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Research Papers

Models for Materials Damping, Loss Factor, and Coefficient of Restitution

[+] Author and Article Information
Hany A. Sherif

Professor
Department of Mechanical Engineering,
College of Engineering,
Qassim University,
P.O. Box 6677,
Buraidah 51452, Saudi Arabia
e-mail: hasherif@qec.edu.sa

Fahad. A. Almufadi

Associate Professor
Department of Mechanical Engineering,
College of Engineering,
Qassim University,
P.O. Box 6677,
Buraidah 51452, Saudi Arabia
e-mail: almufadi@qec.edu.sa

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received March 19, 2019; final manuscript received July 1, 2019; published online August 2, 2019. Assoc. Editor: Khaled Morsi.

J. Eng. Mater. Technol 142(1), (Aug 02, 2019) (12 pages) Paper No: MATS-19-1052; doi: 10.1115/1.4044281 History: Received March 19, 2019; Accepted July 16, 2019

Common parameters between metallic and polymeric materials are the coefficient of restitution, the damping coefficient, and loss factor. Although the relationship between the coefficient of restitution and the loss factor is quite direct, their dependence on the damping coefficient is not so simple and mainly affected by the adopted model used to describe the material response under impact. In the present study, Kelvin–Voigt linear model and Hunt–Crossley complex model are analyzed to describe how the coefficient of restitution depends on the viscous damping coefficient of impact. The correlation between the theoretical models and the experimental data is also shown. A simple method to predict the impact damping factor of both polymeric and metallic materials from the measured temporal signal of the impact force is demonstrated.

Copyright © 2019 by ASME
Topics: Damping , Polymers , Metals , Signals
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References

Yigit, A. S., and Christoforou, A. P., 1994, “On the Impact of a Spherical Indenter and an Elastic-Plastic Transversely Isotropic Half Space,” Compos. Eng., 4(11), pp. 1143–1152. [CrossRef]
Yigit, A. S., Christoforou, A. P., and Majeed, M. A., 2011, “A Nonlinear Visco-Elastoplastic Impact Model and the Coefficient of Restitution,” Nonlinear Dyn., 66(4), pp. 509–521. [CrossRef]
Sherif, H. A., and Almufadi, F. A., 2016, “Identification of Contact Parameters From Elastic-Plastic Impact of Hard Sphere and Elastic Half Space,” Wear, 368–369, pp. 358–367. [CrossRef]
Gilardi, G., and Sharf, I., 2002, “Literature Survey of Contact Dynamics Modelling,” Mech. Mach. Theory, 37(10), pp. 1213–1239. [CrossRef]
Thornton, C., 2013, “Coefficient of Restitution for Collinear Collisions of Elastic—Perfectly Plastic Spheres,” ASME J. Appl. Mech., 64(2), pp. 383–386. [CrossRef]
Coaplen, J., Stronge, W. J., and Ravani, B., 2004, “Work Equivalent Composite Coefficient of Restitution,” Int. J. Impact Eng., 30(6), pp. 581–591. [CrossRef]
Atanackovic, T. M., and Spasic, D. T., 2004, “On Viscoelastic Compliant Contact-Impact Models,” ASME J. Appl. Mech., 71(1), pp. 134–138. [CrossRef]
Mangwandi, C., Cheong, Y. S., Adams, M. J., Hounslow, M. J., and Salman, A. D., 2007, “The Coefficient of Restitution of Different Representative Types of Granules,” Chem. Eng. Sci., 62(1–2), pp. 437–450. [CrossRef]
Cross, R., 2002, “Measurements of the Horizontal Coefficient of Restitution for a Superball and a Tennis Ball,” Am. J. Phys., 70(5), p. 482. [CrossRef]
Stronge, W. J., 1990, “Rigid Body Collisions With Friction,” Proc. R. Soc. London Ser. A, 431, pp. 169–181. [CrossRef]
Lubarda, V. A., 2010, “The Bounds on the Coefficients of Restitution for the Frictional Impact of Rigid Pendulum Against a Fixed Surface,” ASME J. Appl. Mech., 77(1), pp. 1–7. [CrossRef]
Butcher, E. A., and Segalman, D. J., 2000, “Characterizing Damping and Restitution in Compliant Impacts Via Modified K-V and Higher-Order Linear Viscoelastic Models,” ASME J. Appl. Mech., 67(4), pp. 831–834. [CrossRef]
Gharib, M., and Hurmuzlu, Y., 2012, “A New Contact Force Model for Low Coefficient of Restitution Impact,” ASME J. Appl. Mech., 79(6), p. 064506. [CrossRef]
Alves, J., Peixinho, N., da Silva, M. T., Flores, P., and Lankarani, H. M., 2015, “A Comparative Study of the Viscoelastic Constitutive Models for Frictionless Contact Interfaces in Solids,” Mech. Mach. Theory, 85, pp. 172–188. [CrossRef]
Ahmad, M., Ismail, K. A., and Mat, F., 2016, “Impact Models and Coefficient of Restitution: A Review,” J. Eng. Appl. Sci., 11(10), pp. 6549–6555.
Stronge, W. J., 2000, Impact Mechanics, Cambridge University Press, Cambridge.
Ismail, K. A., and Stronge, W. J., 2008, “Impact of Viscoplastic Bodies: Dissipation and Restitution,” ASME J. Appl. Mech., 75(6), p. 061011. [CrossRef]
Flugge, W., 1967, “Viscoelasticity,” Blaisdell Publishing Company, Waltham, MA.
Hunt, K. H., and Crossley, F. R. E., 1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42(2), pp. 440–445. [CrossRef]
Jacobs, D. A., and Waldron, K. J., 2015, “Modeling Inelastic Collisions With the Hunt–Crossley Model Using the Energetic Coefficient of Restitution,” ASME J. Comput. Nonlin. Dyn., 10(2), p. 021001. [CrossRef]
Johnson, K., 1985, Contact Mechanics, Cambridge University Press, Cambridge.
Sherif, H. A., and Almufadi, F. A., 2019, “Polymer Modulus of Elasticity and Hardness From Impact Data,” ASME J. Eng. Mater. Technol., 141(1), p. 011010. [CrossRef]
Chakravartula, A., and Komvopoulos, K., 2006, “Viscoelastic Properties of Polymer Surfaces Investigated by Nanoscale Dynamic Mechanical Analysis,” Appl. Phys. Lett., 88(13), pp. 131901. [CrossRef]

