Katsumasa Tanaka

Finite element modelling and simulations for golf impact

The objective of this study was to construct a finite element model of a golf ball and an impact simulation model between the ball and a club, and to devise a method for the construction of simulation models by investigating the factors affecting the behaviour of the ball during and after impact. A ball model with hyperelasticity and viscoelasticity was constructed using solid elements, and the relationship between the material properties and the ball behaviour at impact was revealed by varying several material constants of the ball model. A finite element model of a club with elasticity was created from a computer-aided design surface model of a commercially available driver. The club head and shaft were modelled using solid and shell elements, respectively. The effects of initial conditions at impact on the rebound behaviour of the ball, that is, the velocity, angle and spin rate, were investigated from impact simulations by varying the impact points of the ball and the postures of the club. Then, methods for the construction of simulation models were proposed based on these relationships. Impact experiments were also conducted to obtain the ball behaviour. The results simulated using the models, constructed by the proposed methods, closely matched the experimental results.

Construction of a finite element model for collisions of a golf ball with a club during swing

The objective of this study was to construct a finite element model for simulating the mechanical behaviour of a golf club and ball from swing to impact. An experiment using a golf robot was conducted to obtain the motion of the shaft grip during the swing, and the behaviour of the club and ball during the swing and impact. The swing model was developed by inputting the positional coordinate data of the grip, which was obtained from an experiment, into the grip model. The simulation results generally matched the experimental results for the swing motion, the behaviour of the shaft during the swing and the clubhead velocity and orientation at impact. The modelling of the grip contributed to the accuracy of the simulation results by precisely representing swing motion and suppressing the generation of vibration in the shaft grip. This indicates that the components of the proposed modelling method may also be suitable for representing the swing using data obtained from the robot test, and that the model and the approach for modelling may have potential to be used as a predictable tool to supplement robot tests, reducing the dependency on prototypes.

Finite-Element Analysis of the Collision and Bounce between a Golf Ball and Simplified Clubs (P271)

The objective of this study was to develop a finite-element (FE) model which could accurately simulate the behaviour of golf impacts, and to investigate the effect of a shaft on the clubhead upon the rebound of a ball, by conducting FE analysis on a ball colliding with a simplified club. The clubs were constructed by holding simplified clubheads by a locking ring fitted onto a steel shaft. The clubheads were designed based on the mass, volume and position of the centre of gravity (CoG) of commercial clubheads, so as to enable a typical golf impact. Three circular, hollow, titanium alloy bodies of constant mass, with increasing loft angles, were manufactured. FE models with linear elasticity of the clubs, which consisted of the clubheads, a locking ring and a shaft, were constructed. The FE model of the ball consisted of 8-node solid elements, and the material model was expressed as a hyper-elastic/viscoelastic model. Impact experiments were also conducted for comparison to confirm the accuracy of the FE models. The results of the impact simulations closely matched the experimental results. Impact behaviour was analysed by varying the impact point of the ball colliding with the full clubs and the lone clubheads and then comparing the ball/club and ball/clubhead collision results. The differences between the two most extreme values for the rebound angle and spin rate tended to be smaller in the club impact cases than in the clubhead impact cases. This tendency was estimated to depend on the relationship between the shaft position and the loft angle/CoG of the clubhead.