Sliotar Impact Response

1. Sliotar Impact Response Simulation of the Impact Response of a Sliotar Core with a Non-Linear Contact Model Kevin Hanley, Kevin Cronin, Edmond Byrne Dept. of Process & Chemical Engineering, University College Cork, Fiachra Collins, Dermot Brabazon, Kieran Moran School of Mechanical and Manufacturing Engineering, Dublin City University, Ireland

2. Sliotar Impact Response HURLING Hurling is one of the national Irish sports governed by the Gaelic Athletic Association (GAA) in which a ball is struck by a wooden stick known as a hurley. The ball, known as a sliotar, consists of a leather skin and a solid core. The sliotar typically has a mass of 90 g, a diameter of 70 mm and consists of a leather skin around either a Cork core (traditional) or Polymer core (more recent). Hurley/sliotar impact speeds can range from zero up to 38 m/s. The response of the ball when struck by a hurley is dominated by the behaviour of the core material.

3. Sliotar Impact Response HURLING

4. Sliotar Impact Response UCC AND HURLING Irish Universities compete in the Fitzgibbon Cup (named after a UCC Academic) with the competition dating from 1912. UCC lead the Roll of Honour with 37 titles (8 in a row in the 1980’s). Ray Cummins, Nicky English, Joe Deane 1988 1997

5. Sliotar Impact Response PROJECT MOTIVATION Regulations concerning a sliotar are viewed as inadequate (mainly concerned with dimensions, construction and water pick-up and not with impact response). Much less stringent compared to cricket, tennis, baseball. GAA commissioned DCU to examine the impact characteristics of currently used sliotar cores with a view to standardisation. Project motivated by concerns about variability in sliotar performance in major games.

6. Sliotar Impact Response MEDIA COMMENTS behaved like a ping-pong ball…” – Sunday Times, 20/07/2003 “…ball is travelling too far…” – Sunday Times, 03/08/2003 “Croke Park suspects that Cork introduced their own balls into the All-Ireland final” –Sunday Times, 22/02/2004 “…going too far… crazy to see puck-outs nearly reach the full-forward lines…” –Sunday Times, 18/09/2005 “…bounced wildly…” – Sunday Times, 02/07/2006 “…too light… travelled too fast… almost impossible to control…” – Irish Times,20/04/2007 “...spends most of its time in the air... hardly any midfield play anymore... making a mockery of the game...” – Irish Independent, 01/07/2010

7. Sliotar Impact Response BALL RESPONSE Players’ perception of ball performance can be related to impact parameters (Contact Duration, Max. Impact Force, Max. Impact Deflection, Coefficient Of Restitution). For instance too short a contact time results in a very high impact force and ball appears to be too ‘hard’. Too high a COR and ball is too ‘lively’ and uncontrollable. Excessive deflection or deformation affects ball durability The coefficient of restitution is the only impact parameter that is precisely regulated at present; it must lie between 0.522 and 0.576 when measured from a drop height of 1.8 m. (an impact speed of around 6 m/s) Compare to tennis ball (0.74), baseball (0.54), cricket ball (0.58)

8. Sliotar Impact Response TEST IMPACT CONDITIONS To facilitate comparison between different core types a standard impact configuration was examined rather than actual hurley/sliotar contact. The chosen configuration was the direct, normal, impact of a non-rotating ball core against a static, heavy steel plate. The plate was assumed to be infinitely stiff compared to the ball core so that no momentum was exchanged during the impact.

9. Sliotar Impact Response IMPACT MODELLING Continuous contact dynamic models insert some combination of conceptual springs (contact stiffness) and dashpots (contact damping) at the contact point between bodies. The dashpots dissipate energy while the springs provide the required elastic behaviour. Ball core is subject to a force from each component.

10. Sliotar Impact Response IMPACT MODELLING Assuming the impact between the ball and the flat plate may be treated as a single degree of freedom problem. Damping and Stiffness terms are proportional to impact velocity, x’(t) and displacement, x(t) respectively and the corresponding coefficients are usually given a power law dependence on displacement. Note hysteresis effects between the loading and unloading periods are not explicitly accounted for nor is any strain rate dependence of κ (expect it to be larger with increasing impact speed). .

11. Sliotar Impact Response PHYSICAL SOURCES OF NON-LINEARITY 1] Geometric Hertzian Contact – stiffness force has a non-linear relationship with displacement. 2] Damping Force depends on the product of displacement and its derivative, velocity. 3] Material Constitutive Characteristics (Stress-Strain Curve is non-linear even at low load levels).

