Extrusion Introduction An extruder is a common machine in industry ...

With boundary conditions occur at r = R o (z), r = R i (z), z = 0 and z = L, the inner and
outer surface profile can be determined as follows.
R ( z )
i
exp
2
i
r
(1 r
2
i
) / w ( z )
p
i
(1 w ( z ))
w ( z )
2
i
r
1 / 2
(12)
R
o
( z )
R
2
i
( z )
(1 r
2
i
w ( z )
)
1 / 2
(13)
w
( z ) exp
z
(14)
w L
ln
w o
(15)
where r i and r o are known as the die geometry factors (i.e., inner and outer diameters of
exit of the die), w o is output rate at die exit and w L is the take-off velocity.
Sample Calculations
Figure 7 through 9 provide the theoretical predictions given by the equations (12) through
(15) for the following conditions:
the outer radius of the die, r o : 2.788 mm (7/32” diameter)
the inner radius of the die, r i : 1.588 mm (1/8” diameter)
draw span, L :
viscosity, :
50 cm
1000 Pa-s
density, : 0.92 g/cm 3
mass flow rate, m :
take-up speed, w(L) :
internal pressure, p i :
50 g/min
40 cm/s
0 ~60 Pa