Finite element model of a tennis ball impact with a racket

Previous authors have produced analytical models which accurately simulate tennis impacts. However, currently there are few published studies on the simulation of tennis impacts using finite-element (FE) technique. The purpose of this study was to produce accurate FE models of tennis impacts, which will serve as design tools as well as aid in furthering the understanding of how the ball, string-bed and racket behave during play.

An FE model of a pressurised tennis ball was produced in Ansys/LS-DYNA 10.0 and validated against experimental data. The ball model was updated to simulate the extreme playing temperatures of 10 and 400C and validated against experimental data, obtained inside a climate chamber. Following validation of the ball model, an FE model of a head-clamped racket was produced and validated against experimental data. The validation included a range of inbound velocities, angles and spin rates, for impacts at a number of nominal locations on the string-bed. Finally, an FE model of a freely suspended racket was constructed and validated against experimental data. Impacts were simulated at a number of nominal impact locations on the string-bed, with a range of ball inbound velocities, angles and spin rates. The impacts were recorded using two Phantom 4.2 high-speed cameras and analysed in 3D. The FE models were all in good agreement with the experimental data, for the individual stages of the validation.

A parametric modelling program was produced to be used in conjunction with the model. This program enables the user to adjust a variety of parameters, such as the inbound velocity of the ball, impact location and mass of the racket, and run simulations without any specialist knowledge of the FE model. This program was used to analyse the model against ball to racket impact data obtained during player testing. There was relatively good agreement between the model and player testing data.

Finally, the model was used to determine the influence of racket structural stiffness, mass and the position of the balance point, when performing a typical topspin forehand. It was found that using a head-heavy racket, with high structural stiffness and mass, will increase the rebound velocity and topspin of the ball, for a shot of this type at the centre of the string-bed.

Keywords: tennis ball, tennis racket, high speed cinematograph, finite-element modelling.