FEA of a Golf Driver and Golf Ball

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FEA of a Golf Driver and Golf Ball

• Solid Mechanics - ES 240
• Adrian Podpirka
• ABAQUS Project

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Outline of Work

• Introduction to Golf
• Goal of Research
• Theory
• Modeling
• Results

• Discussion
• Analysis
• Conclusion
• Citations

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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

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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

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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.

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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.
• Allows for wave dispersion before coming in
  contact with the club face edge.

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Materials

• Golf Ball
• Driver Head
• Driver Shaft

T. Iwatsubo et al B. Wang et al
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Geometry of Equipment

• Golf Ball
• Golf Club - Wood Driver

40 cm
44 cm
Shaft length - 1.05 m
Height - 40 mm Width - 90 mm Depth - 65 mm
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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.

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Golf Ball Results
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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

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The hollow bodied club face has a lower frequency
then the solid body, closer matching that of the
balls.
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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.

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Stress
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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.
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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.

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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

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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