A Critical Study of the Applicability of Rigid-Body Collision Theory

1996 ◽  
Vol 63 (2) ◽  
pp. 307-316 ◽  
Author(s):  
D. Stoianovici ◽  
Y. Hurmuzlu
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Equations Of Motion ◽  
Coefficient Of Restitution ◽  
Electrical Circuit ◽  
Experimental Results ◽  
Critical Study ◽  
Low Velocity ◽  
Steel Bars ◽  
Body Theory

This article deals with the collision of steel bars with external surfaces. The central issue of the article is the investigation of the fundamental concepts that are used to solve collision problems by using rigid-body theory. We particularly focus on low-velocity impacts of relatively rigid steel bars to test the applicability of these concepts. An experimental analysis was conducted to study the rebound velocities of freely dropped bars on a large external surface. A high-speed video system was used to capture the kinematic data. The number of contacts and the contact time were determined by using an electrical circuit and an oscilloscope. Tests were performed by using six bar lengths and varying the pre-impact inclinations and the velocities of the bars. The experimental results were used to verify the applicability of Coulomb’s law of friction and the invariance of the coefficient of restitution in the class of impacts considered in this study. Then, given the unusual variation the coefficient of restitution as a result of changing pre-impact inclinations, a theoretical model was developed to explain this variation. A discrete model of the bar was used to obtain the equations of motion during impact. Computed and experimental results were compared to establish the accuracy of numerical model. The internal vibrations of the bar and multi impacts between the bar and the surface were found to be two main factors that cause the variation of the coefficient of restitution. Furthermore, a slenderness factor was proposed to identify the subset of collision problems where the coefficient of restitution was invariant to the inclination angle.

Dynamics of a Radially Rotating Beam With Impact, Part 1: Theoretical and Computational Model

1990 ◽  
Vol 112 (1) ◽  
pp. 65-70 ◽  
Author(s):  
A. S. Yigit ◽  
A. G. Ulsoy ◽  
R. A. Scott
Keyword(s):  
Rigid Body ◽  
Computational Model ◽  
Computational Algorithm ◽  
Coefficient Of Restitution ◽  
Experimental Results ◽  
Body Motion ◽  
Momentum Balance ◽  
Rotating Beam ◽  
Before And After ◽  
Simulation Results

A model is presented for the dynamics of a radially rotating beam with impact. The model uses a momentum balance method and a coefficient of restitution, and enables one to predict the rigid body motion as well as the elastic motion before and after impact. A computational algorithm is also developed to implement the model. In Part 2 simulation results will be compared with experimental results to investigate the validity of the model.

On Planar Impacts of Cylinders and Balls

2019 ◽  
Vol 86 (7) ◽  
Author(s):  
Khalid Alluhydan ◽  
Pouria Razzaghi ◽  
Yildirim Hurmuzlu
Keyword(s):  
Rigid Body ◽  
Coefficient Of Restitution ◽  
Experimental Results ◽  
Discretization Method ◽  
Stiffness Ratio ◽  
Hertz Model ◽  
Local Contact ◽  
Contact Models ◽  
Simulation Results ◽  
Number Of Segments

In this paper, we studied planar collisions of balls and cylinders with an emphasis on the coefficient of restitution (COR). We conducted a set of experiments using three types of materials: steel, wood, and rubber. Then, we estimated the kinematic COR for all collision pairs. We discovered unusual variations among the ball–ball (B–B) and ball–cylinder (B–C) CORs. We proposed a discretization method to investigate the cause of the variations in the COR. Three types of local contact models were used for the simulation: rigid body, bimodal linear, and bimodal Hertz models. Based on simulation results, we discovered that the bimodal Hertz model produced collision outcomes that had the greatest agreement with the experimental results. In addition, our simulations showed that softer materials need to be segmented more than harder ones. Softer materials are materials with smaller collision stiffness values than harder ones. Moreover, we obtained a relationship between the collision stiffness ratio and the number of segments of softer materials to produce physically accurate simulations of B–C CORs. We validated this relationship and the proposed method by conducting two additional sets of experiments.

scholarly journals Experimental Study on Rockfall Mechanism of Platy Rock on a Complex Slope

