Abstract
Cryogenic cooling helps to improve the machining performance and reduce the tool wear. Cryogenic condition could activate these substructures such as deformation twins and dislocation cells. The effects of the substructures are not taken into consideration in the conventional machining models. The conventional models cannot characterize the dynamics in cryogenic machining, i.e., the evolutions of cutting force and temperature with time. Here, considering the effect of the substructures, a new analytical model for metal cutting was proposed to predict the dynamics in cryogenic orthogonal machining. To validate the applicability of the proposed model, the experiments of orthogonal cutting copper at liquid nitrogen temperature and room temperature were conducted. Transmission electron microscope observations show that nanotwins formed in cryogenic cutting copper. The comparisons between experimental cutting forces and the proposed model or the conventional models validate the rationality of the nanotwin-based analytical model. Numerical calculations were further carried out to reveal the underlying mechanism. The periodic oscillation of cutting force in liquid nitrogen condition is a phenomenon of Hopf bifurcation resulting from the formation of nanotwins.
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Abbreviations
- t 0 :
-
precut thickness
- t c :
-
chip thickness
- w :
-
workpiece thickness
- ϕ :
-
shear angle
- V :
-
cutting speed
- F c :
-
cutting force
- ρ :
-
mobile dislocation density
- t :
-
time
- d :
-
mean grain size
- τ y :
-
shear yield strength
- R TW :
-
mean radius of nanotwin
- h TW :
-
thickness of nanotwin
- k a :
-
annihilation constant
- ρ 0 :
-
initial dislocation density
- γ SF :
-
stacking fault energy
- b :
-
modulus of Burgers vector
- G :
-
shear modulus
- T :
-
temperature
- τ :
-
flow shear stress
- \( \hat{t} \) :
-
dimensionless time
- \( \hat{d} \) :
-
dimensionless grain size
- a11(T), a12(T), a13, a14, b11, b12, b13 :
-
dimensionless coefficients
- f nt :
-
volume fraction of nanotwin
- N TW :
-
concentration of active twins
- η :
-
fraction of plastically dissipated energy
- ε D :
-
energy of dislocation line per unit length
- Δ:
-
mean distance of nanotwins
- V nt :
-
speed of nanotwin formation
- V D :
-
dislocation motion velocity
- n 0 :
-
total number of twinning system
- ρ anh :
-
annihilation rate of dislocation
- τ g :
-
shear yield strength of deformed grains
- τ nt :
-
shear yield strength of nanotwinned grains
- A 1 :
-
coefficient 1 for deformed grains
- A 2 :
-
coefficient 2 for deformed grains
- B 1 :
-
coefficient 1 for nanotwinned grains
- B 2 :
-
coefficient 2 for nanotwinned grains
- τ 0 :
-
dislocation gliding frictional stress
- α :
-
dislocation interaction term
- k TW :
-
coefficient of twinning strengthening
- \( \hat{\tau} \) :
-
dimensionless flow shear stress
- \( \hat{\rho} \) :
-
dimensionless dislocation density
- \( {\hat{\rho}}^{\ast } \) :
-
equilibrium dislocation density
- \( {f}_{\mathrm{nt}}^{\ast } \) :
-
equilibrium nanotwin volume fraction
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Funding
This study was funded by the National Key Research and Development Program of China (grant number 2017YFB0702003), the National Natural Science Foundation of China (grant numbers 12072327 and 11802013), Fundamental Research Funds for the Central Universities (grant number FRF-TP-18-020A2), China Scholarship Council (grant number 201909110036), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant numbers XDB22040302 and XDB22040303), and the Key Research Program of Frontier Sciences (grant number QYZDJSSW-JSC011).
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Liu, Y., Cai, S., Chen, Y. et al. A nanotwin-based analytical model to predict dynamics in cryogenic orthogonal machining copper. Int J Adv Manuf Technol 111, 3189–3205 (2020). https://doi.org/10.1007/s00170-020-06303-9
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DOI: https://doi.org/10.1007/s00170-020-06303-9