A New Class of Asynchronous Rotordynamic Response in High-Speed Rotors

2007 ◽  
Author(s):  
Fredric F. Ehrich
Keyword(s):  
High Speed ◽  
Critical Frequency ◽  
Piecewise Linear ◽  
Dominant Frequency ◽  
Data Points ◽  
Subharmonic Response ◽  
Single Mass ◽  
Similar Appearance ◽  
The Individual ◽  
Representative Points

Virtually all of the nonlinear rotordynamic phenomena studied in the past result in excitation of rotor response at a dominant frequency at or near the critical frequency at rotational speeds other than the critical speed. In experimental work on a “macro-rig” of a micro-rotor in development some years ago at the Gas Turbine Laboratory of MIT, an unforeseen array of asynchronous response frequencies at other than the critical were noted when the rotor was operated at both subcritical and supercritical speeds. However, those responses were not explored in detail at the time. The patterned responses were apparently related to subharmonic and ultra-subharmonic response, but at frequencies lower than the critical frequency. More recently, the author noted a similar pattern of rotordynamic response in the course of operation at subcritical of an experimental turbomachinery component which was experiencing a local rub between the rotor and stator of an interstage seal. Data from that incident revealed a pattern of asynchronous response that had a very similar appearance to the earlier observation. Using a simple numerical model of a rotor employing a single mass mounted on a massless shaft and a piecewise linear (that is, a bilinear) bearing support stiffness to represent the system, it was possible to replicate the response at individual representative points over a range of sub-, trans-, and supercritical high-speed rotor operation. A generalized expression was derived inductively to represent the individual data points. The resultant pattern of data replicated the patterns of data from the two test vehicles which originally inspired the investigation and suggested the means of their suppression where their presence might be undesirable.

Fitting Functions to Data in High Dimensional Design Space

1999 ◽  
Author(s):  
Xiaoou Wang ◽  
Yingying Liu ◽  
Erik K. Antonsson
Keyword(s):  
Piecewise Linear ◽  
Region Of Interest ◽  
Multivariate Adaptive Regression Splines ◽  
High Dimensional ◽  
Linear Quadratic ◽  
Data Set ◽  
Data Points ◽  
Adaptive Regression ◽  
Representative Points ◽  
Adaptive Regression Splines

Abstract One approach to rapidly exploring large design spaces is to evaluate the performance of a small number of representative points in the space, then based on those points, construct an approximation to the response over a region of interest. Linear, piecewise linear, quadratic and multivariate adaptive regression splines (MARS) models are fit to an example 5-dimensional data set representative of information available in preliminary engineering design. When the number of data points representing a high-dimensional response is small, all of the approximation models appear to perform nearly equally.

Spontaneous Sidebanding at Subharmonic Peaks of Rotordynamic Nonlinear Response

1997 ◽  
Author(s):  
Fredric Ehrich ◽  
Marc Berthillier
Keyword(s):  
Natural Frequency ◽  
Rotational Speed ◽  
High Speed ◽  
Nonlinear Response ◽  
Dominant Frequency ◽  
Critical Set ◽  
Whole Number ◽  
Subharmonic Response ◽  
Intermittent Contact ◽  
Response Peak

Abstract One of the authors has shown in previous papers (Enrich, 1995; Ehrich, 1996) that, when high speed rotors are operated in the transcritical range with the rotor located eccentrically in its rotor/stator clearance with the rotor in intermittent contact with the stator, a nonlinear response, at speeds both slightly above and slightly below the critical speed, is induced. The response at a particular speed will include significant components at an asynchronous frequency which is approximately equal to the natural frequency of the system. In particular, when the speed (normalized by the natural frequency) S is approximately (J+1)/J, the dominant frequency (normalized by the natural frequency) F is precisely J/(J+1) times S or approximately 1 (where values of the whole number J < 1 give the subcritical set of speeds and values J > 1 give the supercritical set of speeds). The phenomenon has been termed spontaneous sidebanding. Observations of similar asynchronous responses noted in a Campbell diagram of the rotordynamic response of an actual high speed rotor clustered around a subharmonic response peak at a rotational speed twice the natural frequency suggest that the phenomenon is also possible at any subharmonic pseudo-critical response peak. In this more general case, we would expect that at rotational speeds in the vicinity of the M th subharmonic pseudo-critical normalized speed where S is approximately (MJ+1)/J and the dominant normalized frequency F is precisely J/(MJ+1) times S or approximately 1 [where values of the whole number J < 1 give the sub(pseudo)critical set of speeds and values J > 1 give the super(pseudo)critical set of speeds]. A simple numerical model of the nonlinear system verifies that these asynchronous responses are indeed possible. Operation of the model at a rotational speed approximately double the natural frequency yields data which closely reproduce the asynchronous response seen in the actual machine.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics

1991 ◽  
Vol 113 (1) ◽  
pp. 50-57 ◽  
Author(s):  
F. F. Ehrich
Keyword(s):  
Numerical Model ◽  
High Speed ◽  
Chaotic Behavior ◽  
Narrow Region ◽  
System A ◽  
Vibratory Response ◽  
Local Contact ◽  
Jeffcott Rotor ◽  
Subharmonic Response ◽  
Static Part

