Modeling of Impact Dynamics of a Tennis Ball With a Flat Surface

2005 ◽  
Author(s):  
Syed Muhammad Mohsin Jafri ◽  
John M. Vance
Keyword(s):  
Flat Surface ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Rolling Contact ◽  
Tennis Ball ◽  
Computationally Efficient ◽  
Mass Model ◽  
Experimental Findings ◽  
Tennis Balls ◽  
The Impact

A model of impact of a tennis ball with a flat surface is developed based on a planar, two-mass, linear, four degree of freedom vibration system idealization. The impact is assumed to be incident on a flat surface with friction. The incident parameters of the ball include the centre of mass translational velocity, angle of impact with the surface and the incident angular spin of the ball. The linear, piecemeal vibration model predicts the corresponding rebound parameters of the tennis ball. The model also predicts the duration of contact of the tennis ball with the flat surface, the transition of motion of the tennis ball during contact with the ground from sliding to rolling contact, and the resulting contact forces developed between the tennis ball and the flat surface. The model is computationally efficient because the governing differential equations of motion are linear and their standard solutions can be easily implemented on a personal computer. Predictions of the rebound parameters from the model are compared with experimental findings on tennis balls which are incident on a flat surface with various angles, velocities and angular spins (zero spin, topspin and backspin). For selected parameters of the two-mass model, the comparisons show excellent agreement between the model and the measurements.

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.

A Methodology to Detect the Precise Instant of Contact in Multibody Dynamics

2011 ◽  
Author(s):  
Paulo Flores
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Time Step ◽  
Dynamic Simulations ◽  
Integration Algorithm ◽  
Current Time ◽  
Impact Time ◽  
System Equations ◽  
The Impact

The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step for the contact and non contact periods in multibody dynamics. The basic idea of the described methodology is to ensure that the first impact within a multibody system does not occur with a large value for relative bodies’ penetration in order to avoid the artificially large contact forces associated. The detection of the instant of contact takes place when the distance between two bodies change the sign between two discrete moments in time. In fact, in theory, the contact starts when this distance is zero, or a very small value to prevent the round-off errors. Thus, during the numerical solution of the system equations of motion if the first penetration is below this small value previously specified, then the current time is taken as the impact time. On the other hand, if the first penetration is larger than the specified tolerance, then the current time step is beyond the impact time. In this case, integration algorithm is forced to go back and take a smaller time step until a step can be taken within the acceptable tolerance. The main features of this approach are the easiness to implement and the good computational efficiency. In addition, it can easily deal with the transitions between non contact and contact cases in multibody dynamics. Finally, results obtained from dynamic simulations are presented and discussed to study the validity of the methodology proposed in this work.

scholarly journals Statistical Analysis of Table-Tennis Ball Trajectories

2018 ◽  
Vol 8 (12) ◽  
pp. 2595
Author(s):  
Ralf Schneider ◽  
Lars Lewerentz ◽  
Karl Lüskow ◽  
Marc Marschall ◽  
Stefan Kemnitz
Keyword(s):  
Statistical Analysis ◽  
Graphics Processing Units ◽  
Initial Conditions ◽  
Statistical Significance ◽  
Equations Of Motion ◽  
Distribution Functions ◽  
Tennis Ball ◽  
Table Tennis ◽  
Ball Size ◽  
The Impact

In this work, the equations of motion for table-tennis balls were numerically solved on graphics processing units (GPUs) using Compute Unified Device Architecture (CUDA) for systematical statistical studies of the impact of ball size and weight, as well as of net height, on the distribution functions of successful strokes. Half a billion different initial conditions involving hitting location, initial spin, and velocities were analyzed to reach sufficient statistical significance for the different cases. In this paper, an advanced statistical analysis of the database generated by the simulation is presented.

Modeling of Tread Block Contact Mechanics Using Linear Viscoelastic Theory3

2008 ◽  
Vol 36 (3) ◽  
pp. 211-226 ◽  
Author(s):  
F. Liu ◽  
M. P. F. Sutcliffe ◽  
W. R. Graham
Keyword(s):  
High Speed ◽  
Slip Rate ◽  
Material Model ◽  
Contact Forces ◽  
Block Modeling ◽  
Rate Dependent ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
The Impact ◽  
Good Agreement

Abstract In an effort to understand the dynamic hub forces on road vehicles, an advanced free-rolling tire-model is being developed in which the tread blocks and tire belt are modeled separately. This paper presents the interim results for the tread block modeling. The finite element code ABAQUS/Explicit is used to predict the contact forces on the tread blocks based on a linear viscoelastic material model. Special attention is paid to investigating the forces on the tread blocks during the impact and release motions. A pressure and slip-rate-dependent frictional law is applied in the analysis. A simplified numerical model is also proposed where the tread blocks are discretized into linear viscoelastic spring elements. The results from both models are validated via experiments in a high-speed rolling test rig and found to be in good agreement.

