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ratio max(μt/μ)=1 380 and is in a correct range. The results
show that the thin residual wall gained in simulation is close to the experiment results[7–9]. The coupling between load pressure p and flow rate qL is shown in Fig. 6. The approximate equation can be written as
polymer melt cavity filling flow in molding injection[17–18].
= BL
2
qL ,
(6)
The equation is
(˙,T , p) =
0 (T , p) ,
* 1−n
(2)
AL
where AL is the cross section area of mould cavity and BL is
where
1+(0˙ )
⎛TB ⎞⎟
the equivalent load visco-damping coefficient which can be
given by CFD simulation or WAIM experiments.
Table 2. Cross model parameters of polymer
Polymer
0 (T , p) = B exp⎜⎜
⎟⎟exp( p).
(3)
Model parameter
PA66 ABS
⎜⎝ T ⎠
100 K higher than vitrification temperature Tg. This is applicable in GAIM. However, the temperature of polymer melts may drop to T<Tg+100, and the Cross-William- Landel-Ferry (Cross-WLF) model shall be used as[19–21]
Viscosity at Tg ηg/(MPa • s) 35 190.0 916.5
⎛− − ⎞⎟
(T , p) =
exp⎜⎜
C1 (T Tg )⎟⎟exp( p),
(4)
Fig. 4. Calculation field of CFD simulation
0 g ⎜⎜ C
+T −T ⎟
⎝ 2 g ⎠
where B, TB, , τ*, C1 and C2 are model parameters of the Cross model. Table 2 shows model parameters of Nylon 66 and acrylonitrile butadiene styrene(ABS), two polymer
If inertia, elasticity and viscosity are all involved in the load characteristics, the transfer function between the load pressure and flow rate can be estimated as
2
materials in common use. These parameters show great
G (s) =
p = mL s + BL s + kL .
(7)
L 2
difference between the two materials, which is general
instance in polymer materials. The apparent viscosity is decided by temperature, shear stain rate and pressure. The load pressure p can be given as
qL AL s
The linear control model of the system can be built and simulated with this assumption of visco-elastic load.
·422·
ZHOU Hua, et al: Water-Assisted Injection Molding System Based on Water Hydraulic
Proportional Control Technique
of pressure cylinder are written as
pA A1 = pB A2 + pL A3 + m˙x˙+ Bp x˙ + f ,
(9)
q = A x˙ + C
( p − p ) + C p
+ V1 p˙ ,
(10)
A 1 ip1
A B ep1 A