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Effect and feasibility analysis of the smoothening functions for clearance-type nonlinearity in a practical driveline system

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Abstract

Discontinuous dynamic characteristics in gear backlash often cause convergence problems when a nonlinear torsional system is simulated. This clearance-type nonlinearity can be mathematically modeled by using smoothening functions which change the dynamic responses of the system under discontinuous ranges into continuous ones. However, the effect of the smoothening functions is not well known and difficult to anticipate under various nonlinear conditions. Thus, a new smoothening function is proposed. The effect and feasibility of the model were investigated with a practical vehicle driveline system. To examine the key factors of the smoothening function, the harmonic balance method was used with an ‘n’th order polynomial function and compared with hyperbolic-type smoothening functions. The harmonic balance method and numerical analysis were compared for nonlinear system responses that include much high order of the super-harmonic components with respect to impulsive contact motions to understand the limits of the method. The smoothening function is applicable for simulating gear impact phenomena with limit conditions.

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Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01058183).

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Authors and Affiliations

  1. Department of Mechatronics Engineering, Incheon National University, (Songdo-dong) 119 Academy-ro, Yeonsu-gu, Incheon, 22012, Republic of Korea

    Jong-Yun Yoon

  2. School of Mechanical Engineering, Yeungnam University, 280, Daehak-ro, Gyeongsan-si, Gyeongsangbuk-do, 712-749, Republic of Korea

    Byeongil Kim

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  1. Jong-Yun Yoon
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  2. Byeongil Kim
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Correspondence to Byeongil Kim.

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Yoon, JY., Kim, B. Effect and feasibility analysis of the smoothening functions for clearance-type nonlinearity in a practical driveline system. Nonlinear Dyn 85, 1651–1664 (2016). https://doi.org/10.1007/s11071-016-2784-3

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  • DOI: https://doi.org/10.1007/s11071-016-2784-3

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