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Solitary Waves to Assess the Internal Pressure and the Rubber Degradation of Tennis Balls

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Abstract

Rubber is a material present in many commodities, including tennis balls. The characteristics of tennis balls are specified by the International Tennis Federation and are evaluated using standard tests that are too cumbersome to be staged easily and quickly. In this article we present an experimental method based on the propagation of highly nonlinear solitary waves (HNSWs) to determine the internal pressure of tennis balls and to estimate rubber degradation. HNSWs are compact waves that can form and travel in a closely-packed assembly of systematically arranged particles that generally interact according to the Hertz contact law. In the study presented here, we developed a model that predicts the internal pressure of tennis balls and estimates rubber degradation by observing the waves propagating within a chain in contact with the ball to be estimated. The model was validated experimentally, by testing 18 identical balls played over a few weeks period. We found that the dynamic interaction between the waves and the rubber can successfully detect changes in internal pressure and bouncing characteristics and that these changes were barely detected using a conventional rebound test. In the future, the findings of this study may be expanded to characterize any rubber of any shape.

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References

  1. (ITF) ITF International Tennis Fedration (ITF) (2018) http://www.itftennis.com/technical/balls/approval-tests.aspx Accessed Feb 2018

  2. Technical I. http://www.itftennis.com/technical/. Accessed 2 March 2018

  3. Steele C (2006) Tennis ball degradation. © Carolyn Steele

  4. International Tennis Fedration (ITF). http://www.itftennis.com/media/278130/278130.pdf

  5. Cross R (1999) Dynamic properties of tennis balls. Sports Eng 2:23–34

    Article  Google Scholar 

  6. Haron A, Ismail K (2012) Coefficient of restitution of sports balls: a normal drop test. In: IOP conference series: materials science and engineering. vol 1. IOP Publishing, p 012038

  7. Bridge NJ (1998) The way balls bounce. Phys Educ 33(3):174

    Article  Google Scholar 

  8. Hubbard M, Stronge W (2001) Bounce of hollow balls on flat surfaces. Sports Eng 4(2):49–61

    Article  Google Scholar 

  9. Andersen T (1999) Collisions in soccer kicking. Sports Eng 2(2):121–125

    Article  Google Scholar 

  10. Haake S, Carre M, Goodwill S (2003) The dynamic impact characteristics of tennis balls with tennis rackets. J Sports Sci 21(10):839–850

    Article  Google Scholar 

  11. Goodwill S, Haake S (2004) Modelling of tennis ball impacts on a rigid surface. Proc Inst Mech Eng C J Mech Eng Sci 218(10):1139–1153

    Article  Google Scholar 

  12. Nagurka M, Huang SA (2004) Mass-spring-damper model of a bouncing ball. In: American Control Conference, 2004. Proceedings of the 2004. IEEE, pp 499–504

  13. Wadhwa A (2009) Measuring the coefficient of restitution using a digital oscilloscope. Phys Educ 44(5):517

    Article  Google Scholar 

  14. Wadhwa A (2012) Measuring the rebound resilience of a bouncing ball. Phys Educ 47(5):620

    Article  Google Scholar 

  15. Wadhwa A (2013) Study of the dynamic properties and effects of temperature using a spring model for the bouncing ball. Eur J Phys 34(3):703

    Article  Google Scholar 

  16. Bagheri A, Rizzo P (2017) Assessing the pressure of tennis balls using nonlinear solitary waves: a numerical study. Sports Eng 20(1):53–62

    Article  Google Scholar 

  17. Nasrollahi A, Rizzo P, Orak MS (2018) Numerical and experimental study on the dynamic interaction between highly nonlinear solitary waves and pressurized balls. J Appl Mech 85(3):031007–031011. https://doi.org/10.1115/1.4038990

    Article  Google Scholar 

  18. Nasrollahi A, Orak MS, Kosinski K, James A, Weighardt L, Rizzo P (2018) An alternative noninvasive approach to characterize tennis balls. J Nondestr Eval Diagn Progn Eng Syst (in press)

  19. Yang J, Silvestro C, Khatri D, De Nardo L, Daraio C (2011) Interaction of highly nonlinear solitary waves with linear elastic media. Phys Rev E 83(4):046606

