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The Numerical Solutions and Their Applications in 2K-H Planetary Gear Transmission Systems

  • Shuli Guo
  • Lina Han
Chapter

Abstract

Classical Range Kutta (RK) methods are introduced and analyzed.  And some important algorithms are outlined. The nonlinear dynamic differential equation of 2K-H planetary gear transmission, which takes into consideration of clearance, is presented in this chapter. Based on some RK algorithm, various chaotic characteristics of the numerical solution system, such as the largest Lyapunov exponent, Poincaré section, FFT spectrum, and the phase locus are collected.  As the existence of clearance, the Jacobi matrix of the numerical solution system does not exist at the boundary.  A new method on the Largest Lyapunov Exponent of the system is deduced based on the definition of Lyapunov Exponent.   Numerical simulation results are carried out on the periodic movement, quasiperiodic movement and chaotic movement of the system.

Notes

Acknowledgements

This work is Supported by National Key Research and Development Program of China (2017YFF0207400).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Key Laboratory of Complex System Intelligent Control and Decision, School of AutomationBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Cardiovascular Internal Medicine of Nanlou Branch, National Clinical Research Center for Geriatric DiseasesChinese PLA General HospitalBeijingChina

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