Stability of the Unison Response for a Rotating System With Multiple Tautochronic Pendulum Vibration Absorbers

1997 ◽  
Vol 64 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Chang-Po Chao ◽  
S. W. Shaw ◽  
Cheng-Tang Lee
Keyword(s):  
Equations Of Motion ◽  
Vibration Absorbers ◽  
Rotating System ◽  
Total Moment ◽  
Equivalent Viscous Damping ◽  
Future Paper ◽  
The Stability ◽  
The Individual ◽  
Special Case ◽  
Selection Of

Due to spatial and balancing considerations, the implementation of centrifugal pendulum absorbers (CPVA’s) invariably requires that the total absorber inertia be divided into several absorber masses and stationed about the center of rotation. To achieve the designed-for performance, the CPVA’s are expected to move in exact unison, since the selection of the total absorber mass is made by assuming an equivalent single absorber mass. In this paper, we determine the conditions under which the unison motion of a system of several identical CPVA’s is dynamically stable. This is done for the special case of tautochronic absorbers subjected to a purely harmonic torque. The stability criterion is obtained by an asymptotic method that exploits certain symmetries in the equations of motion and is based on the assumption that total moment of inertia of the absorbers is much smaller than that of the entire rotating system—an assumption that is almost always satisfied in practice. It is expressed in terms of a critical torque level that is proportional to the square root of the equivalent viscous damping of the individual absorbers. The result is verified by numerical simulations of the system near the critical parameter conditions. A future paper will consider the post-critical response of the system.

Incidence Stability of Space Shuttles During Re-Entry

1974 ◽  
Vol 25 (4) ◽  
pp. 266-270
Author(s):  
R Arho ◽  
S Virtanen
Keyword(s):  
Space Shuttle ◽  
Equations Of Motion ◽  
Stability Conditions ◽  
Free Oscillations ◽  
Long Period ◽  
Short Period ◽  
The Stability ◽  
Oscillation Equation ◽  
Special Case ◽  
Critical Damping

SummaryThe equations of motion of a vehicle entering the earth’s atmosphere (space shuttle) are expanded to give the incidence oscillation equation. The stability conditions for small free oscillations are deduced. These stability conditions apply equally to short-period and long-period oscillations. A special case of critical damping is investigated and more explicit stability conditions are derived for that case.

Accounting for Roller Dynamics in the Design of Bifilar Torsional Vibration Absorbers

2009 ◽  
Author(s):  
Ryan J. Monroe ◽  
Steven W. Shaw ◽  
Alan H. Haddow ◽  
Bruce K. Geist
Keyword(s):  
Equations Of Motion ◽  
Tuning Parameter ◽  
System Response ◽  
Vibration Absorbers ◽  
State Response ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
The Common ◽  
Roller System ◽  
First Time ◽  
Selection Of

Centrifugal pendulum vibration absorbers are used for reducing torsional vibrations in rotating machines. The most common configuration of these devices utilizes a bifilar suspension in which the absorber mass rides on a pair of rollers, whose mass is small compared to that of the absorber. These rollers are typically solid steel cylinders that allow the CPVAs to move along a prescribed path relative to the rotor, determined by the shape of machined cutouts on the rotor and the absorber mass. Previous studies have considered how to account for the roller dynamics in selecting the linear tuning characteristics of the absorber system, but have not quantified the errors induced by the common approximations that either ignores their effects completely, or does not account for the nonlinear aspects of their dynamics. In this paper we systematically investigate these effects. Specifically, we first show that there exists an absorber path for which the absorber/roller system maintains the same frequency of free oscillation over all physically possible amplitudes. This tautochronic path has been well known for the case with zero roller inertia, and herein, for the first time, the corresponding path with rollers is shown to exist and is constructed. In addition, we carry out an analysis of the steady-state response of the rotor/absorber/roller system in order to quantify the effects of various approximations commonly used in regards to the roller dynamics. This analysis is based on the equations of motion, scaled in such a manner so that they are amenable to a perturbation analysis, which includes the effects of rollers in the perturbation terms. It is shown that if one accounts for the linear tuning aspects of the rollers, the system response is essentially insensitive to the selection of the nonlinear tuning parameter, so long as it is close to the tautochronic value. This implies that the approximation commonly used for selecting absorber paths with rollers is adequate.

Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness

2002 ◽  
Vol 125 (1) ◽  
pp. 91-101 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Parametric Excitation ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Fourier Series Expansion ◽  
Time Varying ◽  
Algebraic Equations ◽  
Rotating System ◽  
Mathieu’S Equation ◽  
The Stability

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu’s equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant for these algebraic equations. The validity of this research is proven by comparing the stability chart with the time responses of the vibration model suggested by prior research. This research shows that the waviness in the ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 i=1,2,3,….

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.

Tuning for Performance and Stability in Systems of Nearly Tautochronic Torsional Vibration Absorbers

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Steven W. Shaw ◽  
Bruce Geist
Keyword(s):  
Torsional Vibration ◽  
Center Of Mass ◽  
Vibration Absorbers ◽  
Nonlinear Perturbations ◽  
Operating Range ◽  
The Subject ◽  
And Performance ◽  
The Stability ◽  
Stability Results ◽  
Selection Of

This paper considers the dynamic response and performance characteristics of a special class of centrifugal pendulum torsional vibration absorbers. The absorbers of interest are designed by selection of the path that their center of mass follows, such that their dynamics are linear or nearly so, out to large amplitudes of motion, thereby avoiding the nonlinear-induced detuning that typically accompanies such responses. These order-tuned, tautochronic or isochronic, absorbers have been the subject of previous investigations, including analyses of the synchronous and certain nonsynchronous responses of systems comprised of a set of identical absorbers. The analysis and experiments have demonstrated that the synchronous response of such absorber systems can experience an instability that results in nonsynchronous responses in which a subset of absorbers have significantly larger amplitude than the corresponding synchronous response. In this study, we present results that generalize these stability results to include absorbers whose dynamics differ slightly from tautochronic by varying the absorber path such that both linear and nonlinear perturbations of perfect tuning are included. It is shown by analysis and verified by simulations that the perfect tuning case is quite special, specifically that the instability described above occurs for tunings very close to ideal and that the synchronous response can be made stable over the entire feasible operating range by employing small levels of linear and/or nonlinear detuning. Such detuning is known to have the additional benefit of resulting in smaller absorber responses and an attendant larger operating range albeit at the expense of absorber performance in terms of attenuating rotor torsional vibrations. The main conclusion of these results is that one can select a very small amount of detuning to avoid this undesirable instability and that such detuning does not have a significant effect on absorber effectiveness. The analytical results derived also provide a quantitative means of predicting synchronous absorber response amplitudes and the associated rotor torsional vibration levels, as well as the stability properties of these responses, results are very useful for the design of absorber systems.

Nonlinear Interactions in Systems of Multiple Order Centrifugal Pendulum Vibration Absorbers

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Brendan J. Vidmar ◽  
Steven W. Shaw ◽  
Brian F. Feeny ◽  
Bruce K. Geist
Keyword(s):  
Equations Of Motion ◽  
System Stability ◽  
System Response ◽  
Nonlinear Interactions ◽  
Vibration Absorbers ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
System Equations ◽  
Improved Performance ◽  
Nonlinear Equations Of Motion ◽  
Selection Of

