubber
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Persson, B. N. J., 2001, “Theory of Rubber Friction and Contact Mechanics,” J. Chem. Phys., 115(8), pp. 3840–3860. [CrossRef]
Grosch, K. A., 1963, “The Relation Between the Friction and Visco-Elastic Properties of Rubber,” Proc. R. Soc. Lond. Ser. A, 274(1356), pp. 21–39. [CrossRef]
Persson, B. N. J., Albohr, O., Tartaglino, U., Volokitin, A. I., and Tosatti, E., 2005, “On the Nature of Surface Roughness With Application to Contact Mechanics, Sealing, Rubber Friction and Adhesion,” J. Phys.: Condens. Matter, 17(1), pp. R1–R62. [CrossRef] [PubMed]
Persson, B. N. J., 2006, “Rubber Friction: Role of Flash Temperature,” J. Phys.: Condens. Matter, 18(32), pp. 7789–7823. [CrossRef] [PubMed]
Persson, B., 1998, “On the Theory of Rubber Friction,” Surf. Sci., 401(3), pp. 445–454. [CrossRef]
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Williams, M. L., Landel, R. F., and Ferry, J. D., 1955, “The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids,” J. Am. Chem. Soc., 77(14), pp. 3701–3707. [CrossRef]
Gent, A. N., and Walter, J. D., 2005, The Pneumatic Tyre, National Highway Traffic Safety Administration, Washington, DC.
Klüppel, M., and Fritzsche, J., 2009, “Viscoelastic Properties of Filler Reinforced Elastomers,” Constitutive Models for Rubber VI, CRC Press, Dresden, Germany, pp. 111–118.
Fletcher, W. P., and Gent, A. N., 1957, “Dynamic Shear Properties of Some Rubber-Like Materials,” Br. J. Appl. Phys., 8(5), pp. 194–201. [CrossRef]
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Fig. 2

Generic master curve (solid) of rubber friction against sliding speed log(v). On rough surface, adhesion and viscoelastic friction mechanisms (dashed) are blended into a single friction master curve (adapted from Ref. [8, p. 67, Chap. 2]).

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Fig. 1

Schematic representation of the interaction between the rubber block and a generic wave undulation of length λ; the vectors of the rubber block sliding velocity v, the vertical load Fz, and friction force Ff are also represented

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Fig. 3

Storage moduli and loss modulus curves for SBR compound at varying frequency. The storage moduli curves have been extracted from Refs. [9] and [10] while the loss modulus curve is provided in Ref. [2].

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Fig. 4

Log of shift factor aT for SBR. The reference temperature is Tref = 20 °C. The log shift at 0 °C is also highlighted for reference given that in Ref. [2] Tref = 0 °C.

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Fig. 5

Power spectral density C(q) of a strip of silicon carbide paper (commercially known as “safety walk paper”) at varying wave number q. The macro roughness (q0) and cut-off (q1) wave numbers are highlighted.

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Fig. 6

Simulated hysteretic friction master curves of Grosch–Fletcher and Grosch–Klüppel compounds on silicon carbide paper. The curves are compared with Grosch's measured master curve on clean silicon carbide paper. Each colored segment in the simulated curves corresponds to a different compound temperature T.

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Fig. 7

The tan(δ) curves of the simulated materials peak at similar frequencies. The shaded area locates the frequency range where the loss tangents measured by Grosch [2] and by Fletcher and Gent [10] are maximum.

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Fig. 8

Comparison between the adapted storage modulus and the storage moduli of the Grosch–Klüppel and the Grosch–Fletcher materials

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Fig. 9

Comparison between the tan(δ) of the adapted material with those of the Grosch–Klüppel and the Grosch–Fletcher materials

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Fig. 10

Simulated friction master curve generated by the adapted material. The curve is compared to Grosch's experimental curve on clean paper.

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Fig. 11

Simulated friction master curve generated by the adapted material. The curve is compared to the experimental curves on clean and dusted paper.




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