A mass-spring-damper model of a bouncing ball (original) (raw)

A Mass-Spring-Damper Model of a Bouncing Ball (Conference proceeding)

2005

The mechanical properties of a vertically dropped ball, represented by an equivalent mass-spring-damper model, are related to the coefficient of restitution and the time of contact of the ball during one bounce with the impacting surface. In addition, it is shown that the coefficient of restitution and contact time of a single bounce are related to the total number of bounces and the total time elapsing between dropping the ball and the ball coming to rest. For a ball with significant bounce, approximate expressions for model parameters, i.e., stiffness and damping or equivalently natural frequency and damping ratio, are developed. Experimentally based results for a bouncing pingpong ball are presented

Simple models of bouncing ball dynamics and their comparison

2010

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time, approximating sinusoidal motion and making analytical computations possible, is assumed as quadratic and cubic functions of time, respectively.

Simple Model of Bouncing Ball Dynamics

Differential Equations and Dynamical Systems, 2012

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincaré map, describing evolution from an impact to the next impact, is described. Displacement of the limiter is assumed as periodic, cubic function of time. Due to simplicity of this function analytical computations are possible. Several dynamical modes, such as fixed points, 2-cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands are created from fixed points after first period doubling in a corner-type bifurcation. Equation for the time of the next impact is solved exactly for the case of two subsequent impacts occurring in the same period of limiter's motion making analysis of chattering possible.

Feedback Control of Impact Dynamics: the Bouncing Ball Revisited

Proceedings of the 45th IEEE Conference on Decision and Control, 2006

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The proposed control law uses the impact times as the sole feedback information. We show that the acceleration of the table at impact plays no role in the stability analysis but is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution.

Nonlinear impact model of a tennis racket and a ball

Journal of Mechanical Science and Technology, 2012

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.

Aerodynamic effects in a dropped ping-pong ball experiment

2003

This paper addresses aerodynamic modeling issues related to a simple experiment in which a pingpong ball is dropped from rest onto a table surface. From the times between the ball-table impacts, the initial drop height and the coefficient of restitution can be determined using a model that neglects aerodynamic drag. The experiment prompts questions about modeling the dynamics of a simple impact problem, including the importance of accounting for aerodynamic effects. Two nonlinear aerodynamic models are discussed in the context of experimental results.

Experimental Validation of Theoretical Model for Centric Dumped Collision between Two Balls

2012

In everyday life one can meet collision phenomena characterized by sudden variation of kinematical and dynamical parameters in diverse aspects. An important feature of these consists in high values of impact forces occurring during the contact time. In order to estimate the values of these forces it is required to know the time variation of characteristic parameters. Recent researches present models, from simple to complex, of impact phenomenon. An important issue is experimental validation of theoretical models. The present work treats some qualitative aspects concerning experimental validation using a shock sensor, of a centric dumped collision model for two balls.

Review of the Dynamic Behaviour of Sports Balls during Normal and Oblique Impacts

In this paper are review of impact experiment to study the dynamic behaviour of sports ball during oblique and normal impacts. In previous studies, the investigation was done on the dynamic behaviour of a sports ball during oblique and normal impacts from experimental, numerical, and theoretical viewpoints. The experimental results are analysed and compared with the theories, in order to understand the dynamics behaviours based on the phenomenological occurrence. Throughout the experimental studies previously, there are results of dynamics behaviours examined by many researchers such as the coefficient of restitution, tangential coefficient, local deformation, dynamic impact force, contact time, angle of impact (inbound and rebound), spin rate of the ball, ball stiffness and damping coefficient which dependable of the initial or impact velocity.

Rebound Property in Low Velocity Impact of Two Equivalent Balls

The present study focuses on an impact phenomenon of two spheres and its rebound property. The collision of two spheres is a fundamental problem with impact phenomenon. The coefficient of restitution characterizes the property of impact phenomenon and has been estimated in general by experiment. In addition, it has been tried to estimate the coefficient by analytical and numerical methods. Considering body deformation, the body is deflected rapidly in collision and the strain rate occurred in the body is significantly high. It is well known the yield stress of the specific industrial material depends on the strain rate. However, it has not been proved the relationship between the coefficient of restitution and the strain rate in details yet. The present paper discusses the coefficient of restitution in low velocity impact of two equivalent balls. The impact experiments were conducted for the balls with different diameters by a pendulum impact apparatus. And the balls are numerically analyzed based on the finite element method considering the dependence of yield stress on strain rate as the material property of the balls. In conclusion, the strain rate decreases with the increment of the ball diameter and, it causes the coefficient of restitution to decrease.