We consider nonlinear interactions in systems of order-tuned torsional vibration absorbers with sets of absorbers tuned to different orders. In all current applications, absorber systems are designed to reduce torsional vibrations at a single order. However, when two or more excitation orders are present and absorbers are introduced to address different orders, nonlinear interactions become possible under certain resonance conditions. Under these conditions, a common example of which occurs for orders n and 2n, crosstalk between the absorbers, acting through the rotor inertia, can result in instabilities that are detrimental to system response. In order to design absorber systems that avoid these interactions, and to explore possible improved performance with sets of absorbers tuned to different orders, we develop predictive models that allow one to examine the effects of absorber mass distribution and tuning. These models are based on perturbation methods applied to the system equations of motion, and they yield system response features, including absorber and rotor response amplitudes and stability, as a function of parameters of interest. The model-based analytical results are compared against numerical simulations of the complete nonlinear equations of motion, and are shown to be in good agreement. These results are useful for the selection of absorber parameters to achieve desired performance. For example, they allow for approximate closed form expressions for the ratio of absorber masses at the two orders that yield optimal performance. It is also found that utilizing multiple order absorber systems can be beneficial for system stability, even when only a single excitation order is present.

On the Effects of Imperfections and Mistuning on the Performance of Subharmonic Vibration Absorbers

1997 ◽  
Author(s):  
Chang-Po Chao ◽  
Steven W. Shaw
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Vibration Absorbers ◽  
Performance Indices ◽  
External Excitation ◽  
Rotating System ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Applicable Range ◽  
Subharmonic Vibration ◽  
Steady State Solutions

Abstract A pair of centrifugal pendulum vibration absorbers (CPVA’s) riding on half-order epicycloidal paths have recently been found to be very effective at reducing torsional vibration levels in a rotating system that is subjected to a harmonic external torque. Previous analyses of this system have assumed perfectly manufactured and exactly tuned paths for the absorber masses. The primary goal of this study is to explore the effects that manufacturing and other imperfections and intentional mistunings have on the performance of this absorber system. To this aim, the equations of motion are first derived for a simplified model. The basic system has two and a half degrees of freedom with a one-to-one internal resonance and two-to-one resonant external excitation. Utilizing the method of averaging, the steady-state solutions are obtained and used to evaluate the absorber performance via two performance indices: the rotor acceleration and the applicable range of the disturbing torque. Finally, some guidelines are provided for designers in terms of how one should choose and/or control intensional mistuning and imperfections of the absorber paths.

Implications of Person Fluctuation for the Stability and Validity of Test Scores

Methodology ◽  
2006 ◽  
Vol 2 (4) ◽  
pp. 142-148 ◽  
Author(s):  
Pere J. Ferrando
Keyword(s):  
Item Response ◽  
Test Scores ◽  
Temporal Stability ◽  
Person Fit ◽  
Item Parameters ◽  
Individual Trait ◽  
The Stability ◽  
The Individual ◽  
Different Levels ◽  
Fluctuation Model

In the IRT person-fluctuation model, the individual trait levels fluctuate within a single test administration whereas the items have fixed locations. This article studies the relations between the person and item parameters of this model and two central properties of item and test scores: temporal stability and external validity. For temporal stability, formulas are derived for predicting and interpreting item response changes in a test-retest situation on the basis of the individual fluctuations. As for validity, formulas are derived for obtaining disattenuated estimates and for predicting changes in validity in groups with different levels of fluctuation. These latter formulas are related to previous research in the person-fit domain. The results obtained and the relations discussed are illustrated with an empirical example.

Pengaruh Persepsi Kegunaan, Persepsi Kemudahan, Kecepatan, Keamanan 75 dan Kerahasiaan Serta Kesiapan Teknologi Informasi Wajib Pajak terhadap Penggunaan e-Filing Bagi Wajib Pajak Orang Pribadi Di Kota Tangerang, Kecamatan Karawaci

2016 ◽  
Vol 8 (1) ◽  
pp. 75-91 ◽  
Author(s):  
Shelby Devina ◽  
Waluyo Waluyo
Keyword(s):  
Ease Of Use ◽  
Perceived Usefulness ◽  
Security And Privacy ◽  
Primary Data ◽  
Perceived Ease Of Use ◽  
Analysis Technique ◽  
Convenience Sampling ◽  
The Individual ◽  
Tax Payers ◽  
Selection Of