Figures

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Fig. 1

Surface displacement–time curve due to impact

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Fig. 2

Variation of the damping factor with the time ratio

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Fig. 3

Variation of the normalized damping coefficient with coefficient of restitution

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Fig. 4

Scheme of pendulum test setup

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Fig. 5

Measured angular velocity of sphere indenter (d = 2.0 mm) striking polymer sample P2

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Fig. 6

Measured coefficient of restitution of polymer samples with velocity of impact

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Fig. 7

Mean values of the coefficient of restitution for the six-polymer samples tested

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Fig. 8

Effect of velocity of impact on the temporal signal of normal contact force of polymer sample P2

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Fig. 9

Measured coefficient of restitution of metal samples versus velocity of impact

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Fig. 10

Effect of velocity of impact on the temporal signal of normal contact force of metal sample M3

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Fig. 11

Variation of predicted damping coefficient c¯l of polymer samples with velocity of impact

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Fig. 12

Variation of predicted damping coefficient c¯n of polymer samples with velocity of impact (n = 1.5)

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Fig. 13

Variation of predicted damping coefficient c¯l of metal samples with velocity of impact

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Fig. 14

Variation of predicted damping coefficient c¯n of metal samples with velocity of impact (n = 1.5)

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Fig. 15

Variation of the damping coefficient c¯l of polymer samples with coefficient of restitution e

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Fig. 16

Variation of the damping coefficient c¯n of polymer samples with coefficient of restitution e (n = 1)

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Fig. 17

Variation of the damping coefficient c¯n of polymer samples with coefficient of restitution e (n = 1.5)

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Fig. 18

Variation of the damping factor c¯l of metal samples with the coefficient of restitution

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Fig. 19

Variation of the damping factor c¯n of metal samples with the coefficient of restitution (n = 1)

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Fig. 20

Variation of the damping factor c¯n of metal samples with the coefficient of restitution (n = 1.5)

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Fig. 21

Dependence of damping factor ζ of polymer samples on time ratio tc/t* of force–time signal

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Fig. 22

Effect of polymer hardness and velocity of impact on the time ratio tc/t* of polymer samples

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Fig. 23

Dependence of damping factor of metal samples on time ratio tc/t* of force–time signal

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Fig. 24

Variation of loss factor of polymer samples with the velocity of impact

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Fig. 25

Variation of loss factor of metal samples with the velocity of impact

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Fig. 26

Variation of loss factor of some polymer samples with the force frequency

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