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

R o
2
z
p
1
u
r
2
R o
z
w
z
1
u
2
r
2
R
o
u
z
z
R o
u
z
z
w
r
w
r
R o
z
0
2
w
z
(5)
(6)
At r = R i (z),
u
R i
2
z
p p i
R i
z
w
u
r
1
0
w
z
2
R i
z
1
u
2
r
2
R
i
u
z
z
R i
u
z
z
w
r
w
r
0
R i
z
2
w
z
(7)
(8)
(9)
Here (4) and (7) are the kinematic conditions, (5) and (8) the tangential stress balances,
and (6) and (9) are the normal stress balances at the outer and the inner surfaces of the
tube. In (9), p i is the pressure inside the tube (i.e., internal pressure) that can be
controlled. That is, the inner (hence the outer) radius can be controlled by varying the
internal pressure when other conditions are fixed.
At z = 0,
R i
ri
, R o ro
, w w o
(10)
At z = L,
w w L
(11)
Here w o is the average velocity in the axial direction that is determined once the output
flow rate and the die geometry (i.e., r i and r o ) are specified. the axial velocity at z = L
(i.e., position the fiber is quenched or solidified instantaneously). w L is also known as the
take-up velocity (v t ) that is controlled by the take-up device.