An Analysis Method for the Dynamic Compaction Processes of Powder Media Within a Die

1988 ◽  
Vol 110 (1) ◽  
pp. 28-34
Author(s):  
Yukio Sano
Keyword(s):  
Equations Of Motion ◽  
Approximate Solutions ◽  
Rigid Bodies ◽  
Jump Conditions ◽  
Rigid Plastic ◽  
Von Neumann ◽  
Powder Medium ◽  
Plastic Type ◽  
Particle Velocities ◽  
Compaction Processes

A method of analysis for the multishock compaction process of die-contained powder media with a plug at one end and an impacting punch at the other end is presented. In the method assumptions are made that the media are of a simple rigid-plastic type, and compressed only at the fronts of the shock waves passing through, and furthermore the punch and plug are rigid bodies. Based on the assumptions, particle velocities of elements between the punch surface and a shock wave front are the same and equal to the punch velocity, while velocities of elements between the front and the plug surface are equal to a velocity of the plug surface, i.e., zero. Therefore, it is possible to use jump conditions at the front and equations of motion for the punch and medium moving with the same velocity as it, instead of partial differential equations, i.e., conservation equations which were used in other methods. The equations of motion, together with the jump conditions and rigid-plastic constitutive relation equations provide two sets of equations governing the process. It is shown that there exist unique solutions of the equations of motion, and the equations are analyzed for a copper powder medium. Exact solutions obtained are compared with approximate solutions analyzed previously by the von Neumann and Richtmyer method. A fairly good agreement of the solutions by both the methods indicates that the approximate solutions are effective.

Experimental Verification of the Similarity of Dynamic Compaction Processes of a Copper Powder Medium in Dies of Elementary Shapes

1987 ◽  
Vol 109 (4) ◽  
pp. 306-313
Author(s):  
Kiyohiro Miyagi ◽  
Yukio Sano ◽  
Takuo Hayashi
Keyword(s):  
Cross Section ◽  
Copper Powder ◽  
Similarity Theory ◽  
Rigid Bodies ◽  
Dynamic Compaction ◽  
Wall Friction ◽  
Simple Type ◽  
One Dimensional ◽  
Powder Medium ◽  
Compaction Processes

The similarity of dynamic compaction processes was investigated theoretically and predicted in our previous report, where powder media in a die were assumed to be of a simple type, and the punch and plug to be rigid bodies. The predictions were based on a set of one-dimensional equations and a set of nondimensionalized one-dimensional equations. The objective of this study is to examine the similarity experimentally and to present the results of compaction experiments in order to verify the existence predicted. The experiments were carried out on a copper powder medium in dies having inner cross-section in elementary shapes such as circle, square and triangle. The pressure of the medium at a point contacting the end of the plug, the density distribution and mean density of the green compacts were measured in the experiment. From the analysis of the experimental data the validity of the dynamic similarity theory was demonstrated and the similarity was verified to exist despite the differences in size and shape between the dies used, which implies that the copper powder medium in the dies of elementary shapes is of a simple type. Relations between the density and the shape coefficients showed that the density reached maximum as the coefficients decreased approaching a certain point with a decreasing influence of the die wall friction, while past that point, contrary to the prediction by the theory, it began to decrease due to an increasing influence of the elastic deformation of the punch and plug.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

The Flutter of a Helicopter Rotor Blade in Forward Flight

1970 ◽  
Vol 21 (1) ◽  
pp. 18-48 ◽  
Author(s):  
C. W. Stammers
Keyword(s):  
Equations Of Motion ◽  
Approximate Solutions ◽  
Speed Ratio ◽  
Forward Speed ◽  
Forward Flight ◽  
Helicopter Blade ◽  
Integer Multiple ◽  
Tip Speed Ratio ◽  
Half Integer ◽  
Helicopter Rotor Blade

SummaryThe nature of flapping torsion flutter of a helicopter blade in forward flight is discussed. The essential complication in the analysis is the presence of periodic coefficients in the equations of motion; approximate solutions are obtained by use of a perturbation procedure. An unusual behaviour of the flutter equations which occurs when the fundamental frequency of flutter is a half-integer multiple of rotational speed is studied. Two different instability mechanisms can be distinguished and are related to the two energy sources in the system, namely the rotation of the rotor and the forward speed of the helicopter. It is found that forward flight can have a significant stabilising influence on flutter and that, as the tip speed ratio increases, flutter occurs predominantly at half-integer frequencies. The results are confirmed by the use of a numerical method.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

Formulation of the Equations of Motion of RRPR Robot Manipulator

2000 ◽  
Author(s):  
Hazem Ali Attia ◽  
Tarek M. A. El-Mistikawy ◽  
Adel A. Megahed
Keyword(s):  
Dynamic Analysis ◽  
Efficient Solution ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Second Law ◽  
Equivalent System ◽  
Constraint Forces ◽  
Dynamic Formulation ◽  
System Of Particles

Abstract In this paper the dynamic analysis of RRPR robot manipulator is presented. The equations of motion are formulated using a two-step transformation. Initially, a dynamically equivalent system of particles that replaces the rigid bodies is constructed and then Newton’s second law is applied to derive their equations of motion. The equations of motion are then transformed to the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality. For open chains, this process automatically eliminates all of the non-working constraint forces and leads to an efficient solution and integration of the equations of motion. The results of the simulation indicate the simplicity and generality of the dynamic formulation.

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