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Research Papers

Nonlinear Analysis of a Torsional Vibration of a Multidegrees-of-Freedom System With Centrifugal Pendulum Vibration Absorbers and Its Suppression

[+] Author and Article Information
Keiyu Kadoi

Department of Mechanical Science Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan

Tsuyoshi Inoue

Mem. ASME
Department of Mechanical Science Engineering,
Nagoya University,
Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan
e-mail: inoue.tsuyoshi@nagoya-u.jp

Junichi Kawano, Masahiko Kondo

Nissan Motor Co., Ltd.,
Okatsukoku 560-2,
Atsugi-shi 243-0192, Kanagawa, Japan

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 3, 2017; final manuscript received April 16, 2018; published online May 14, 2018. Assoc. Editor: John Judge.

J. Vib. Acoust 140(6), 061008 (May 14, 2018) (12 pages) Paper No: VIB-17-1044; doi: 10.1115/1.4040042 History: Received February 03, 2017; Revised April 16, 2018

Centrifugal pendulum vibration absorber (CPVA) has been used as a torsional vibration suppression device. Recently, downsizing turbotechnology is widespread and it causes a torsional vibration in the drivetrains of automobiles, and CPVA is used for torsional vibration suppression. In such cases of vibration suppression of the drive-train shaft, it should be modeled as a multi degrees-of-freedom system and considered the suppression of its multiple modes. However, most of researches on CPVA so far have focused on a one degree-of-freedom system, and the vibration analysis and its suppression of the torsional vibration caused in the multi degrees-of-freedom system has been hardly investigated. In this paper, the dynamical characteristic of torsional vibration of the multi degrees-of-freedom system with CPVAs is investigated both theoretically and experimentally. Vibration suppression mechanism of CPVA on the torsional vibration of the multi degrees-of-freedom system is studied by the eigenvalue analysis. The vibration suppression effect of CPVA on the harmonic resonances, and the occurrence of superharmonic resonances in multiple modes are observed by the numerical simulation. Then, nonlinear theoretical analyses of harmonic resonances and superharmonic resonances are performed and the vibration suppression effects of CPVA are explained. These obtained theoretical results are confirmed by experiments.

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References

Lee, C. T. , and Shaw, S. W. , 1995, “ Torsional Vibration Reduction in Internal Combustion Engines Using Centrifugal Pendulums,” ASME Design Engineering Technical Conference, Boston, MA, Sept. 17–20.
SAE, 2016, “ Vibration and Noise of Drive-Train,” Automotive Engineering Handbook, Society of Automotive Engineers of Japan, Chiyoda-Ku, Japan, pp. 464–474 (in Japanese).
Kato, J. , Isaka, K. , Ban, H. , Kudo, R. , and Kobayashi, K. , 1985, “ Development of Engine Flywheel With Torsional Damper,” Toyota Engineering, 35(1), pp. 114–119 (in Japanese).
Ito, H. , Kamei, N. , Numajiri, S. , and Kanda, K. , 2001, “ A Study on Optimum Regulation Value of Rubber Damper for Torsional Vibration of Crank Shafts,” Jpn. Soc. Des. Eng., 36(6), p. 34 (in Japanese).
Kawano, D. , 2016, “ The Environment and the Automobile Industry,” Automot. Tech., 70(8), pp. 22–23 (in Japanese).
Maeda, Y. , 2016, “ Gasoline Engines,” Automot. Tech., 70(8), pp. 96–97 (in Japanese).
Den Hartog, J. P. , 1998, Mechanical Vibrations, McGraw-Hill, New York.
Newland, D. E. , 1964, “ Nonlinear Aspects of the Performance of Centrifugal Pendulum Vibration Absorbers,” Trans. ASME, J. Eng. Ind., 86(3), pp. 257–263.
Monroe, R. J. , Shaw, S. W. , Haddow, A. H. , and Geist, B. K. , 2011, “ Accounting for Roller Dynamics in the Design of Bifilar Torsional Vibration Absorbers,” ASME J. Vib. Acoust., 133(6), p. 061002.
Chao, C. P. , Lee, C. T. , and Shaw, S. W. , 1997, “ Stability of the Unison Response for a Rotating System With Multiple Tautochronic Pendulum Vibration Absorbers,” ASME J. Appl. Mech., 64(1), pp. 149–156.
Lee, C. T. , and Shaw, S. W. , 1997, “ The Non-Linear Dynamics Response of Paired Centrifugal Pendulum Vibration Absorbers,” J. Sound Vib., 203(5), pp. 731–743.
Chao, C. P. , Lee, C. T. , and Shaw, S. W. , 1997, “ Non-Unison Dynamics of Multiple Centrifugal Pendulum Vibration Absorbers,” J. Sound Vib., 204(5), pp. 769–794.
Alsuwaiyan, A. S. , and Shaw, S. W. , 2002, “ Performance and Dynamic Stability of General-Path Centrifugal Pendulum Vibration Absorbers,” J. Sound Vib., 252(5), pp. 791–815.
Issa, J. S. , and Shaw, S. W. , 2015, “ Synchronous and Non-Synchronous Responses of Systems With Multiple Identical Nonlinear Vibration Absorbers,” J. Sound Vib., 348, pp. 105–125.
Monroe, R. J. , and Shaw, S. W. , 2013, “ Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part II: Experimental Results,” ASME J. Vib. Acoust., 135(1), p. 011018.
Vidmar, B. J. , Shaw, S. W. , Feeny, B. F. , and Geist, B. K. , 2013, “ Nonlinear Interactions in Systems of Multiple Order Centrifugal Pendulum Vibration Absorbers,” ASME J. Vib. Acoust., 135(6), p. 061012.
Ishida, Y. , Inoue, T. , Kagawa, T. , and Ueda, M. , 2008, “ Nonlinear Analysis and Experiments on Torsional Vibration of Rotor With Centrifugal Pendulum Vibration Absorber,” J. Syst. Des. Dyn., 2(3), pp. 715–726.
Ishida, Y. , Inoue, T. , Fukami, T. , and Ueda, M. , 2009, “ Torsional Vibration Suppression by Roller Type Centrifugal Vibration Absorbers,” ASME, J. Vib. Acoust., 131(5), p. 051012.

