Abstract
In this paper, a finite element model for investigating the restitution characteristics of the golf ball colliding with club-head is proposed. The solid elements are used to construct the finite element model of golf ball. Solid and shell elements are used for modeling the club-head. The material properties of club-head are considered as isotropic elastic. The proposed model of golf ball is divided into two parts. The cover of ball is considered as an isotropic elastic material while the core of ball is treated as a shape-memory alloy. The restitution characteristics of a golf ball colliding with club-head were simulated by LS-DYNA commercial code. This paper attempts to explore the possibility of modeling COR of golf ball behavior during impact using SMA model for the core material. The verification experiment was conducted using a ball projected by air cannon toward a resting club-head without shaft or grip to measure the coefficient of restitution.
One benefit of SMA model is that we could easily control the percentage of energy loss, which is critical for COR, through the four points of SMA model. The other benefit of SMA model is that it requires no special tensile machine and only two additional COR test data are needed to accomplish the analysis. And the experimental result agreed with the proposed finite element model. The developed model is useful to investigate the design parameters of a golf club.
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References
Procedure for Measuring the Velocity Ration of a Club Head for Conformance to Rule 4-1e, Appendix 2. United States Golf Association, February, 1999.
Charles E. Smith and Pao-Pao Liu, Coefficient of restitution. Journal of Applied Mechanics,59 (1992), 963–969.
Ujihashi Sadayuki, Hirabara Yasuharu, Adachi Tadaharu and Matsumoto Hiroyuki, Measurement and evaluation of restitution characteristics of golf balls. Transactions of the Japan Society of Mechanical Engineers, Part C, 60, No. 577 (1994), 3150–3156.
Ujihashi Sadayuki, Inou Norio, Tanaka Katsumasa, Tanaka Takanori, Sato Fuminobu and Kaneko Yasunori, Analysis of the restitution characteristics of golf balls colliding with thin plates. Transactions of the Japan Society of Mechanical Engineers, Part C,68, No. 2 (2002), 555–561.
Tom Mase, Eric Nelson, Jeff Brennan and Bruce Pettibone, USGA Rule 4-1e optimization of a golf driver head using LS-DYNA and Altair HyperStudy. 7th International LS-DYNA Users Conference, Session 17 — Simulation Technology, 2002, 5.1–5.8.
D.C. Winfield and Teong E. Tan, Optimization of the clubface shape of a golf driver to minimize dispersion of off-center shots. Computer and Structures,58, No. 6 (1996), 1217–1224.
Ferdinando Auricchio, Robert L. Taylor and Jacob Lubliner, Shape-memory alloys: Macro modeling and numerical simulations of the super elastic behavior. Computer Methods Applied Mechanics Engineering,146 (1997), 281–312.
Ferdinando Auricchio and Robert L. Taylor, Shape-memory alloys: Modeling and numerical simulations of the finite-strain super elastic behavior. Computer Methods Applied Mechanics Engineering,143 (1997), 175–194.
Livermore Software Technology Corporation, LS-DYNA KEYWORD USER’S MANUAL. California, 2001.
Douglas C. Montgomery, Design and Analysis of Experiments (2nd edition). John Wiley & Sons, 1984, 21–32.
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Chiu, JT., Shen, CL. Analysis of the restitution characteristics of a golf ball colliding with a club-head. Japan J. Indust. Appl. Math. 22, 429–442 (2005). https://doi.org/10.1007/BF03167493
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DOI: https://doi.org/10.1007/BF03167493