Dan B. Marghitu

Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres

The current work presents a different methodology for modeling the impact between elasto-plastic spheres. Recent finite element results modeling the static deformation of an elasto-plastic sphere are used in conjunction with equations for the variation of kinetic energy to obtain predictions for the coefficient of restitution. A model is also needed to predict the residual deformation of the sphere during rebound, or unloading, of which several are available and compared in this work. The model predicts that a significant amount of energy will be dissipated in the form of plastic deformation such that as the speed at initial impact increases, the coefficient of restitution decreases. This work also derives a new equation for the initial critical speed which causes initial plastic deformation in the sphere that is different than that shown in previously derived equations and is strongly dependant on Poisson’s Ratio. For impacts occurring above this speed, the coefficient of restitution will be less than a value of one. This work also compares the predictions between several models that make significantly different predictions. The results of the current model also compare well with some existing experimental data. Empirical fits to the results are provided for use as a tool to predict the coefficient of restitution.

Three-Dimensional Rigid-Body Collisions With Multiple Contact Points

This article deals with three-dimensional collisions of rigid, kinematic chains with an external surface while in contact with other surfaces. We concentrate on a special class of kinematic chain problems where there are multiple contact points during the impact process. A differential formulation based algorithm is used to obtain solutions that utilize the kinematic, kinetic, and the energetic definitions of the coefficient of restitution. Planar and spatial collisions of three-link chain with two contact points are numerically studied to compare the outcomes predicted by each approach. Particular emphasis is placed on the relation between the post and pre-impact energies, slippage and rebounds at the contact points, and differences among planar and nearly planar three-dimensional solutions.

Nonlinear dynamics of an elastic rod with frictional impact

A model is presented for the impact with friction of a flexible body in translation and rotation. This model consists of a system of nonlinear differential equations which considers the multiple collisions as well as frictional effects at the contacting end, and allows one to predict the rigid and elastic body motion after the impact. The kinetic energy is derived by utilizing a generalized velocity field theory for elastic solids. The model uses a dry coefficient of friction and a nonlinear contact force. We introduce a finite number of vibrational modes to take into account the vibrational behavior of the body during impact. The vibrations, the multiple collisions, and the angle of incidence angle, are found to be important factors for the kinematics of frictional impact. Analytical and experimental results were compared to establish the accuracy of the model.

Dynamics of children with torsional anomalies of the lower limb joints

Abstract In this study we used the techniques of nonlinear dynamics to analyze the stability of normal and pathological gait in children. We based the analysis on the assumption that a human at steady-state locomotion can be represented as a nonlinear periodic system. Kinematic data for the lower limb joints were used to construct phase plane portraits and first return maps for the hip, the knee and the ankle joints. Anomalies in the joint rotations of pathological individuals were graphically depicted by comparing the phase plane portraits and first return maps. Using the Floquet theory, an index of dynamic stability was used to compare normal and pathological gait.

Nonlinear dynamics in orthogonal turning process

Abstract In this paper, the nonlinear dynamics methods were applied to analyze the experimental data captured during the orthogonal turning process. The analyzed data were the acquired time series represented by the cutting and thrust forces acting on the cutting tool. Workpieces of aluminum alloy, ductile cast iron, and gray cast iron were machined. The false nearest neighbors and the largest Lyapunov methods were considered to study the nonlinear phenomena occurring in turning process. An index of stability was also defined and used to compare the turning processes of all tested workpieces.

Dynamics Analysis of Ground Contact Pressure of English Pointer Dogs

In this study force sensing resistors were used to determine thepressure on the central area of each of the weight bearing pads of thefore and hind paws of dogs at the walk. Six adult normal healthy EnglishPointer dogs were used in this project. Pressure data were collected byaffixing a force sensing resistor to the central area of the groundcontact surface of each weight bearing paw pad of the right fore andhind limbs. Pressure signal data from stance phase during walking wereanalyzed. Within paw pads, the pressure graphs were consistent in formand magnitude. Within paws, there were significant pressure differencesamong pads on both fore and hind limbs. The coefficient of restitution,the embedding dimension, and the Lyapunov exponents were calculated. Theability to measure and analyze pressure on individual paw pads providesinsight into soft tissue stresses on the palmar/plantar surface of thepaw. Pressure at a wound site on the pads has a detrimental effect onwound healing and a better understanding these stresses will be ofbenefit when suturing and bandaging pad wounds. Such information isespecially important in athletic and working dogs, e.g. search andrescue dogs.

Control of a Parametrically Excited Flexible Beam Undergoing Rotation and Impacts

The linear control of a parametrically excited impacting flexible link in rotational motion is considered. The equation of motion for such a system contains time-periodic coefficients. To suppress the vibrations resulting after impact with an external rigid body, a linear controller is designed via Lyapunov–Floquet transformation. In this approach, the equations of motion with time-periodic coefficients are transformed into a time-invariant form suitable for the application of standard time-invariant controller design techniques. The momentum balance method and an empirical coefficient of restitution is used to model the collision between the two bodies.

An analysis of greyhound gait using wavelets

In this paper we present a method of analysing gait of quadrupedal animals using wavelets. Time series data such as joint trajectories can be decomposed by the discrete wavelet transform to represent components of different frequency bandwidth. Differences between two similar trajectories can be detected by comparing the components of the same bandwidth. We analysed kinematic data of the hindlimbs of three greyhounds with normal gait and with tibial nerve paralysis. Abnormalities in the gait patterns were detected and quantified by comparing the energy contribution of the components that were present at the same level of the wavelet transform.

Experimental and theoretical study of the oblique impact of a tennis ball with a racket

The normal and the oblique impact of a tennis ball with a racket has been studied. An accurate setup has been built in order to provide consistent initial conditions for the impacts. Experiments have been done for a wide range of impact angles and initial velocities. The motion of the ball before, during and after the impact has been recorded using a high-speed camera with 10,000 frames per second. The impact has been divided into two phases, compression and restitution. An expression for the contact force has been provided. The coefficient of restitution and effective coefficient of friction have been analyzed experimentally. For low impact velocities, the coefficient of restitution is constant at different impact angles. The effective coefficient of friction changes as a function of the impact angle. The contact force expression has been determined for the compression and the restitution phases using the experimental data from normal impact experiments. The simulation and experimental results are compared and verified for the normal and the oblique impacts.

Dynamics and Fuzzy Control of a Levitated Particle

This paper deals with the control in both horizontal and vertical directions of a nonlinear magnetic spherical particle suspension. A pair of horizontal electromagnets were added to the typical magnetic levitation system in order to handle the horizontal unexpected displacements of the particle. A fuzzy logic controller was designed to bring the particle to the operating location situated on the symmetry axis. Simulations with different initial position conditions of the particle are provided. It was shown that the controller has a good behavior for almost any initial conditions.