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Dynamic milling stability prediction of thin-walled components based on VPC and VSS combined method

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Abstract

In the milling process, the coupling deflection and the dynamic characteristics of the cutter–workpiece system are time variant as the material removal and the change of cutter position. The milling stability of the system is dynamic because of the time-varying stiffness. In this study, the model of time-varying system has been developed. Variable pitch cutter (VPC) and variable spindle speed (VSS) are, respectively, typical method of passive control and active control to suppress the chatter, and two methods are compatible. The arithmetic of VPC and VSS combined method has been developed and verified effectively. Dynamic milling stability prediction of stiffness time-varying system for thin-walled components based on VPC and VSS combined method has been developed. And then, the dynamic milling stability of stiffness time-varying system for thin-walled components has been predicted.

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Abbreviations

a e :

Nominal radial depth of cutting (mm)

B 0 :

Initial thickness of workpiece (mm)

d t :

Deflection of cutter (mm)

d w :

Deflection of workpiece (mm)

d c :

Coupling deflection of cutter–workpiece system (mm)

N :

Sum of nodes on contact location of cutter and workpiece

G y :

Relativity frequency response function of cutter–workpiece system in y-direction (mm/N)

G y(t) :

Frequency response function of cutter in y-direction (mm/N)

G y(w) :

Frequency response function of workpiece in y-direction (mm/N)

δ y(t) :

Displacement of cutter in y-direction (mm)

δ y(w) :

Displacement of workpiece in y-direction (mm)

N c :

Number of teeth

Δψ :

Pitch increment (°)

ψ 0 :

Basic pitch variation (°)

η :

Initial phase angle (°)

Ω0 :

Nominal spindle speed value (r/min)

T :

Time period (s)

a p :

Axial depth of cutting (mm)

hj(t):

Chip thickness (mm)

k t :

Cutting force coefficient in tangential direction (N/m2)

k r :

Cutting force coefficient in radial direction (N/m2)

q :

Cutting force exponent

ϕ st :

Start angle (°)

ϕ ex :

Exit angle (°)

f z :

Mean feed per tooth (mm/tooth)

m :

Modal mass (kg)

c :

Damping coefficient (N s/m)

k :

Modal stiffness (N/mm)

ξ :

Damping ratio

ω n :

Natural frequency (Hz)

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51905082), the Fundamental Research Funds for the Central Universities (Grant No. N2023024), Scientific Research Initiation Funds for Northeastern University at Qinhuangdao (Grand No. XNY201807), and National Defense Key Funds for Equipment Pre-research (Grant No. 61409230103).

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Authors and Affiliations

  1. School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China

    Li Zhang, Bo Hao, Dongping Xu & Mingqiang Dong

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  1. Li Zhang
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  2. Bo Hao
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  3. Dongping Xu
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Correspondence to Li Zhang.

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Technical Editor: Adriano Fagali de Souza.

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Zhang, L., Hao, B., Xu, D. et al. Dynamic milling stability prediction of thin-walled components based on VPC and VSS combined method. J Braz. Soc. Mech. Sci. Eng. 42, 336 (2020). https://doi.org/10.1007/s40430-020-02419-x

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  • DOI: https://doi.org/10.1007/s40430-020-02419-x

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