Subharmonic response in rotordynamics may be encountered when a rotor is operated with its rotational centerline eccentric to that of a close clearance static part, so that local contact can take place during each orbit when the rotor is excited by residual unbalance. The rotor will tend to bounce at or near its fundamental frequency when the rotor is operated at or near a speed which is a whole number [n] times that frequency. Using a simple numerical model of a Jeffcott rotor mounted on a nonlinear spring, it is found that the vibratory response in the transition zone midway between adjacent zones of subharmonic response has all the characteristics of chaotic behavior. The transition from subharmonic to chaotic response has a complex substructure which involves a sequence of bifurcations of the orbit with variations in speed. This class of rotordynamic behavior was confirmed and illustrated by experimental observations of the vibratory response of a high-speed turbomachine, operating at a speed between 8 and 9 times its fundamental rotor frequency when in local contact across a clearance in the support system. A narrow region between zones of 8th order and 9th order subharmonic response was identified where the response had all the characteristics of the chaotic motion identified in the numerical model.

The biological basis of aptitude: the endurance runner

1981 ◽  
Vol 13 (S7) ◽  
pp. 103-112 ◽  
Author(s):  
Clyde Williams
Keyword(s):  
Oxygen Transport ◽  
High Speed ◽  
Endurance Athlete ◽  
Endurance Athletes ◽  
High Rate ◽  
Type I ◽  
Carbon Dioxide Elimination ◽  
Endurance Runner ◽  
Genetic Endowment ◽  
The Individual

SummaryAptitude for a particular sport is governed by many factors, not least of which are obvious environmental influences. There are, however, individuals who, through genetic endowment, have the necessary biological characteristics which identify them as potentially elite athletes. These characteristics have been described more fully for endurance athletes because prolonged, almost steady-state running, lends itself more readily to investigation by biologists, than do the more complex sports.These studies show that the potentially elite endurance athlete is an individual endowed with an above average cardio-respiratory system, capable of a high rate of oxygen transport and carbon dioxide elimination. Not only does the elite endurance athlete have a greater rate of oxygen transport than the average sportsman or sportswoman, but the muscles receiving the oxygen are composed mainly of type I, i.e. low-twitch oxidative fibres, which are designed for endurance exercise. Furthermore, the elite endurance athlete also appears to be pre-programmed genetically to lay down less fat, in the form of sub-cutaneous adipose tissue, than the average sportsman or sportswoman of the same age and sex.Although genetic endowment dictates the potential ability of an individual for sustained high speed running, only appropriate training will allow the realization of this potential and so enable the individual to join the fraternity of the world's elite endurance athletes.

THE PROBLEM OF MORAL EDUCATION OF THE INDIVIDUAL IN THE CONDITIONS OF MODERN RUSSIA

2020 ◽  
Vol 10 (6) ◽  
pp. 114-123
Author(s):  
ALEXANDER OZEROV ◽  
◽  
Keyword(s):  
Moral Education ◽  
High Speed ◽  
Digital Technologies ◽  
Sociological Research ◽  
Russian Society ◽  
Social Changes ◽  
Life Attitudes ◽  
Patriotic Education ◽  
Systemic Crisis ◽  
The Individual

The article is devoted to the problem of spiritual and moral education of personality in the conditions of modern Russia. Some aspects of the existing meaning of life attitudes, spiritual and moral characteristics of society are considered, ways of solving problems of a legal and moral nature in conditions of social changes are proposed. Particular attention is paid to examining the relationship between morality, law and patriotism in the system of personal perception. In modern conditions, great attention must be paid to monitoring the spiritual and moral characteristics of Russian society, its moral and ethical state. Specific data from such studies will make it possible to draw a conclusion taking into account specific territories, forming a visual “matrix” with territories where improvements are needed in relation to spiritual and moral values. The results of sociological research will help to see exactly where such work is needed. This is especially true of patriotic education, forms and methods, according to which it is recommended to carry out this kind of activity. In the process of creating methods, it is necessary to abandon the experience of building patriotism based on ineffective measures, without taking into account the historical specifics and specific statistics. It is important to take into account the situation on the ground, public opinion, the presence or absence of a systemic crisis, the situation in the field of human rights. In addition, it would be very useful to create patriotic applications on smartphones, where it would be possible, in a game or other form of active interaction, to gain knowledge about Russian history, heroic deeds of the past, and about the prospects for people with developed moral and ethical qualities. Outside of the separation from digital technologies, it is possible to give meaning to life not only to young people, but also to those who are already of age, by teaching them how to use the latest digital technologies and take advantage of high-speed Internet. It is necessary to create a complex toolkit, which would take into account all aspects of the conditions and circumstances under which effective and comprehensive patriotic and spiritual and moral education is possible.

