Research Papers

Experimental Characterizations and Estimation of the Natural Frequency of Nonlinear Rubber-Damped Torsional Vibration Absorbers

[+] Author and Article Information
Wen-Bin Shangguan, Yiming Guo, Yuming Wei

School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou 510641, China

Subhash Rakheja

School of Mechanical and
Automotive Engineering,
South China University of Technology,
Guangzhou 510641, China;
CONCAVE Research Center,
Mechanical & Industrial Engineering,
Concordia University,
Montreal, QC H4B 1R6, Canada
e-mail: 349733684@qq.com

Weidong Zhu

University of Maryland,
Baltimore County,
Baltimore, MD 21250

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 25, 2015; final manuscript received March 19, 2016; published online June 2, 2016. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 138(5), 051006 (Jun 02, 2016) (12 pages) Paper No: VIB-15-1138; doi: 10.1115/1.4033579 History: Received April 25, 2015; Revised March 19, 2016

The natural frequency of a rubber-damped torsional vibration absorber (TVA) depends on the excitation amplitudes and frequencies in a highly nonlinear manner. This is due to nonlinear shear properties of the rubber ring. In this study, the nonlinear static and dynamic shear characteristics of a rubber ring, and the natural frequency of a nonlinear TVA are experimentally characterized firstly. Since a rubber ring employed in a rubber-damped TVA is usually in the compression state, its static and dynamic shear properties depend upon the compression ratio and dimensions apart from the chemical ingredients in a highly complex manner. The prediction of the natural frequency of a rubber-ring TVA thus poses considerable complexities. In this study, a special fixture is designed and fabricated for characterizing shear properties of a rubber ring subject to different compression ratios. The shear properties are subsequently characterized using different constitutive models, and a methodology for identifying the model parameters is presented considering the measured properties. Second, a methodology for estimating the natural frequency of the TVA is proposed, and the effectiveness of the proposed method is demonstrated through comparisons of the estimated natural frequency with the measured values. The results of the study suggest that the model using fractional derivatives to characterize nonlinear shear properties of a rubber ring can be effectively used to obtain accurate estimation of natural frequency of a nonlinear TVA over a wide range of excitations. The natural frequency of a TVA can thus be accurately estimated before prototyping using the experimental and modeling methods developed in this paper.

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Fig. 1

(a) Rubber-damped TVA for an engine crankshaft and (b) fixture for measuring shear properties of a rubber specimen (1-moveable block; 2,10-clamping plates; 2,6-fastening bolts; 4,7-locking blocks; 5-intermediate block; 8-rubber specimens; 9-gaskets)

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Fig. 2

Measured characteristics of the rubber specimen under different compression ratios: (a) force–displacement (excitation amplitude: 5 mm; frequency: 0.2 Hz) and (b) dynamic stiffness (excitation amplitude: 0.1 mm)

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Fig. 3

Models for the rubber specimen (a) Kelvin–Voigt model, (b) Maxwell model, and (c) fractional derivative model

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Fig. 4

Typical force–displacement characteristics of a rubber subject to large magnitude deformation at a slow rate

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Fig. 5

Constitutive models for describing shear dynamic properties of rubbers based on: (a) Kelvin–Voigt model, (b) Maxwell model, and (c) Fractional derivative model

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Fig. 6

Deformation of the rubber specimen under a shear load

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Fig. 7

Comparison of dynamic shear stiffness obtained from the identified Kelvin–Voigt model with the measured data of the rubber specimen (compression ratio: 50%; Excitation amplitude: 0.1 mm)

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Fig. 8

Identifications of elastic stiffness ke, maximum friction force Ffmax, and displacement × 1/2 corresponding to half the maximum friction force from the measured force–displacement characteristics of the rubber specimen under 20% compression ratio

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Fig. 9

Comparisons of estimated dynamic shear stiffness of the rubber specimen with the measured data: (a) Maxwell constitutive model and (b) fractional derivative constitute model (compression ratio: 50%, excitation amplitude: 0.1 mm)

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Fig. 10

Experimental setup for measurements of frequency response function (FRF) of the rubber-damped TVA (1-excitation shaft; 2-hub; 3-inertia ring; 4,5-accelerometers)

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Fig. 11

Measured frequency response characteristics of the TVA: (a) magnitude ratio and phase responses under 0.01 deg oscillation angle amplitude and (b) magnitude ratio under different oscillation angle amplitudes

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Fig. 12

TVA model employing different models of the rubber ring: (a) Kelvin–Voigt model, (b) Maxwell model, and (c) fractional derivative model

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Fig. 13

TVA with an irregularly shaped hub (1-inertia ring; 2-rubber specimen; 3-hub)

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Fig. 14

Frequency response of the rubber-damped TVA employing Maxwell mode of the inertia ring (compression ratio: 40%; excitation amplitude: 0.01 deg)

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Fig. 15

Comparisons of natural frequencies predicted from the rubber-damped TVA models with those obtained from the measured frequency response characteristics under different excitation amplitudes



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