FEA of a Golf Driver and
Golf Ball
Solid Mechanics - ES 240
Adrian Podpirka
ABAQUS Project
Outline of Work
Introduction to
Golf
Goal of
Research
Discussion
Analysis
Conclusion
Theory
Citations
Modeling
Results
Golf
Invented in Scotland around 1450s.
Requires hitting a small ball roughly 200-500
yards into a small hole.
Different clubs are used depending on distance
and arc required.
During the first shot, the golfer tries to hit it down
course as far as possible
Goals of Project
To determine stress distributions in a golf ball and
in a driver.
To determine natural frequency of the golf ball
and driver.
Attempt to determine percentage of sweet spot
and effect of driving distance.
Learn ABAQUS
FEA & Golf
Only recently has FEA been used to design clubs.
Programs are being made specifically to cater to
the golf industry.
Used to analyze swings, slicing, tendency to
hook, etc.
Theories
Golf Ball
Internal Stresses in the golf ball will arise due
to sudden impact and different properties of
the two materials
Ball will deform as drastically as seen in the
picture to the right.
Frequency Measurement
A closer natural frequency between the ball
and the club will lead to an increase in
distance.
Stress Propagation
Sweet spot occurs symmetrically from
propagating waves.
Materials
Young’s
Modulus E
(GNm^-2)
Poisson’s
Ration
Density (kg
m^-3)
Note
Golf Ball
Butadien
Rubber
.0392
.45 1150
Inner Core of Golf Ball
Driver Head
Iononer
Resin
.294
.40
Outer Core of Golf Ball
Ti-6Al-4V
118
.34 4507
Standard Driver Head
Material
Carbon
Fiber
17.2
.31 1545
Standard Shaft Material
Driver Shaft
950
T. Iwatsubo et al
B. Wang et al
Geometry of
Equipment
Golf Ball
40 cm
Golf Club - Wood Driver
44 cm
Shaft length - 1.05 m
Height - 40 mm
Width - 90 mm
Depth - 65 mm
Golf Ball
loaded linearly ramping to 15000 N.
Golf Ball
Sweep meshed with 1600 elements
Modeled a 44 cm diameter area and partitioned off middle section.
Traction load placed in between 7 & 9
Boundary Condition placed directly opposite
Results
Internal stresses develop as a result of mismatch of materials on the order of 40 kN.
Golf ball is seen to deform. This is analogous to the picture shown before.
Golf Ball Results
QuickTime™ and a
BMP decompressor
are needed to see this picture.
QuickTime™ and a
BMP decompressor
are needed to see this picture.
Natural Frequency
The closer the frequency between club and ball, the better energy transfer and
therefore, farther distance.
We will test the difference between hollow and solid clubs
Golf Ball
Meshed with 124 elements
Circular edge boundary conditions
Driver
Meshed with roughly 169 & 171 elements
Pinned at top
The hollow bodied club face has a lower
frequency then the solid body, closer
matching that of the balls.
2D Stress
Distribution
Assume traction loading on face of of driver.
Large deformation occurs in shaft of carbon fiber.
Stress waves still occurs in driver face but much less then with coupled shaft.
QuickTime™ and a
BMP decompressor
are needed to see this picture.
QuickTime™ and a
BMP decompressor
are needed to see this picture.
Stress
QuickTime™ and a
BMP decompressor
are needed to see this picture.
3D Stress
Note: The full 3D
club could not be
meshed because
of element
assignment errors
in ABAQUS. The
Natural frequency
of the club could
not be found.
QuickTime™ and a
BMP decompressor
are needed to see this picture.
QuickTime™ and a
BMP decompressor
are needed to see this picture.
Analysis
Full Analysis of all data and values will be given in the paper.
The golf balls deformed as theory and practice indicated.
By tuning golf balls to different clubs, better distances can be obtained. This would
require changing either the parameters on the ball or club.
Since ABAQUS was not able to mesh the merged structure, I had to forgo on the
natural frequency aspect of the 3D driver.
Recommendations
Many of the articles could not be located since
Harvard did not have a subscription to them.
Many parameters
Using different material parameters in order to
optimize values.
Dynamically loading and setting contact
parameters
Citations
Wang et al. “Modal Properties of Golf Club Wood Driver in Different Boundary Conditions”
Hocknell et al. “Hollow Club Hear Modal Characteristics: Determination and Impact Applications”
Hocknell et al. “Experimental Analysis of Impacts with Large Elastic Deformation: I. Linear Motion”
Iwatsubo et al. “Numerical Analysis of Golf Club Head and Ball”
Penner, A. “The Physics of Golf: The Convex Face of a Driver”
Newman et al. “The Dynamic Flexing of a Golf Club Shaft During a Typical Swing”
Arakawa et al. “Dynamic Contact Behavior of a Golf Ball during an Oblique Impact”
H. Kolsky. Stress Waves in Solids. Dover Publications Inc.
Axe et al. “The vibrational mode structure of a golf ball”