Dynamic analysis of vibration-driven systems moving based on frictional locomotion principles

2011 ◽  
Vol 226 (7) ◽  
pp. 1787-1799 ◽  
Author(s):  
A Kamali Eigoli ◽  
GR Vossoughi
Keyword(s):  
Dynamic Analysis ◽  
Longitudinal Vibration ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Normal Contact ◽  
Driven Systems ◽  
Proposed Model ◽  
Linear Equations Of Motion ◽  
And Control ◽  
Good Agreement

In this article, we investigate the dynamic analysis of vibration-driven systems moving based on frictional locomotion principles. Symmetrically actuating particles with longitudinal harmonic forces or with longitudinal vibration of the base does not lead to the net motion, unless the generated slip varies during back and forth motion. Harmonically varying the normal contact force and employing asymmetric friction coefficients are two approaches for obtaining frictional locomotion principles. In order to study the simultaneous effect of these required conditions of generating net displacement, a mathematical model is developed, and the resulting non-linear equations of motion are analytically solved. We have shown that the proposed model can be simply generalized to many other frictional, vibration-induced principles, such as the friction drive and the directional friction concepts. The obtained results are in good agreement with those achieved from numerical integration and experiments, reported in the literature. The presented theoretical findings can be effectively used for the design and control of this type of oscillators.

Formulation of Multiple Belt System and its Dynamic Analysis

1993 ◽  
Author(s):  
Takuzo Iwatsubo ◽  
Shiro Arii ◽  
Kei Hasegawa ◽  
Koki Shiohata
Keyword(s):  
Computer Program ◽  
Dynamic Analysis ◽  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Transient Responses ◽  
Fundamental Idea ◽  
Linear Equations Of Motion ◽  
Simulation Results ◽  
Belt System

Abstract This paper presents a method for analyzing the dynamic characteristics of driving systems consisting of multiple belts and pulleys. First, the algorithm which derives the linear equations of motion of arbitrary multi-coupled belt systems is shown. Secondly, by using the algorithm, the computer program which formulates the equations of motion and calculates the transient responses of the belt system is presented. The fundamental idea of the algorithm is as follows: Complicated belt systems consisting of multiple belts and pulleys are regarded as combinations of simple belt systems consisting of a single belt and some pulleys. Therefore, the equations of motion of the belt systems can be derived by the superposition of the equations of motion of the simple belt systems. By means of this method, the responses of arbitrary multi-coupled belt systems can be calculated. Finally, to verify the usefulness of this method, the simulation results are compared with the experimental results.

scholarly journals INVESTIGATION OF THE DYNAMICS OF AN OVERHEAD CRANE LIFTING PROCESS IN A VERTICAL PLANE

Transport ◽  
2005 ◽  
Vol 20 (5) ◽  
pp. 176-180 ◽  
Author(s):  
Marijonas Bogdevičius ◽  
Aleksandr Vika
Keyword(s):  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Asynchronous Motor ◽  
Linear Equations ◽  
Vertical Plane ◽  
Overhead Crane ◽  
Dynamic Forces ◽  
Planet Gear ◽  
Linear Equations Of Motion ◽  
Non Linear Equations

The paper analyses the dynamic behaviour of supporting structure of an overhead crane during the operation of a hoisting mechanism. The crane is expected to operate with a hook and to carry 50 kN of weight. The electric hoist consists of an asynchronous motor with a magnetic brake, a two‐level planet gear, a load drum and an upper block. Non‐linear equations of motion of a crane hoisting mechanism are derived. Real dynamic forces and their influence on the hoisting crane behaviour are obtained. Numerical results of the crane are derived considering two hoisting regimes during the operation of the hoisting.

Modelling the flight dynamics of the hang glider

2005 ◽  
Vol 109 (1102) ◽  
pp. I-XX ◽  
Author(s):  
M. V. Cook ◽  
M. Spottiswoode
Keyword(s):  
Complex Geometry ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flight Dynamics ◽  
Control Analysis ◽  
Stability Margins ◽  
Stability And Control ◽  
Centre Of Gravity ◽  
Weight Shift ◽  
And Control

AbstractThe development of the non-linear equations of motion for the hang glider from first principles is described, including the complex geometry of control by pilot ‘weight shift’. By making appropriate assumptions the linearised small perturbation equations are derived for the purposes of stability and control analysis. The mathematical development shows that control is effected not by pilot weight shift, but by centre of gravity shift and that lateral-directional control by this means is weak, and is accompanied by significant instantaneous adverse response.The development of a comprehensive semi-empirical mathematical model of the flexible wing aerodynamics is described. In particular, the modelling attempts to quantify camber and twist dependencies. The performance of the model is shown to compare satisfactorily with measured hang glider wing data obtained in earlier full scale experiments. The mathematical aerodynamic model is then used to estimate the hang glider stability and control derivatives over the speed envelope for substitution into the linearised equations of motion.Solution of the equations of motion is illustrated and the flight dynamics of the typical hang glider are described. In particular, the dynamic stability properties are very similar to those of a conventional aeroplane, but the predicted lateral directional stability margins are significantly larger. The depth of mathematical modelling employed enables the differences to be explained satisfactorily. The unique control properties of the hang glider are described in some detail. Pitch and roll control of the hang glider is an aerodynamic phenomenon and results from the pilot adjusting his position relative to the wing in order to generate out of trim aerodynamic control moments about the centre of gravity. Maximum control moments are limited by hang glider geometry which is dependent on the length of the pilot‘s arm. The pilot does not generate control moments directly by shifting his weight relative to the wing. The modelling thus described would seem to give a plausible description of the flight dynamics of the hang glider.

Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link

1988 ◽  
Vol 110 (4) ◽  
pp. 416-421 ◽  
Author(s):  
Enrique Barbieri ◽  
U¨mit O¨zgu¨ner
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Quantitative Comparison ◽  
Mode Shapes ◽  
Dimensional Model ◽  
Finite Dimensional ◽  
Linear Equations Of Motion ◽  
Aluminum Beam

The linear equations of motion of a uniform flexible slewing link which were derived via Hamilton’s Extended Principle are considered. These equations account for the coupling between bending and rigid modes. Unconstrained and constrained mode expansions are investigated and a quantitative comparison is made between the frequency equations and associated mode shapes. A finite dimensional model is derived using the assumed modes method and the theoretical frequencies are verified with an experimental counterbalanced aluminum beam.

Dynamic Analysis of the Ultrasonic Machining Process

1996 ◽  
Vol 118 (3) ◽  
pp. 376-381 ◽  
Author(s):  
Z. Y. Wang ◽  
K. P. Rajurkar
Keyword(s):  
Dynamic Analysis ◽  
Material Removal ◽  
Removal Rate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamic Contact ◽  
Machining Process ◽  
Ultrasonic Machining ◽  
Factors Affecting ◽  
Good Agreement

This paper presents a dynamic analysis of the ultrasonic machining process based on impact mechanics. Equations representing the dynamic contact force and stresses caused by the impinging of abrasive grits on the work, are obtained by solving the three-dimensional equations of motion. The factors affecting the material removal rate have been studied. It is found that the theoretical estimates obtained from the dynamic model are in good agreement with the experimental results.

Calculations for anemometry with fine hot wires

1968 ◽  
Vol 32 (1) ◽  
pp. 9-19 ◽  
Author(s):  
W. W. Wood
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Close Agreement ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Measured Data ◽  
Hot Wire ◽  
Linear Equations Of Motion ◽  
Hot Wires ◽  
Non Linear Equations

The heat transfer appropriate to low Reynolds number hot-wire anemometry is calculated from the full non-linear equations of motion and of heat transfer by an iterative method starting with the Oseen solution and its heat flux analogue. The second and third iterates yield close agreement with measured data.

Detection of Cracks in Rotating Timoshenko Shafts Using Axial Impulses

1991 ◽  
Vol 113 (1) ◽  
pp. 74-78 ◽  
Author(s):  
K. R. Collins ◽  
R. H. Plaut ◽  
J. Wauer
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Effective Means ◽  
Linear Equations ◽  
Free Vibrations ◽  
Frequency Spectra ◽  
Time Histories ◽  
Rotating Shafts ◽  
Linear Equations Of Motion

A rotating Timoshenko shaft with a single transverse crack is considered. The crack opens and closes during motion and is represented by generalized forces and moments. The shaft has simply supported ends, and the six coupled, piecewise-linear equations of motion (including longitudinal, transverse, and torsional displacements) are integrated numerically after application of Galerkin’s method with two-term approximations for each of the six displacements. Time histories and frequency spectra are compared for shafts with no crack and with a crack for which the crack depth is one-fifth of the shaft diameter. Free vibrations and the responses to a single axial impulse and periodic axial impulses are analyzed. The last case appears to provide an effective means for detecting cracks in rotating shafts.

Inviscid Shear Flow Analysis of Corner Eddies Ahead of a Channel Flow Contraction

1985 ◽  
Vol 107 (2) ◽  
pp. 212-217
Author(s):  
R. N. Meroney
Keyword(s):  
Shear Flow ◽  
Velocity Distribution ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flow Analysis ◽  
Inviscid Fluid ◽  
Flow Vorticity ◽  
Flow Geometry ◽  
Linear Shear ◽  
Linear Equations Of Motion

The steady rotational flow of an inviscid fluid in a two-dimensional channel toward a sink or a contraction is treated. The velocity distribution at upstream infinity is approximated by a linear combination of uniform flow, linear shear flow, and a cosine curve. The combinations were adjusted to simulate flows ranging from laminar to turbulent. Vorticity is assumed conserved on streamlines. The resulting linear equations of motion are solved exactly. The solution show the dependence of the corner eddy separation and reattachment on flow geometry and approach flow vorticity and velocity distribution typified by a shape factor.

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