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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 Theory Modeling Results. Discussion Analysis Conclusion Citations. Golf. Invented in Scotland around 1450s.

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fea of a golf driver and golf ball
FEA of a Golf Driver and Golf Ball
  • Solid Mechanics - ES 240
  • Adrian Podpirka
  • ABAQUS Project
outline of work
Outline of Work
  • Introduction to Golf
  • Goal of Research
  • Theory
  • Modeling
  • Results
  • Discussion
  • Analysis
  • Conclusion
  • Citations
  • 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
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
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.
  • 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.

Young’s Modulus E (GNm^-2)

Poisson’s Ration

Density (kg m^-3)


Butadien Rubber




Inner Core of Golf Ball

Iononer Resin




Outer Core of Golf Ball





Standard Driver Head Material

Carbon Fiber




Standard Shaft Material

  • Golf Ball
  • Driver Head
  • Driver Shaft

T. Iwatsubo et al

B. Wang et al

geometry of equipment
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

golf ball
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.
natural frequency
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
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.
3d stress
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.

  • 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.
  • 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
  • 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”