1. ANALYSIS OF NONCONFORMING COEFFICIENTS OF RESTITUTION IN GOLF DRIVERS USING A FINITE ELEMENT APPROACH
Engineering Project by: Brian Hill
Main Advisor: Ernesto Gutierrez-Miravete
Co-Advisor: Ken Brown
Second Progress Report

2. Goals Investigate the effect clubface thickness has on COR.
Investigate the effect swing speed at impact has on COR.
Use USGA COR test method as a basis to create a suitable ANSYS FE model.
Plot comparative results of COR vs. face thickness at different swing speeds.

3. ANSYS Modeling Properties
2-d model of representative clubface and 3 piece golf ball with axisymmetry
Ball modeled as concentric semicircles and plate modeled as rectangles.
LS-DYNA explicit 2-d solid 162 elements
Quads only, 2d
Plastic kinematic properties for titanium plate
Impact could be close to yield stress at small face thicknesses
Mooney-Rivlin hyper-elastic properties for ball
Core, Mantle, and Cover of 3 piece ball modeled using material properties from previous articles.
SI units used

4. Titanium Plate Geometry

5. LS-DYNA Analysis Options
Nodal component created for the ball
Initial velocity placed in –y direction on nodal component
Contact definition: “2d Surface to Surface” contact in lieu of “automatic”
Contact time defined as .005 seconds
Output ASCII file matsum for averaged nodal velocities for each part (core, cover, mantle, plate)
Mass taken from d3hsp file - automatically produced

6. Axisymmetric Model Cross Section
Areas Defined
Mesh Created
Materials Defined

7. Expanded Axisymmetric Model

8. Analysis Runs
-110
0.1375
-100
-90
0.1250
0.1125
0.1000
0.0875
0.0750

9. Impact Video – Element Displacement

10. Impact Video – Velocity Solution

11. Velocity Results

12. COR Results

13. References:
K. Tanaka et al., Construction of the finite-element models of golf balls and simulations of their collisions, Proc. of the Institution of Mechanical Engineers, Part L: J of Materials: Design and Applications 220 (1) (2006), pp. 13–22.
Petersen, Willem et al., Shape optimization of golf clubface using finite element impact models, International Sports Engineering Organization, December 2009
September 21, 2010.
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GOLF CHANNEL Newsroom. “USGA, R&A Rule on 'Spring-Like' Effect.” thegolfchannel. August 6, September 21, 2010
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“What is C.O.R.? What is CT?” wishongolf. September 21, 2010
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“Conflicts surrounding the Callaway ERC driver.” golftoday. September 21, 2010
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“Coefficient of restitution.” wikipedia. September 21, 2010
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Kelley, Brent. “Clubhead Speed.” about. September 26, 2010
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