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

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ryan J. Monroe ◽  
Steven W. Shaw ◽  
Alan H. Haddow ◽  
Bruce K. Geist
Keyword(s):  
Finite Amplitude ◽  
Tuning Parameter ◽  
System Response ◽  
Vibration Absorbers ◽  
Engine Order ◽  
Constant Rate ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Roller System ◽  
First Time ◽  
Selection Of

Centrifugal pendulum vibration absorbers are used for reducing engine-order torsional vibrations in rotating machines. The most common configuration of these devices utilizes a bifilar suspension in which the absorber mass is suspended by a pair of cylindrical rollers that allow it to move along a prescribed path that is determined by the shape of machined cutouts on the rotor and the absorber mass. Previous studies have considered how to account for the roller inertia in selecting the linear (small amplitude) tuning characteristics of the absorber system. Here, we describe a systematic study of the nonlinear (finite amplitude) aspects of this system and 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 when the rotor spins at a constant rate. 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 a method for its construction is presented. In addition, we carry out a perturbation analysis of the steady-state dynamic response of the rotor/absorber/roller system in order to quantify the effects of various approximations commonly used with regard to the roller dynamics. The results show that if one accounts for the rollers in the linear absorber tuning, the nonlinear system response is essentially insensitive to the selection of the nonlinear tuning parameter, so long as it is close to the tautochronic value.

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.

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.

Analysis and Design of Multiple Order Centrifugal Pendulum Vibration Absorbers

2012 ◽  
Author(s):  
Brendan J. Vidmar ◽  
Steven W. Shaw ◽  
Brian F. Feeny ◽  
Bruce K. Geist
Keyword(s):  
Equations Of Motion ◽  
System Response ◽  
Torsional Vibrations ◽  
Nonlinear Interactions ◽  
Vibration Absorbers ◽  
Analysis And Design ◽  
Engine Order ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
System Equations ◽  
Nonlinear Equations Of Motion

We consider nonlinear interactions in systems of order-tuned torsional vibration absorbers. These absorbers, which consist of centrifugally driven pendulums fitted to a rotor, are used to reduce engine-order torsional vibrations in rotating machines, including automotive engines, helicopter rotors, and light aircraft engines. 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, undesirable 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, we develop predictive models that allow one to select proper tuning and sizing of the absorbers. 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 for 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.

The Effects of Gravity on the Response of Centrifugal Pendulum Vibration Absorbers

2021 ◽  
pp. 1-61
Author(s):  
Darryl Tchokogoue ◽  
Ming Mu ◽  
Brian F. Feeny ◽  
Bruce K. Geist ◽  
Steven W. Shaw
Keyword(s):  
Equations Of Motion ◽  
Operating Conditions ◽  
Vibration Absorbers ◽  
Cyclic Symmetry ◽  
Passive Devices ◽  
Engine Order ◽  
Gravity Effects ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Automotive Powertrain ◽  
Linearized Model

Abstract This paper describes the effects of gravity on the response of systems of identical, cyclically arranged, centrifugal pendulum vibration absorbers (CPVAs). CPVAs are passive devices composed of movable masses suspended on a rotor, suspended such that they reduce torsional vibrations at a given engine order. These absorbers are becoming prevalent in automotive powertrain components in order to expand fuel-efficient engine operating conditions. Gravitational effects acting on the absorbers can be important for a horizontal rotor/CPVA system spinning at relatively low rotation speeds, for example, during engine idle conditions. The main goal of this investigation is to predict the response of a CPVA/rotor system in the presence of gravity. A linearized model which includes the effects of gravity and an order n torque acting on the rotor is analyzed by exploiting the cyclic symmetry of the system. The results show that the N absorbers respond in one or more groups, where the absorbers in each group respond with identical waveforms but shifted phases. The number of groups depends on the engine order n and the ratio Nn. It is shown that there are special resonant effects if the engine order is n = 1 or n = 2, the latter of which is particularly important in applications. In addition, it is shown that for N > 1 the rotor response is not affected by gravity, due to the symmetry of the gravity effects. The analytical predictions are verified by direct simulations of the equations of motion.

