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

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.

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

Titanium Plate Geometry

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

Axisymmetric Model Cross Section Areas Defined Mesh Created Materials Defined

Expanded Axisymmetric Model

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

Impact Video – Element Displacement

Impact Video – Velocity Solution

Velocity Results

COR Results

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 www.fanklygolf.com, September 21, 2010. <http://www.franklygolf.com/driver-cor-springlike-effect.aspx> GOLF CHANNEL Newsroom. “USGA, R&A Rule on 'Spring-Like' Effect.” thegolfchannel. August 6, 2002. September 21, 2010 <http://www.thegolfchannel.com/tour-insider/usga-ra-rule-spring-like-effect-6874/> “What is C.O.R.? What is CT?” wishongolf. September 21, 2010 <http://www.wishongolf.com/faq_tech_answer.php?techKey=1> “Conflicts surrounding the Callaway ERC driver.” golftoday. September 21, 2010 <http://www.golftoday.co.uk/news/yeartodate/news01/callaway.html> “Coefficient of restitution.” wikipedia. September 21, 2010 <http://en.wikipedia.org/wiki/Coefficient_of_restitution> Kelley, Brent. “Clubhead Speed.” about. September 26, 2010 <http://golf.about.com/od/golfterms/g/clubheadspeed.htm>