    Article  Google Scholar 

  20. Bagheri A, La Malfa Ribolla E, Rizzo P, Al-Nazer L, Giambanco G (2015) On the use of l-shaped granular chains for the assessment of thermal stress in slender structures. Exp Mech 55(3):543–558

    Article  Google Scholar 

  21. Nesterenko V (1983) Propagation of nonlinear compression pulses in granular media. J Appl Mech Tech Phys 24(5):733–743

    Article  Google Scholar 

  22. Nesterenko V, Lazaridi A, Sibiryakov E (1995) The decay of soliton at the contact of two “acoustic vacuums”. J Appl Mech Tech Phys 36(2):166–168

    Article  Google Scholar 

  23. Nesterenko VF (2013) Dynamics of heterogeneous materials. Springer Science & Business Media, New York

    Google Scholar 

  24. Lazaridi A, Nesterenko V (1985) Observation of a new type of solitary waves in a one-dimensional granular medium. J Appl Mech Tech Phys 26(3):405–408

    Article  Google Scholar 

  25. Coste C, Falcon E, Fauve S (1997) Solitary waves in a chain of beads under hertz contact. Phys Rev E 56(5):6104

    Article  Google Scholar 

  26. Daraio C, Nesterenko V, Herbold E, Jin S (2005) Strongly nonlinear waves in a chain of Teflon beads. Phys Rev E 72(1):016603

    Article  Google Scholar 

  27. Daraio C, Nesterenko V, Herbold E, Jin S (2006) Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. Phys Rev E 73(2):026610

    Article  Google Scholar 

  28. Job S, Melo F, Sokolow A, Sen S (2005) How Hertzian solitary waves interact with boundaries in a 1D granular medium. Phys Rev Lett 94(17):178002

    Article  Google Scholar 

  29. Job S, Melo F, Sokolow A, Sen S (2007) Solitary wave trains in granular chains: experiments, theory and simulations. Granul Matter 10(1):13–20

    Article  MATH  Google Scholar 

  30. Carretero-González R, Khatri D, Porter MA, Kevrekidis P, Daraio C (2009) Dissipative solitary waves in granular crystals. Phys Rev Lett 102(2):024102

    Article  Google Scholar 

  31. Yang J, Daraio C (2013) Frequency-and amplitude-dependent transmission of stress waves in curved one-dimensional granular crystals composed of diatomic particles. Exp Mech 53(3):469–483

    Article  Google Scholar 

  32. Yang J, Gonzalez M, Kim E, Agbasi C, Sutton M (2014) Attenuation of solitary waves and localization of breathers in 1D granular crystals visualized via high speed photography. Exp Mech 54(6):1043–1057

    Article  Google Scholar 

  33. Li K, Rizzo P (2015) Energy harvesting using arrays of granular chains and solid rods. J Appl Phys 117(21):215101

    Article  Google Scholar 

  34. Li K, Rizzo P (2015) Energy harvesting using an array of granules. J Vib Acoust 137(4):041002

    Article  Google Scholar 

  35. Li K, Rizzo P, Bagheri A (2015) A parametric study on the optimization of a metamaterial-based energy harvester. Smart Mater Struct 24(11):115019

    Article  Google Scholar 

  36. Li K, Rizzo P (2017) Experimental parametric analysis of an energy harvester based on highly nonlinear solitary waves. J Intell Mater Syst Struct 28(6):772–781

    Article  Google Scholar 

  37. Daraio C, Nesterenko V, Herbold E, Jin S (2006) Energy trapping and shock disintegration in a composite granular medium. Phys Rev Lett 96(5):058002

    Article  Google Scholar 

  38. Deng W, Nasrollahi A, Rizzo P, Li K (2016) On the reliability of a solitary wave based transducer to determine the characteristics of some materials. Sensors 16:5. https://doi.org/10.3390/s16010005

    Article  Google Scholar 

  39. Nasrollahi A, Deng W, Rizzo P, Vuotto A, Vandenbossche JM (2017) Nondestructive testing of concrete using highly nonlinear solitary waves. Nondestr Testing Eval 32(4):381–399. https://doi.org/10.1080/10589759.2016.1254212

