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.

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.

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.

Torsional Vibration Suppression by a Centrifugal Pendulum Vibration Absorber

2005 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue ◽  
Taishi Kagawa ◽  
Motohiko Ueda
Keyword(s):  
Torsional Vibration ◽  
Large Amplitude ◽  
Vibration Suppression ◽  
Torsional Vibrations ◽  
Vibration Absorbers ◽  
Harmonic Vibrations ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Automobile Engines ◽  
Large Amplitude Vibration ◽  
Driving Torque

Driving torque of rotating machinery, such as automobile engines, changes periodically. As a result, torsional vibrations occur and cause serious noise and vibration problems. In this study, the dynamic characteristics of centrifugal pendulum vibration absorbers restraining torsional vibration is investigated both theoretically and experimentally. In the theoretical analysis, the nonlinear characteristics are taken into consideration under the assumption of large amplitude vibration of pendulum. It is clarified that the centrifugal pendulum, although it has remarkable effects on suppressing harmonic vibration, induces large amplitude harmonic vibrations, the second and third superharmonic resonances, and unstable vibrations of harmonic type. We propose various methods to suppress these secondarily induced vibration and show that it is possible to suppress torsional vibrations to substancially zero amplitude in all through the rotational speed range.

The Dynamics of a Ball-Type Balancer System Equipped with a Pair of Free-Moving Balancing Masses

2001 ◽  
Vol 123 (4) ◽  
pp. 456-465 ◽  
Author(s):  
Jaan-Rong Kang ◽  
Chang-Po Chao ◽  
Chun-Lung Huang ◽  
Cheng-Kuo Sung
Keyword(s):  
High Speed ◽  
Multiple Scales ◽  
Design Guidelines ◽  
Disk Drives ◽  
Rotating System ◽  
Radial Vibrations ◽  
First Order ◽  
System A ◽  
Autonomous Differential Equations ◽  
Steady State Solutions

This study is devoted to evaluate the performance of a ball-type balancer system that is installed in high-speed optical disk drives. The ball-type balancer system, composed of a circular runway and free-moving balls inside, is designed for reducing radial vibrations induced by the inherent unbalance of the rotating system. A balancer system equipped with a pair of balls is considered in this study for its capability to reach possible near-elimination of radial vibrations as opposed to the serious sizing problem of a single balancing-ball system. A mathematical model is first established to describe the dynamics of the balls and rotor system. Utilizing the method of multiple scales and assuming the smallness of radial vibrations, the system dynamics on the slow time scale is represented by eight first-order autonomous differential equations, which accommodate the radial vibratory motions and ball behaviors. The steady-state solutions of these slow equations are then solved and their stability analyzed to predict settling ball positions. The residual vibrations are computed to evaluate the performance of the balancer system and then the design guidelines are distilled for engineers to design the balancer system.

Nonlinear Aspects of the Performance of Centrifugal Pendulum Vibration Absorbers

1964 ◽  
Vol 86 (3) ◽  
pp. 257-263 ◽  
Author(s):  
D. E. Newland
Keyword(s):  
Torsional Vibration ◽  
Large Amplitude ◽  
Vibration Absorbers ◽  
Aircraft Engines ◽  
Reciprocating Engines ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Large Amplitude Motion

Centrifugal pendulums have been used for many years to limit the torsional vibration of reciprocating engines. Recently small pendulums, designed to swing through amplitudes of about 45 deg, have been tested for lightweight aircraft engines. These have not functioned properly, and have been found to swing through much larger angles than expected, damaging the stops limiting motion of the pendulum counterweight. This paper investigates the large-amplitude motion of centrifugal-pendulum vibration absorbers.

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.

scholarly journals Developments in the Design of Centrifugal Pendulum Vibration Absorbers

2020 ◽  
Vol 25 (2) ◽  
pp. 266-277
Author(s):  
David E. Newland
Keyword(s):  
Torsional Vibration ◽  
System Performance ◽  
Vibration Absorbers ◽  
Aircraft Engines ◽  
Current State ◽  
Practical Design ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Automobile Engines ◽  
The Subject ◽  
Design Requirements

For over 60 years, the torsional vibration of reciprocating aircraft engines has been controlled by centrifugal pendulum vibration absorbers. Loose weights attached to an engine's crankshaft act as tuned-mass absorbers by oscillating at a frequency in proportion to rotational speed. More recently, similar loose masses have been attached to the flywheels of automobile engines. The need to achieve increased power from fewer cylinders, while reducing weight and improving economy, has exacerbated torsional vibration of the drive train. The dynamics of a wheel carrying many centrifugal pendulums of bifilar design has been the subject of a growing literature, but much less has been written about roller-type pendulums and about overall system performance. This paper is a new analysis of bifilar and roller systems and their design requirements. The current state of knowledge about practical design limitations is explained and the need for further research discussed.

An Analytical Investigation of the Impact of Design Parameters on the Performance of Centrifugal Pendulum Vibration Absorbers

2019 ◽  
Author(s):  
Bahadir Sarikaya ◽  
Murat Inalpolat ◽  
Hyun Ku Lee ◽  
Moo Suk Kim
Keyword(s):  
Dynamic Model ◽  
Translational Motion ◽  
Vibration Reduction ◽  
Analytical Investigation ◽  
Design Parameters ◽  
Vibration Absorbers ◽  
Modeling Framework ◽  
Centrifugal Pendulum Vibration Absorbers ◽  
Fast Prediction ◽  
The Impact

Abstract A generalized nonlinear time-varying, planar dynamic model of bifilar centrifugal pendulum vibration absorbers (CPVA) is proposed. This dynamic model enables fast prediction of vibration reduction performance of any CPVA design considering the impact of absorber rollers, gravity, end stops and translational motion of the system. The modeling framework provides comparative, simultaneous simulation results for numerous different design possibilities, and thus can be used to optimize CPVA designs. The dynamic model is generic and can handle N individually designed absorbers on a rotor with numerous path options ranging from circular to cycloid. Absorbers can be designed to be equally or unequally spaced. In this study, first the dynamic model of the bifilar CPVAs is derived. Then, case studies are provided to showcase the capabilities of the modeling framework. Initially, maximum applicable dynamic torque to a CPVA and vibration reduction performance are investigated by considering the effect of tuning order and different absorber path options for different operating speeds. Then, impact of different modelling features on system frequency response and limit dynamic torque is investigated. Interactions between the important design parameters are highlighted. Finally, the influence of end stop positioning on the CPVA dynamic response is illustrated.

Sign in / Sign up

Export Citation Format

Share Document