Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery

1996 ◽  
Vol 118 (3) ◽  
pp. 485-490 ◽  
Author(s):  
H. Ashrafiuon ◽  
A. M. Whitman
Keyword(s):  
Numerical Modeling ◽  
Steady State ◽  
Asymptotic Analysis ◽  
Degree Of Freedom ◽  
Torsional Vibrations ◽  
Transient Vibration ◽  
Asymptotic Expressions ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Good Agreement

A class of two degree of freedom reciprocating machines is analyzed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.

Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery

1995 ◽  
Author(s):  
Hashem Ashrafiuon ◽  
Alan M. Whitman
Keyword(s):  
Numerical Modeling ◽  
Steady State ◽  
Asymptotic Analysis ◽  
Degree Of Freedom ◽  
Torsional Vibrations ◽  
Transient Vibration ◽  
Asymptotic Expressions ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Good Agreement

Abstract A class of two degree of freedom reciprocating machines is analysed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.

Effects of Chip Seizure on Steady State Motion of a Machine-Tool

2009 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Machine Tool ◽  
Systems Theory ◽  
Degree Of Freedom ◽  
Continuous Systems ◽  
Discontinuous Systems ◽  
Mechanical Analogy ◽  
Steady State Motion ◽  
Two Degree Of Freedom

The steady state motion of a machine-tool is numerically predicted with interaction of the chip/tool friction boundary. The chip/tool friction boundary is modeled via a discontinuous systems theory in effort to validate the passage of motion through such a boundary. The mechanical analogy of the machine-tool is shown and the continuous systems of such a model are governed by a linear two degree of freedom set of differential equations. The domains describing the span of the continuous systems are defined such that the discontinuous systems theory can be applied to this machine-tool analogy. Specifically, the numerical prediction of eccentricity amplitude and frequency attribute the chip seizure motion to the onset or route to unstable interrupted cutting.

Computer Simulation of a Test Rig to Model Sloshing in Spin-Stabilized Satellites

1992 ◽  
Vol 114 (4) ◽  
pp. 689-698 ◽  
Author(s):  
D. R. Flugrad ◽  
L. A. Obermaier
Keyword(s):  
Model Simulation ◽  
Test Rig ◽  
Dynamic Motion ◽  
Experimental Project ◽  
Rotating Structure ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Good Agreement

Certain communications satellites carry liquid stores on board for station tending and attitude adjustment. However, sloshing of the liquid can cause an undesirable nutational motion of the spin-stabilized vehicle. In previous work a test rig was designed, built and instrumented to study the interaction between the rotating structure and liquid. To augment that experimental project, a computer model of the test rig has been developed to simulate the dynamic motion of the system for various parameter values. The sloshing liquid was replaced by a two degree-of-freedom pendulum in the mathematical model. Simulation results were compared with those from a general multibody dynamics program and with experimental measurements of the test rig motion to demonstrate the mathematical model’s validity. Good agreement was achieved in both instances.

The Galloping Response of a Two-Degree-of-Freedom System

1974 ◽  
Vol 41 (4) ◽  
pp. 1113-1118 ◽  
Author(s):  
R. D. Blevins ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Natural Frequencies ◽  
Analytic Solutions ◽  
Degree Of Freedom ◽  
Approximate Analysis ◽  
Stability Criteria ◽  
Integer Multiple ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.

Forced Oscillations of Non-Linear Two-Degree-of-Freedom Systems

1966 ◽  
Vol 8 (3) ◽  
pp. 252-258 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Numerical Integration ◽  
Transient Response ◽  
Internal Resonance ◽  
Perturbation Technique ◽  
Degree Of Freedom ◽  
Forced Oscillations ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom ◽  
Good Agreement

This paper shows how the Lighthill-Poincaré perturbation technique may be used to determine the transient response of ‘lightly coupled’ non-linear multi-degree-of-freedom oscillatory systems subject to arbitrary forcing functions. The results in general are complex but simplify in many important cases. A comparison is made between the analytical results and results obtained by a numerical integration of the equations on a computer. Good agreement is noted. The method fails under conditions of ‘internal resonance’ of the system.

Coronas and the space charge problem

1991 ◽  
Vol 2 (1) ◽  
pp. 43-81 ◽  
Author(s):  
Chris Budd
Keyword(s):  
Steady State ◽  
Asymptotic Analysis ◽  
Space Charge ◽  
Large Time ◽  
Steady State Solution ◽  
Travelling Wave ◽  
Macroscopic Motion ◽  
The Relationship ◽  
Charged Ions ◽  
Good Agreement

This paper presents a detailed analysis of a model for a positive corona discharge, and discusses the relationship between the model and the space charge equations which predict the macroscopic motion of charged ions in a gas. The study is restricted to the asymptotic behaviour of the discharge for large time, and it does not consider its initial or burst phases in detail.One prediction of this model is the existence of a steady state solution to the space charge equations that may lose stability to a travelling wave disturbance which then grows into a strongly pulsed oscillation.We compare some numerical calculations with an asymptotic analysis of the discharge and find good agreement.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

scholarly journals Two-degree-of-freedom control of a multilink flexible manipulator using filtered inverse feedforward controller and strain feedback controller

2019 ◽  
Keyword(s):  
Research Paper ◽  
Feedback Controller ◽  
Degree Of Freedom ◽  
Flexible Manipulator ◽  
Transient Vibration ◽  
Rapid Decay ◽  
Hybrid Solution ◽  
Manipulator Arm ◽  
Feedforward Controller ◽  
Two Degree Of Freedom

This research paper presents a hybrid solution to both residue vibration and transient vibration as addressed using filtered inverse feedforward controller and strain feedback controller on a 3D 2 links flexible manipulator. The feedforward filtered inverse will minimize on the transient vibration due to sudden starting followed sudden stopping of the manipulator arm while the strain feedback will ensure rapid decay of the residue vibrations. Transient and residue vibrations stand in the way to reaping all the numerous advantages of the flexible manipulator. Transient vibration refers to vibrations resulting from sudden changes in the direction of the links while residue vibrations means that the arm takes too long to settle to do some useful work. Modelling of the manipulator and development of the inverse controller was carried out in Maple, MapleSim and MATLAB softwares. Experiments carried out in dSPACE control desk environment considering the manipulator without load and a case where a load of 100g was attached at the distal end of link 2.

Lateral Dynamics and Stability of the Skateboard

1979 ◽  
Vol 46 (4) ◽  
pp. 931-936 ◽  
Author(s):  
M. Hubbard
Keyword(s):  
Critical Speed ◽  
Experimental Validation ◽  
Degree Of Freedom ◽  
Forward Speed ◽  
Stability Criteria ◽  
Vehicle Model ◽  
Inertia Effects ◽  
Lateral Dynamics ◽  
Parameter Values ◽  
Two Degree Of Freedom

The natural lateral dynamic behavior of a skateboard is described in the absence of rider control. The effects of vehicle and rider parameters are investigated and stability criteria are derived in terms of these parameters. It is shown that for certain parameter values a simple one-degree-of-freedom vehicle model predicts a critical speed above which inertia effects can stabilize the roll motion, and that the frequency of roll oscillations is a function of forward speed. A more complicated two-degree-of-freedom vehicle model, including independent roll of both the board and of the rider, is also derived and is shown to have the possibility of speed stabilization as well. Experimental validation of the first theory is included.

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