A study of thickness optimization of golf club heads to maximize release velocity of balls

Abstract

SUMMARYIn the present study, the shape optimization of a golf club head is investigated. The problem of maximizing the release velocity of the ball after impact is treated under the constraint of a speciÿed weight of club head. The thickness distribution of the clubface is chosen as the design variable for optimization. The basis vector method, which is an approximating method for optimization problems in which the sensitivity cannot be derived analytically, is employed. The basis vector represents a fundamental change of shape, and it is preferable to obtaining e ective results that the basis vectors be mutually independent. A simple approach to create the basis vectors using eigenmodes is also presented. The theory of impedance matching is conÿrmed numerically by a two-dimensional example. A three-dimensional example is given to show that this approach is e ective for optimal design of the golf club head.

Shape optimization of golf clubface using finite element impact models

“…It also allows for a three-dimensional parameterization of the shape in a shape optimization of the face geometry that maximizes the launch velocity for central impacts. This is in contrast to the approach of Nakai et al [5], who optimized the thickness over a flat face geometry using shell elements.…”

“…The first basis shape (shape 0) is introduced to allow thinner clubfaces; it is created by simply moving the nodes on the back face in the normal direction to its surface. The second and third design variables, shape 1 and shape 2, are created by concentrating the masses along an elliptical ring around the centroid of the clubface and as an ellipsoidal dome in the centroid of the clubface, respectively, as proposed by Nakai et al [5]. The optimizations in every stage are performed using the adaptive response surface optimization routine.…”

Golf Clubhead Optimization Based on Contribution of Eigenmodes

“…To these problems, the authors have proposed an approach using basis vector method for the optimization of clubface. [Nakai et al (2004); Wu et al (2004)]. In this study, we try to extend the optimization of thickness distribution to the entire clubhead.…”

“…Twelve basis vectors are used in this example to express the thickness distribution. Five of them are generated with sensitivity functions of eigenvalues by proposed method, and others are generated by a former method [Nakai et al (2004); Wu et al (2004)]. Besides these vectors, one additional vector is created to express the change of the loft angle, and two additional vectors are created to express the changes of lumped masses set at the back of the clubhead.…”

“…However, much research concerning the optimization of a golf club was limited to the parametric optimization with few design variables, such as loft angle, bulge angle, and concentrated mass; the total design of the clubhead including shape or thickness distribution of the head was scarce since the sensitivity is difficult to be derived analytically in impact problems, and then the sensitivity-based approaches cannot be applied. As an attempt to avoid this difficulty, the authors have proposed an approach using basis vector method for the thickness optimization to maximize the initial velocity and the flying distance of a golf ball [Nakai et al (2004); Wu et al (2004)]. In these studies, the optimization of thickness distribution was limited to the clubface part.…”