Modelling of tennis ball impacts on a rigid surface

2004 ◽  
Vol 218 (10) ◽  
pp. 1139-1153 ◽  
Author(s):  
S R Goodwill ◽  
S J Haake
Keyword(s):  
Contact Time ◽  
Momentum Flux ◽  
Viscoelastic Model ◽  
Coefficient Of Restitution ◽  
Model Parameters ◽  
Total Force ◽  
Tennis Ball ◽  
Rigid Surface ◽  
Ball Impact ◽  
The Impact

A viscoelastic model of a tennis ball impact at normal incidence on a rigid surface is presented in this study. The ball model has three discrete elements that account for the structural stiffness, material damping and momentum flux loading. Experiments using a force platform are performed to determine the force that acts on the ball during impact, for a range of ball inbound velocities. The inbound and rebound velocities of the ball are measured using speed gates. The contact time and coefficient of restitution for the impact are also determined in these experiments. The model parameters are determined such that the values of the coefficient of restitution and contact time that are calculated by the model are consistent with those values determined experimentally. The model can be used to calculate the force that acts on the ball during impact. Generally, the force-time plots calculated by the model were consistent with those determined experimentally. Furthermore, the model can be used to calculate the three components of the force that acts on the ball during impact. It is shown that the main component of the force during the first 0.6 ms of impact is that due to momentum flux loading. This is approximately equal in magnitude for each ball type and explains why the total force acting on each ball is very similar during this period.

Phenomenological Modeling of Carpeted Surface for Drop Simulation of Portable Electronics

2019 ◽  
Vol 141 (2) ◽  
Author(s):  
Abhi Sirimamilla ◽  
Hua Ye ◽  
Yinan Wu
Keyword(s):  
Mechanical Response ◽  
Viscoelastic Model ◽  
Single Layer ◽  
Material Model ◽  
Impact Testing ◽  
Consumer Electronics ◽  
Model Parameters ◽  
Portable Devices ◽  
Impact Surface ◽  
The Impact

Using finite element (FE) analysis to simulate drop impact is widely adopted by the consumer electronics industry in the design process of portable devices. Most of such simulations model impact surface as a rigid or simple elastic surface. While this approach is valid for many common hard surfaces such as wood, tile, or concrete, it often does not provide a realistic risk assessment if the impact surface is a soft surface such as carpet. This paper describes a methodology to create a material model for carpeted impact surface that is suited for FE drop simulation. A multilayer hyperelastic–viscoelastic material model is used to model the mechanical response of the carpet under mechanical impact. Quasi-static and impact testing on the industrial carpet were performed to calibrate the model parameters with the help of optimization. Validation of the model was done by comparing the simulation predictions with measurements from the impact tests performed at different heights. Much better correlation between experimental measurements and simulation predictions were observed when using the multilayer hyper-viscoelastic model for carpet than using a single layer homogenous model. This approach can provide a better estimate and a more accurate representation for device drop risk on carpeted surfaces for design and development of portable products. The methodology can also be used to derive material models for other similar impact surfaces.

The Impact of an Elastic Sphere on a Thin Elastic Plate Supported by a Winkler Foundation

1975 ◽  
Vol 42 (1) ◽  
pp. 133-135 ◽  
Author(s):  
H. D. Fisher
Keyword(s):  
Thin Plate ◽  
Contact Time ◽  
Viscoelastic Plate ◽  
Coefficient Of Restitution ◽  
Solution Technique ◽  
Rigid Sphere ◽  
Winkler Foundation ◽  
Thin Elastic Plate ◽  
Continuous Contact ◽  
The Impact

This paper investigates the elastic impact of a sphere on a thin plate which is in continuous contact with a foundation. The reaction pressure is considered to be proportional to the local deflection (Winkler hypothesis). A solution technique, which was originally developed to analyze the impact of a rigid sphere on a viscoelastic plate, is modified for application in the present study. The contact force, the coefficient of restitution, and the contact time are computed for a wide variation in the two dimensionless parameters which are required to describe a given problem. For the limiting cases of impact on a half space and impact on a thin plate supported by a rigid foundation, the contact time computed here is shown to correlate with the calculations of earlier investigators.

scholarly journals Characterisation of ball impact conditions in professional tennis: Matches played on hard court

