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Dynamics modeling and simultaneous identification of force coefficients for variable pitch bull-nose cutter milling considering process damping and cutter runout

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Abstract

Regenerative chatter is a common challenge in milling large and difficult-to-cut complex curved parts, which seriously affects the machining efficiency and quality. Variable pitch cutters (VPCs) and process damping are known to be effective in suppressing chatter. However, the complex multiple interactions between process damping and variable pitch bull-nose cutters (VPBNCs) have been rarely investigated due to unavoidable runout and multiple modes of the milling system. In addition, the simultaneous identification of shearing force coefficients and ploughing force coefficients presents a challenge when the dynamic characteristics of VPCs are considered. To this end, this paper first establishes the geometric parametric modeling of VPBNCs, and a mechanical model is proposed to uniformly handle shearing force and process damping force, which accounts for cutter runout. Secondly, the multiple interactions comprehensive dynamics model of VPBNCs milling system is developed. The milling system involves multiple regeneration delays, multiple modes and process damping effects. A modified hybrid multi-step method (MHMSM) is employed to analyze milling stability. Then, combined with the mechanical model considering cutter vibration, a multi-parameter synchronous calibration method (MPSCM) is proposed to identify ploughing force coefficients and runout parameters. Finally, experimental validation is performed to verify the proposed model and calibration method. The results show good agreement between simulation and experimental results. Furthermore, the joint influences of process damping and pitch angle variation on stability in different speed ranges are explored in detail.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. U22A20202 and No.52205516) and the China Postdoctoral Science Foundation(Grant No. 2022M720641).

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Authors and Affiliations

  1. State Key Laboratory of High-Performance Precision Manufacturing, School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Shikang Li, Danian Zhan, Shuoxue Sun & Yuwen Sun

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  1. Shikang Li
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  2. Danian Zhan
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  3. Shuoxue Sun
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Contributions

Methodology, investigation, software, writing—original draft: SL; methodology, writing—review and editing: DZ; investigation, writing—review and editing: SS; methodology, writing—review, supervision: YS.

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Correspondence to Shuoxue Sun.

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Appendix

Appendix

1.1 Detailed derivations of Eq. (62)

$$\begin{array}{c}\left\{\begin{array}{c}{S}_{1}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta z/sin{k}_{1}cos{\varphi }_{j,1}\left({t}_{i}\right)\\ {L}_{1}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}_{j,1}\left(t\right)\Delta z/sin{k}_{1}cos{\varphi }_{j,1}\left({t}_{i}\right) \\ {S}_{2}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta zsin{\varphi }_{j,1}\left({t}_{i}\right) \\ {L}_{2}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}_{j,1}\left(t\right)\Delta zsin{\varphi }_{j,1}\left({t}_{i}\right) \\ {S}_{3}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta zcot{k}_{1}sin{\varphi }_{j,1}\left({t}_{i}\right) \\ {L}_{3}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}^{st}\Delta zcot{k}_{1}sin{\varphi }_{j,1}\left({t}_{i}\right) \\ {S}_{4}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta z/sin{k}_{1}sin{\varphi }_{j,1}\left({t}_{i}\right) \\ {L}_{4}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}_{j,1}\left(t\right)\Delta z/sin{k}_{1}sin{\varphi }_{j,1}\left({t}_{i}\right) \\ {S}_{5}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta zcos{\varphi }_{j,1}\left({t}_{i}\right) \\ {L}_{5}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}_{j,1}\left(t\right)\Delta zcos{\varphi }_{j,1}\left({t}_{i}\right) \\ {S}_{6}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta zcot{k}_{1}cos{\varphi }_{j,1}\left({t}_{i}\right) \\ {L}_{6}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}^{st}\Delta zcot{k}_{1}cos{\varphi }_{j,1}\left({t}_{i}\right) \\ {S}_{7}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta zcot{k}_{1} \\ {L}_{7}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}_{j,1}\left(t\right)\Delta zcot{k}_{1} \\ {S}_{8}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){h}_{j,1}\left({t}_{i},p\right)\Delta z \\ {L}_{8}\left({t}_{i}\right)=-{\sum }_{j=1}^{{N}_{t}}{g}_{j,1}\left({t}_{i}\right){S}^{st}\Delta z \\ \end{array}\right.\end{array}$$

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Li, S., Zhan, D., Sun, S. et al. Dynamics modeling and simultaneous identification of force coefficients for variable pitch bull-nose cutter milling considering process damping and cutter runout. Int J Adv Manuf Technol 130, 2877–2898 (2024). https://doi.org/10.1007/s00170-023-12777-0

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