Shape optimization of golf clubface using finite element impact models

To model the impact dynamics of a golf drive, high-fidelity finite element models of the ball and the clubhead are created and combined to simulate the collision of the two bodies. A three-piece golf ball is modelled using only solid elements, while the clubhead is modelled using solid elements for the crucial area of the impact, i.e. the clubface, and using shell elements for the rest of the clubhead to improve the computational efficiency of the simulation. The correct transfer of forces and moments in the transition area between the shell and solid elements is assured by introducing kinematic nodal constraints using rigid elements. The finite element model of the clubhead is parameterized with three shape variables that are varied during an optimization of the launch velocity for central impacts. The optimization process is performed in three stages. After analyzing the modal behaviour of each body involved in the impact, the first stage minimizes the natural frequency of the clubhead so that it better matches that of the ball, according to the theory of impedance matching. This first stage only requires structural analyses of the clubface. In the second stage, the ball is included and impacted on the stationary clubhead. The rebound velocity is maximized and the final shape is used as the initial shape in the last optimization stage, to save time during optimization iterations. In the final stage, the entire clubhead model is used and driven into the ball, to determine the clubface geometry that maximizes the launch velocity of the golf ball for central impacts. A final clubface shape is reached and a total improvement of 4.8 m/s over the initial design is obtained. This is a 7% gain in launch velocity, which results in a driving length advantage of approximately 20 meters until the first contact with the ground. The optimization results are compared against those obtained using the principle of impedance matching.