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