The Quasi-Static and Dynamic Testing of Damping in Golf Clubs Shafts

Sporting Actions • Although there are a great variety of sports there are a number of common actions involved • Propelling a projectile by an athlete or athlete-driven implement Golf, hockey, cricket, tennis, shot putt, javelin, squash, badminton • Controlling a vehicle around a track Skiing, skating, motorsport, snowboarding, horseracing • Propelling a vehicle by the athlete Snowboarding, toboggan, luge, cycling, rowing General Requirements • Conservation of momentum and energy • Mechanical efficiency is needed • Stiffness needs to be controlled • Component mass needs to be minimised • These share many similarities with aerospace so that sports equipment often ‘borrows’ materials from aerospace, e.g. Ti-based alloys and composites Sports Pecularities • The use of much sports equipment involves large strains and high strain rates. • The athlete is more intimately connected to the equipment and so force transfer to the human needs to be controlled • Damping is therefore an important dynamic materials property in sports equipment • Force reduction is important in injury reduction, but force transfer is an important feedback mechanism for athletes and so is needed for control • These requirements are not part of the material development for aerospace applications and so it is unlikely that the structures and properties are optimised for sports equipment use Improving Performance • Improved performance (faster, higher, longer) comes from more efficient energy transfer • The dynamic behaviour of materials and equipment needs to be determined • The interaction with the athlete needs to be addressed • Currently many sport equipement items are tested statically or quasi-statically. • Is this sufficient? Strains and Strain Rates • Some equipment can be strain gauged and used in sporting simulators (e.g. golf robots) or by real athletes (provided low intrusion of measuring devices) Maximum Strain rates: Golf club shafts < 0.1 s-1 Archery Bows < 2 s-1 Ice Hockey Sticks < 8 s-1 Modulus and Stiffness • Efficient energy transfer (and aerodynamics) requires high stiffness and so high specific modulus materials • Most modulus / stiffness measurements are quasi-static, but dynamic values are needed for sporting applications Modulus and Stiffness • Impact testing can then identify the strain rate range for which the modulus of composites become rate-dependent Modulus and Stiffness • For many sports quasi-static modulus / stiffness measurements are sufficient and these can be designed through appropriate laminate stacking design codes 100 80 Predicted modulus 60 40 20 Experimental Young's Modulus (GPa) Modulus Young's Static 0 modulus Lay-Up Damping • The strong interaction between athlete and equipment for handles and shafts means that damping to control forces transmitted to the athlete is necessary • Excess force transfer can lead to short- or long-term injury, e.g. tennis elbow. • Under damping can lead to large oscillations of the equipment (during a swing for example). • Excess damping leads to removal of a feedback loop to the athlete • Viscoelasticity can be effective in providing damping, e.g. shoe foams, running track surfaces, but this is strain and strain rate dependent Damping Characterisation •Each panel was clamped at cantilever length of 50 mm. •Each panel was fitted with a Kyowa uniaxial strain gauge (type KFG) to monitor the oscillation •Using the signal generator the panel was forced to oscillate through a swept sine frequency. •This was passed through a Fast Fourier Transform (FFT) where the damping and fundamental bending frequency was calculated. •Strain and strain rate was altered by changing the magnitude of the oscillation Strain Rate Sensitivity on Damping 0.0045 •Strain rates in golf 0.004 typically fall under 0.2 s-1 (Slater and Betzler, 2009) 0.0035 10 •No noticeable change in 0.003 damping can be seen in 20 the range applicable to 0.0025 30 golf. 0.002 40 •This agrees with Slater Loss Factor (n) Factor Loss and Betzler (2009), where 50 0.0015 no change in stiffness was 90 noticed through the same 0.001 range. 0.0005 0 0.01 0.1 1 Strain Rate (s-1) Damping Modelling • Theoretical based on 0 and 90° 0.009 panels. 0.008 • Good agreement 0.007 between theoretical 0.006 and experimental. ) η 0.005 • Only 4 ply panels were tested 0.004 Theoretical however CLT is Loss Factor ( Factor Loss Experimental 0.003 only valid for thin laminates so model 0.002 may fail for much 0.001 thicker laminates 0 Lay-Up Free-body Measurement • Golf shafts along with bats and rackets are amenable to instrumentation using gauges and accelerometers • The dynamic behaviour of balls is more difficult to quantify • Many balls are characterised by coefficient of restitution measurements by recording speeds prior to and after impacts with rigid or semi-rigid targets • This gives a measure of the ball performance, but does not indicate how that performance is achieved Free-body Measurement • CoR gives overall effects, e.g. the decrease in ball 0.90 CoR with increasing inbound speed 0.85 • Increased strain rate 0.80 would increase the CoR stiffness, reducing hysteresis and therefore 0.75 A increasing CoR. B C 0.70 • An increase in strain leads 10 20 30 40 50 60 Impact Speed to greater hysteresis and therefore and decrease in CoR. Showing strain the more dominant feature. Free-body Measurement • Whilst targets can be instrumented to give forces during impact and contact times the ball deformation needs to be measured in a non-contact manner Core Deformation 7000 Material Choice 6000 5000 • Compression test balls, 4000 0.02 mm/s cores and constituent Force (N) 301200 materials 2000 10 • Same deformation as 1000 8 impact, but at range of 0 0 2 4 6 8 10 12 slow strain rate (2 mm/s) Displacement (mm) 6 7000 • Measure energy losses Deformation (mm) 4 6000 • Predict ball performance 2 Ball A 5000 Ball B Ball C based on component part 0 4000 properties 0 2 4 6 8 10 12 14 3000 Hysteresis (J) 2 mm/s Force (N) • Use as basis of FE 2000 modelling 1000 0 0 2 4 6 8 10 12 Displacement (mm) Normal / Oblique Impact • The approach above is very successful for normal impact, and carries through to other sports, e.g. hockey • However this is only part of the answer as most shots involve oblique where significant rates of back spin are generated Normal / Oblique Impact • To address this the strains in different parts of the ball are needed, i.e. large deformation in the cover to give interaction with grooves and large core deformation to generate contact area • Large core deformation should result in large viscoelastic energy losses • In this aspect the strain rate is also important, not on loading, but on unloading Use of Hard Mantle 75 70 Ball D •Harder mantles deform 65 Ball E more elastically - force 60 soft core to recover 55 faster than normal Shore D ShoreHardness D 50 •Reduces viscous part 45 of deformation unloading 40 0 5 10 15 20 25 Radial Distance (mm) Conclusions • Sports equipment performance can be improved provided that the mechanism behind the action can be determined • Accurate strain and strain rate determination is needed in order to characterise the equipment and component materials under sports- specific conditions. • Static testing for equipment fabricated from composites/polymers maybe be sufficient. Some application dynamic testing is required. .

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