# Determination of Coefficient of Restitution for Golf Club Using Experimental Modal Analysis

This guest post on Innovation Intelligence was written by TechPassion. Their software, VMAP, is a Noise, Vibration and Harshness analysis tool available through the Altair Partner Alliance.

Coefficient of Restitution (COR) is a parameter used to classify golf clubs. A coefficient of restitution of 0.8 means that a ball traveling at 100 M.P.H. will rebound off a metal plate at 80 M.P.H. COR is measured using standardized tests. The most commonly used test is the USGA canon test. In this test, the speeds of the golf ball before and after impact are measured to compute COR. Though it sounds like a simple test, it has the following drawbacks:

1. The test requires expensive equipment for creating impact and recording the speeds
2. The test requires lot of space
3. COR value obtained is specific to both the golf club head and the golf ball
4. There is considerable standard deviation in the recorded COR value with the measurements made with the a pair of golf club and ball

An alternative method [1] that combines modal test data and simple analytical modeling can potentially replace this test. It uses simple and inexpensive tools and has been shown to yield precise results. The method consists of the following steps

Step 1: Perform experimental modal analysis of the golf club

Step 2: Obtain the modal parameters (mass, stiffness, damping) of the golf club using curve fitting methods

Step 3: Setup a simulation to model the impact of the ball on the golf club

Step 4: Compute the COR using the velocity output from the simulation model.

Modal testing can be an alternative to the canon test. In addition to this benefit, modal analysis can be used to design golf clubs. Modal analysis gives a fundamental understanding of the dynamic characteristics of the structure. During the early stages in the design process, finite element method based modal analysis can be used to explore different designs and materials. In the later stages of the design, with prototypes, experimental modal analysis (EMA) can be used to measure the dynamic properties of the golf club. For instance, damping can be measured precisely using experimental modal analysis. A golf club can be thought of as a beam with a mass at its end. For a component such as this, modal analysis is a simple yet powerful tool to design and will open doors to innovative designs.

Tools such as VMAP can be used to perform modal test and modal parameter estimation. More information about modal analysis and VMAP can be found by visiting www.techpassiontech.com or by writing directly to support@techpassiontech.com

1. “Determination of Coefficient of Restitution Based on Modal Data”, Fan, F.H., In Proceedings of the 21st International Modal Analysis Conference, Orlando, USA, February 2003.

Sridhar Ravikoti is the Technical Director of Global Partner Programs at Altair. He has been with Altair since 2000, gaining experience in engineering product development and software program management. In his current role as a technical lead for the Altair Partner Alliance, Sridhar drives a synergetic relationship between Altair offering and its Partners. He holds a Bachelor’s degree from Osmania University in India, and a Master’s degree from the University of Nebraska-Lincoln, with a major in Mechanical Engineering and a minor degree in Applied Mechanics.