Racket Frame Research Articles

Material selection in a sustainable manufacturing practice of a badminton racket frame using Elimination and Choice Expressing Reality (ELECTRE) Method

Badminton is one of the leading sports in the world. It has its own set of rules on the equipments used and general game play. One of the main equipment used is the badminton racket. Each sections of a badminton racket have its own design requirements and one of it is the racket’s material selection. Therefore, material selection is very important to improve the usage of a badminton racket. This study describes the use of the Elimination and Choice Expressing Reality (ELECTRE) method in the material selection of a badminton racket frame with reference to the sustainable manufacturing practice of the frame. By categorizing the materials of the badminton racket frame according to mechanical, physical, chemical and environmental properties, and further detailed sub criteria were set according to the usage of these frames, the ELECTRE I method was used to determine the dominant material. Out of the six materials usually used in the manufacturing of a badminton racket frame, carbon fibre was the dominant material selected from three out of the four properties which are the mechanical, chemical and most importantly the environmental properties, as to comply with the sustainable manufacturing practice of these frames.

Tennis Racket Vibrations and Shock Transmission to the Wrist during Forehand Drive.

This study aimed to investigate the effects of two different racket models and two different forehand drive velocities on the three-dimensional vibration behavior of the racket and shock transmission to the player’s wrist under real playing conditions. Nine tennis players performed a series of crosscourt flat forehand drives at two velocities, using a lightly and a highly vibrant racket. Two accelerometers were fixed on the racket frame and the player’s wrist. The analysis of vibration signals in both time and frequency domains showed no interaction effect of velocity and racket conditions either on the racket vibration behavior or on shock transmission. An increase in playing velocity enlarged the amount of vibrations at the racket and wrist, but weakly altered their frequency content. As compared to a racket perceived as highly vibrating, a racket perceived as lightly vibrating damped longer in the out-of-plane axis of the racket and shorter on the other axis of the racket and on the wrist, and displayed a lower amount of energy in the high frequency of the vibration signal at the racket and wrist. These findings indicated that the playing velocity must be controlled when investigating the vibration loads due to the racket under real playing conditions. Similarly, a reduced perception of vibration by the tennis player would be linked to decreased amplitude of the racket vibration signal, which may concentrate the signal energy in the low frequencies.

Measurement of Main Strings Movement and its Effect on Tennis Ball Spin

Ball spin plays an important role in the modern game of tennis. Previous work has shown that reducing the number of cross strings in a tennis racket can increase rebound ball spin. The aim of this study was to further our understanding of the effect of the number of cross strings on ball spin generation. Two rackets were tested, one with 16 main and 19 cross strings and the other with 16 main and 12 cross strings. The racket frame was fully-constrained and a ball was fired onto the strings at inbound angles of 24 and 38°. Inbound velocity was set at 30 m/s and inbound spin was varied from 0 to 500rad/s. Ball velocity and spin, and lateral main string deflections during impact, were measured from high-speed video footage. Lateral string deflections were consistently larger for the racket with fewer cross strings. The racket with fewer cross strings produced slightly higher rebound spin and lower horizontal rebound velocity, which was attributed to the main strings returning during the restitution phase of the impact.

Finite-Element Study on Effect of String Tension toward Coefficient of Restitution of a Badminton Racket String-Bed

Understanding of racket parameters is important for players to gain the best racket which could improve their games performances. This present study was aimed to investigate the effect of string tension toward performance of coefficient of restitution (COR) by neglecting the effect of racket frame stiffness. A finite element simulation of collision between ball and string-bed was performed in Abaqus explicit. The ball was dropped onto the centre of mass (CM) of the string-bed area with different values of string tension. From the results, the increasing values of string tension lead to increase values of COR. This finding will contribute to the enlargement of sweet spot in badminton racket as well as improving the player performances.

