An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc.

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1 [Type text] [Type text] [Type text] ISSN : Volue 10 Issue 24 BioTechnology 2014 An Indian Journal FULL PAPER BTAIJ, 10(24), 2014 [ ] Mechanical analysis of tennis racket and ball during ipact based on finite eleent ethod Li Jiude College of Physical Education, Linyi University, Linyi,Shandong, , (CHINA) ABSTRACT Mechanical analysis of tennis racket and ball during ipact is of utost iportance to advance developent of sports activities. Finite eleent analysis is often applied to further our understanding of the echanics of sports equipent. Based on the finite eleent ethod, in the present paper FE odel of tennis racket and eshing can be developed. The effect of incident angle and velocity of ball, tennis racket aterial and the relationship with incident/rebound velocity of ball are researched in detail to deonstrate the internal relation during the racket/ball ipact. It is found that the incident angle and velocity, the racket aterial and the ratio of incident/rebound velocity are ain influencing factors. KEYWORDS Mechanical analysis; Tennis racket; Incident angle; FE odel; Racket/ball ipact. Trade Science Inc.

2 BTAIJ, 10(24) 2014 Li Jiude INTRODUCTION Tennis sport, which has a rich history and the first rules were laid down in 1873, is a beautiful and intense, netting separated without body contact sporting events. As the training ethod of updating, the odern tennis copetition has becoe the gae which should be deanded to have the coprehensive abilities with the faster speed, larger angle, ore rotation and higher strength. For exaple, a professional tennis player can serve an extraordinarily fast ball through an arcshaped oveent of his ar. So it requires that the player has not only strong uscle power but also the ability to control his ar dynaics so that it can ake sure to defeat the other players. No atter what the players are professional or aateur tennis enthusiasts, they enjoy the joy of tennis sports but trouble with the pain of injures. The statistics has suggested that over 50% of all people playing tennis regularly have suffered pain at the elbow region at least once in their lifeties [1-3]. Therefore, it is of utost iportance to research echanical analysis of tennis racket and ball during ipact. Many experiental and analytical studies [2-3] were used in the past to research various racket paraeters and deterine their effect on ball return velocity, but these studies only analyzed the duration of ball contact. And ost of studies also suarized in their analysis the hand reaction forces during racket/ball ipact. Casolo and Ruggieri [2] have developed a different approach by eans of an analytical odel to take into account the inertia of the ar, forear, and hand in addition to the racket. Several others investigators [4-6] deonstrated experientally that ball-rebound velocity after an eccentric ipact against a tennis racket reains unchanged for two extree conditions of grip firness, i.e., when the grip is firly claped and when it is allowed to stand freely on its butt. Over the past decades, a nuber of authors have developed tennis ball/bat ipact odels of varying coplexity. Jaes et al. (2012) [7] presents a rigid body odel of a tennis bat based on Newtonian echanics. Sith and Singh [8] present a finite eleent (FE) odel of a cricket ball/bat ipact. A linear visco-elastic aterial odel was applied to the ball, with aterial coefficients selected to provide agreeent with a load-tie curve for a ball ipacting a load cell at 27/s. A linear elastic aterial odel was applied to the handle of the bat and a linear orthotropic aterial odel was applied to the blade. The FE odel for the ball/bat ipact was shown to be in good agreeent with experiental data, in ters of the rebound speed of the ball. However, despite independent characteristic of the ball for an ipact on a fixed rigid surface, the aterial coefficients applied to the ball required further adjustent to achieve the level of fit presented for the ball/bat odel. The process of ipact tennis racket is a aterial nonlinearity, geoetric nonlinearity and contact nonlinear ipact process. The objective of this paper was to analyze and validate the internal relation during the racket/ball ipact. Based on the finite eleent ethod, in the present paper FE odel of tennis racket and eshing can be developed. The effect of incident angle and velocity of ball, tennis racket aterial and the relationship with incident/rebound velocity of ball are researched in detail. MECHANICAL ANALYSIS MODEL BY FEM Generally speaking, atheatical size odel of tennis racket and ball in detail is shown in the Figure 1. The tennis racket is ade up of racket upper, iddle part and botto (see Figure 1). Every part can be ade by various kinds of aterials, such as wooden, GRP and CFRP and so on. Consequently, it ay lead to different echanical perforance, the ipact zone and rebound velocity. In this paper, the finite eleent ethod is utilized to siulate the echanical process during racket/ball ipacting. Based on ANSYS software, FE odel was developed by eshing the different eleents of parts (see Figure 2) Racket upper; 2 Racket iddle part; 3 Racket botto Figure 1 : Matheatical size odel of tennis racket and ball The study on the tennis racket and nonlinear ipact theory odel has been researched by a few of scholars. However, ost of the presented odels are regarded to be just reduced to the syste coposed of quality, play tennis spring