2016 ◽  
Vol 230 (4) ◽  
pp. 236-245 ◽  
Author(s):  
Ben Lane ◽  
Paul Sherratt ◽  
Hu Xiao ◽  
Andy Harland
Keyword(s):  
Research And Development ◽  
Tennis Ball ◽  
Ball Impact ◽  
Total Data ◽  
Ball Tracking ◽  
Professional Tennis ◽  
Post Impact ◽  
Tennis Balls ◽  
The Impact

To assess ball performance for research and development purposes requires greater understanding of the impact conditions a tennis ball experiences in professional tournament play. Ball tracking information taken from three consecutive years of an ATP 250 tour event played on hard court was analysed. The frequency of first serves, second serves, racket impacts and surface impacts was assessed per game and extrapolated to show how many impacts a single ball is subjected to. Where applicable the pre- and post-impact velocities and angles were found, and the distribution of each was analysed. In total, data from 65 matches comprising 1505 games were analysed. On average, each game contained 70.26 (±16.23) impacts, of which 9.23%, 3.16%, 37.78% and 49.83% were first serves, second serves, racket impacts and surface impacts, respectively. As a result, assuming all balls in play are used evenly, a single ball is expected to be subjected to 105 (±24) impacts over the course of the nine games that it is in play. The results of the investigation could be used to design a wear protocol capable of artificially wearing tennis balls in a way that is representative of professional play.

Bouncing-Ball Model of ‘Dry’ Motions of a Tethered Buoy

2000 ◽  
Vol 123 (3) ◽  
pp. 333-339 ◽  
Author(s):  
R. H. Plaut ◽  
A. L. Farmer ◽  
M. M. Holland
Keyword(s):  
Coefficient Of Restitution ◽  
Critical Force ◽  
Mooring Line ◽  
Wave Forces ◽  
Axial Component ◽  
Rigid Surface ◽  
Fluid Inertia ◽  
Sea Floor ◽  
Ball Bouncing ◽  
The Impact

The motions of a buoy moored to the sea floor by a cable are considered. The buoy is modeled both as a point mass and as a sphere. It is assumed that the mooring line has no effect when it is slack, and that when it becomes taut it exerts an instantaneous impulsive force on the buoy, analogous to the impact of a ball bouncing on a rigid surface. The magnitude of the axial component of the velocity is reduced at this time. Fluid inertia and damping are not included, and the wave forces are assumed to be harmonic. The effects of the coefficient of restitution and the forcing frequency on two types of critical force are examined. Trajectories of the motion are plotted and the impact velocities are computed and analyzed. Knowledge of the number and magnitude of these impacts is useful in assessing fatigue of the mooring line.

scholarly journals Numerical Study on Pounding between Two Adjacent Buildings under Earthquake Excitation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
H. Naderpour ◽  
R. C. Barros ◽  
S. M. Khatami ◽  
R. Jankowski
Keyword(s):  
Impact Force ◽  
Viscoelastic Model ◽  
Coefficient Of Restitution ◽  
Earthquake Excitation ◽  
Structural Pounding ◽  
Adjacent Buildings ◽  
Impact Forces ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Model ◽  
The Impact

Seismic excitation, which results in large horizontal relative displacements, may cause collisions between two adjacent structures due to insufficient separation distance between them. Such collisions, known as earthquake-induced structural pounding, may induce severe damage. In this paper, the case of pounding between two adjacent buildings is studied by the application of single degree-of-freedom structural models. Impact is numerically simulated with the use of a nonlinear viscoelastic model. Special attention is focused on calculating values of impact forces during collisions which have significant influence of pounding-involved response under ground motions. The results of the study indicate that the impact force time history is much dependent on the earthquake excitation analyzed. Moreover, the peak impact forces during collision depend substantially on such parameters as gap size, coefficient of restitution, impact velocity, and stiffness of impact spring element. The nonlinear viscoelastic model of impact force with the considered relation between the damping coefficient and the coefficient of restitution has also been found to be effective in simulating earthquake-induced structural pounding.