scholarly journals Resonance Suppression in Multi-Degree-of-Freedom Rotating Flexible Structures Using Order-Tuned Absorbers

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Serif Gozen ◽  
Brian J. Olson ◽  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Structural Model ◽  
Flexible Structures ◽  
Coupled System ◽  
Degree Of Freedom ◽  
Tuning Parameter ◽  
Vibration Absorbers ◽  
Resonance Zone ◽  
Engine Order ◽  
Rotating Structure ◽  
Structural Mode

This paper considers the dynamic response and order-tuning of vibration absorbers fitted to a rotating flexible structure under traveling wave (TW) engine order excitation. Of specific interest is the extension of previous results on the so-called no-resonance zone, that is, a region in linear tuning parameter space in which the coupled structure/absorber system does not experience resonance over all rotation speeds. The no-resonance feature was shown to exist for cyclic rotating structures with one structural and one absorber degree of freedom (DOF) per sector. This work uses a higher-fidelity structural model to investigate the effects of higher modes on the cyclically-coupled system. It is shown that the no-resonance zone is replaced by a resonance-suppression zone in which one structural mode is suppressed, but higher-order resonances still exist with the addition of the absorbers. The results are general in the sense that one vibration mode can be eliminated using a set of identically-tuned absorbers on a rotating structure with arbitrarily many DOFs per sector.

Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part II: Experimental Results

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Ryan J. Monroe ◽  
Steven W. Shaw
Keyword(s):  
Torsional Vibration ◽  
Companion Paper ◽  
Experimental Results ◽  
Circular Path ◽  
Vibration Absorbers ◽  
Automotive Engine ◽  
Engine Order ◽  
Applied Torque ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Nonlinear Transient

This paper presents results from an experimental investigation of the transient response of centrifugal pendulum vibration absorbers, including a comparison with the analytical results derived in the companion paper, Part I. The focus of the study is the overshoot experienced by pendulum-type torsional vibration absorbers when a rotor running at a constant speed is suddenly subjected to an applied fluctuating torque. The experiments are carried out using a fully instrumented spin rig controlled by a servo motor that can provide user-specified engine order disturbances, including those that simulate automotive engine environments. The absorber overshoot depends on the absorber tuning relative to the excitation order, the absorber damping, the amplitude of the applied torque, and on the system nonlinearity, which is set by the absorber path and/or kinematic coupling between the rotor and the absorber. Two types of absorbers are used in the study, a simple circular path pendulum, for which the path nonlinearity is dominant, and a nearly tautochronic path pendulum with a bifilar support, for which the path and coupling nonlinearities are both small. It is found that the experimental results agree very well with the analytical predictions from the companion paper. In addition, it is confirmed that the general path pseudoenergy prediction (which depends on a single parameter) provides a useful, conservative upper bound for most practical absorber designs, provided the absorber damping is small.

Nonlinear Dynamics of Flexible Rotating Shafts With Centrifugal Pendulum Vibration Absorbers

2015 ◽  
Author(s):  
Mustafa A. Acar ◽  
Steven W. Shaw ◽  
Brian F. Feeny
Keyword(s):  
Torsional Vibration ◽  
Perturbation Methods ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Vibration Modes ◽  
Vibration Absorbers ◽  
Engine Order ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Rotating Shafts ◽  
Practical Implications

We consider the nonlinear vibration response of rotating flexible shafts fitted with centrifugally driven pendulum vibration absorbers (CPVAs) that are used to address engine-order torsional vibrations. The model used to represent the behavior of the flexible shaft consists of two lumped inertial elements with an interconnecting stiffness element, which captures the rigid body and fundamental torsional vibration modes of the rotor. The absorbers are centrifugally driven pendulums fitted to a rotor element, such that their natural frequencies scale with the rotor speed, and can thus tuned to a given order of rotation. Previous analysis of a linearized version of this coupled rotor-absorber system revealed frequency veering behavior as the rotation speed varies, and showed that one can detune the absorber to eliminate key system resonances. In this paper the behavior of the system is analyzed for large absorber amplitudes using perturbation methods and numerical simulations. It is shown that the absorbers remain effective in reducing torsional vibration when moving through large amplitudes, and that the resonance avoidance is similarly robust. This has practical implications for the tuning of absorbers in certain applications.

