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.

Design of Pendulum Absorbers for Transverse Vibration Attenuation of Rotating Beams

1997 ◽  
Author(s):  
Yenkai Wang ◽  
Steven W. Shaw ◽  
Chang-Po Chao
Keyword(s):  
Transverse Vibration ◽  
Design Strategy ◽  
Simplified Model ◽  
Vibration Absorbers ◽  
Rotating Beam ◽  
External Excitation ◽  
Rotating Beams ◽  
Transverse Vibrations ◽  
Vibration Attenuation ◽  
Centrifugal Pendulum Vibration Absorbers

Abstract This paper considers the placement, sizing and tuning of centrifugal pendulum vibration absorbers for the reduction of transverse vibrations in rotating beams. A simplified model describing the linearized dynamics of a rotating beam with external excitation and attached absorbers is used for the analysis. A design strategy is offered wherein individual absorbers are designed to reduce vibration amplitudes and stress levels caused by troublesome resonances. It is shown that this procedure offers significant reduction in vibratory stresses, even in the case of excitations composed of multiple harmonics.

Optimal Tuning of Centrifugal Pendulum Vibration Absorbers

2013 ◽  
Author(s):  
Chengzhi Shi ◽  
Robert G. Parker ◽  
Steven W. Shaw
Keyword(s):  
Equations Of Motion ◽  
Turbine Blades ◽  
Vibration Absorbers ◽  
Wind Turbine Blades ◽  
Optimal Tuning ◽  
Translational Vibration ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Rotational Vibration ◽  
Reaction Forces ◽  
Analytical Proof

This note provides an analytical proof of the optimal tuning of centrifugal pendulum vibration absorbers (CPVAs) to reduce in-plane translational and rotational vibration for a rotor with N cyclically symmetric substructures attached to it. The reaction forces that the substructures (helicopter or wind turbine blades, for example) exert on the rotor are first analyzed. The linearized equations of motion for the vibration are then solved by a gyroscopic system modal analysis procedure. The solutions show that the rotor translational vibration at order j is reduced when one group of CPVAs is tuned to order jN − 1 and the other is tuned to order jN + 1. Derivation of this result is not available in the literature. The current derivation also yields the better known result that tuning CPVAs to order jN reduces rotational rotor vibration at order j.

Nonlinear Localization in Systems of Tautochronic Vibration Absorbers

1997 ◽  
Author(s):  
Chang-Po Chao ◽  
Steven W. Shaw
Keyword(s):  
Dynamic Instability ◽  
Vibration Absorbers ◽  
Worst Case ◽  
Nonlinear Localization ◽  
Synchronous Motion ◽  
Applied Torque ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Autonomous Differential Equations ◽  
Steady State Solutions ◽  
Angular Transformation

Abstract The system considered consists of a rigid rotor and N centrifugal pendulum vibration absorbers (CPVAs) riding on epicycloidal paths tuned to order n, the same as the dominant order of the applied torque. An investigation is carried out to determine the effects that a dynamic instability of the synchronous motion of CPVAs has on the system performance. Using various co-ordinate transformations, including a group-theory-based transformation and an angular transformation, the system dynamics are modeled by a set of 2N first-order, averaged, autonomous differential equations. A bifurcation analysis of these equations shows that in the post-bifurcation dynamic, one of the N absorbers moves out of step and at a much larger amplitude than its partners. This localized response is dynamically stable and leads to the worst-case (that is, the smallest) operating torque range of all the possible post-critical steady-state solutions. Analytical estimates of the torque range and the rotor acceleration are derived based on a truncated version of the equations, and more accurate estimates are obtained from a numerical solution of the non-truncated equations. The results are found to be very accurate when compared to numerical simulations.

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.

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 Analysis of a Torsional Vibration of a Multidegrees-of-Freedom System With Centrifugal Pendulum Vibration Absorbers and Its Suppression

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Keiyu Kadoi ◽  
Tsuyoshi Inoue ◽  
Junichi Kawano ◽  
Masahiko Kondo
Keyword(s):  
Torsional Vibration ◽  
Degrees Of Freedom ◽  
Vibration Suppression ◽  
Dynamical Characteristic ◽  
Vibration Absorbers ◽  
Multiple Modes ◽  
Suppression Effect ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Suppression Mechanism ◽  
Theoretical Analyses

Centrifugal pendulum vibration absorber (CPVA) has been used as a torsional vibration suppression device. Recently, downsizing turbotechnology is widespread and it causes a torsional vibration in the drivetrains of automobiles, and CPVA is used for torsional vibration suppression. In such cases of vibration suppression of the drive-train shaft, it should be modeled as a multi degrees-of-freedom system and considered the suppression of its multiple modes. However, most of researches on CPVA so far have focused on a one degree-of-freedom system, and the vibration analysis and its suppression of the torsional vibration caused in the multi degrees-of-freedom system has been hardly investigated. In this paper, the dynamical characteristic of torsional vibration of the multi degrees-of-freedom system with CPVAs is investigated both theoretically and experimentally. Vibration suppression mechanism of CPVA on the torsional vibration of the multi degrees-of-freedom system is studied by the eigenvalue analysis. The vibration suppression effect of CPVA on the harmonic resonances, and the occurrence of superharmonic resonances in multiple modes are observed by the numerical simulation. Then, nonlinear theoretical analyses of harmonic resonances and superharmonic resonances are performed and the vibration suppression effects of CPVA are explained. These obtained theoretical results are confirmed by experiments.

Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers

2011 ◽  
Author(s):  
Ryan J. Monroe ◽  
Steven W. Shaw
Keyword(s):  
Equations Of Motion ◽  
Torque Converter ◽  
Transient Dynamics ◽  
Circular Path ◽  
Vibration Absorbers ◽  
Approximate Analytical Expression ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Nonlinear Transient ◽  
System Equations ◽  
Minimal Mass

This paper describes an analytical and experimental investigation of the transient dynamics of centrifugal pendulum vibration absorbers, which are used for reducing torsional vibrations in rotating machines. Recently these absorbers have been proposed for use in automotive engines, to aid with fuel saving technologies such as cylinder deactivation and torque converter lockup. In order for them to operate effectively with minimal mass, they must be designed to allow for large amplitude, nonlinear responses. In this paper we consider the transient dynamics of these absorbers, focusing on the response during startup. During these transient events the absorbers experience a beating type motion, resulting in overshoot of the absorber response before reaching steady state conditions. Using a perturbation analysis of the system equations of motion, an approximate analytical expression for nonlinear overshoot is derived, relating the overshoot to the system and excitation parameters. These predictive results are derived for a general class of absorbers, and are verified by simulations of the full equations of motion and by experiments using a fully instrumented spin rig. It is found that the overshoot for absorbers with softening nonlinearity, such as circular path absorbers, can be well over the 100% upper limit for a linear absorber, and can be as high as 173%. For absorbers with tautochronic paths, the overshoot remains quite close to that of the linearized system, even for large amplitudes. These results provide a useful tool for the design of absorbers to meet transient response specifications.

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.

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.

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