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Bifurcation and chaos analysis of the closed-loop gear system of the 3D braiding machine

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Abstract

To research the special transmission system type of the multistage closed-loop gear system of the 3D braiding machine, a multi-degree of freedom nonlinear dynamic model was established by using the lumped mass method, taking into account parameters such as meshing stiffness, static transmission error, backlash, and meshing damping. To reduce the computational complexity, a gear system with 12 gears was selected and solved using the Runge-Kutta method. Using meshing frequency, backlash, and meshing damping ratio as control parameters, we analyzed the bifurcation and chaos of the system under different conditions through bifurcation diagrams. Simultaneously using sequence diagram, phase plane diagrams, Poincare maps, and FFT diagrams to accurately display the motion state of the system. The analysis results indicate that with the increase of meshing frequency and backlash, the system exhibits a range of motion states, such as period-one motion, multi-periodic motion, quasi-periodic motion, and chaotic motion. Meanwhile, increasing the damping ratio can effectively suppress the chaotic state of the gear system and also reduce the maximum vibration displacement of the gear system.

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Acknowledgments

This work was supported by Major technical equipment research projects of the National Development and Reform Commission (Grant No.2102-320905-89-05-514710), China and Basic Research Project on the Application of Textile Light (Grant No. J202202), China.

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Authors and Affiliations

  1. College of Mechanical Engineering, Donghua University, Shanghai, 201620, China

    Zhijun Sun & Yongbing Liu

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  1. Zhijun Sun
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  2. Yongbing Liu
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Correspondence to Zhijun Sun.

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Zhijun Sun received his Ph.D. from Donghua University, China, in 2013. He is currently an Associate Professor at Donghua University. He is mainly engaged in research on mechanical design and theory, mechatronics integration technology and applications, complex system modeling and analysis.

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Sun, Z., Liu, Y. Bifurcation and chaos analysis of the closed-loop gear system of the 3D braiding machine. J Mech Sci Technol 38, 1669–1681 (2024). https://doi.org/10.1007/s12206-024-0304-9

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  • DOI: https://doi.org/10.1007/s12206-024-0304-9

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