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
MmmMVVe
in
out
Axisymmetric Model Cross Section
Areas Defined
Mesh Created
Materials Defined
Expanded Axisymmetric Model
Analysis Runs
VycftVy
cftVycft
-110
0.1375
-100
0.1375
-90
0.1375
0.1250 0.1250 0.1250
0.1125 0.1125 0.1125
0.1000 0.1000 0.1000
0.0875 0.0875 0.0875
0.0750 0.0750 0.0750
Impact Video – Element Displacement
Impact Video – Velocity Solution
Velocity Results
Final Velocity vs. Clubface Thickness for Different Swing Speeds
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0.05 0.075 0.1 0.125 0.15
Clubface Thickness (inches)
Fin
al V
elo
cit
y (m
ph
)
110 MPH Swing Speed
100 MPH Swing Speed
90 MPH Swing Speed
COR Results
COR vs. Clubface Thickness for Different Swing Speeds
0.920
0.930
0.940
0.950
0.960
0.970
0.980
0.05 0.075 0.1 0.125 0.15
Clubface Thickness (inches)
CO
R
110 MPH Swing Speed
100 MPH Swing Speed
90 MPH Swing Speed
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>