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Research Papers

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

[+] Author and Article Information
Ryan J. Monroe

Air and Missile Defense Department,
The Johns Hopkins University
Applied Physics Laboratory,
Laurel, MD 20723
e-mail: Ryan.Monroe@jhuapl.edu

Steven W. Shaw

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

As shown in the companion paper [1], the tuning order for a circular path absorber with a single point suspension is ñ/$β$; however, for convenience, here we define this quantity as given in Eq. (2).

Compared to the companion paper [1], the tuning orders here are a bit different, since the experimental absorbers used were set by hardware of the test rig rather than designed to address three-cylinder excitation.

The experimental results presented in Ref. [5] were limited in amplitude such that they match very closely those for an exact tautochronic path.

For a linear system, the percent overshoot is independent of the input amplitude.

Recall that a tautochronic path system with λe is slightly softening (ξt < 0) in the near tautochronic theory and is linear (ξc = 0) in the general path theory. For the near tautochronic theory, the level of softening increases as the excitation order n and tuning order ñ increase (see Eq. (16) in Ref. [1]).

1Address all correspondence to this author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received February 8, 2012; final manuscript received July 15, 2012; published online February 4, 2013. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 135(1), 011018 (Feb 04, 2013) (7 pages) Paper No: VIB-12-1030; doi: 10.1115/1.4007560 History: Received February 08, 2012; Revised July 15, 2012

## Abstract

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.

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## References

Monroe, R. J., and Shaw, S. W., 2013, “Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory,” ASME J. Vibr. Acoust.135(1), p. 011017.
Nester, T., Haddow, A. G., and Shaw, S. W., 2003, “Experimental Investigation of a System With Multiple Nearly Identical Centrifugal Pendulum Vibration Absorbers,” Proceedings of the ASME 19th Biennial Conference on Mechanical Vibration and Noise, Chicago, IL, September 2-6, ASME Paper No. DETC2003/VIB-48410, pp. 913–921.
Haddow, A. G., and Shaw, S. W., 2003, “Centrifugal Pendulum Vibration Absorbers: An Experimental and Theoretical Investigation,” Nonlinear Dyn., 34(3–4), pp. 293–307.
Vidmar, B. J., Feeny, B. F., Shaw, S. W., Haddow, A. G., Geist, B. K., and Verhanovitz, N. J., 2012, “The Effects of Coulomb Friction on the Performance of Centrifugal Pendulum Vibration Absorbers,” Nonlinear Dyn., 69(1–2), pp. 589–600.
Shaw, S. W., Schmitz, P. M., and Haddow, A. G., 2006, “Tautochronic Vibration Absorbers for Rotating Systems,” J. Comput. Nonlinear Dyn., 1(1), pp. 283–293.
Palmer, D., 2005, “Theoretical and Experimental Investigation Into the Transient Behavior of Centrifugal Pendulum Vibration Absorbers,” M.S. thesis, Michigan State University, East Lansing, MI.
Shaw, S. W., Orlowski, M. B., and Haddow, A. G., 2008, “Transient Dynamics of Centrifugal Pendulum Vibration Absorbers,” Proceedings of the 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, HI, February 17-22, p. 119.
Nester, T. M., Haddow, A. G., Schmitz, P. M., and Shaw, S. W., 2004, “Experimental Observations of Centrifugal Pendulum Vibration Absorbers,” 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-10) , Honolulu, HI, March 7-11, Paper No. ISROMAC10-2004-043.
Schmitz, P. M., 2003, “Experimental Investigation Into Epicycloidal Centrifugal Pendulum Vibration Absorbers,” M.S. thesis, Michigan State University, East Lansing, MI.
Shaw, S. W., 2007, “Engine Excitation Harmonics and Applications to MDS Transitions,” Michigan State University, Report No. 2007H.
Taylor, B. N., and Kuyatt, C. E., 1994, “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results,” National Institute of Standards and Technology (NIST) Technical Note No. 1297.
Shaw, S. W., and Geist, B. K., 2010, “Tuning for Performance and Stability in Systems of Nearly Tautochronic Torsional Vibration Absorbers,” ASME J. Vibr. Acoust., 132(4), p. 041005.

## Figures

Fig. 3

An experimentally simulated cylinder deactivation event showing the torque input and the resulting transient absorber response. (a) Input torque applied to the rotor by the servo motor; (b) absorber transient amplitude response to the input torque; (c) zoom-in of the input torque at the transition point; (d) zoom-in of the absorber response at the transition point.

Fig. 2

Absorber pendulums: (a) near tautochronic absorber (dark gray), suspended by two steel bands that wraparound cheeks, generating the desired path, shown with an encoder attached; (b) circular path absorber (inverted “T”), suspended by a pin and needle bearing, as indicated (encoder not shown)

Fig. 1

The experimental apparatus with components: (A) computer for system control and data processing, (B) motor controller, (C) servo motor, (D) rotor encoder, (E) absorber with encoder

Fig. 4

Comparison of theory and experiments for the circular path absorber, varying n and Γc. Percent overshoot versus n for (a) Γc = 0.223, (b) Γc = 0.372, and (c) Γc = 0.50. Percent overshoot versus Γc for (d) n = 1.27, (e) n = 1.28, and (f) n = 1.30.

Fig. 5

Comparison of theory and experiments for the near tautochronic path absorber, varying n and Γt. Percent overshoot versus n for (a) Γt = 0.11, (b) Γt = 0.184, and (c) Γt = 0.21. Percent overshoot versus Γt for (d) n = 1.41, (e) n = 1.43, and (f) n = 1.44.

Fig. 6

Comparisons of theory and experiments for the (a) circular path absorber and the (b) near tautochronic path absorber; percent overshoot versus χc

Fig. 7

Bounding the experimental data using simulations of the damped general path averaged equations for the (a) circular path absorber and (b) the near tautochronic path absorber; percent overshoot versus χc

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