    Article  Google Scholar 

  40. Rizzo P, Nasrollahi A, Deng W, Vandenbossche J (2016) Detecting the presence of high water-to-cement ratio in concrete surfaces using highly nonlinear solitary waves. Appl Sci 6(4):104

    Article  Google Scholar 

  41. Schiffer A, Alkhaja A, Yang J, Esfahani E, Kim T-Y (2017) Interaction of highly nonlinear solitary waves with elastic solids containing a spherical void. Int J Solids Struct

  42. Ni X, Rizzo P (2012) Highly nonlinear solitary waves for the inspection of adhesive joints. Exp Mech 52(9):1493–1501

    Article  Google Scholar 

  43. Singhal T, Kim E, Kim T-Y, Yang J (2017) Weak bond detection in composites using highly nonlinear solitary waves. Smart Mater Struct 26(5):055011

    Article  Google Scholar 

  44. Schiffer A, Lee D, Kim E, Kim TY (2018) Interaction of highly nonlinear solitary waves with rigid polyurethane foams. Int J Solids Struct. https://doi.org/10.1016/j.ijsolstr.2018.05.010

  45. Yang J, Sangiorgio SN, Borkowski SL, Silvestro C, De Nardo L, Daraio C, Ebramzadeh E (2012) Site-specific quantification of bone quality using highly nonlinear solitary waves. J Biomech Eng 134(10):101001

    Article  Google Scholar 

  46. Bathe K-J (2006) Finite element procedures. Prentice Hall, Pearson Education, Inc. K-J Bathe, London

  47. Belytschko T, Liu WK, Moran B, Elkhodary K (2013) Nonlinear finite elements for continua and structures. Wiley, West Sussex

    MATH  Google Scholar 

  48. Goodwill S, Kirk R, Haake S (2005) Experimental and finite element analysis of a tennis ball impact on a rigid surface. Sports Eng 8(3):145–158

    Article  Google Scholar 

  49. Frey PJ, George PL (2000) Mesh generation: application to finite elements. Hermes Science Europe, Oxford

    MATH  Google Scholar 

  50. Goodwill S, Haake S (2004) Ball spin generation for oblique impacts with a tennis racket. Exp Mech 44(2):195–206

    Article  Google Scholar 

  51. Cross R (2014) Oblique bounce of a rubber ball. Exp Mech 54(9):1523–1536

    Article  Google Scholar 

  52. Herbold EB (2008) Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials. University of California, San Diego

    Google Scholar 

  53. Sissler L (2012) Advanced modelling and design of a tennis ball. © Lise Sissler, Loughborough

  54. Sissler L, Jones R, Leaney P, Harland A (2010) Viscoelastic modelling of tennis ball properties. In: IOP conference series: materials science and engineering. vol 1. IOP Publishing, p 012114

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Acknowledgments

This project was supported by the University of Pittsburgh CRDF seed funding. The second author conducted this research as part of a Pittsburgh Allderdice High School research class, where high school students work on projects much like the undergraduate research experience. The mentoring effort of Dr. Janet R. Waldeck, National Board Certified Teacher, is very much appreciated. Finally, we thank Drs. Vidic and Fazzari for using the test samples and providing fruitful comments and suggestions about the serviceability of tennis balls.

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Authors and Affiliations

  1. Laboratory for Nondestructive Evaluation and Structural Health Monitoring Studies, Department of Civil and Environmental Engineering, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA, 15261, USA

    A. Nasrollahi & P. Rizzo

  2. Allderdice High-School, Pittsburgh, PA, USA

    R. Lucht

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  1. A. Nasrollahi
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  2. R. Lucht
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  3. P. Rizzo
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Correspondence to P. Rizzo.

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Nasrollahi, A., Lucht, R. & Rizzo, P. Solitary Waves to Assess the Internal Pressure and the Rubber Degradation of Tennis Balls. Exp Mech 59, 65–77 (2019). https://doi.org/10.1007/s11340-018-0432-1

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  • DOI: https://doi.org/10.1007/s11340-018-0432-1

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