2020 ◽  
Vol 10 (8) ◽  
pp. 2849
Author(s):  
Xiaohui Liao ◽  
Qi Ouyang ◽  
Haiyang Liu ◽  
Juanjuan Sun ◽  
Xueliang Wang ◽  
...  
Keyword(s):  
Experimental Study ◽  
High Speed ◽  
Slope Angle ◽  
Coefficient Of Restitution ◽  
Experimental Results ◽  
Rock Fall ◽  
Restitution Coefficient ◽  
Hazard Control ◽  
Before And After ◽  
Control Work

The rock fall trajectory and its mechanisms are the most difficult to predict, owing to the complexity of the slope and the Irregular shape of falling rocks. To acquire a better knowledge of the rock fall mechanism of platy rock and to investigate the influence of various impact parameters, a comprehensive physical model experimental study was undertaken based on 3D printing technology using a high-speed camera and specially developed block release system. Based on the experimental results, the effects of the slope angle on the stopping position, the instantaneous kinetic energy and collision position of platy rock block were analyzed. Meanwhile, the effects of movement forms of platy rock before and after collision on the normal coefficient of restitution and the tangent coefficient of restitution were discussed. It is observed that rock fall trajectory depends not only on slope material characteristics, slope angle but also on factors related to the platy block (weight, size and shape). The experimental results showed the value of restitution coefficient exceeding 1 has an important relation with the combination of various movement forms (including the flip motion) and the change of movement forms of platy rock before and after the collision. A new feasible experimental method for research and prevention of rock fall disaster was put forward. It would be important and helpful to the geo-hazard control work.

Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part I—Element Level Equations

1990 ◽  
Vol 112 (2) ◽  
pp. 203-214 ◽  
Author(s):  
S. Nagarajan ◽  
David A. Turcic
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Realistic Model ◽  
Open Loop ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Elastic Links

Equations of motion are derived using Lagrange’s equation for elastic mechanism systems. The elastic links are modeled using the finite element method. Both rigid body degrees of freedom and the elastic degrees of freedom are considered as generalized coordinates in the derivation. Previous work in the area of analysis of general elastic mechanisms usually involve the assumption that the rigid body motion or the nominal motion of the system is unaffected by the elastic motion. The nonlinear differential equations of motion derived in this work do not make this assumption and thus allow for the rigid body motion and the elastic motion to influence each other. Also the equations obtained are in closed form for the entire mechanism system, in terms of a minimum number of variables, which are the rigid body and the elastic degrees of freedom. These equations represent a more realistic model of light-weight high-speed mechanisms, having closed and open loop multi degree of freedom chains, and geometrically complex elastic links.

Yaw Galloping of a TLWP Platform Under High Speed Currents by Analytical Methods and its Comparison With Experimental Results

2017 ◽  
Author(s):  
Francisco Lamas ◽  
Miguel A. M. Ramirez ◽  
Antonio Carlos Fernandes
Keyword(s):  
High Speed ◽  
Production Systems ◽  
Experimental Tests ◽  
Experimental Results ◽  
Analytical Methodology ◽  
New Approach ◽  
Laboratory Facilities ◽  
Polynomial Curve ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Analyses

Flow Induced Motions are always an important subject during both design and operational phases of an offshore platform life. These motions could significantly affect the performance of the platform, including its mooring and oil production systems. These kind of analyses are performed using basically two different approaches: experimental tests with reduced models and, more recently, with Computational Fluid Dynamics (CFD) dynamic analysis. The main objective of this work is to present a new approach, based on an analytical methodology using static CFD analyses to estimate the response on yaw motions of a Tension Leg Wellhead Platform on one of the several types of motions that can be classified as flow-induced motions, known as galloping. The first step is to review the equations that govern the yaw motions of an ocean platform when subjected to currents from different angles of attack. The yaw moment coefficients will be obtained using CFD steady-state analysis, on which the yaw moments will be calculated for several angles of attack, placed around the central angle where the analysis is being carried out. Having the force coefficients plotted against the angle values, we can adjust a polynomial curve around each analysis point in order to evaluate the amplitude of the yaw motion using a limit cycle approach. Other properties of the system which are flow-dependent, such as damping and added mass, will also be estimated using CFD. The last part of this work consists in comparing the analytical results with experimental results obtained at the LOC/COPPE-UFRJ laboratory facilities.

