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Thixoforming : Semi-solid Metal Processing

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406j 10 Thixoforging and Rheoforging of Steel and Aluminium Alloys<br />

List of Symbols and Abbreviations<br />

w circular frequency of the resonant circuit<br />

s Stefan–Boltzmann constant<br />

r density<br />

m magnetic permeability<br />

l heat conduction coefficient<br />

k electric conductivity<br />

e emissivity factor<br />

d penetration depth<br />

a ratio of ring side area to piston side area<br />

Wout measured temperature at the surface<br />

Win<br />

temperature at the middle of the billet<br />

We<br />

temperature of the environment<br />

Wdesired<br />

desired surface temperature<br />

_Fðr; tÞ volume power density<br />

Ak<br />

piston area<br />

Bv<br />

value flow gain<br />

ber(), bei() Kelvin functions<br />

CNC Computerized numerical control<br />

cp<br />

^Ef<br />

specific heat capacity<br />

electric field<br />

FDM finite difference method<br />

FL<br />

load<br />

FR<br />

friction force<br />

^Hz<br />

magnetic field strength<br />

Hsurrounding convective heat transmission<br />

^Ic<br />

coil current peak value<br />

J0, J1<br />

modified Bessel functions of first kind, zero and first order<br />

kf0<br />

flow stress<br />

kv<br />

value dynamic gain<br />

Lc<br />

coil length<br />

Nc<br />

number of turns<br />

PID proportional–integral–derivative<br />

Pk i<br />

induced power in the scale i at the time step k.<br />

PLC programmable logic controller<br />

pN<br />

pressure<br />

Pv<br />

supply pressure<br />

R radius of coil<br />

Tsurrounding temperature of environment<br />

Ttool<br />

temperature of tools<br />

Tv<br />

time constant of the value<br />

TZM molybdenum-based alloy<br />

u(t) voltage<br />

v(t) velocity of the piston

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