Resonance Suppression in Multi-DOF Rotating Flexible Structures Using Order-Tuned Absorbers

2009 ◽  
Author(s):  
Serif Gozen ◽  
Brian J. Olson ◽  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Structural Model ◽  
Vibration Mode ◽  
Flexible Structures ◽  
Coupled System ◽  
Tuning Parameter ◽  
Vibration Absorbers ◽  
Resonance Zone ◽  
Engine Order ◽  
Rotating Structure ◽  
Structural Mode

This paper considers the dynamic response and order-tuning of vibration absorbers fitted to a rotating flexible structure under traveling wave (TW) engine order excitation. Of specific interest is the extension of previous results on the so-called no-resonance zone, that is, a region in linear tuning parameter space in which the coupled structure/absorber system does not experience resonance over all rotation speeds. The no-resonance feature was shown to exist for cyclic rotating structures with one structural and one absorber degree-of-freedom (DOF) per sector. This work uses a higher-fidelity structural model to investigate the effects of higher modes on the cyclically-coupled system. It is shown that the no-resonance zone is replaced by a resonance-suppression zone in which one structural mode is suppressed, but higher-order resonances still exist with the addition of the absorbers. The results are general, in the sense that one vibration mode can be eliminated using a set of identically-tuned absorbers on a rotating structure with arbitrarily many DOFs per sector.

Experimental Investigation of a System With Multiple Nearly Identical Centrifugal Pendulum Vibration Absorbers

2003 ◽  
Author(s):  
Tyler M. Nester ◽  
Alan G. Haddow ◽  
Steven W. Shaw
Keyword(s):  
Experimental Investigation ◽  
Theoretical Background ◽  
Experimental Results ◽  
Circular Path ◽  
Vibration Absorbers ◽  
Test Apparatus ◽  
Controlled Experiments ◽  
Theoretical Predictions ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
First Time

This paper presents experimental results from tests completed on a rotor system fitted with nearly-identical circular path centrifugal pendulum vibration absorbers. A brief review of theoretical background for the absorbers is given along with an overview of the test apparatus. The experimental results for one absorber and for four absorbers are presented and compared with theoretical predictions and expectations. To the best knowledge of the authors, this is the first time that systematic, controlled experiments that monitored both the response of the absorbers and the rotor have been undertaken.

Competition of Verb Aspects and Its Resolution as a Creative Act (Based on the Material of Aspects Variants in the Texts by F. M. Dostoevsky)

2020 ◽  
Vol 81 (2) ◽  
pp. 56-63
Author(s):  
S. A. Karpukhin
Keyword(s):  
Traditional Method ◽  
Contextual Analysis ◽  
Verb Aspect ◽  
Component Theory ◽  
Two Component ◽  
Artistic Interpretation ◽  
New Perspective ◽  
First Time ◽  
Selection Of ◽  
Aspectual Meaning

The article considers the competition of verbal aspects from a new perspective. Instead of employing the traditional method of demonstrating this phenomenon — an empirical replacement of the aspect of a verb in a phrase with the opposite — the author examines Dostoevsky’s choice between the variants found in different manuscripts of the same text. For the first time, based on a two-component theory of the semantic invariant of a verb type, the aspectual meaning of the selection of a verb aspect is revealed and, as a result of contextual analysis, an artistic interpretation of the selected type is proposed.

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