Truck Tire Operating Temperatures on Flat and Curved Test Surfaces

2005 ◽  
Vol 33 (3) ◽  
pp. 156-178 ◽  
Author(s):  
T. J. LaClair ◽  
C. Zarak
Keyword(s):  
Flat Surface ◽  
Operating Temperature ◽  
Operating Conditions ◽  
Load Pressure ◽  
Truck Tire ◽  
Endurance Testing ◽  
Operating Temperatures ◽  
The Impact ◽  
Tread Rubber ◽  
Cylindrical Test

Abstract Operating temperature is critical to the endurance life of a tire. Fundamental differences between operations of a tire on a flat surface, as experienced in normal highway use, and on a cylindrical test drum may result in a substantially higher tire temperature in the latter case. Nonetheless, cylindrical road wheels are widely used in the industry for tire endurance testing. This paper discusses the important effects of surface curvature on truck tire endurance testing and highlights the impact that curvature has on tire operating temperature. Temperature measurements made during testing on flat and curved surfaces under a range of load, pressure and speed conditions are presented. New tires and re-treaded tires of the same casing construction were evaluated to determine the effect that the tread rubber and pattern have on operating temperatures on the flat and curved test surfaces. The results of this study are used to suggest conditions on a road wheel that provide highway-equivalent operating conditions for truck tire endurance testing.

scholarly journals Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface

2021 ◽  
Vol 11 (2) ◽  
pp. 466
Author(s):  
Włodzimierz Kęska ◽  
Jacek Marcinkiewicz ◽  
Łukasz Gierz ◽  
Żaneta Staszak ◽  
Jarosław Selech ◽  
...  
Keyword(s):  
Dynamic Properties ◽  
Decisive Role ◽  
Force Sensor ◽  
Contact Forces ◽  
Correct Selection ◽  
Contact Parameter ◽  
Cereal Grain ◽  
Wide Range ◽  
The Impact ◽  
Selection Of

The continuous development of computer technology has made it applicable in many scientific fields, including research into a wide range of processes in agricultural machines. It allows the simulation of very complex physical phenomena, including grain motion. A recently discovered discrete element method (DEM) is used for this purpose. It involves direct integration of equations of grain system motion under the action of various forces, the most important of which are contact forces. The method’s accuracy depends mainly on precisely developed mathematical models of contacts. The creation of such models requires empirical validation, an experiment that investigates the course of contact forces at the moment of the impact of the grains. To achieve this, specialised test stations equipped with force and speed sensors were developed. The correct selection of testing equipment and interpretation of results play a decisive role in this type of research. This paper focuses on the evaluation of the force sensor dynamic properties’ influence on the measurement accuracy of the course of the plant grain impact forces against a stiff surface. The issue was examined using the computer simulation method. A proprietary computer software with the main calculation module and data input procedures, which presents results in a graphic form, was used for calculations. From the simulation, graphs of the contact force and force signal from the sensor were obtained. This helped to clearly indicate the essence of the correct selection of parameters used in the tests of sensors, which should be characterised by high resonance frequency.

scholarly journals Dynamics of Multibody Systems With Spherical Clearance Joints

2005 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Contact Forces ◽  
Force Model ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Dynamics Of Multibody Systems ◽  
The Impact

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Development of an End-Effector for Mitigation of Collisions

2021 ◽  
Author(s):  
Domenico Tommasino ◽  
Matteo Bottin ◽  
Giulio Cipriani ◽  
Alberto Doria ◽  
Giulio Rosati
Keyword(s):  
Numerical Simulations ◽  
Industrial Applications ◽  
Operating Conditions ◽  
Contact Forces ◽  
Design Parameters ◽  
End Effector ◽  
Linear Behavior ◽  
Stable Mechanism ◽  
Robot Tasks ◽  
The Impact

Abstract In robotics the risk of collisions is present both in industrial applications and in remote handling. If a collision occurs, the impact may damage both the robot and external equipment, which may result in successive imprecise robot tasks or line stops, reducing robot efficiency. As a result, appropriate collision avoidance algorithms should be used or, if it is not possible, the robot must be able to react to impacts reducing the contact forces. For this purpose, this paper focuses on the development of a special end-effector that can withstand impacts and is able to protect the robot from impulsive forces. The novel end-effector is based on a bi-stable mechanism that decouples the dynamics of the end-effector from the dynamics of the robot. The intrinsically non-linear behavior of the end-effector is investigated with the aid of numerical simulations. The effect of design parameters and the operating conditions are analyzed and the interaction between the functioning of the bi-stable mechanism and the control system is studied. In particular, the effect of the mechanism in different scenarios characterized by different robot velocities is shown. Results of numerical simulations assess the validity of the proposed end-effector, which can lead to large reductions in impact forces.

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Daniel Dopico
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Automatic Differentiation ◽  
Time Integration ◽  
General Purpose ◽  
Contact Forces ◽  
Design Parameters ◽  
Computational Techniques ◽  
Computationally Efficient ◽  
Integration Algorithm

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

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