Figures

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Fig. 4

Natural frequency diagram for the system shown in Fig. 1 without CPVA. Ordinate and abscissa are dimensionless value for standard value ω̂ST. Line Ω=2ω is added.

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Fig. 3

Theoretical model of CPVA (case that multiple CPVAs are attached to rotor 2)

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Fig. 2

Natural frequencies and mode shapes of all three modes for the case without CPVA: theoretical system is shown in Fig. 1 and parameter values are shown in Table 1

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Fig. 1

Theoretical model of three degrees-of-freedom system with CPVA (case that CPVA is attached to rotor 2)

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Fig. 5

Resonance curves of amplitude of torsional vibration at rotors 2, 3, and 4 for the system shown in Fig. 1 without CPVA. Peaks p01−Ω,p02−Ω,p03−Ω show harmonic resonances of three modes.

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Fig. 6

Influence of the CPVA's mass on the resonance curves (numerical simulation using Eq. (4) with four CPVAs. m̂p is the mass of each CPVA) of torsional vibration of rotors 2, 3, 4, and CPVA for the case with CPVA. Abscissa are dimensionless value for standard value ω̂ST, and ordinate is dB value of vibration angle (rad). Dashed line designates the resonance curve for the case without CPVA (m̂p= 0 kg) as reference. Symbols ◻, ◯, and △ designate the resonance curves for the cases with each CPVA's mass are m̂p=1.97×10−2,3.85×10−2,7.70×10−2 kg, respectively. (a) Amplitude of torsional vibration θ2 at rotor 2, (b) amplitude of torsional vibration θ3 at rotor 3, (c) amplitude of torsional vibration θ4 at rotor 4, and (d) amplitude of torsional vibration φ of CPVA.

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Fig. 7

Natural frequency diagram of the system shown in Fig. 1 for the case with CPVA (unison motion)

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Fig. 8

Natural frequency diagram of the one degree-of-freedom system with CPVA (unison motion)

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Fig. 12

Influence of CPVA's mass on the resonance curves of torsional vibration of rotors 2, 3, 4, and CPVAs (unison motion). Each CPVA's mass is mp = 7.70 × 10−2 kg. (a) Resonance curve of the torsional vibration amplitude of rotor 2, (b) resonance curve of the torsional vibration amplitude of rotor 3, (c) resonance curve of the torsional vibration amplitude of rotor 4, and (d) resonance curve of the amplitude of CPVA (unison motion).

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Fig. 13

Spectrum at the resonance p3−2Ω (ω̂=115.0 rad/s, (ω=ω̂/ω̂ST=1.024)) in the case with four CPVAs

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Fig. 14

Spectrum at the resonance p2−3Ω (ω̂=52.5 rad/s, (ω=ω̂/ω̂ST=0.467)) in the case with four CPVAs

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Fig. 15

Resonance curve of the theoretical analysis for superharmonic resonance p3−2Ω (CPVA in unison motion) and comparison with the numerical simulation. Each CPVA's mass is mp = 3.85 × 10−2 kg.

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Fig. 9

Resonance curve of the theoretical analysis for harmonic resonance (CPVA in unison motion) and comparison with numerical simulation. Each CPVA's mass is mp = 3.85 × 10−2 kg.

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Fig. 10

Enlarged figure of Fig. 9 at around the resonance p1−Ω

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Fig. 11

Influence of CPVA's mass on the resonance curves of torsional vibration of rotors 2, 3, 4, and CPVAs (unison motion). Each CPVA's mass is mp = 3.85 × 10−2 kg. (a) Resonance curve of the torsional vibration amplitude of rotor 2, (b) resonance curve of the torsional vibration amplitude of rotor 3, (c) resonance curve of the torsional vibration amplitude of rotor 4, and (d) resonance curve of the amplitude of CPVA (unison motion).

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Fig. 16

Experimental system (a) whole view of experimental system and (b) CPVA part with four CPVAs

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Fig. 17

schematic of experimental system

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Fig. 18

Experimental result: resonance curve of torsional vibration at rotors 2, 3, and 4 (θ2,θ3,and θ4) for the case without CPVA (ω̂ST = 1000 rpm)

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Fig. 19

Experimental result: resonance curves of torsional vibration of rotors 2 (θ2) for the case with CPVA at rotor 2. Influence of the total mass of CPVA (ω̂ST = 1000 rpm).

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Fig. 20

Experimental result: resonance curves of torsional vibration of rotors 2 (θ2) for the case with CPVA. Influence of the position of CPVA (ω̂ST = 1000 rpm).

Tables

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