Five-axis flank milling stability prediction by considering the tool-workpiece interactions and speed effect

Abstract

Chatter is one of the challenging topics in the field of metal cutting. The dynamic characteristics of five-axis milling system are complex and variable. Especially in high-speed milling process, the influence of the tool-workpiece interactions and speed effect on milling stability is more obvious. It is necessary to investigate the influence of various interaction effects on milling stability. In this paper, the dynamical model of spindle system was established, and then the model was applied to investigate the influence of gyroscopic effect and centrifugal force on the dynamical characteristics of the tool tip. In order to solve the chatter problem of five-axis flank milling, the extended dynamical model of five-axis flank milling which considers the tool-workpiece interactions and speed effect was established. Based on the established milling dynamical model, the influence mechanism of the spindle system-tool-workpiece interaction effects on five-axis flank milling stability was investigated. The stability lobe diagrams of five-axis flank milling which contains the tool-workpiece interactions and speed effect can be obtained. Experimental results show that the proposed five-axis flank milling dynamical model can predict the milling state more reliable than the traditional ones. The research results are of great significance in preventing five-axis flank milling chatter.

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Change history

  • 06 June 2020

    This original article contained a mistake.

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Funding

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51375055 and 51575055).

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Correspondence to Yongjian Ji.

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The original version of this article was revised: Equation 39 is missing in the original published paper.

Appendices

Appendix 1. Details of Tx1(90°),Tx2(90°),Ty(θB), Tz(θC),(TF‐ to ‐W)−1in Eq.(17)

$$ {\mathrm{T}}_{x1}\left({90}^{{}^{\circ}}\right)=\left[\begin{array}{ccc}1& 0& 0\\ {}0& \cos \left({90}^{{}^{\circ}}\right)& -\sin \left({90}^{{}^{\circ}}\right)\\ {}0& \sin \left({90}^{{}^{\circ}}\right)& \cos \left({90}^{{}^{\circ}}\right)\end{array}\right]\kern0.5em ,\kern0.5em {\mathrm{T}}_{x2}\left({90}^{{}^{\circ}}\right)=\left[\begin{array}{ccc}1& 0& 0\\ {}0& \cos \left({90}^{{}^{\circ}}\right)& \sin \left({90}^{{}^{\circ}}\right)\\ {}0& -\sin \left({90}^{{}^{\circ}}\right)& \cos \left({90}^{{}^{\circ}}\right)\end{array}\right] $$
(48)
$$ {\mathrm{T}}_y\left({\theta}_B\right)=\left[\begin{array}{ccc}\cos {\theta}_B& -\sin {\theta}_B& 0\\ {}\sin {\theta}_B& \cos {\theta}_B& 0\\ {}0& 0& 1\end{array}\right]\kern0.5em ,\kern0.5em {\mathrm{T}}_z\left({\theta}_C\right)=\left[\begin{array}{ccc}\cos {\theta}_C& -\sin {\theta}_C& 0\\ {}\sin {\theta}_C& \cos {\theta}_C& 0\\ {}0& 0& 1\end{array}\right] $$
(49)
$$ {\left({\mathrm{T}}_{\mathrm{F}\hbox{-} \mathrm{to}\hbox{-} \mathrm{W}}\right)}^{-1}=\left[\begin{array}{ccc}\cos {\alpha}_{\mathrm{F}}\cos {\gamma}_{\mathrm{F}}& \sin {\alpha}_{\mathrm{F}}& -\cos {\alpha}_{\mathrm{F}}\sin {\gamma}_{\mathrm{F}}\\ {}-\sin {\alpha}_{\mathrm{F}}\cos {\gamma}_{\mathrm{F}}& \cos {\alpha}_{\mathrm{F}}& \sin {\gamma}_{\mathrm{F}}\sin {\alpha}_{\mathrm{F}}\\ {}\sin {\gamma}_{\mathrm{F}}& 0& \cos {\gamma}_{\mathrm{F}}\end{array}\right] $$
(50)