12. Sliotar Impact Response LINEAR KELVIN-VOIGT IMPACT MODEL Letting the exponents We obtain the standard linear model: m mass of the ball kg λ(c) ball (viscous) damping coefficient Ns/m κ(k) Ball stiffness N/m

13. Sliotar Impact Response LINEAR KELVIN-VOIGT IMPACT MODEL Advantages: 1] Simplicity. 2] Parameters of the model have a physically meaningful interpretation. 3] Can be solved analytically for impact velocity and displacement as a function of time. Weaknesses: 1] Model predicts that contact forces at the beginning of the impact are discontinuous (physically unrealistic). 2] Small attractive force terms appear directly prior to the separation of the bodies (physically unrealistic). 3] Coefficients of restitution have no dependence on impact velocity (contrary to experiments).

14. Sliotar Impact Response LINEAR KELVIN-VOIGT IMPACT MODEL Sliotar core impacts will be under-damped (ζ < 1 in fact ζ ≈ 0.17). Impact displacement versus time will be Impact force versus time Contact duration will be Coefficient of restitution will be

15. Sliotar Impact Response LINEAR IMPACT MODEL Force versus Deflection Characteristic

16. Sliotar Impact Response NON-LINEAR IMPACT MODEL Letting the exponents We obtain a four parameter impact model (Hunt & Crossley) that gives results more consistent with experimental findings. The appropriate value for n comes from the geometry of contact (sphere impacting a flat plate) suggesting the Hertzian value of 1.5. m Ball mass kg λ Damping Parameter Ns/m2.5 κ Stiffness Parameter N/m1.5

17. Sliotar Impact Response NON-LINEAR IMPACT MODEL No analytical solution for impact quantities but an implicit relationship between velocity, v and displacement, x does exist.

18. Sliotar Impact Response NON-LINEAR IMPACT MODEL: PARAMETER DETERMINATION The parameters λ and κ come from ball energy absorption and stiffness characteristics. It can be shown that they are inter-related with two experimentally measurable quantities: The initial impact velocity, v0 The coefficient of restitution, ε

19. Sliotar Impact Response NON-LINEAR IMPACT MODEL The Stiffness Parameter can be related to the asymptotic Hertzian stiffness, KH at very low impact speeds where E (Modulus of Elasticity), ν (Poisson’s Ratio) and R (Core radius) are ball elastic and geometric properties.

20. Sliotar Impact Response SLIOTAR CORE COMPOSITIONS Diameters, masses and compositions of each sliotar core used in this study

21. Sliotar Impact Response STATIC LOADING TESTS Quasi static loading of whole cores and core prisms at low strain rates (0.01 mm/s, 0.5 mm/s and 1 mm/s) and up to different maximum deflection levels (3 mm, 6 mm and 10 mm).

22. Sliotar Impact Response DYNAMIC LOADING TESTS Each of the four cores was tested at three impact speeds; 5 m/s, 15 m/s 25 m/s.

23. Sliotar Impact Response NON-LINEAR IMPACT MODEL SOLUTION Algorithm written in MATLAB (using the implicit differential equation solver). Magnitudes of the stiffness and damping parameters found by physical reasoning and data analysis. Stiffness parameter is constant for each ball type but damping parameter depends on impact speed.

24. Sliotar Impact Response STATIC LOADING - FORCE versus DEFLECTION Results agree with Hertz Theory (Force vs. Deflection follows a 1.5 exponent power law).

25. Sliotar Impact Response IMPACT LOADING: FORCE versus DEFLECTION

26. Sliotar Impact Response IMPACT LOADING: DEFLECTION versus TIME

27. Sliotar Impact Response IMPACT LOADING: CONTACT TIME versus IMPACT SPEED

28. Sliotar Impact Response NON-LINEAR IMPACT MODEL RESULTS Model predictions agreed well with experimental measurements. Maximum contact force is very sensitive to impact speed rising from 750 N at 5 m/s up to 4500 N at 25 m/s. Maximum impact deflection also varies with impact speed rising from 3 mm at 5 m/s up to 10 mm at 25 m/s. Contact duration decreases from 2.14 ms at 5 m/s down to 1.58 ms at 25 m/s. Core C gave the ‘hardest’ contact with a large impact force and short contact duration. Overall though impact velocity is much more significant in determining response than core type.

29. Sliotar Impact Response MODEL PARAMETER STUDIES By selecting a representative fixed displacement, xR, for each impact condition, the non-linear model can be linearly approximated as Equivalent viscous damping coefficient and equivalent linear stiffness can be defined as Ball mass, m can be adjusted (within limits) by varying density of the core material. Ball stiffness, κ can be adjusted by varying Modulus of Elasticity for the core. Ball damping, λ can be adjusted by varying Loss Modulus of the core material.

30. Sliotar Impact Response PARAMETER STUDIES Output quantities of interest such as contact time and coefficient of restitution can be related to ball properties of mass, m, damping λ and stiffness κ. For instance selecting a core material with a greater modulus of elasticity will give shorter contact times and higher coefficients of restitution.

31. Sliotar Impact Response CONCLUSIONS Non-Linearity of the sliotar impact process must be accounted for. A relatively simple modelling approach can give good results. Selection of model parameters requires experimental data and cannot be done a priori. Model can then be used to suggest strategies to achieve required performance targets.