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Research Papers

Vibration Modes and Natural Frequency Veering in Three-Dimensional, Cyclically Symmetric Centrifugal Pendulum Vibration Absorber Systems

[+] Author and Article Information
Chengzhi Shi

Graduate Student
University of Michigan-Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China

Robert G. Parker

L. S. Randolph Professor and Head
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: r.parker@vt.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 13, 2013; final manuscript received October 8, 2013; published online November 13, 2013. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 136(1), 011014 (Nov 13, 2013) (11 pages) Paper No: VIB-13-1159; doi: 10.1115/1.4025678 History: Received May 13, 2013; Revised October 08, 2013

This paper investigates the vibration mode structure of three-dimensional, cyclically symmetric centrifugal pendulum vibration absorber (CPVA) systems. The rotor in the system has two translational, one rotational, and two tilting degrees of freedom. The equations of motion for the three-dimensional model, including the rotor tilting, are derived to study the modes analytically and numerically. Only three mode types exist: rotational, translational-tilting, and absorber modes. The rotational and absorber modes have identical properties to those of in-plane models. Only the translational-tilting modes contain rotor tilting. The veering/crossing behavior between the eigenvalue loci is derived analytically.

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Figures

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Fig. 1

Bases and coordinates used in the three-dimensional, cyclically symmetric CPVA system. COM denotes the rotor-shaft center of mass.

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Fig. 2

Structured vibration modes of three-dimensional CPVA system with six equally spaced, identical absorbers and the system parameters given in Table 1. The horizontal axis labels denote the system degrees of freedom. The modes are normalized such that ψ¯TCψ=1, where ψ and C are defined in a later section.

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Fig. 3

Eigenvalues of three-dimensional CPVA system with six equally spaced, identical absorbers and the system parameters given in Table 1 for varying rotor speed. Rotational modes are shown by solid (blue) lines, translational-tilting modes are shown by dashed (red) lines, and absorber modes are shown by dotted (black) lines. The inset figures zoom in on the highlighted regions A, B, C, and D.

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Fig. 4

Translational-tilting mode eigenvalues of three three-dimensional CPVA systems for varying rotor speed. Each system has six equally spaced, identical absorbers, and the system parameters are given in Table 1, except for the tuning order n and distance between the rotor-shaft center of mass and rotor plane L. The translational-tilting mode eigenvalue loci of the systems with (a) n=2, L=0.5m, (b) n=2, L=0.8m, and (c) n=0.8, L=0.5m are shown by dashed (red), solid (blue), and dotted (black) lines, respectively.

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