Effects of Tennis Racket Frame Size and String Tension on the Change of Ball Speed and Tennis Racket Movement during Impact

Effects of Tennis Racket Frame Size and String Tension on the Change of Ball Speed and Tennis Racket Movement during Impact

Research on Material Features in Design Technique of Tennis Materials

Tennis is being loved by more and more people now. Moreover, it is gradually becoming an important leisure and recreation activity. As for this, material features involved with tennis design is currently widely studied and noticed by scholars domestic and overseas. Based on the positive results obtained by researchers domestic and overseas, the paper further summarized and generalized the development process of tennis racket frame and the material features of tennis racket string. Besides, the technical process of tennis racket design is also analyzed. Eventually, by integrating the pressure carrying feature of tennis racket, by taking carbon fiber tennis racket as the example, the paper has calculated related mechanical indexes, so as to high-lighten its excellent performance. In addition, racket string also has significant influence on ball speed and accuracy rate. By looking up related literatures, the intrinsic relationship is also revealed.

Nonlinear impact model of a tennis racket and a ball

A nonlinear impact model of a ball impacting on a tennis racket was developed to investigate the impact characteristics of this collision. The impact model included a tennis ball, the tennis racket frame and string bed in a tennis racket. The governing equations for the impact model were derived and were solved by applying numerical analysis. Extensive parametric studies were conducted to study the effects of the system parameters including ball dynamic stiffness, ball damping ratio, racket head size, string tension, string axial rigidity, etc. The analysis results showed that although head size and string axial rigidity have negligible effects on the dwell time and velocity ratio of the ball, string tension can have a significant effect on the dwell time and velocity ratio of the ball.

A computer simulation model of tennis racket/ball impacts

A forward dynamics computer simulation for replicating tennis racket/ball impacts is described consisting of two rigid segments coupled with two degrees of rotational freedom for the racket frame, nine equally spaced point masses connected by 24 visco-elastic springs for the string-bed and a point mass visco-elastic ball model. The first and second modal responses both in and perpendicular to the racket string-bed plane have been reproduced for two contrasting racket frames, each strung at a high and a low tension. Ball/string-bed normal impact simulations of real impacts at nine locations on each string-bed and six different initial ball velocities resulted in <3% RMS error in rebound velocity (over the 16–27 m/s range observed). The RMS difference between simulated and measured oblique impact rebound angles across nine impact locations was 1°. Thus, careful measurement of ball and racket characteristics to configure the model parameters enables researchers to accurately introduce ball impact at different locations and subsequent modal response of the tennis racket to rigid body simulations of tennis strokes without punitive computational cost.

Poster Session I, July 14th 2010 — Abstracts The effects of ball impact location on wrist flexion for one-handed tennis backhand groundstrokes

A torque-driven, 3D computer simulation model of an arm-racket system was used to investigate the effects of ball impact location (nine locations on the stringbed) on wrist flexionfor one-handed tennis backhand groundstrokes. The model consists of nine segments with three rotational degrees of freedom at the shoulder, two at the elbow, two at the wrist, three at the grip and two between the racket handle and racket head. Seven pairs of torque generators were used to control joint angle changes with each pair of torque generators representing the torque exerted by the corresponding agonist-antagonist muscles across a joint. The torque exerted during a simulation was determined by multiplying maximum voluntary torque and the corresponding torque activation level which was specified as a function of time using flexor and extensor torque activation profiles. The stringbed was represented by nine point masses connected to each other and the racket frame with elastic springs and three torsional springdampers between the hand and the racket were used to represent grip tightness. The model was designed so that the ball could contact the racket at any of the nine point mass locations and therefore allow simulations for different ball impact locations. The starting point of all simulations was a matched centre impact trial with all parameters in the model kept at the values used in the matching simulation apart from ball impact location. For each perturbation of ball impact location, simulations were run for a 50 ms period starting with ball-racket impact. The effect of ball impact location on the movement of the racket and wrist could be clearly grouped into three impact locations; above the longitudinal axis of the racket, on the longitudinal axis of the racket and below the longitudinal of the racket. Simulations showed that during off-centre impacts below the longitudinal axis of the racket, the wrist was forced to flex up to 16∘ more due to substantial racket rotation within the hand when compared to a matched centre impact simulation. As a consequence off-centre impacts below the longitudinal axis of the racket may be a substantial contributing factor for tennis elbow injuries due to forced wrist flexion and eccentric contraction of the wrist extensors.

