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Torsional vibration analysis of a planetary gear type antiresonant vibration isolator using transfer matrix method, Part I: System modeling

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Abstract

Recently, a new type of vibration isolator called a dynamic antiresonant vibration isolator (DAVI) has been studied for torsional systems as well as translational systems. In the DAVI for torsional systems, the inertia coupling for the anti-resonance effect is generated by a planetary gear that connects control inertia and inertias at the input and output terminals. In this research, an analytical modeling approach called the transfer matrix method is applied to design a planetary gear type DAVI for complex systems such as an automotive powertrain. Unlike a previous study, inertias of the pinion gears are newly included in the transfer matrix model to improve the model accuracy in this paper. In this part 1 of series papers, the internal configuration of a planetary gear type DAVI system is described and its dynamic model is derived using the transfer matrix method. The derived transfer matrix model is then validated by comparing its frequency response with those obtained by conventional and numerical methods. Finally, the effects of different gear ratios and pinion gear inertia are examined using the derived transfer matrix model.

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Abbreviations

c :

Viscous damping coefficient (N·s/m)

i :

Imaginary unit, √-1

I :

Mass moment of inertia (kg·m2)

k :

Stiffness of the torsional spring (Nm/rad)

N :

Number of gear teeth

T :

Torque

α :

Angular acceleration of an inertia element (rad/s2)

β :

The gear ratio between sun gear and ring gear

γ :

Gear ratio between pinion gear and ring gear

θ :

Angular displacement

θ̇ :

Angular velocity

θ̈ :

Angular acceleration

Γij :

Transfer matrix for the element with terminal i and j

ω :

Angular frequency (rad/s)

Ω:

Angular velocity of an inertia element (rad/s)

a :

Classical dynamic absorber

ar :

Anti-resonance of the system

C :

Carrier in the planetary gear set

i :

Input

I :

Isolator

o :

Output

P :

Pinion in the planetary gear set

R :

Ring gear in the planetary gear set

r :

Resonance of the system

S :

Sun gear in the planetary gear set

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1057332).

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Authors and Affiliations

  1. School of Automotive Engineering, Kyungpook National University, 2559 Gyeongsangdaero, Sangju, Kyungbuk, 37224, Korea

    Hyeongill Lee

  2. Department of Mechanical Engineering, College of Engineering, The University of Alabama, Box 870276, Tuscaloosa, Alabama, 35487-0276, USA

    Hwan-Sik Yoon

Authors
  1. Hyeongill Lee
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  2. Hwan-Sik Yoon
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Corresponding author

Correspondence to Hwan-Sik Yoon.

Additional information

Recommended by Editor No-cheol Park

Hyeongill Lee is a Professor in School of Automotive Engineering at Kyungpook National University in Korea. Professor Lee is teaching Dynamics, Automatic Control and Mechanical Vibration, etc. His research interests include automotive NVH, brake squeal, and sound radiation from vibrating structures.

Hwan-Sik Yoon is an Associate Professor in Mechanical Engineering at The University of Alabama. He received his Ph.D. degree in Mechanical Engineering from The Ohio State University, Columbus, Ohio, U.S.A. His research interests include modeling, simulation, and control of automotive systems and construction equiment.

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Lee, H., Yoon, HS. Torsional vibration analysis of a planetary gear type antiresonant vibration isolator using transfer matrix method, Part I: System modeling. J Mech Sci Technol 34, 1005–1012 (2020). https://doi.org/10.1007/s12206-020-0203-7

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  • DOI: https://doi.org/10.1007/s12206-020-0203-7

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