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Research Papers

Nonlinear Frequency Response Analysis of a Multistage Clutch Damper With Multiple Nonlinearities

[+] Author and Article Information
Jong-Yun Yoon

School of Mechanical and
Automotive Engineering,
Kyungil University,
33 Buho-ri, Hayang-eup, Gyeongsan-si,
Gyeongsangbuk-do 712-701, Korea
e-mail: yoon3932@kiu.kr

Hwan-Sik Yoon

Department of Mechanical Engineering,
The University of Alabama,
P.O. Box 870276,
Tuscaloosa, AL 35487
e-mail: hyoon@eng.ua.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 10, 2013; final manuscript received November 12, 2013; published online February 13, 2014. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 9(3), 031007 (Feb 13, 2014) (10 pages) Paper No: CND-13-1178; doi: 10.1115/1.4026036 History: Received July 10, 2013; Revised November 12, 2013

This paper presents the nonlinear frequency response of a multistage clutch damper system in the framework of the harmonic balance method. For the numerical analysis, a multistage clutch damper with multiple nonlinearities is modeled as a single degree-of-freedom torsional system subjected to sinusoidal excitations. The nonlinearities include piecewise-linear stiffness, hysteresis, and preload all with asymmetric transition angles. Then, the nonlinear frequency response of the system is numerically obtained by applying the Newton–Raphson method to a system equation formulated by using the harmonic balance method. The resulting nonlinear frequency response is then compared with that obtained by direct numerical simulation of the system in the time domain. Using the simulation results, the stability characteristics and existence of quasi-harmonic response of the system are investigated. Also, the effect of stiffness values on the dynamic performance of the system is examined.

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Figures

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Fig. 1

Multistage clutch damper system model: (a) A single DOF nonlinear torsional system model and (b) piecewise-linear clutch torque profile [2-4]

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Fig. 2

Torque profile due to nonlinear stiffness of a multistage clutch damper [2]: (a) Experimentally measured clutch torque; (b) clutch torque induced by piecewise-linear stiffness with asymmetric transition angles; (c) clutch torque induced by hysteresis with asymmetric transition angles; and (d) clutch torque induced by preload

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Fig. 4

Linear and nonlinear frequency responses. Key: red •, HBM with Nmax = 12 and ρ = 2 (stable solution); blue + , HBM with Nmax = 12 and ρ = 2 (unstable solution); and black dashed line, linear analysis.

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Fig. 8

Comparison of system responses obtained by HBM (Nmax = 12 and ρ = 2) and NS in phase planes: (a) System responses at 14.7 Hz and (b) system responses at 18.8 Hz. Key: red •, HBM; blue solid line, NS.

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Fig. 9

Comparison of frequency responses obtained by HBM (Nmax = 12 and ρ = 2) and NS: (a) Maximum, mean, and minimum values of θf(t) during frequency up- and down-sweeping and (b) dynamic behaviors at jumping area and quasi-periodic regimes. Key: black solid line, HBM; red circle, NS with frequency up-sweeping; blue +, NS with frequency down-sweeping.

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Fig. 10

Effect of stiffness values KC3 and KC4 on the multistage clutch damper: (a) Effect of KC3 and (b) effect of KC4. Key: black dotted line, 0.5 × KC3 (or 0.5 × KC4); red dashed line, 0.8 × KC3 (or 0.8 × KC4); blue solid line, KC3 (or KC4); green dotted-dashed line, 1.2 × KC3 (or 1.2 × KC4).

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Fig. 3

Up and down frequency sweeping processes

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Fig. 6

Effect of damping ratio on the HBM results with Nmax = 12 and ρ = 2: (a) θrms with respect to ω¯ and (b) zoomed-in view of the superharmonic regime. Key: black dotted line, ζ = 0.02; red dashed line, ζ = 0.03; and blue solid line, ζ = 0.05.

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Fig. 7

Time responses obtained by HBM (Nmax = 12 and ρ = 2) and NS at different excitation frequencies: (a) Time responses at 14.7 Hz and (b) time responses at 18.8 Hz. Key: red circle, HBM; blue solid line, NS.

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Fig. 5

Comparison of the HBM results using different numbers of harmonic terms: (a) Comparison of maximum, mean, and minimum values of θf(t) during frequency up-sweeping and (b) zoomed-in views of superharmonic regimes. Key: black dashed line, Nmax = 1 and ρ = 1; red dotted line, Nmax = 3 and ρ = 1; and blue solid line, Nmax = 12 and ρ = 2.

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