Measuring Agreement Among Ranks

2016 ◽  
Vol 7 (1) ◽  
pp. 45-62 ◽  
Author(s):  
Kathleen Campbell Garwood ◽  
Alicia Graziosi Strandberg
Keyword(s):  
Specific Pattern ◽  
Comparison Methods ◽  
The People ◽  
Data Points ◽  
Good For ◽  
The Individual ◽  
Measuring Agreement ◽  
Different Sources ◽  
Kendall’S W

Is it possible to compare rankings from different sources when the individual rankings of the top x elements differ? To investigate this question, 2015 sustainable rankings from 4 sources that have ranked the top globally most sustainable corporations are considered (Corporate Knights, Fortune's World's Most Admired Companies, Newsweek's Green Rankings, and Harris). These rankings are analyzed using common rank comparison methods (Spearman's ?, Kendall's t). Then, they are analyzed to see if the sources ranking the data are doing so at random or if there is a specific pattern of agreement (Kendall's W and a method by Alvo, Cabilio & Feigin (1982)). The insights from these methods as well as possible limitations are considered. A truly sustainable corporation would transcend all definitions and be good for the environment and the people relying on the company. This paper will attempt to identify data points that tend to cluster close together in one or more groups, thereby justifying the feasibility of identifying sets of companies that are truly the “most” sustainable.

PL Link Isotopy, Essential Knotting and Quotients of Polynomials

1991 ◽  
Vol 34 (4) ◽  
pp. 536-541 ◽  
Author(s):  
Dale Rolfsen
Keyword(s):  
Knot Theory ◽  
Piecewise Linear ◽  
Rational Functions ◽  
Isotopy Class ◽  
Link Invariants ◽  
Link Theory ◽  
The Individual

AbstractPiecewise-linear (nonambient) isotopy of classical links may be regarded as link theory modulo knot theory. This note considers an adaptation of new (and old) polynomial link invariants to this theory, obtained simply by dividing a link's polynomial by the polynomials of the individual components. The resulting rational functions are effective in distinguishing isotopy classes of links, and in demonstrating that certain links are essentially knotted in the sense that every link in its isotopy class has a knotted component. We also establish geometric criteria for essential knotting of links.

The local extinction and the nonlinear behaviors of a premixed methane/air flame under low-frequency acoustic excitation

2020 ◽  
Vol 34 (13) ◽  
pp. 2050138 ◽  
Author(s):  
Yongchao Sun ◽  
Mingbo Sun ◽  
Jiajian Zhu ◽  
Yang Xie ◽  
Hongbo Wang ◽  
...  
Keyword(s):  
High Speed ◽  
Excitation Frequency ◽  
Dominant Frequency ◽  
Local Extinction ◽  
Acoustic Excitation ◽  
Flame Extinction ◽  
Buoyant Force ◽  
Hot Gas ◽  
Nature Frequency ◽  
Production Zone

The local extinction and the nonlinear behavior of a premixed methane/air flame under acoustic excitation are investigated experimentally. High-speed photography and high-speed schlieren imaging are used to investigate the oscillation characteristics of the premixed methane/air flame. The flame structure shows a periodic fluctuation when the acoustic excitation is performed to the flame. The local flame extinction can be observed during the flame evolution process. During the local flame extinction process, the flame is found to be cut into two components, then the downstream one extinguishes shortly. The Particle Image Velocimetry (PIV) results suggest that the lower velocity at the separation point is one of the reasons for the flame local extinction. The flame without the acoustic excitation oscillates with a dominant frequency of 18 Hz, which is shown by the schlieren images to be related to the evolution of the hot gas around the flame driven by the buoyant force. When the acoustic excitation frequency is 100 Hz, the structure of the hot gas is destroyed, meanwhile the amplitude of the nature frequency decreases significantly. The hot gas structure appears regularly with the increasing excitation frequency. As a result, the amplitude of the nature frequency also increases gradually. Proper Orthogonal Decomposition (POD) analysis shows that the dominant frequency of the flame without the acoustic excitation is mainly caused by the evolution of the production zone of the flame and the fluctuation of the flame tip. The evolution of the production zone is driven by the buoyant force, which indicates that the result from POD method is consistent with the conclusion obtained from the high-speed schlieren images. Two dominant modes are obtained when the excitation frequencies are 100 and 200 Hz. The two modes are mainly caused by the process of the local flame extinction and the increasing flame length.

scholarly journals Using Artificial Neural Networks for Equalizing Time Series Considering Seasonal Fluctuations

2019 ◽  
Vol 71 ◽  
pp. 01003
Author(s):  
J. Vrbka ◽  
J. Horák ◽  
V. Machová
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Artificial Neural Networks ◽  
Seasonal Fluctuations ◽  
Republic Of China ◽  
The People ◽  
Data Points ◽  
Artificial Neural ◽  
The Individual

The objective of this contribution is to prepare a methodology of using artificial neural networks for equalizing time series when considering seasonal fluctuations on the example of the Czech Republic import from the People´s Republic of China. If we focus on the relation of neural networks and time series, it is possible to state that both the purpose of time series themselves and the nature of all the data are what matters. The purpose of neural networks is to record the process of time series and to forecast individual data points in the best possible way. From the discussion part it follows that adding other variables significantly improves the quality of the equalized time series. Not only the performance of the networks is very high, but the individual MLP networks are also able to capture the seasonal fluctuations in the development of the monitored variable, which is the CR import from the PRC.

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