Validated dynamic analysis of real sports equipment using finite element; a case study using tennis rackets

An explicit finite element (FE) model of a tennis ball impact on a freely suspended racket was produced in Ansys/LS-DYNA 10.0. The geometry for the racket frame was reproduced in the FE model using a non-contact laser scanner. The model was validated against experimental data obtained using the fully automated International Tennis Federation Racket Power Machine. The root mean squared error between the model and experimental data was 1 m⋅s−1 for the rebound velocity of the ball for typical velocities of over 40 m⋅s−1. The method can be applied to different rackets and other sports equipment to determine rapidly the performance characteristics of new designs.

DESIGN ASPECTS OF A TENNIS RACKET

Over the last years, the racket design had many improvements. The racket heads have grown larger, on frames that have become lighter. The racket frame and strings are of great importance for the player performance. The paper proposes a racket model having the frame made by light-weight graphite and the strings made by nylon fiber. The racket shape and dimensions can be established by the designer. The racket design was performed using CATIA V5R16. The racket model can be implemented in numerical analysis software in order to study the mechanical properties of the racket, especially the impact between tennis ball and string bed of the racket.

Customising a tennis racket by adding weights

Most elite tennis players customise their rackets by adding weights at various points to enhance the performance of the racket and to improve its balance and feel. The additional weights also alter the swing weight, vibration frequency, amplitude and node location, the centre of percussion, apparent coefficient of restitution and racket power. In this paper, experimental data is presented on the effects of adding a 30-g mass at several points on the racket frame. The data is consistent with a one-dimensional, nonuniform beam model of the racket, with a few minor exceptions. Mass added at the tip of a racket is more effective in increasing racket power than mass added at any other location, and has the additional advantage of shifting the point of maximum power towards the tip of the racket. For a serve, the point of maximum power can be shifted to a point near the tip of the racket, giving the player a significant height advantage. For a groundstroke, the added mass will shift the point of maximum power to a point near the centre of the strings, where players normally impact the ball.

Experimental designs in sport implement research: Application to the tension loss in tennis strings

The aim of this study was to quantify the influence of five experimental variables (style of play, sheath and central structure of synthetic strings, racket frame, and game court) on the tension loss in tennis strings in field situations, using experimental design methodology. Sixteen experiments were defined using a fractional factorial design 2(5–1). The tension loss in tennis strings was calculated by the difference between the tension measured just before and just after one hour of play. Multiple linear regression was performed to express the tension loss as a function of the five experimental variables and their first‐order interactions. The results showed that the tension loss was influenced by three main experimental variables: game court, racket frame, and string‐sheath, and by four two‐factor interactions, including the style of play and string central structure interaction term. The tension loss in tennis strings was minimal when playing with an 18‐main‐string racket frame strung with an S1‐coated string on a hard court. This work suggested that experimental designs could help researchers to highlight the sport implements’ behaviour in field situations.

Decoupling of the tennis racket frame decreases grip vibrations

Decoupling of the tennis racket frame decreases grip vibrations

A25 テニスラケットのエネルギ損失と反発係数におよぼすフレーム面内フープ振動の影響(野球2・他)

A25 テニスラケットのエネルギ損失と反発係数におよぼすフレーム面内フープ振動の影響(野球2・他)

String vibration dampers do not reduce racket frame vibration transfer to the forearm

In this study, we examined the effect of string vibration damping devices on reducing racket frame vibration transfer to the forearm. Twenty participants volunteered to hold a tennis racket stationary in a forehand and backhand stroking position while tennis balls were fired at 20 m · s−1 towards two impact locations, the node of vibration and the dead spot. A three-way analysis of variance with repeated measures on damping condition, impact location and stroke condition was performed on the data. The resonant frequency of the hand-held racket was found to be ∼120 Hz. No significant differences in amplitude of vibration at the resonant frequency were found for the wrist or the elbow when damped and non-damped impacts were compared. Impacts at the dead spot produced greater amplitudes of vibration (P < 0.01) but no interaction between impact location and string dampers was evident. The string dampers had no effect on the grip force used or the muscle electrical activity in the forearm after impact. In conclusion, we found that string dampers do not reduce the amount of racket frame vibration received at the forearm. We suggest that string dampers remain a popular accessory among tennis players because of their acoustic effects and psychological support rather than any mechanical advantage.