Oblique Impact of Thick Walled Pressurized Spheres as Used in Tennis

2005 ◽  
Vol 219 (11) ◽  
pp. 1179-1189 ◽  
Author(s):  
S J Haake ◽  
M J Carré ◽  
R Kirk ◽  
S R Goodwill
Keyword(s):  
Coefficient Of Friction ◽  
Momentum Flux ◽  
High Speed ◽  
Reaction Force ◽  
Oblique Impact ◽  
Tennis Ball ◽  
The Coefficient Of Friction ◽  
Impact Phase ◽  
Rotation Set ◽  
The Impact

A model is presented in which the normal impact of a thick walled pressurized sphere, such as a tennis ball, is modelled as a non-linear viscoelastic spring and damper, coupled with momentum-flux forces where the shell wall deforms with high stiffness and damping. These momentum-flux forces are only present in the impact phase and do not appear during restitution. Rotation set up during an oblique impact causes the momentum-flux forces at the front and rear of the sphere to be different such that the total vertical reaction force acts in front of the centre of mass when topspin is present. The sphere was allowed to deform and this caused both the torque and the effective moment of inertia of the sphere to decrease. The result of this is that the deformed sphere gains sufficient spin during impact for reverse slip to occur when the ball reforms towards the end of impact. Tennis balls were projected at two similarly constructed surfaces with a coefficient of friction of 0.51 and 0.62. It was found that displacements and rotations from the model compared well with experimental results recorded using a high-speed video running at 7100 frames per second. The model was able to predict these results with only the coefficient of friction as the varying parameter.

Viscoelastic Evaluation of Soft Materials at Subsonic Level by Ball Impact Test

2014 ◽  
Author(s):  
Katsuya Igarashi ◽  
Naoki Torii ◽  
Atsushi Sakuma
Keyword(s):  
Numerical Simulation ◽  
Impact Test ◽  
Viscoelastic Model ◽  
Soft Materials ◽  
Soft Material ◽  
Test Method ◽  
Material Behavior ◽  
Hertzian Contact ◽  
Ball Impact ◽  
The Impact

Mechanical evaluation of soft material is required in the precise design fields of machines concerning car accident, airplane bird strike, and so on because the inaccuracy of mechanical design causes economic loss. In the design field of crash problems on the soft material, precise analysis of the material at subsonic level is required for practical realization of accurate numerical simulation. Then a shock impact test method for the material at the subsonic level using an airsoft gun is developed to identify the mechanical behavior of the soft material. In the impact test, the viscoelastic characteristics of specimens are evaluated by analyzing the stress response using the extended Hertzian contact theory and wave equation at the moment when a simple ball bullet is shot at the specimen using the airsoft gun. An obvious relationship between quasi-static and impact responses of the specimen is observed subjectively in the experimental results of the test. The deformation resistance modules of impact test method for the specimens at the subsonic level are higher than that of quasi-static examination in all materials. The evaluated viscoelastic relationship is applied to crash simulations of soft material by using the fundamental viscoelastic constitutive equation and the material parameters derived from the impact test, and the simulation is computed using the identified parameters. In the simulated results of impact test using the viscoelastic model applied material behavior of soft material, the deformation behavior of the soft materials can be evaluated for the applicable form to numerical simulation.

Dynamics of a bouncing table tennis ball from the acoustic signature using an optical fibre sensor

2021 ◽  
Author(s):  
James Farai Jena ◽  
Shukree Wassin ◽  
Tim Gibbon
Keyword(s):  
Undergraduate Students ◽  
Optical Fibre ◽  
Impact Force ◽  
Early Warning Systems ◽  
Coefficient Of Restitution ◽  
Tennis Ball ◽  
Table Tennis ◽  
Optical Fibre Sensor ◽  
Fibre Sensor ◽  
The Impact

Abstract We describe an optical fibre-based method to estimate impact force and collision duration using time measurements recorded from acoustic signals of a table tennis ball bouncing on a table. The technique combines measurements obtained from a polarisation dependent optical fibre sensor with graphical analysis and kinetics through numerical calculations. The presented coefficient of restitution, collision time, impact force, and elastic deformation during each bounce of the table tennis ball were obtained using corresponding time series measurements and numerical analysis. A peak impact force of 38.4N was estimated for a ball of mass 2.83g and 39.7mm diameter dropped from a height of 31.5cm. The impact duration for the associated bounce was 0.68ms with a centre of gravity shift of 0.40mm and coefficient of restitution of 0.88. While the observed results are unique to the ball and table surface, the approach is an attempt to fully quantify collision parameters from basic measurement and instrumentation applicable to undergraduate students. The sensor developed in this paper finds application in sports performance monitoring, infrastructural health early warning systems and pressure sensitive manufacturing processes.

Sign in / Sign up

Export Citation Format

Share Document