3 15432 Mechanical analysis of tennis racket and ball during ipact based on finite eleent ethod BTAIJ, 10(24) 2014 and daper. The line is viewed as a nonlinear spring bed and the ball string as a linear elastic aterial siulated by the truss eleent. In the previous analysis, the frae of racket treated as a rigid body has the effect of siplified calculation, to reduce the coputational accuracy. What s ore, in the calculated results the tennis racket of elastic deforation force and the effect of oveent could not be taken into account. In the present paper, assuing the racket as deforation, the elasticity of the racket and the influence of deforation on the ball have been considered, showing to be in good agreeent with the actual situation. The physical paraeters of aterial (Young's odulus, density, poisson's ratio) in every part of tennis racket are shown in the TABLE 1. Figure 2 : ANSYS odel of tennis racket TABLE 1 : Physical paraeters of aterial Racket parts Young's odulus Density, ρ ( 10 E (GPa) kg/ 3 Poisson's ratio ) υ Frae of racket Racket botto Prince RESULTS AND DISCUSSION The effect of incident angle and velocity of ball The incident angle is fored by the ipact with tennis balls and tennis rackets (see Figure 3). Maeda et al. has studied on the friction characteristics of holding a tennis racket to produce 30 to 45, which is verified as the ost eaningful angles. So in this paper incident angles of 30 and 45 are chosen to calculate and consider its influence. The ball is usually ipacted by the two styles of flattening and rotation, which is used to copare each other. Relationship with incident velocity of the ball and the reaction force of the racket is shown in the Figure 4. Fro the graph, it is easily found that the relation between incident velocity of the ball and the reaction force of the racket has the liner relationship as the following: Fy = av + b (1) For the other thing, the reaction force with incident Angle of ball 45 is bigger than the one with 30. When it has the sae speed, reaction force produced by the different incident angles is greater to hit the ball. Therefore, it suggests that the greater the incidence angle, the stronger the rotation; the faster the ball speed, the ore difficult to ipact. z Noral of racket Incident angle Ball Racket x Figure 3 : The diagra of incident angel definition

4 BTAIJ, 10(24) 2014 Li Jiude a) Flattening style b) Rotation Figure 4 : Relationship with incident velocity of the ball and the reaction force of the racket The effect of tennis racket aterial Torsion and displaceent results of various tennis racket aterials are shown in TABLE 2. It is found that the best ipact zone of ball with three kinds of tennis rackets (wooden, GRP, CFRP) can be vividly depicted by the pictures. It is usually of great significance to the training of the tennis athletes so that it can iprove the copetitive power. TABLE 2 : Torsion and displaceent results of various tennis racket aterials Racket aterial Weight E Bending stiffness Torsion stiffness (g) ( 10 5 kg/c 2 ) EI ( 10 6 kg/c 2 ) GIK ( 10 6 kg/c 2 ) θ Δ Wooden GRP CFRP c 26.8c 24.5c 32.4c 25c 32.6c Figure 5 : The best ipact zone of ball with three kinds of tennis rackets The relationship with incident and rebound velocity of ball Figure 6 shows results for the ball and racket ipact. The experiental data shows the ratio of rebound/incident velocity decreased as incident velocity increased. The relationship with incident and rebound velocity of ball can be well found as shown in the Figure 6 and 7. It is shown in good agreeent with the results by Sith and Singh in the year of 2008 [8].

5 15434 Mechanical analysis of tennis racket and ball during ipact based on finite eleent ethod BTAIJ, 10(24) 2014 Figure 6 : Relationship with rebound to incident velocity during ball/racket ipact Figure 7 : Racket deforation:(a) FE odel; (b) experiental results CONCLUSIONS This paper has shown the echanical analysis of tennis racket and ball during ipact based on finite eleent ethod. By eans of tennis racket odel developed by ANSYS, the ain conclusions in this paper can be briefly suarized as the following: (1) The effect of incident angle and velocity of ball was clearly studied and suggested that the relation between incident velocity of the ball and the reaction force of the racket is linear. And it suggests that the greater the incidence angle, the stronger the rotation; the faster the ball speed, the ore difficult to ipact. (2) Through the result coparison with three kinds of tennis racket aterials, the best ipact zone of ball can be found and it benefits to the exercise of tennis players. The relationship with incident and rebound velocity of ball also suggests that the ratio of rebound/incident velocity decreased as incident velocity increased. REFERENCES [1] Hiroshi Maeda, Masaaki Okauchi; Friction Properties of the Face of a Hand-Held Tennis Racket[J], Procedia Engineering, 34, (2012). [2] F.Casolo, G.Ruggieri; Dynaic analysis of the ball-racket Ipact in the Gae of Tennis[J], Meccanica, 26, (1991). [3] C.H.Yang, P.C.Lin, Y.J.Chiu; The influence of vibration ode on response of tennis racket[j], Journal of Bioechanics, 40(S2), (2007). [4] Linin Li, Sund Hanyang, H.Chang-soon et al; Effects of string tension and ipact location on tennis playing[j], Journal of Mechanical Science and Technology, 23, (2009). [5] T.I.Tijana, J.Bojan, D.Swetta et al; Tennis chapion of the future[j], Coplex Sports Biodynaics Cognitive Systes Monographs, 2, (2009). [6] M.Buechler, L.Espino, G.Thopson et al; Vibration odeling and suppression in tennis racket[r], 21 st Int. Modal Analysis Conf. (IMACXXI), (2003). [7] D.Jaes, D.Curtis, T.Allen et al.; The validity of a rigid body odel of a cricket ball-bat ipact, In: Edited by Drane, P., Sherwood, J. (Ed), The Engineering of Sport 9-Proceedings of 9th ISEA conference, Procedia Engineering, 34, (2012). [8] L.Sith, H.Singh; An exaination of cricket bat perforance, In: Estivalet, M., Brisson, P. (Ed), The Engineering of Sport 7-Proceedings of 7th ISEA conference, Springer, Biarritz, (2008).

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