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Volume 50 Issue 11
Nov.  2024
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Journal of Beijing University of Aeronautics and Astronautics  > 2024  >  50(11): 3566-3577.
XU W S，XU T Q，MA H X，et al. Dynamic characteristics of flexible micro-positioning platforms based on transfer matrix method[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（11）：3566-3577 （in Chinese） doi: 10.13700/j.bh.1001-5965.2022.0845
Citation: XU W S，XU T Q，MA H X，et al. Dynamic characteristics of flexible micro-positioning platforms based on transfer matrix method[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（11）：3566-3577 （in Chinese） doi: 10.13700/j.bh.1001-5965.2022.0845
shu

Dynamic characteristics of flexible micro-positioning platforms based on transfer matrix method

doi: 10.13700/j.bh.1001-5965.2022.0845
  • 1.

    School of Mechanical Engineering，Jiangnan University，Wuxi 214122，China

  • 2.

    Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment & Technology，Wuxi 214122，China

Funds:  National Natural Science Foundation of China (51375209); The Six Talent Peaks Project in Jiangsu Province (ZBZZ-012); Program of Introducing Talents of Discipline to Universities (B18027); The Excellent Technology Innovation Team Fundation of Jiangsu Province (2019SK07)
More Information
  • Corresponding author: E-mail：caoyi@jiangnan.edu.cn
  • Received Date: 10 Oct 2022
  • Accepted Date: 02 Dec 2022
    • Available Online: 23 Dec 2022
  • Publish Date: 15 Dec 2022
    Abstract

  • With the development of precision micro-positioning technology, the research on dynamic characteristics of flexible micro-positioning platforms is necessary. As an effective method to analyze the dynamics of multi-body systems, the transfer matrix method (TMM) has the advantages of convenient modeling and high calculation accuracy. Therefore, a dynamics model of the micro-positioning platform was established based on TMM to analyze its dynamic characteristics. The basic idea of TMM was introduced, and the transfer equation of flexible mechanism was established. Its instantaneous dynamic response under arbitrary excitation was deduced. An XY flexible micro-positioning platform based on the flexible hinge and flexible beam was designed, and the transfer matrix of its branch chain and the whole platform was derived. Based on vibration theory, the transfer matrix of the main characteristic elements of the platform was derived. Finally, in order to verify the validity of the theoretical model, the natural frequency and instantaneous dynamic response of the platform were studied based on the TMM, finite element method (FEM), and equivalent mass method (EMM), respectively. The results show that the transfer matrix can be programmatically constructed based on the TMM to analyze the dynamic characteristics of the platform without establishing complicated dynamics equations. Compared with EMM, TMM can calculate the higher-order natural frequency of the platform. The maximum relative error between theoretical and simulated natural frequencies of the platform is just 2.4%, and the theoretical and simulated dynamic responses basically agree with each other, which proves the validity of the model based on TMM.

     

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