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Numerical and experimental study of end-milling process of titanium alloy with a cryogenic internal coolant supply

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Abstract

Cryogenic machining is an environmentally friendly process; liquid nitrogen (LN2) is sprayed onto cutting tool to reduce cutting temperature, increasing tool life. Cutting temperature and force were numerically predicted during cryogenic assisted milling with an internal coolant-assisted tool holder (internal cryogenic milling) for Ti-6Al-4V alloy. The influence of LN2 on the material temperature throughout the machining was estimated; a numerical model to simulate the initial temperature of work material was discussed by consideration of LN2 injective mechanism. A modified Johnson-Cook model including the cryogenic temperature range was adopted to model material plasticity. The predictive models were validated based on side-milling test. The predicted values captured the trend of experimental result; the minimum and maximum temperature errors were 0.1% and 8.6%, and those for the cutting force were 0.2% and 34.4%. Moreover, comprehensive experimental studies for the cutting temperature, cutting force, chip morphology, and chip composition were performed to understand the effect of cryogenic cooling condition. In internal cryogenic milling, the cutting temperature and force tended to be lower than dry machining. Based on the morphological analysis of the generated chip, the coefficient of sliding friction at tool-chip interface under the internal cooling was reduced by 21.4% as compared to the dry condition.

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Abbreviations

σ :

flow stress (MPa)

A :

material model parameter, yield stress (MPa)

B :

material model parameter, strain hardening coefficient

n :

material model parameter, strain hardening exponent

C :

material model parameter, strain rate coefficient

λ, m :

material model parameter, thermal coefficient

ε :

plastic strain

\( {\dot{\varepsilon}}^{\ast } \) :

dimensionless strain rate

T :

temperature variable (°C)

T r :

room temperature (°C)

T m :

melting temperature (°C)

ΔT SZ :

elevated temperature at shear zone by plastic deformation (°C)

ΔT Work :

heat conducted into work material (°C)

β :

proportion value of heat transferred to work material

ρ :

density of work material (kg/m3)

S :

specific heat of work material (J/kg-°C)

t 1 :

cutting depth (m)

w :

machining width (m)

F S :

shear force (N)

Φ:

shear angle (rad)

α n :

rake angle of cutting tool (rad)

V C :

cutting speed (m/s)

K Work :

thermal conductivity of work material (W/m-°C)

ΔT C :

average temperature rise in chip (°C)

θ :

angle in slip-line field (rad)

λ f :

frictional angle (rad)

φ :

rotating angle of cutting tool (rad)

f :

feed (m/rev/tooth)

d R :

radial depth (m)

D Tool :

Diameter of cutting tool (m)

h :

convective coefficient of LN2 (W/m2-°C)

K LN2 :

thermal conductivity of LN2 (W/m-°C)

Pr :

Prandtl number of LN2

Re :

Renold number of LN2

D :

diameter of injective nozzle (m)

A Nozzle :

correlation coefficient of injective nozzle

L :

characteristic distance for LN2 injection (m)

T m p :

temperature of work material at position and time of m and p (°C)

T ∞ :

temperature of LN2 (°C)

Fo :

Fourier number

Bi :

Biot number

α Work :

thermal diffusivity of work material (m2/s)

Δt :

time for step simulation (s)

Δx :

distance between adjacent points for step simulation (m)

RPM :

Number of revolutions per minute of cutting tool

ΔT Cryo :

temperature change due to cryogenic heat source (°C)

q Cryo :

cryogenic heat source (W/m2)

V Chip :

cutting speed of chip (m/s)

K 0 :

modified Bessel function with second order of zero

R, R ' , R ' ':

distance from cryogenic heat source (m)

T Chip :

temperature of chip surface (°C)

T LN2 :

temperature of LN2 (°C)

X, x, Z:

Cartesian coordinate representing location of simulated temperature

t ch :

deformed chip thickness (m)

T Work, Machined :

work material temperature at machined surface (°C)

T Material :

temperature of raw material (°C)

ν, δ, Ψ:

temperature factors

ΔT Initial :

temperature change caused by initial temperature reduction (°C)

ΔT Cryogenic − Shear :

temperature change caused by cryogenic heat source at shear zone (°C)

ΔT Cryogenic − Chip :

temperature change caused by cryogenic heat source at tool-chip interface (°C)

ΔT M :

maximum temperature rise in chip (°C)

l Contact :

tool-chip contact length

P1, P2, P3 :

cutting forces in cutting, tangential, radial directions (N)

Cs :

side cutting angle (rad)

F C, F T, F R :

cutting force components (N)

k AB :

shear flow stress at shear zone (Pa)

k Chip :

shear flow stress at tool-chip interface (Pa)

σ AB :

normal flow stress at shear zone (Pa)

σ Chip :

normal flow stress at tool-chip interface (Pa)

i :

inclination angle (rad)

η :

chip flow angle (rad)

F X, F Y, F Z :

cutting forces in x, y, z directions (N)

r f :

cutting ratio

PC :

distance between teeth of serrated chip (mm)

P:

height of serrated chip (mm)

μ :

frictional coefficient at interface of tool and chip

r :

nose radius (m)

d :

cutting depth (m)

Q :

amount of heat transferred (W-s)

Δt C :

time for heat transfer (s)

A C :

area for heat transfer (m2)

T M :

temperature of work material at machined surface (°C)

T n :

temperature of thermocouple at position of n (°C)

d n :

distance between machined surface and thermocouple position of n (m)

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Funding

This research was supported by the technology innovation program (10053248, Development of Manufacturing System for CFRP (Carbon Fiber Reinforced Plastics) Machining) funded by the Ministry of Trade, industry & Energy (MOTIE) of Korea and the Mid-career Researcher Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT of Korea (No. 2018R1A2B3007806).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ulsan National Institute of Science and Technology, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan, 689-798, Republic of Korea

    Do Young Kim & Hyung Wook Park

  2. Dongnam Regional Division, Korea Institute of Industrial Technology, 25, Yeonkkot-ro 165 beon-gil, Jeongchon-myeon, Jinju-si, 52845, Gyeongsangnam-do, Republic of Korea

    Dong Min Kim

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  1. Do Young Kim
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Correspondence to Hyung Wook Park.

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Research highlights

We developed the numerical model of end milling with the internal cryogenic cooling.

Experimental validations of cutting forces and temperatures were performed.

Morphologies of the chips were analyzed to observe the friction at tool-chip interface.

The numerical model can capture the trend of the experiments.

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Kim, D.Y., Kim, D.M. & Park, H.W. Numerical and experimental study of end-milling process of titanium alloy with a cryogenic internal coolant supply. Int J Adv Manuf Technol 105, 2957–2975 (2019). https://doi.org/10.1007/s00170-019-04425-3

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  • DOI: https://doi.org/10.1007/s00170-019-04425-3

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