The objective of this research was to examine the effect of perceived usefulness, perceived ease of use, speed, security and privacy and readiness technology tax payers information to e-Filing usage. The object of this study is the individual tax payers in Tangerang City, Karawaci District. The selection of the sample is determined based on convenience sampling method. Data used in this study was primary data, id est: questionnaires. The respondent in this study were 110. Data analysis technique in this study using multiple linear regression. The result of this study were (1) perceived usefulness have a significant impact towards e-Filing usage; (2) perceived ease of use have a significant impact towards e-Filing usage; (3) speed does not have a significant impact towards e-Filing usage; (4) security and privacy does not have a significant impact towards e-Filing usage; (5) readiness technology tax payers information does not have a significant impact towards e-Filing usage; (6) perceived usefulness, perceived ease of use, speed, security and privacy and readiness technology tax payers information all simultaneously, have a significant impact towards e-Filing usage. Keywords: e-Filing usage, perceived usefulness, perceived ease of use, readiness technology tax payers information, security and privacy.

PROBLEM ASPECTS OF THE IMPLEMENTATION OF CRIMINAL PROCEDURAL NORMS OF PROTECTION OF THE VICTIMS FROM CRIME

2020 ◽  
pp. 72-76
Author(s):  
Яна Валерьевна Самиулина
Keyword(s):  
Preventive Measure ◽  
Criminal Procedure ◽  
Legal Rights ◽  
Criminal Proceedings ◽  
Effective Mechanism ◽  
The Russian Federation ◽  
The Individual ◽  
The Right ◽  
To Receive ◽  
Selection Of

В настоящей статье предпринята попытка исследовать отдельные проблемные аспекты института потерпевшего в российском уголовном процессе. В этих целях подвергнуты анализу правовые нормы, регламентирующие его процессуальный статус. Раскрываются отдельные пробелы уголовно-процессуального законодательства в сфере защиты законных прав и интересов потерпевшего. Автор акцентирует внимание на том, что совершенствование уголовно-процессуального законодательства в части расширения правомочий потерпевшего по отстаиванию своих нарушенных преступлением прав следует продолжить. На основании проведенного исследования действующего законодательства в части регламентации прав потерпевшего от преступления предлагается расширить перечень получаемых им копий постановлений, указанных в п. 13 ч. 2 ст. 42 УПК РФ. Автор предлагает включить в перечень указанной законодательной нормы право получения потерпевшим копии постановления об избрании конкретного вида меры пресечения, избранного в отношении подозреваемого (обвиняемого). Для создания действенного механизма защиты интересов потерпевших от преступления юридических лиц предлагаем ч. 9 ст. 42 УПК РФ изложить в следующей редакции: «в случае признания потерпевшим юридического лица его процессуальное право в уголовном процессе осуществляет представляющий его профессиональный адвокат». This article attempts to investigate certain problematic aspects of the institution of the victim in the Russian criminal process. For this purpose, analyzed the individual norms governing his procedural status. Separate gaps of the criminal procedure legislation in the sphere of protection of the legal rights and interests of the victim are disclosed. The author emphasizes that the improvement of the criminal procedure legislation in terms of the extension of the victim’s authority to defend his rights violated by the crime should be continued. On the basis of the study of the current legislation regarding the regulation of the rights of the victim of a crime, it is proposed to expand the list of decisions received by him, referred to in paragraph 13, part 2 of article 42 Code of Criminal Procedure. The author proposes to include in the list of the indicated legislative norm the right to receive the victim a copy of the decision on the selection of a specific type of preventive measure, selected in relation to the suspect (accused). To create an effective mechanism for protecting the interests of legal entities victims of a crime, we offer part 9 of art. 42 of the Code of Criminal Procedure of the Russian Federation shall be reworded as follows: «if a legal entity is recognized as a victim, his procedural right in criminal proceedings is exercised by the professional lawyer representing him».

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