Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Leonardo Sanches ◽  
Guilhem Michon ◽  
Alain Berlioz ◽  
Daniel Alazard
Keyword(s):  
Equations Of Motion ◽  
Experimental Results ◽  
Resonance Phenomenon ◽  
Experimental Setup ◽  
Numerical Investigations ◽  
Ground Resonance ◽  
Stability Chart ◽  
The Stability ◽  
Theoretical Results ◽  
Theoretical Developments

Recent works have studied ground resonance in helicopters under the aging or damage effects. Indeed, blade lead-lag stiffness may vary randomly with time and differ from blade to blade. The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon was determined through numerical investigations into the periodic equations of motion, treated using Floquet's theory. A stability chart highlights the appearance of new instability zones as a function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup was designed and developed. The ground resonance instabilities were investigated using different rotors and the boundaries of stability were determined. A good correlation between both theoretical and experimental results was obtained and the new instability zones, found in asymmetric rotors, were verified experimentally. The temporal responses of the measured signals highlighted the exponential divergence in the instability zones.

Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments

2012 ◽  
Author(s):  
Leonardo Sanches ◽  
Guilhem Michon ◽  
Alain Berlioz ◽  
Daniel Alazard
Keyword(s):  
Equations Of Motion ◽  
Resonance Phenomenon ◽  
Aging Effects ◽  
Ground Resonance ◽  
Different Types ◽  
Stability Chart ◽  
Instability Regions ◽  
The Stability ◽  
Theoretical Results ◽  
Theoretical Developments

Recent works study the ground resonance in helicopters under the aging effects. Indeed, the blades lead-lag stiffness may vary randomly with time and be different from each other (i.e.: anisotropic rotor). The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon is determined through numerical investigations on the periodical equations of motion, treated by using Floquet’s theory. Stability chart highlights the appearance of new instability zones as function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup is designed and developed. The ground resonance instabilities are investigated for different types of rotor configurations (i.e.: isotropic and anisotropic rotors) and the boundaries of stability are determined. A good correlation between both theoretical and experimental results is obtained and the new instability zones, found in asymmetric rotors, are verified experimentally. The temporal responses of the measured signals highlight the exponential divergence at the instability regions.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

Similarity and stability of the laminar boundary layer in a streamwise corner

1981 ◽  
Vol 377 (1770) ◽  
pp. 269-288 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Conclusive Evidence ◽  
Experimental Results ◽  
Solid Surfaces ◽  
Boundary Layer Problem ◽  
Streamwise Pressure Gradient ◽  
The Stability ◽  
Limiting Case ◽  
Theoretical Results

The study of laminar viscous flow along the line of intersection of two solid surfaces at right angles is examined in its present state, and out­standing differences between various experimental and theoretical results are analysed. New experimental results are presented in which the stability of the corner boundary layer is examined in terms of the degree of streamwise similarity of its velocity profiles. Conclusive evidence is found that the layer does not exist in stable laminar form when the streamwise pressure gradient is zero and the Reynolds number much above about 10 4 . The new results also help to explain the differences between various experimental results, and between theory and experi­ment, which have characterized the corner boundary layer problem for several years. By extrapolation, an approximate prediction is obtained of what the velocity profile of the corner boundary layer would be in the limiting case of zero pressure gradient, if the layer were stable in that state. The predicted profile is compared with the results of current theories.

ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF TWO IMPACTING OSCILLATORS WITH DAMPING

2004 ◽  
Vol 14 (11) ◽  
pp. 3931-3947 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Periodic Motion ◽  
Equations Of Motion ◽  
Analytical Determination ◽  
Stable Periodic Solution ◽  
Numerical Investigations ◽  
Stable Periodic ◽  
Existence Of Periodic Solutions ◽  
The Stability

A system that consists of two impacting oscillators with damping has been considered in this paper. In the first part, a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions are presented. The results of the computations carried out by these methods have been illustrated with a few examples. In the second part of the paper, the results of some numerical investigations are presented. The goal of these studies is to determine, in which regions of parameters characterizing the system, the periodic motion with one impact per period exists and is stable.

Self-Excited Vibrations and Damping in Circulatory Systems

2014 ◽  
Vol 81 (10) ◽  
Author(s):  
Peter Hagedorn ◽  
Manuel Eckstein ◽  
Eduard Heffel ◽  
Andreas Wagner
Keyword(s):  
Transmission Lines ◽  
Mechanical Engineering ◽  
Equations Of Motion ◽  
The Self ◽  
Engineering Systems ◽  
Common Assumption ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Ground Resonance ◽  
The Stability

Self-excited vibrations in mechanical engineering systems are in general unwanted and sometimes dangerous. There are many systems exhibiting self-excited vibrations which up to this day cannot be completely avoided, such as brake squeal, the galloping vibrations of overhead transmission lines, the ground resonance in helicopters and others. These systems have in common that in the linearized equations of motion the self-excitation terms are given by nonconservative, circulatory forces. It has been well known for some time, that such systems are very sensitive to damping. Recently, several new theorems concerning the effect of damping on the stability and on the self-excited vibrations were proved by some of the authors. The present paper discusses these new mathematical results for practical mechanical engineering systems. It turns out that the structure of the damping matrix is of utmost importance, and the common assumption, namely, representing the damping matrix as a linear combination of the mass and the stiffness matrices, may give completely misleading results for the problem of instability and the onset of self-excited vibrations. The authors give some indications on improving the description of the damping matrix in the linearized problems, in order to enhance the modeling of the self-excited vibrations. The improved models should lead to a better understanding of these unwanted phenomena and possibly also to designs oriented toward their avoidance.