Appendix 2. Details of p1, p2, p3, p4, e1, e2, e3, e4, o1, o2, o3, o4, f1, f2, f3, f4 in Eq. (47)

$$ {p}_1=\frac{-{m}_y{k}_x+{m}_{xy}{k}_{yx}}{m_x{m}_y-{m}_{xy}{m}_{yx}},{p}_2=\frac{-{m}_y{k}_{xy}+{m}_{xy}{k}_y}{m_x{m}_y-{m}_{xy}{m}_{yx}},{p}_3=\frac{-{m}_{yx}{k}_x-{m}_x{k}_{yx}}{m_x{m}_y-{m}_{xy}{m}_{yx}},{p}_4=\frac{-{m}_{yx}{k}_{xy}-{m}_x{k}_y}{m_x{m}_y-{m}_{xy}{m}_{yx}} $$
(51)
$$ {e}_1=\frac{-{m}_y{C}_x+{m}_{xy}{C}_{yx}}{m_x{m}_y-{m}_{xy}{m}_{yx}},{e}_2=\frac{-{m}_y{C}_{xy}+{m}_{xy}{C}_y}{m_x{m}_y-{m}_{xy}{m}_{yx}},{e}_3=\frac{-{m}_{yx}{C}_x-{m}_x{C}_{yx}}{m_x{m}_y-{m}_{xy}{m}_{yx}},{e}_4=\frac{-{m}_{yx}{C}_{xy}-{m}_x{C}_y}{m_x{m}_y-{m}_{xy}{m}_{yx}} $$
(52)
$$ {o}_1=\frac{-{m}_y\cdotp {h}_{2,11}+{m}_{xy}\cdotp {h}_{2,21}}{m_x{m}_y-{m}_{xy}{m}_{yx}},\kern0.5em {o}_2=\frac{-{m}_y\cdotp {h}_{2,12}+{m}_{xy}\cdotp {h}_{2,22}}{m_x{m}_y-{m}_{xy}{m}_{yx}} $$
(53)
$$ {o}_3=\frac{m_{yx}\cdotp {h}_{2,11}-{m}_x\cdotp {h}_{2,21}}{m_x{m}_y-{m}_{xy}{m}_{yx}},\kern0.5em {o}_4=\frac{m_{yx}\cdotp {h}_{2,12}-{m}_x\cdotp {h}_{2,22}}{m_x{m}_y-{m}_{xy}{m}_{yx}}, $$
(54)
$$ {f}_1=\frac{-{m}_y\cdotp {c}_{\mathrm{p}3,x}+{m}_{xy}\cdotp {c}_{\mathrm{p}3, yx}}{m_x{m}_y-{m}_{xy}{m}_{yx}},\kern0.5em {f}_2=\frac{-{m}_y\cdotp {c}_{\mathrm{p}3, xy}+{m}_{xy}\cdotp {c}_{\mathrm{p}3,y}}{m_x{m}_y-{m}_{xy}{m}_{yx}} $$
(55)
$$ {f}_3=\frac{m_{yx}\cdotp {c}_{\mathrm{p}3,x}-{m}_x\cdotp {c}_{\mathrm{p}3, yx}}{m_x{m}_y-{m}_{xy}{m}_{yx}},\kern0.5em {f}_4=\frac{m_{yx}\cdotp {c}_{\mathrm{p}3, xy}-{m}_x\cdotp {c}_{\mathrm{p}3,y}}{m_x{m}_y-{m}_{xy}{m}_{yx}} $$
(56)

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Ji, Y., Wang, X., Liu, Z. et al. Five-axis flank milling stability prediction by considering the tool-workpiece interactions and speed effect. Int J Adv Manuf Technol 108, 2037–2060 (2020). https://doi.org/10.1007/s00170-020-05251-8

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Keywords

  • Milling stability prediction
  • Five-axis
  • Flank milling
  • Tool-workpiece interactions
  • Speed effect