CAE of Tennis Rackets with Impact Phenomena. Prediction of Racket Response and a View of Restitution in Racket-Ball Impact.

TLDR: In this article, the authors investigated the impact force and impact duration of a tennis racket, considering the strong nonlinearity of the restoring force of the ball and strings, and estimated the coefficient of restitution of the tennis racket using a personal computer.

Abstract: There are a number of unclarified points regarding the impact phenomena and the optimum design of tennis rackets. The present study is based on the idea that the dynamics of a racket consists of the dynamics of a rigid body with an arm swing given at a grip as a boundary condition, an impact between a ball and strings with racket frame as an input force, and the structural vibration of the racket. In this paper, impact force and impact duration are investigated, considering the strong nonlinearity of the restoring force of ball and strings. Furthermore, the coefficient of restitution of the tennis racket is estimated using a personal computer on the basis of the impact phenomena and the experimental modal analysis. In order to predict the contact duration, which has an influence on the racket vibration, a simple impact model has been proposed, i.e., that the contact duration is determined by the natural period of a whole system composed of the mass of the ball, the stiffness of the ball and strings, and the reduced mass of the racket at the impact point on the racket face. The calculated results agree fairly well with the experimental results.