Finite Element Analysis of Wood and Composite Structured Hockey sticks

Transcription

1 Finite Element Analysis of Wood and Composite Structured Hockey sticks 605 Finite Element Analysis Professor Ian Grosse May 15, 2003 By: Michael O Brien

2 Project Statement The direction of this project is to understand the nature of the construction of composite shafts and then use that knowledge to assess the proper dimensions necessary to deal with bending forces.

3 Various Materials Wood (Rock Elm) Aluminum Composite

4 Feel Stick selection how the puck feels when it comes in contact with the stick Flex The snap action associated with the stick Weight Durability The ability of the stick to endure repeated loading and unloading Cost Weight, Flex and Durability are the most important

5 Applied Force Input bending picture F = m*v^2/2 d d is an ideal distance of m (mass =.170 kg) A shot at 100 mph (44.6 m/s) would have would require a force of 560N. (Physics of Hockey, Hache, p 86) Al MacInnis (photo: Kevin Frayer)

6 Deflection Pecca picture With the applied force of 560 N it is possible for sticks to bend up to 30 degrees, thus creating a deflection of 15 cm. (Physics of Hockey, Hache, p 93) Michael Pecca (photo:david Duprey)

7 Analysis Wooden Stick Properties of Rock Elm Young's Modulus Max Tensile Max Compression Poisson's Ratio 8963 M Pa 15 M Pa 11 M Pa 0.35 Force 560 N - With these values we can set up an optimization of the solid wooden shaft Data from: Carmichael, Colin Kent s Mechanical Engineers Handbook 12th Edition Hache, Alain The Physics of Hockey

8 Modeling Assumptions Zero displacement in all DOF at the butt end of stick Zero displacement in Y direction at the heel Load placement 3/4 along the shaft All force is perpendicular to the shaft maximum deflection is 15 cm Element types Beam 3 for optimization Plane 82 for stress analysis with appropriate dimensions

9 Optimization Results W = 2.6 cm H = 1.64 cm Von Mises Stress = K Pa Volume = 5.11 * 10 ^ -4 m^3 - This stress is below the critical compression stress. However, repeated loading would quickly cause considerable damage to the wood fibers.

10 Real Dimension W = 3.0 cm H = 2.0 cm Stress (max) = 5209 k Pa Volume = 7.2 * 10 ^-4 m^3

11 Conclusions about wooden shaft A 15 cm deflection in a wooden shaft produces a volume of 5.11 *10^-4 m^3, which would endure a stress of K Pa. This stress is very close to the max compression stress of the material. If a wooden stick, with real dimensions, was introduced to this degree of deflection it would more often than not fail.

12 The Composite Stick - Composites are made up of multiple layers which are oriented at various angles so as to effectively handle different types of stresses. -Orthotropic vs. Isotropic -Orientation - Longitudinal - 45 degrees

13 Composite Material Properties Dyneema Sk60 High strength Polyetuylene Fiber (used in sports and auto composites) Properties Density MaxTensile Stress Modulus of Elasticity 970 kg/m^ M Pa 110 G Pa (

14 Modeling Assumptions Force applied to center of shaft (ease in modeling) Same displacement constrains as wooden shaft Symmetric about the mid-point Elements Plane 42 (to mesh face) Solid 45 (to sweep entire volume)

15 Longitudinal Orientation

16 Further Work Optimize the thickness of the transverse and longitudinal layers. Make Weight comparisons Wood Shaft density 514 kg/m^3 mass = Kg Composite Density 970 kg/m^3 mass (roughly) = Kg

17 Future Considerations Introduce torsion into both wood and composite models.

18 Works Cited Books Carmichael, Colin. Kent s Mechanical Engineers Handbook 12th Edition. John Wiley and Sons, Inc. New york, NY Hache, Alain, The Physics of Hockey The Johns Hopkins University Press. Baltimore, MD Websites plastics.about.com/library/data/blc-gy htm www/popsci.com/popsci/science/article/0,12543,383877,00.html