Chaotic Vibration in Aircraft Braking Systems

1995 ◽  
Author(s):  
M. Akif Özbek ◽  
Steve Y. Liu ◽  
James T. Gordon ◽  
David S. Newman ◽  
Ali R. Atilgan
Keyword(s):  
Time Delay ◽  
Singular System ◽  
High Amplitude ◽  
Vibration Modes ◽  
Chaotic Vibration ◽  
Chaotic Region ◽  
Wide Range ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Model Equations

Abstract Typical vibration modes of aircraft braking systems are discussed in this paper. Special attention is given to squeal vibrations of carbon brakes. From flight tests, a wide range of response amplitudes are analyzed to determine the nature of the motion. Fourier analysis indicates the presence of a high amplitude limit cycle which seems to be initiated by a transient chaotic region. A singular system approach based on a time delay embedding confirms this finding. Time delay analysis makes it possible to contruct model equations via which intrinsic dynamics of the system can be recovered, and opens up the possibility of preventing large amplitude vibration by controlling the chaotic motion.

Synchronous whirl mode maps for rotor vibration with stator interaction across clearance annuli in multiple planes

2012 ◽  
Vol 227 (2) ◽  
pp. 261-275 ◽  
Author(s):  
Matthew OT Cole ◽  
Theeraphong Wongratanaphisan
Keyword(s):  
Rotational Symmetry ◽  
High Amplitude ◽  
Current Theory ◽  
Magnetic Bearing ◽  
Rotor Vibration ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Auxiliary Bearing ◽  
Stiffness Characteristics ◽  
Model Equations

For rotating machines having rotor–stator structures with non-linear stiffness characteristics or finite clearances between rotor and stator parts, there can be a multiplicity of possible vibration behaviours for any given operating speed. When the dynamic characteristics of the machine structure possess rotational symmetry, possible vibration modes arising due to unbalance can be calculated exactly from the frequency response of the structure. This study extends current theory by considering systems for which rotor–stator contact interaction may occur in multiple transverse planes. Damping and friction effects arising from contact mechanics are also accounted for. The model equations can be used to compute a complete set of vibration solutions involving circular whirl and thereby establish parametric regions where a low amplitude whirl can transgress to a high amplitude one with rotor–stator contact in one or more planes. Experimentally identified whirl modes for a flexible rotor system interacting with two clearance bearings show a good correlation with the theoretical predictions and thus indicate the suitability of the approach as a tool for prediction and design. The results are pertinent to the design of magnetic bearing and auxiliary bearing systems but are also relevant to a wide range of machines where rotor vibration may exceed clearance limits or boundaries of linearity.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

The structure of weakly compressible grid-generated turbulence

2001 ◽  
Vol 432 ◽  
pp. 219-283 ◽  
Author(s):  
G. BRIASSULIS ◽  
J. H. AGUI ◽  
Y. ANDREOPOULOS
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
High Amplitude ◽  
Time Dependent ◽  
Wide Range ◽  
Dynamical Flow ◽  
Set Up ◽  
Decay Exponent

A decaying compressible nearly homogeneous and nearly isotropic grid-generated turbulent flow has been set up in a large scale shock tube research facility. Experiments have been performed using instrumentation with spatial resolution of the order of 7 to 26 Kolmogorov viscous length scales. A variety of turbulence-generating grids provided a wide range of turbulence scales with bulk flow Mach numbers ranging from 0.3 to 0.6 and turbulent Reynolds numbers up to 700. The decay of Mach number fluctuations was found to follow a power law similar to that describing the decay of incompressible isotropic turbulence. It was also found that the decay coefficient and the decay exponent decrease with increasing Mach number while the virtual origin increases with increasing Mach number. A possible mechanism responsible for these effects appears to be the inherently low growth rate of compressible shear layers emanating from the cylindrical rods of the grid. Measurements of the time-dependent, three dimensional vorticity vectors were attempted for the first time with a 12-wire miniature probe. This also allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. It was found that the fluctuations of these quantities increase with increasing mean Mach number of the flow. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause.

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