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Bifurcation and chaos analysis of cutter head-spindle system of VH-CATT gear machine tool considering time-varying stiffness

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Abstract

The stability of power system in variable hyperbolic circular arc tooth trace (VH-CATT) gear machine tool determines the surface accuracy and mechanical properties of the VH-CATT gear. Due to the existence of several time-varying parameters, the power system is a typical nonlinear dynamic system. To study the influence of the design parameters of the spindle and cutter head on the motion stability of the power system, a nonlinear dynamic model of the cutter head-spindle system is established based on the cutting principle, which considers the time-varying stiffness, clearance and excitation. According to the potential function and phase portrait, the existence of intersect homoclinic orbit is proved, and the concrete expression is derived. The threshold values of the parameters for occurrence of the homoclinic bifurcation are obtained by means of Melnikov method. The analytical predictions have been verified through numerical simulations, and good agreement is observed, which presents the dynamic behaviors of the system include 1 T-periodic, nT-periodic, and chaotic motion. Additionally, combined with bifurcation diagrams, time histories, phase portraits, Poincaré sections, and power spectra, the global bifurcation of the system and the transition between various motion states are revealed. The research results offer reference for the parameter selection of the cutter head-spindle system and also provide a theoretical basis for the subsequent experimental analysis.

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Acknowledgements

The authors sincerely thanks to Mr. Hou and Mr. Chen for their critical discussion and guidance during manuscript preparation.

Funding

This research has been supported by the National Natural Science Foundation of China under Grant no. Grant No. 51875370.

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Authors and Affiliations

  1. School of Mechanical Engineering, Sichuan University, Chengdu, 610065, China

    Shuang Liang, Li Hou, Haiyan Zhang, Lan Luo, Yang Wu & Pei Luo

  2. School of Mechanical & Electronical Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Lan Luo

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  1. Shuang Liang
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  2. Li Hou
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  3. Haiyan Zhang
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  4. Lan Luo
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  5. Yang Wu
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  6. Pei Luo
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Contributions

Liang wrote the manuscript, and was in charge of the simulation. Hou established an initial protocol for the study. Luo and Wu assisted with Model establishment and result analysis. Zhang contribute to review and edition. All authors read and approved the final manuscript.

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Correspondence to Shuang Liang.

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Liang, S., Hou, L., Zhang, H. et al. Bifurcation and chaos analysis of cutter head-spindle system of VH-CATT gear machine tool considering time-varying stiffness. Int J Adv Manuf Technol 124, 3995–4008 (2023). https://doi.org/10.1007/s00170-021-08360-0

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  • DOI: https://doi.org/10.1007/s00170-021-08360-0

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