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 Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Ryan J. Monroe ◽  
Steven W. Shaw
Keyword(s):  
Transient Response ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Torque Converter ◽  
Companion Paper ◽  
Transient Dynamics ◽  
Circular Path ◽  
Vibration Absorbers ◽  
Automotive Engines ◽  
Minimal Mass

Transient dynamics of centrifugal pendulum vibration absorbers, which are used for reducing torsional vibrations in rotating machines, are investigated using analysis and simulations of a dynamical model. These absorbers are being implemented in automotive engines to smooth vibrations and aid with fuel saving technologies, such as cylinder deactivation and torque converter lockup. In order for the absorbers to operate effectively with minimal mass, they must be designed to accommodate large amplitude, nonlinear responses, and in automotive engines they will experience a variety of transient environments. Here we consider the most severe transient environment, that of sudden activation near resonance, which leads to beating behavior of a nonlinear oscillator coupled to a driven rotor. An approximate method for predicting the percent overshoot of the beating transient response is derived, based on perturbation analysis of the system equations of motion. The main result is expressed in terms of the system and excitation parameters, and is found to accurately predict results from direct simulations of the model equations of motion. It is shown that absorbers with near-tautochronic paths behave much like linear absorbers, and when lightly damped and start from small initial conditions, they have an overshoot close to 100%. For absorbers with softening paths, such as the commonly used circular path absorbers, the overshoot can reach up to 173%, depending on system and input parameters, far exceeding predictions from linear analysis. These results provide a useful tool for design of absorbers to meet transient response specifications. In the following companion paper an experimental investigation is used to verify the analytical predictions.

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 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.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

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.

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.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1992 ◽  
Vol 114 (2) ◽  
pp. 280-283
Author(s):  
H. Ashrafiuon
Keyword(s):  
Optimal Design ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Flexible Models

This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. Optimal design parameters are computed and compared for the rigid, and flexible models of the base as well as different levels of base flexibility.

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.

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.

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