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Nonlinear chatter of CNTs-reinforced composite boring cutter considering unstable region

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Abstract

The nonlinear dynamic analysis of rotating composite boring round bar containing carbon nanotubes (CNTs) in boring system is investigated. Firstly, according to both the Halpin–Tsai model and the micro-mechanical theory, the resultant properties of filled-CNT composite material are estimated. Subsequently, the equations in terms of the energies and virtual works for the composite boring bar are derived by taking into the Von Kármán geometric nonlinearity account. Then, the extended Hamilton principle is used to establish the nonlinear dynamic model of the machining system, which includes periodic regenerative chatter cutting force, periodic frictional force, viscoelastic and process damping force. Both methods of Galerkin approximation and multiple time scales for nonlinear equation are utilized to obtain steady-state response of the boring process. The stability of the boring system is explored considering the effects of CNT-related parameters, fiber volume fraction and orientations, stacking sequences, damping coefficient, and cutter geometry features. The results obtained demonstrate that the CNTs inclusion has a considerable effect on the dynamic behavior of the boring process. Furthermore, it is also concluded that the unstable area can be reduced by increasing damping and that the stability of boring process will be enhanced.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. 11672166) and the Natural Science Foundation of Shandong Province (Grant no. ZR202103070107).

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Authors and Affiliations

  1. College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao, China

    Jinfeng Zhang, Zhong Wang, Junlei Jia, Zhenfang Tong, Yongsheng Ren & Peisi Zhong

  2. Engineering and Training Center, Shandong University of Science and Technology, Qingdao, China

    Chao Feng

  3. College of Ocean Science and Engineering, Shandong University of Science and Technology, Qingdao, China

    Xionglong Cao

  4. Advanced Manufacturing Technology Center, Shandong University of Science and Technology, Qingdao, China

    Jinfeng Zhang & Peisi Zhong

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Appendix A

Appendix A

The transformed material constants of the kth layer of the composite boring bar are defined as,

$$\overline{Q}_{11} = Q_{11} \cos^{4} \theta^{(k)} + 2(Q_{12} + 2Q_{66} )\cos^{2} \theta^{(k)} \sin^{2} \theta^{(k)} + Q_{22} \sin^{4} \theta^{(k)}$$
(57)

where θ(k) is the layered angle of each layer of material.

The expression for Q11, Q1, Q22, Q66 is as follows,

$$Q_{11} = \frac{{E_{11} }}{{1 - \nu_{12} \nu_{21} }},\quad Q_{22} = \frac{{E_{22} }}{{1 - \nu_{12} \nu_{21} }}\quad Q_{12} = \frac{{\nu_{21} E_{11} }}{{1 - \nu_{12} \nu_{21} }},\quad Q_{66} = G_{12}$$
(58)

where \(\nu_{21} = \frac{{\nu_{12} E_{22} }}{{E_{11} }}\).

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Zhang, J., Wang, Z., Feng, C. et al. Nonlinear chatter of CNTs-reinforced composite boring cutter considering unstable region. Arch Appl Mech 93, 4217–4239 (2023). https://doi.org/10.1007/s00419-023-02490-5

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