Spring damper model of an impact between a tennis ball and racket

A model has been derived that determines the ball, stringbed and racket frame motion for an impact between a tennis ball and racket. This paper describes the model and methods used to verify it experimentally. The model incorporated parameters such as racket mass, moment of inertia and ball stiffness. The work was conducted to produce a tool that could be used to identify the importance of each of the parameters on the impact. The ball was modelled as simple spring and damper in parallel while the stringbed was modelled as a spring in series with the ball. The values of these spring and damper parameters were determined experimentally. It was assumed that the racket frame was a rigid body to simplify the analysis. Two different methods of supporting the racket were modelled, and the balls were always projected perpendicular to the string plane. Firstly, the racket was head-clamped and all the balls impacted at the geometric string centre of the racket. Good agreement was found between the experiment and model data for both ball rebound velocity and maximum stringbed deflection during impact. The second method of support involved freely suspending the racket at the tip on a small pin. Three different impact positions along the longitudinal axis of the racket were tested. Good agreement between the experiment and model data was found for the ball rebound velocity for impacts at the geometric string centre of the racket. The model over-predicted the experimental racket rebound velocity (generally by less than 5 per cent) for all impact positions. A qualitative analysis assigned this small difference to the assumption that the frame was a rigid body and therefore vibration losses were not accounted for.

Flexible beam analysis of the effects of string tension and frame stiffness on racket performance

It is generally accepted that a decrease in string tension leads to greater racket power and an increase in tension improves racket control. The increase in power at low string tension can be attributed partly to a decrease in energy loss in the ball and partly to a decrease in the vibrational energy transferred to the racket. Racket control is affected if the ball strikes the strings towards one edge of the frame, in which case the racket will rotate about the long axis through the handle. The angle of rotation is decreased when the string tension is increased. Quantitative estimates of the magnitude of these effects are presented, using a one dimensional flexible beam model to describe the racket and springs to model the ball and strings. For tensions in the range 50–60 lb (220–270 N), commonly used in tennis rackets, and for a ball incident at right angles to the string plane, changes in racket power and control are essentially negligible. However, a significant increase in racket power can be achieved by increasing the stiffness of the racket frame.

Finite Element Analysis of Impact of a Ball on a Tennis Racket. Impact Characteristics of Racket.

For theoretical analysis of impact phenomena in a ball-racket system in tennis, a simple model with few d. o. f. has been used. It is impossible for such a one to express exactly the complex behaviour of the impact between ball and racket. Therefore, finite element analysis using a rigorous model is desired and we are establishing the technique for this analysis. In the present paper a finite element model of racket frame is constructed and is incorporated with formerly developed ball strings finite element model to accomplish total analysis system. Using the developed system, the impact characteristics of a racket are investigated taking account of the effects of incident ball velocity, initial string tension, grip tightness and the racket swing. It is shown that in the region around the center of racket head, the higher velocity of ball rebound is stably acquired under the different incident ball velocities.

Analysis of Impact Phenomena in a Tennis Ball-Racket System : Effects of Frame Vibrations and Optimum Rocket Design

The performance of a tennis racket in terms of the coefficient of restitution (COR) is closely related to impact phenomena. This paper investigates the effects of frame vibrations on the coefficient of restitution and the contact time during impact of a ball/ string system and a simulated frame model, using FEM simulation and modal analysis. The results show that the COR is mainly affected by a rigid motion and a bending vibration with two nodes of racket frame. In addition, the COR increases with an increase of frame rigidity, but then saturates at a certain rigidity depending on the impact velocity. Furthermore, the COR increases as the impact point approaches the center of rotation and the node of racket frame vibration.