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Thermal modeling and experimental investigation on the influences of the process parameters on warm incremental sheet metal forming of titanium grade 2 using electric heating technique

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Abstract

Incremental sheet metal forming (ISMF) is one of the most innovative flexible processes for small volume production of complex sheet metal components. Formability of titanium grade 2 sheets is limited at room temperature and can be improved by forming at elevated temperature. Therefore, warm ISMF process has been explored to enhance the material formability. In this paper, thermal model has been proposed to predict the effect of temperature on the formability of sheet metal in warm ISMF process. Sine law has been used to determine the final thickness of the formed sheets. Experimental investigations on titanium grade 2 sheet at warm temperature has been carried out to study the effects of incremental depth, wall angle, and temperature on formability, geometrical accuracy, and thickness reduction during warm ISMF process using Taguchi L9 orthogonal array. Based on the experimental results, it was found that titanium grade 2 sheets formed with incremental depth of 0.1 mm and temperature of 300 °C showed higher formability with geometrical deviation of 1.52% and thickness reduction of 37.90%. Predictions of thermal model are validated by experimental work, and it has been found that experimental results are in good agreement with the thermal model. Analysis of variance (ANOVA) was used to identify the percentage contribution of each process parameters. To analyze the fracture behavior of the formed component, fractography study has been carried out using scanning electron microscopy (SEM).

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Abbreviations

\( \dot{\mathrm{E}} \) in :

rate of heat energy flows into the system (W)

\( \dot{\mathrm{E}} \) out :

rate of heat energy flows out of the system (W)

\( \dot{\mathrm{E}} \) g :

rate of energy generated (W)

\( \dot{\mathrm{E}} \) st :

rate of change of thermal energy stored by the system (W)

qx, qy, qz :

conduction heat rates along X, Y, Z direction (W)

Qconv :

net heat loss through convection (W)

Qrad :

net heat loss through radiation (W)

I:

input current (A)

t:

time taken to heat the sheet metal (sec)

T:

temperature of the sheet metal (°C)

R(T):

resistance of the sheet material as a function of temperature (ohm)

ρ(T):

electrical resistivity of the sheet material as a function of temperature (ohm-mm).

A1 :

cross-sectional area of the sheet perpendicular to the direction of current flow (mm2)

d:

density of the sheet metal (kg/mm3)

Cp(T):

specific heat capacity of the sheet material as a function of temperature (N mm/Kg.°C)

m:

mass of the sheet metal (kg)

q:

rate of heat conduction through a medium (W)

K(T):

thermal conductivity of the sheet material as a function of temperature (W/mm.oC)

T1 :

initial temperature before heating (°C)

T2 :

final temperature after heating (°C)

ΔT:

difference in temperature (°C)

W1 :

thermal work done to raise the temperature of the sheet material (N-mm)

W2 :

mechanical work done during the forming process (N-mm)

W3 :

work done by the forming tool (N-mm)

W4 :

plastic work done up to fracture (N-mm)

Fz :

axial force exerted by the forming tool (N)

σUTS (T):

ultimate tensile strength of the sheet material as a function of temperature (N/mm2)

dt :

forming tool diameter (mm)

\( \overline{\mathrm{h}} \) :

scallop height (mm)

α:

wall angle (°)

\( \overline{\mathrm{z}} \) :

incremental depth (mm)

zh :

total height of the formed component (mm)

z:

initial thickness of sheet metal (mm)

A2 :

tool contact area during forming process (mm2)

\( \overline{\upsigma} \) :

effective stress (N/mm2)

\( \overline{\upvarepsilon} \) :

effective strain

h:

height of the crack (mm)

K:

strength coefficient of the sheet material (N/mm2)

n:

strain hardening exponent

zf :

final thickness of the formed sheet metal (mm)

\( \overline{\upvarepsilon} \) f :

effective fracture strain

εmajor :

Major in-plane strain

εminor :

minor in-plane strain

R:

average value of the anisotropy coefficient

σ1 and σ2 :

principle stresses (N/mm2)

η:

stress ratio

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  1. Department of Production Engineering, PSG College of Technology, Coimbatore, Tamil Nadu, India

    R. Mohanraj & S. Elangovan

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  1. R. Mohanraj
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Mohanraj, R., Elangovan, S. Thermal modeling and experimental investigation on the influences of the process parameters on warm incremental sheet metal forming of titanium grade 2 using electric heating technique. Int J Adv Manuf Technol 110, 255–274 (2020). https://doi.org/10.1007/s00170-020-05851-4

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