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Research Papers

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

[+] Author and Article Information
Ryan J. Monroe1

Steven W. Shaw, Alan H. Haddow

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

Bruce K. Geist

Chrysler Group, LLC, Auburn Hills, MI, 48326

We have examined the motions of such rollers in an experimental rig and found that they indeed roll without slipping in all situations observed.

Note that many designs require that $ℓ>−0.5$, which according to Fig. 2 means that the roller COM is closer to the rotor center then the pendulum COM. The situation of$ℓ>−0.5$, which is the configuration shown in Fig. 2, is avoided because it can cause out-of-plane instabilities in the absorber motion unless the absorber motion is restricted.

One can also obtain the tautochrone condition by substituting Eq. (9) into Eq. (8) and realizing that tautochronic motion implies that terms proportional to $∂yp/∂s$ must vanish. The present approach, however, is cleaner in terms of keeping conditions on the tuning parameters separate.

Note that achieving a specific geometry that provides the desired value of tuning is a complicated iterative process since the shape of the cutouts, their placement, the location of the absorber COM, the roller paths, and the tuning parameters are all interdependent. This process can be automated in a computer program [12].

1

Corresponding author.

J. Vib. Acoust 133(6), 061002 (Sep 09, 2011) (10 pages) doi:10.1115/1.4003942 History: Received June 24, 2010; Revised December 14, 2010; Published September 09, 2011

## Abstract

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.

###### FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
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## Figures

Figure 1

Picture taken by Steve Shaw of a helicopter rotor with four bifilar absorbers attached (taken aboard the USS Nimitz)

Figure 2

Depiction of a bifilar roller-suspended pendulum (left) attached to a rotor, and the paths of the pendulum COM and rollers’ COM (right)

Figure 3

Influence of roller inertia on the absorber COM path, for ε=0.10 and ℓ=-0.25. (a) Five sample paths: a circle, a cycloid, and three epicycloids, for ñ=1.5. (b) Vertex curvature versus ñ for three values of roller mass.

Figure 4

A table depicting the nine roller mass cases used in the simulations shown in Figs.  56. The zero roller mass (δ=0) case (case x.1) is the same for all three Cases I–III, whereas the δ=1/4 (case x.2) and δ=1/2 (case x.3) roller mass cases will have different linear and nonlinear tuning values as shown. Therefore, seven of the nine total cases have unique pairs of linear and nonlinear tuning values, which is why only seven response curves are shown in Fig. 5 with linetypes indicated in this table.

Figure 5

Steady-state absorber response amplitude z¯ versus applied torque amplitude Γ for the three cases described in the text. The linetypes for the case I responses are indicated in the first row of Fig. 4. The linetypes for the case II responses are indicated in the second row of Fig. 4. The linetypes for the case III responses are indicated in the third row of Fig. 4. Only one response line exists for cases (x.1) because for δ=0 the linear and nonlinear tuning are equal for all three cases. The final three lines of the legend correspond to results from simulations of Eqs. 3,4. Only simulations of case I is depicted since all are very close to one another. Parameter values: ε=0.10, μ=0.30, ℓ=-0.25, and n=1.5.

Figure 6

Order n harmonic amplitude of the rotor response, |w'|n, versus applied torque amplitude Γ for case I. All absorber designs shown in the legend of Fig. 5 result in indistinguishable rotor response amplitudes, but different torque ranges. Only a simulation of the full nonlinear equations using δ=0 (cases x.1) is depicted since the other roller mass values are indistinguishable. Parameter values: ε=0.10, μ=0.30, ℓ=-0.25, and n=1.5.

Figure 7

Steady-state absorber response normalized by the applied torque amplitude Γ versus the rotor angle θ for δ=1/2 from case III (i.e., case III.3). The results demonstrate the hardening nature of the system. Parameter values: ε=0.10, μ=0.30, ℓ=-0.25, and n=1.5.

Figure 8

Steady-state rotor acceleration w' versus rotor angle θ for δ=1/2 from case III (i.e., case III.3). Note that the rotor acceleration is composed of multiple harmonics and the relative contribution of these harmonics depends on the torque amplitude. Parameter values: ε=0.10, μ=0.30, ℓ=-0.25, and n=1.5.

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