Dynamic Behavior of Unbalanced Rigid Shaft Supported on Turbulent Journal Bearings—Theory and Experiment

1990 ◽  
Vol 112 (2) ◽  
pp. 404-408 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Experimental Results ◽  
Fluid Film ◽  
Force Components ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Analytical Expressions

In this paper, the combined effects of turbulence and fluid film inertia on the dynamic behavior of an unbalanced rigid shaft supported horizontally on two identical aligned short journal bearings are investigated theoretically and experimentally. Utilizing analytical expressions for the dynamic fluid film force components considering the effects of turbulence and fluid film inertia, the nonlinear equations of motion for the rotor-bearing systems are solved by the improved Euler’s forward integration method. The journal center trajectories with unbalance eccentricity ratio of εμ = 0, 0.1 and 0.2 are examined theoretically for Reynolds number of Re = 2750, 4580, and 5500, and the theoretical results are compared with experimental results. From the theoretical and experimental results, it was found that the fluid film inertia improves the stability of unbalanced rigid shaft under certain operating conditions.

Analytical and Experimental Analysis of a Self-Compensating Dynamic Balancer in a Rotating Mechanism

1996 ◽  
Vol 118 (3) ◽  
pp. 468-475 ◽  
Author(s):  
Jongkil Lee ◽  
W. K. Van Moorhem
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Circular Disk ◽  
Experimental Results ◽  
Normal Operation ◽  
Rotating System ◽  
Balance System ◽  
Rotor Imbalance ◽  
Low Viscosity ◽  
The Stability

A theoretical and experimental approach was used to investigate the motion and effectiveness of a Self-Compensating Dynamic Balancer (SCDB). This is a device intended to minimize the effects of rotor imbalance and vibratory forces on a rotating system during normal operation. The basic concept of an automatic dynamic balancer has been described in many U.S. patents. The SCDB is composed of a circular disk with a groove containing massive balls and a low viscosity damping fluid. The objective of this research is to determine the motion of the balls and how this ball motion is related to the vibration of the rotating system using both theoretical and experimental methods. The equations of motion the balls were derived by the Lagrangian method. Static and dynamic solutions were derived from the analytic model. To consider dynamic stability of the motion, perturbation equations were investigated by two different methods: Floquet theory and direct computer simulation. On the basis of the results of the stability investigation, ball positions which result in a balance system are stable above the critical speed and unstable at critical speed and below critical speed. To determine the actual critical speed of the rotating system used in the experimental work, a modal analysis was conducted. Experimental results confirm the predicted ball positions. Based on the theoretical and experimental results, when the system operates below and near the first critical speed, the balls do not balance the system. However, when the system operates above the first critical speed the balls can balance the system.

ON THE EXISTENCE OF A STABLE PERIODIC SOLUTION OF AN IMPACTING OSCILLATOR WITH TWO FENDERS

2004 ◽  
Vol 14 (09) ◽  
pp. 3115-3134 ◽  
Author(s):  
KRZYSZTOF CZOLCZYNSKI ◽  
TOMASZ KAPITANIAK
Keyword(s):  
Periodic Solution ◽  
Equations Of Motion ◽  
Analytical Determination ◽  
Stable Periodic Solution ◽  
Numerical Investigations ◽  
Stable Periodic ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Damped Oscillator

A system that consists of a damped oscillator impacting two immovable fenders has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable.

Influence of Multiphysical Effects on the Dynamics of the High Speed Mini Rotors—Part II: Results

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Emre Dikmen ◽  
Peter J. M. van der Hoogt ◽  
André de Boer ◽  
Ronald G. K. M. Aarts
Keyword(s):  
Modal Analysis ◽  
Dynamic Behavior ◽  
High Speed ◽  
Structural Model ◽  
Natural Frequencies ◽  
Experimental Setup ◽  
Flexible Supports ◽  
The Stability ◽  
Surrounding Fluid ◽  
Theoretical Results

In Part I of this work, a theoretical analysis showed that the surrounding air in the closed confinement between rotor and casing has a significant effect on the dynamic behavior of high speed minirotors. In order to validate the developed theoretical model, an experimental setup is designed and the dynamic behavior of the rotor with medium gap confinement is studied. The experimental setup has flexible supports, which consist of beams with adjustable length. The support stiffness is changed by altering the beam length. Modal analysis of the rotor is done in free-free conditions in order to test the capability of the rotordynamic model without the supports and multiphysical effects. The experimental and simulation results agree well with a difference of 1%. Then modal analysis of the whole structure is done at standstill and during operation in the absence of the casing. In this way, multiphysical effects are eliminated and only support effects on the dynamics of the structure are observed. The supports appear to have significant effect on the natural frequencies of the flexural modes of the system. Different support modeling techniques are studied and adequate equivalent models are obtained. These models are then implemented into the structural model of the rotor. Finally, multiphysical effects are tested at different speeds with different support stiffnesses. Experiments are performed with and without the casing for determining the change in the natural frequencies and onset of instability. The surrounding fluid has a significant effect on the stability of the system while the natural frequencies do not change significantly. The experimental and theoretical results are in fair agreement for predicting the natural frequencies and the onset of instability.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

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