The Effect of Strain Rate on the Material Characteristics of Nickel-Based Superalloy Inconel 718

2007 ◽  
Vol 340-341 ◽  
pp. 283-288 ◽  
Author(s):  
Jung Han Song ◽  
Hoon Huh
Keyword(s):  
Dynamic Response ◽  
High Strain Rate ◽  
Strain Rate ◽  
Turbine Blade ◽  
Inconel 718 ◽  
High Speed ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Experimental Results ◽  
Stress Wave Propagation

The dynamic response of the turbine blade materials is indispensable for analysis of erosions of turbine blades as a result of impulsive loading associated with gas flow. This paper is concerned with the dynamic material properties of the Inconel 718 alloy which is widely used in the high speed turbine blade. The dynamic response at the corresponding level of the strain rate should be acquired with an adequate experimental technique and apparatus due to the inertia effect and the stress wave propagation. In this paper, the dynamic response of the Inconel 718 at the intermediate strain rate ranged from 1/s to 400/s is obtained from the high speed tensile test and that at the high strain rate above 1000/s is obtained from the split Hopkinson pressure bar test. The effects of the strain rate on the dynamic flow stress, the strain rate sensitivity and the failure elongation are evaluated with the experimental results. Experimental results from both the quasi-static and the high strain rate up to 3000/s are interpolated in order to construct the constitutive relation that should be applied to simulate the dynamic behavior of the turbine blade made of the Inconel 718.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Experimental Study of Turbulent Macroinstabilities in an Agitated System with Axial High-Speed Impeller and with Radial Baffles

1996 ◽  
Vol 61 (6) ◽  
pp. 856-867 ◽  
Author(s):  
Oldřich Brůha ◽  
Ivan Fořt ◽  
Pavel Smolka ◽  
Milan Jahoda
Keyword(s):  
Experimental Study ◽  
Flow Field ◽  
High Speed ◽  
Experimental Results ◽  
Turbulent Regime ◽  
Frequency Of Occurrence ◽  
Visualization Method ◽  
Entire Flow

The frequency of turbulent macroinstability occurrence was measured in liquids agitated in a cylindrical baffled vessel. As it has been proved by preceding experimental results of the authors, the stochastic quantity with frequency of occurrence of 10-1 to 100 s-1 is concerned. By suitable choosing the viscosity of liquids and frequency of impeller revolutins, the region of Reynolds mixing numbers was covered from the pure laminar up to fully developed turbulent regime. In addition to the equipment making it possible to record automatically the macroinstability occurrence, also the visualization method and videorecording were employed. It enabled us to describe in more detail the form of entire flow field in the agitated system and its behaviour in connection with the macroinstability occurrence. It follows from the experiments made that under turbulent regime of flow of agitated liquids the frequency of turbulent macroinstability occurrence is the same as the frequency of the primary circulation of agitated liquid.

A Wavelength Interleaved DWDM ROF System with 60GHz Optical OFDM Signal

2011 ◽  
Vol 130-134 ◽  
pp. 2245-2248
Author(s):  
Yong Hong Ma ◽  
Chong Xiang Zhang ◽  
Pan Zhang
Keyword(s):  
High Speed ◽  
Radio Over Fiber ◽  
Experimental Results ◽  
Arrayed Waveguide Grating ◽  
Waveguide Grating ◽  
Access System ◽  
Ofdm Signal ◽  
The Future ◽  
Optical Ofdm ◽  
Arrayed Waveguide

we demonstrate a wavelength interleaved DWDM Radio-over-Fiber (ROF) system for providing 1-Gb/s OFDM signal in downlink and 1-Gb/s OOK data in uplink simultaneously. In this scheme, we use only one arrayed waveguide grating device at the remote node to realize both the de-multiplexing and multiplexing functions. The experimental results demonstrate that this scheme is feasible to the future broadband high-speed OFDM-ROF access system.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

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